Philosophical Question: Maths- invented or discovered? [Archive]

renzo_novatore

19th January 2011, 00:27

Math is in my opinion an invention. So, first off, we must discuss math in two different contexts: in theory and in practice. In theory, it is an invention. Think about it - without ears, there'd be no sound; without noses, nothing would smell; without eyes, there'd be nothing to see; and without minds, nothing would make sense. So, in other words, without a mind able to comprehend mathematics, then mathematics would not exist, therefore it is an invention of the human mind - ie 2+2=4 in theory, but without a mind to be able to theoretize, then this would not exist, would it? Theoretical math is therefore an invention.

And then in practice, it is also an invention. In that Blackadder clip, you could have Blackadder thinking that he's showing Baldrick 4 beans when instead Baldrick is really seeing 5 beans. Just because Blackadder doesn't see this extra bean and just because everyone else doesn't see it, doesn't necessarily mean that it doesn't exist, does it? So, mathematics in practice that first off must posit that there are only 2 beans and 2 beans coming together, is an invention - because there could really be 3 beans and 2 beans coming together and you can't know it - in other words, YOU are the one declaring and saying that there are only 2 and 2 beans coming together, the 2 and 2 beans is not a given, which means you came up with how many beans there are and is thus an invention. Or, to put it in another way, you never have simply 2 and 2 beans. Because you have to talk about what a bean is in the first place. Beans is a category that we create - we pigeonhole different things together - the aztecs all called rain, snow, and hail one thing and the inuits have 6 words for snow, so perhaps the bean that you're eating is to someone else not a bean at all - so everything is unique, each individual thing we call a bean is not at all like what we would call other beans. Therefore, how can we say that a bean is a bean? But then you could, to simplify things, say only that I have 2 things and 2 things - therefore I have four things, but then again, what constitutes a thing? What characterizes it? What is a thing? A bean for instance, a single individual thing we call a bean, you could say depends on something different to contrast itself with in order to exist. So, I have 2 things I call beans and 2 other things I call beans, I could say it makes 4 things I call beans, but at the same time I could say it makes 1 thing I call a bean, since that 1 thing I call a bean depended on those other 3 things I call beans for me to know that it exists - in other words that 1 thing I call a bean is not strictly characterized and is limited by its shell - it depends those 3 other things I call beans for its existence, so 2 things I call beans plus 2 things I call beans equals 1 thing I call a bean. In practice, you separate and create the identity of that thing that I call a bean, putting boundaries around it, boundaries that I created, which thus means it is an invention. So, basically, since all identity is an invention, and mathematics must necessarily depend on identity, then mathematics is an invention. Does this make sense? Just know I tried my best to state this as clearly as possible.

In the simplest terms possible - we create identity, identity does not exist in the thing in itself - identity exists in a relationship between the viewer and the object, not necessarily in the object itself, the identity is something that we declare and define (because we're not passive viewers of an external universe, the universe is something that you are making sense of and creating also, you exist in a relationship with it, dogs for instance see a different color green than we do - how do we know then what green is? We can only know what green seems to us, that is all. So, this basically means that since we are active participants in the universe, then each individual is experiencing a universe that they create, their own reality tunnel or reality labyrinth (if you've done enough acid :thumbup:) - and therefore each object depends on its identity from something else, identity is not a given) - so math which needs identity is something that we create.

Oh how I hate my mind.

ComradeMan

19th January 2011, 11:53

^^^^^^ Interesting and fair points.

But on the other hand how do you explain "mathematical matter" or the seemingly mathematical basis of so much in nature independent of the human mind, such as the Fibonacci sequences found in sunflowers, nautilus shells or galaxies? Does it not seem that there is some kind of "code" underlying it all.

You could get into Cartesian-type arguments here too about whether or not something can exist if we can perceive it. Or do we create the perception?

renzo_novatore

19th January 2011, 15:31

But on the other hand how do you explain "mathematical matter" or the seemingly mathematical basis of so much in nature independent of the human mind, such as the Fibonacci sequences found in sunflowers, nautilus shells or galaxies? Does it not seem that there is some kind of "code" underlying it all.

Or it only points to a mathematical nature of the human mind...

ComradeMan

19th January 2011, 20:23

Or it only points to a mathematical nature of the human mind...

Hmmm.... but with or without a human perceiver would the nautilus shell no longer conform to a Fibonacci spiral following mathematical "rules"?

What about this mathematical matter too?

renzo_novatore

22nd January 2011, 07:22

Hmmm.... but with or without a human perceiver would the nautilus shell no longer conform to a Fibonacci spiral following mathematical "rules"?

What about this mathematical matter too?

Well in my opinion I don't think that there is anything that can exist by itself, not even the fibonacci spiral on the nautilus shell.

ZeroNowhere

22nd January 2011, 07:46

Hmmm.... but with or without a human perceiver would the nautilus shell no longer conform to a Fibonacci spiral following mathematical "rules"?
Without a human perceiver, is it still the case that 'bachelors' are unmarried? Well, what would it mean to say that bachelors could then be married? It would be a description of the meaning of the word 'bachelor', whether it could be used to describe something, the rules according to which it may be used. There is nothing inherent to the sound 'bachelor' which makes it applicable or inapplicable, simply the rules by which it is used. To say that a nautilus shell could or could not conform to a Fibonacci spiral without a human perceiver is to simply describe rules for the usage of the phrase 'conforming to a Fibonacci spiral', in what situations it may be used, not to describe how the world is. As such, it could go either way, according to which rule is adopted; on the other hand, there may be no rule at all, similarly to how there isn't necessarily a rule for whether Wittgenstein's inconsistent chair is describable by the word 'chair': a rule could be made, but there needn't be one.

But on the other hand how do you explain "mathematical matter" or the seemingly mathematical basis of so much in nature independent of the human mind, such as the Fibonacci sequences found in sunflowers, nautilus shells or galaxies? Does it not seem that there is some kind of "code" underlying it all.If we are surprised by something, then that is an attitude, it does not imply anything.

ComradeMan

20th February 2011, 12:18

Apparently some insects, a kind of wasp, also have the ability, it seems, to count. It seems that the concept of "number" is not just human.

Black Sheep

21st February 2011, 16:44

Yeah but can it find the area under a curve?

Rosa Lichtenstein

21st February 2011, 16:52

They certainly have the capacity to respond to things we have numbered, but that does not show they can count.

ComradeMan

21st February 2011, 16:59

They certainly have the capacity to respond to things we have numbered, but that does not show they can count.

I'm afraid the evidence suggests they do have the concept of numbers, and prime numbers to be exact.

A certain kind of wasp somehow knows which eggs are going to be males and which females and brings 5 and 10 caterpillars to each egg. Always the same. The 17 year cicada is also interesting? Why 17? Because it's number one enemy lives in 2 year cycles and this way it cheats it's enemy with numbers.

No one is suggesting that an insect can solve Fermat's last theorem, but it does suggest that a numerical perception or the concept of numbers is not a human trait alone.

Rosa Lichtenstein

21st February 2011, 20:12

CM:

A certain kind of wasp somehow knows which eggs are going to be males and which females and brings 5 and 10 caterpillars to each egg. Always the same. The 17 year cicada is also interesting? Why 17? Because it's number one enemy lives in 2 year cycles and this way it cheats it's enemy with numbers.

This no more shows they can count than it shows plants can count when their petals are arranged in fibonacci numbers.

Ravachol

21st February 2011, 20:34

Mathematics, like all systems of human thought aren't static, monolithic pillars of rigid wisdom but evolving systems. The evolution of Set theory from Cantor's initial thoughts through the discovery of paradoxes such as Russell's paradox show how mathematical systems evolve as well.

If we consider the fundamentals of arithmetic, the natural numbers, the idea of them 'naturally occurring' poses some problems. For example, the idea of 2 or 3, etc. exist by virtue of observable similarity. Two apples are considered to be of the same qualitative category and are thus considered quantitative multiples of the same object. Yet, all this rests on an ambiguous perception of difference and similarity. For what we perceive to be two objects of the same qualitative category ('apples') are in fact two infinitely diverse objects which are grouped together by virtue of their seeming similarity. This does not mean that there 'is no such thing as natural numbers' but it does mean that our perception and it's limitations heavily influences the foundations of mathematical structures.

Rosa Lichtenstein

21st February 2011, 20:49

Ravachol:

The evolution of Set theory from Cantor's initial thoughts through the discovery of paradoxes such as Russell's paradox show how mathematical systems evolve as well.

As I have argued here (http://anti-dialectics.co.uk/Godel_letter.htm), since Cantor's diagonalisation 'proof' is defective, Godel's notorious theorems concerning Hilbert's program (http://en.wikipedia.org/wiki/Hilbert's_problems) and Russell's Principia are worthless.

Two apples are considered to be of the same qualitative category and are thus considered quantitative multiples of the same object. Yet, all this rests on an ambiguous perception of difference and similarity. For what we perceive to be two objects of the same qualitative category ('apples') are in fact two infinitely diverse objects which are grouped together by virtue of their seeming similarity. This does not mean that there 'is no such thing as natural numbers' but it does mean that our perception and it's limitations heavily influences the foundations of mathematical structures.

Can I suugest you read Frege (http://plato.stanford.edu/entries/frege/) on this, since overnight he put paid to such views of numbers, and there's no going back, even if his own theory failed, too:

Frege, G. (1953), The Foundations Of Arithmetic (http://en.wikipedia.org/wiki/The_Foundations_of_Arithmetic) (Blackwell, 2nd ed.).

Publius

21st February 2011, 22:47

Ravachol:

As I have argued here (http://anti-dialectics.co.uk/Godel_letter.htm), since Cantor's diagonalisation 'proof' is defective, Godel's notorious theorems concerning Hilbert's program (http://en.wikipedia.org/wiki/Hilbert%27s_problems) and Russell's Principia are worthless.

Can I suugest you read Frege (http://plato.stanford.edu/entries/frege/) on this, since overnight he put paid to such views of numbers, and there's no going back, even if his own theory failed, too:

Frege, G. (1953), The Foundations Of Arithmetic (http://en.wikipedia.org/wiki/The_Foundations_of_Arithmetic) (Blackwell, 2nd ed.).

I don't understand why you think Cantor's diagonalization argument requires or assumes Platonism.

First, we could be Carnapians about the nature of numbers, which would allow us to speak in a Platonic way about numbers without being committed to any ontological claims about them (which are meaningless, on this picture).

Second, I just don't think this result requires Platonism any more than any other result in math does. You could argue that 1 + 1 = 2 assumes Platonism since you could read that as existentially quantifying over entities called 'numbers'.

Whatever we want to say about that, we DON'T want to say that 1 + 1 doesn't equal 2.

Rosa Lichtenstein

21st February 2011, 22:55

Publius:

I don't understand why you think Cantor's diagonalization argument requires or assumes Platonism.

Both he and Godel admit that it does. They were both Platonist mystics, and most mathematicians are Platonists, but not mystics.

They also use the notion of a complete (infinite) set when they tell us one set is bigger than another. But that can only be true if that set already exists before we construct it -- which it can't unless you are a Platonist.

First, we could be Carnapians about the nature of numbers, which would allow us to speak in a Platonic way about numbers without being committed to any ontological claims about them (which are meaningless, on this picture).

No need to if we are committed to the construction of such numbers with an induction.

Second, I just don't think this result requires Platonism any more than any other result in math does. You could argue that 1 + 1 = 2 assumes Platonism since you could read that as existentially quantifying over entities called 'numbers'.

But that only applies to the interpretation of this simple sentence; that is not so with diagonalisation which requires these sets exist before we construct them.

Publius

21st February 2011, 23:51

Both he and Godel admit that it does.

But it's possible that they're wrong about that implication. They may have thought that argument required Platonism to go through, but it's at least not obvious to me.

For example, in Ted Sider's Logic for Philosophy he rigorously runs through the argument in the first few pages, and there's nothing overtly Platonic that I can find about this. Surely we don't want to say all of mathematical logic, or all of math in general, is Platonic, just because Godel and Cantor thought so!

They were both Platonist mystics, and most mathematicians are Platonists, but not mystics.

Maybe it's better to say most mathematicians speak and behave as if they were Platonists, without necessarily accepting the metaphysical or ontological consequences of Platonism. Maybe they do, in fact, have to take the whole theory. But I don't know that.

They also use the notion of a complete (infinite) set when they tell us one set is bigger than another. But that can only be true if that set already exists before we construct it -- which it can't unless you are a Platonist.

Does your objection generalize to all of set theory, then? I don't see how these assumptions about set theory are problematic unless just about all set theory is.

Maybe you could take issue with set theory as a whole. Certainly some do.

But now I think the force of your argument is weakened insofar as you're having us give up a huge and productive branch of mathematics for purely philosophical reasons.

Maybe I'm misunderstanding, but I don't see how defining sets in that way is anything but typical. I assume that's your point. Sets are defined by their members, and sets of numbers require their members to be numbers, which means numbers must exist.

But I don't see why this existential quantification is any worse than the one I point out later in my post.

No need to if we are commited to the construction of such numbers with an induction.

Unless being Carnapians allows us to keep our important and productive fields of math, in which case we have a good practical (not ontologial) reason to remain verbal Platonists while shirking any ontological claims related to the view.

Now I don't want to be a Carnapian about numbers, I want to be a nominalist, but the point is that's a live option (I have some books on the topic I need to read).

But that only applies to the interpretation of this simple sentence; that is not so with diagonalisation which requires these sets exist before we construct them.

1 + 1 = 2 surely requires the numbers to exist before we add them in precisely the same way. The Platonic gloss is just as harmful (or innocuous) in either case.

Maybe I'm just misunderstanding, but is the case of diagonalization supposed to be somehow worse? Why is prima facie Platonism about sets bad but prima facie Platonism about ordinary numbers isn't?

Rosa Lichtenstein

22nd February 2011, 00:29

Publius:

But it's possible that they're wrong about that implication. They may have thought that argument required Platonism to go through, but it's at least not obvious to me.

No, it's an integral part of their proof; others just ignore it, and think the proof works anyway -- which it doesn't if you reject Platonism.

For example, in Ted Sider's Logic for Philosophy he rigorously runs through the argument in the first few pages, and there's nothing overtly Platonic that I can find about this. Surely we don't want to say all of mathematical logic, or all of math in general, is Platonic, just because Godel and Cantor thought so!

Well, I haven't see it so I can't comment, but if it's like the many I have seen, the Platonism is implicit in the enumerative theory of sets [ETS].

Maybe it's better to say most mathematicians speak and behave as if they were Platonists, without necessarily accepting the metaphysical or ontological consequences of Platonism. Maybe they do, in fact, have to take the whole theory. But I don't know that.

Well, as soon as you abandon ETS, the 'proof' falters.

There is also a technical problem with the proof which persists even if you still accept ETS. Using Hilbert's Hotel (http://en.wikipedia.org/wiki/Hilbert's_paradox_of_the_Grand_Hotel), for any new Real Number constructed on the diagonal, we can find a place for it paired one-one with one of the counting numbers on the left by moving each already paired Real Number down one place.

If the counting numbers on the left are infinite, then we can always fit an infinite number of these diagonally constructed Reals into the main list, paired one-one with a counting number. So, even if we accept the logic of this proof, it still fails to show that the Reals have a higher Cardinality than the Natural Numbers.

Does your objection generalize to all of set theory, then? I don't see how these assumptions about set theory are problematic unless just about all set theory is.

Maybe you could take issue with set theory as a whole. Certainly some do.

Well, like Poincare, and Wittgenstein, I do not like set theory, since it turns mathematics into a sort of superscience of collections, especially the ETS interpretation.

But now I think the force of your argument is weakened insofar as you're having us give up a huge and productive branch of mathematics for purely philosophical reasons.

Not so, I think it turns mathematics into something else, as I pointed out above.

And set theory, as I have characterised it, already contains philosophical assumptions, those that your teachers either ignore, cover up, or do not know about.

As Wittgenstein said, he asks questions that children ask, or should ask, before they are silenced into no longer asking them, but which are then buried in the implicit Platonism of mainstream mathematics.

The ruling ideas Marx spoke about also rule in mathematics, you know. [But then you might not accept that as true!]

Maybe I'm misunderstanding, but I don't see how defining sets in that way is anything but typical. I assume that's your point. Sets are defined by their members, and sets of numbers require their members to be numbers, which means numbers must exist.

And that is precisely what is wrong with ETS, for unless you know (i.e., can prove, not just assume) as a result of a rule or an induction that this or that item belongs to a set, then it is just a collection, and set theory becomes merely the superscience of collections.

Unless being Carnapians allows us to keep our important and productive fields of math, in which case we have a good practical (not ontological) reason to remain verbal Platonists while shirking any ontological claims related to the view.

Now I don't want to be a Carnapian about numbers, I want to be a nominalist, but the point is that's a live option (I have some books on the topic I need to read).

Not if it lands you in the mess that Cantor introduced into mathematics.

1 + 1 = 2 surely requires the numbers to exist before we add them in precisely the same way. The Platonic gloss is just as harmful (or innocuous) in either case.

Maybe I'm just misunderstanding, but is the case of diagonalization supposed to be somehow worse? Why is prima facie Platonism about sets bad but prima facie Platonism about ordinary numbers isn't?

And where do they exist, and how do we gain knowledge of them if they aren't in this universe?

Wittgenstein's account of numbers is vastly superior, I think:

http://plato.stanford.edu/entries/wittgenstein-mathematics/

Finally, the simple sentence you quote is the expression of a rule we use to 'balance the books' as it were. No need for Plato, or William of Ockham (and Nominalism) then.:)

Publius

22nd February 2011, 02:02

No, it's an integral part of their proof; others just ignore it, and think the proof works anyway -- which it doesn't if you reject Platonism.

While Platonism is certainly the dominant view among mathematicians (and arguably philosophers), it's certainly not the only view.

And this is the first I've heard of mounting a challenge to Cantor and Goedel's proofs, in this way.

Well, as soon as you abandon ETS, the 'proof' falters.

But that's just to say that once you abandon contemporary set theory the proof falters. But I still don't see why I ought to give up basic set theory.

There is also a technical problem with the proof which persists even if you still accept ETS. Using Hilbert's Hotel (http://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel), for any new Real Number constructed on the diagonal, we can find a place for it paired one-one with one of the counting numbers on the left by moving each already paired Real Number down one place.

If the counting numbers on the left are infinite, then we can always fit an infinite number of these diagonally constructed Reals into the main list, paired one-one with a counting number. So, even if we accept the logic of this proof, it still fails to show that the Reals have a higher Cardinality than the Natural Numbers.

Let's do this formally.

The relevant section of Sider's book (to just take one proof of this theorem) is posted online: http://tedsider.org/books/lfp_sample.pdf

The section starts on page 26. How does the proof Sider gives fail to establish the conclusion that set containing the real numbers is of greater cardinality than the set containing the natural numbers?

Sider does the proof in such a way such that the set R is complete. Thus his exposition of the argument ignores this technical issue, and achieves the desired result.

Well, like Poincare, and Wittgenstein, I do not like set theory, since it turns mathematics into a sort of superscience of collections, especially the ETS interpretation.

I think it's a branch of mathematics on precisely the same footing as every other.

And set theory, as I have characterised it, already contains philosophical assumptions, those that your teachers either ignore, cover up, or do not know about.

Maybe. Or maybe the consequences can be discharged in a harmless way.

As Wittgenstein said, he asks questions that children ask, or should ask, before they are silenced into no longer asking them, but which are then buried in the implicit Platonism of mainstream mathematics.

The ruling ideas Marx spoke about also rule in mathematics, you know. [But then you might not accept that as true!]

I fear you might be tilting at windmills here. Certainly a lot of mathematicians are platonists, but I think among people (mostly philosophers) who study the foundational ontology of math, platonism is only one view among many. Probably you take issue with the other views too, given your philosophical inclinations, but that at least shows the issue isn't just platonism.

And that is precisely what is wrong with ETS, for unless you know (i.e., can prove, not just assume) as a result of a rule or an induction that this or that item belongs to a set, then it is just a collection, and set theory becomes merely the superscience of collections.

I don't see the issue here. You way we need to use mathematical induction, but that commits us to a form of platonism, since to use mathematical induction on numbers, there have to be such things as numbers and properties!

Again, I don't see why the talk of sets is more harmful than ordinary talk of numbers.

And where do they exist, and how do we gain knowledge of them if they aren't in this universe?

Well, I'm not a Platonist either. At best I'm someone who thinks we should talk like Platonists.

Wittgenstein's account of numbers is vastly superior, I think:

http://plato.stanford.edu/entries/wittgenstein-mathematics/

Finally, the simple sentence you quote is the expression of a rule we use to 'balance the books' as it were. No need for Plato, or William of Ockham (and Nominalism) then.:)

Where did you get your PhD in philosophy?

I'm currently applying (Wittgeinstein wouldn't be happy with me!), and have been accepted to a few schools here in the US.

Rosa Lichtenstein

22nd February 2011, 05:42

P:

While Platonism is certainly the dominant view among mathematicians (and arguably philosophers), it's certainly not the only view.

And this is the first I've heard of mounting a challenge to Cantor and Goedel's proofs, in this way.

I agree, but such challenges to Cantor have been around since the 1890s. It's only because explicit and implicit Platonism is the dominant paradigm that other views have now become drowned out.

But that's just to say that once you abandon contemporary set theory the proof falters. But I still don't see why I ought to give up basic set theory.

As Wittgenstein said, and with no disrespect to you: you are welcome to it.

Sider does the proof in such a way such that the set R is complete.

And that is part of the problem, for this assumes that something incomplete (an infinite set) is in fact complete, that is, that it is a Platonic object. A complete finite set (provided it is not so large that we can't survey it, or which we can't define by an induction) is not therefore Platonic. But a complete infinite set must be Platonic since we can't survey it, and the induction that might define it is uncompletable by definition.

Once this is disallowed, the proof falls apart in the way I outlined.

[When my anti-dialectics project is finished I will submit for publication a formal version of my informal argument.]

But, let us suppose that it is complete, then any extra Reals we can generate on the diagonal can be slipped in opposite the very first counting number on the left hand list, and the rest moved down one place a la Hilbert's Hotel. And we can keep doing that indefinitely.

Hence, the Reals are not uncountable, and have the same Cardinality as the natural numbers.

Cantor's 'proof' is defective, therefore, and thus so is Gödel's infamous 'proof'.

[Thanks for that link to Sider's book, by the way!:)]

I think it's a branch of mathematics on precisely the same footing as every other.

Well, not really since set theory is not part of mathematics, but part of some sort of Platonist science fiction.

Maybe. Or maybe the consequences can be discharged in a harmless way.

Well, I'd like to see you (or anyone else for that matter) try.

I fear you might be tilting at windmills here. Certainly a lot of mathematicians are platonists, but I think among people (mostly philosophers) who study the foundational ontology of math, platonism is only one view among many. Probably you take issue with the other views too, given your philosophical inclinations, but that at least shows the issue isn't just platonism.

Well, as we can see with Sider's proof, the Platonism is so deeply hidden not even you spotted it. The same is true of much of mathematics (today and throughout its history), which likewise goes unrecognised.

You can also see that in your reference to its "foundational ontology". Mathematics needs no ontology, unless, of course, we are Platonists of some sort.

I have added an argument here (http://www.revleft.com/vb/all-philosophical-theories-t148537/index.html) in Philosophy (I do not know if you can see it -- if not, I can re-post it in this thread, or in this section) that goes some way toward showing this in relation to traditional philosophy (that all of traditional philosophy is non-sensical), but it would be a minor matter to extend this into any form of ontology in mathematics or elsewhere -- that they too are non-sensical.

No wonder we get all manner of paradoxical results out of Cantor's system -- his entire theory is non-sensical because of its platonist ontology.

[By "non-sensical" I do not mean the same as "nonsensical" -- I explain the difference in the aforementioned post in Philosophy.]

I don't see the issue here. You way we need to use mathematical induction, but that commits us to a form of platonism, since to use mathematical induction on numbers, there have to be such things as numbers and properties!

Not so, all there has to be is an indefinite supply of names and property tokens.

Again, where do these numbers exist?

[You see, you find you have to slip into an unconscious Platonism too!]

Again, I don't see why the talk of sets is more harmful than ordinary talk of numbers.

Well, I have given you my reasons. You need to address them.

Well, I'm not a Platonist either. At best I'm someone who thinks we should talk like Platonists.

Well, it's not just talk is it? You actually think numbers already exist.

Where did you get your PhD in philosophy?

I'm sorry I do not give out personal information on the internet.

I'm currently applying (Wittgenstein wouldn't be happy with me!), and have been accepted to a few schools here in the US.

Well, good luck.

ComradeMan

22nd February 2011, 09:36

CM:

This no more shows they can count than it shows plants can count when their petals are arranged in fibonacci numbers.

Rosa I'm afraid you are wrong.

Scientists have shown that honeybees can count at least up to four and fireflies "count" the number of flahses of other fire flies in order to recognise each other. Some species of ant are also able to measure distance.

http://www.sciencealert.com.au/news/20092901-18730-2.html

http://www.msnbc.msn.com/id/33974286/ns/technology_and_science-science/

http://www.scienceagogo.com/news/20090027230901data_trunc_sys.shtml

Along with other animals

http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0015516

Have a look here:-
The cognitive animal: empirical and theoretical perspectives on animal cognition (http://books.google.it/books?id=T-ztyW8eTnIC&pg=PA197&lpg=PA197&dq=numerical+ability+animals&source=bl&ots=uHrfPzqnIf&sig=X0ulb2wosATmf9l3hqMs96ShX60&hl=it&ei=w4JjTaxdyJI6lur0yQ0&sa=X&oi=book_result&ct=result&resnum=4&ved=0CDkQ6AEwAw#v=onepage&q=numerical%20ability%20animals&f=false)

Marc Bekoff,Colin Allen,Gordon M. Burghardt
Pg. 197

Mr.Awesome

22nd February 2011, 10:23

Well, this is a very interesting question.

In my opinion, maths, or at least the study of maths and the way we use it, is an invention. The way we represent numbers, additions, multiplications, square roots, etc. was invented. Indeed this is one of man's greatest inventions.

But essentially, the basic concept of 1 + 1 = 2 is not one that was invented. If I have one apple and I get another one, I do not need to discover or to invent the fact that I now have two. Its a basic understanding of maths we are all born with.

And so I conclude, the study of mathematics is an invention, based on common sense.

ComradeMan

22nd February 2011, 10:38

The problem with this is that the evidence of a "numerical instinct" in non-human species suggests that perhaps there is something more going on. 100 million years a dinosaur laid perhaps two eggs in each nest, if this is so then something was going on long before humans came around!

Rosa's argument doesn't stand up about this not being evidence and the comparison with Fibonacci sequences in flowers is a bad one.

In the same way it could be argued that humans don't really have the power to count beyond five in terms of recognition of numbers- apparently it's difficult to recognise numbers beyond five however we do have the ability to develop systems and record explanations that animals don't.

On the other hand, if a vastly superior intelligent form of sentient being visited earth on the same basis it might argue that humans only possess rudimentary forms of maths in comparison with its own form and conclude that the Golden Section no more proves we can count than the petals on a flower- afterall, we, like the ants, are just recognising patterns in nature. ;)

Rosa Lichtenstein

22nd February 2011, 14:25

Mr A:

But essentially, the basic concept of 1 + 1 = 2 is not one that was invented. If I have one apple and I get another one, I do not need to discover or to invent the fact that I now have two. Its a basic understanding of maths we are all born with.

You guys really ought to read Frege on this.

As he pointed out, number words attach to concept expressions not objects.

So, even one apple is made of many parts. One apple is also one stalk, plus one skin, plus one pith, plus one core, plus six pips, plus...

Each of the above tells us that the concept word "...is a pip", or "...is a core" is instantiated one or six or... times.

Any object can be broken down like this, and we can do so by attaching number words to the concepts we may legitimately use to do so. But the concept expressions cannot be broken down in this way. So the number words attach to concepts, not objects.

Hence, when we count we instantiate concept expressions, not objects.

Rosa Lichtenstein

22nd February 2011, 14:31

CM:

The problem with this is that the evidence of a "numerical instinct" in non-human species suggests that perhaps there is something more going on. 100 million years a dinosaur laid perhaps two eggs in each nest, if this is so then something was going on long before humans came around!

Rosa's argument doesn't stand up about this not being evidence and the comparison with Fibonacci sequences in flowers is a bad one.

In the same way it could be argued that humans don't really have the power to count beyond five in terms of recognition of numbers- apparently it's difficult to recognise numbers beyond five however we do have the ability to develop systems and record explanations that animals don't.

On the other hand, if a vastly superior intelligent form of sentient being visited earth on the same basis it might argue that humans only possess rudimentary forms of maths in comparison with its own form and conclude that the Golden Section no more proves we can count than the petals on a flower- afterall, we, like the ants, are just recognising patterns in nature.

Once more, you really ought to read Frege on this.

Check out my reply to Mr A above.

Hence, we do not count objects -- nor do birds or dinosaurs, or...--, we instantiate the occurence of concept expressions.

So, unless you can show that these animals have these concepts in their repertoire, your claims won't wash.

Rosa Lichtenstein

22nd February 2011, 14:35

CM:

Rosa I'm afraid you are wrong.

Scientists have shown that honeybees can count at least up to four and fireflies "count" the number of flahses of other fire flies in order to recognise each other. Some species of ant are also able to measure distance.

All they have shown is that there is a causal link between bee and firefly behaviours and sets of instantiated concepts we have already counted.

That no more shows they can count than it shows they can pick one another out in a line up.

ComradeMan

22nd February 2011, 20:38

CM:All they have shown is that there is a causal link between bee and firefly behaviours and sets of instantiated concepts we have already counted.

That no more shows they can count than it shows they can pick one another out in a line up.

Well I am afraid a lot of scientific opinion is against you.

It seems they can actually pick each other out too, apparently.

One might argue that humans can only count based on what they recognise in nature, albeit in a more sophisticated form- afterall, we are only able to subitise numerosities of five basically.

However the ability to subitise and estimate numerosities is well-known in many animals.

I refer you to this paper in English from the University of Padua/Padova.

http://paduaresearch.cab.unipd.it/904/1/FoundationNumericalKnowledge.pdf

and to this work cited in the paper

Chittka, L., & Geiger, K. (1995). Can honey bees count landmarks? Animal
Behaviour 49 (1), 159-164.

Also

Mathematics
Some animals are capable of distinguishing between different amounts and rudimentary counting. Elephants have been known to perform simple arithmetic and rhesus monkeys can count.[8] (http://www.revleft.org/vb/#cite_note-7)[9] (http://www.revleft.org/vb/#cite_note-8) Ants are able to use quantitative values and transmit this information.[10] (http://www.revleft.org/vb/#cite_note-9)[11] (http://www.revleft.org/vb/#cite_note-10) For instance, ants of several species are able to estimate quite precisely numbers of encounters with members of other colonies on their feeding territories.[12] (http://www.revleft.org/vb/#cite_note-11)[13] (http://www.revleft.org/vb/#cite_note-12) Young chimpanzees have outperformed human college students in tasks requiring remembering numbers.[14] (http://www.revleft.org/vb/#cite_note-13) Pigeons (http://www.revleft.org/wiki/Pigeon) have been shown to outperform humans on the Monty Hall problem (http://www.revleft.org/wiki/Monty_Hall_problem), a probability puzzle.[15] (http://www.revleft.org/vb/#cite_note-14)
http://en.wikipedia.org/wiki/Animal_cognition#Mathematics
Notes:
8 Elephants show flair for arithmetic (http://www.timesonline.co.uk/tol/news/world/asia/article4660924.ece)
http://www.timesonline.co.uk/tol/news/world/asia/article4660924.ece (http://www.timesonline.co.uk/tol/news/world/asia/article4660924.ece)
9 Representation of the Numerosities 1-9 by Rhesus Macaques (Macaca mulatto (http://www.columbia.edu/cu/psychology/primatecognitionlab/References/BrannonTerrace2000.pdf)
10 Zhanna Reznikova, Boris Ryabko, "A Study of Ants' Numerical Competence". Electronic Transactions on Artificial Intelligence (http://www.revleft.org/wiki/Electronic_Transactions_on_Artificial_Intelligence ), Issue: Vol. 5(2001): Section B: pp. 111-126
11 Reznikova, Zh. I. (2007). Animal Intelligence: From Individual to Social Cognition. Cambridge University Press
12 Reznikova, Zh. I. (1999). Ethological mechanisms of population dynamic in species ant communities. Russian Journal of Ecology, 30, 3, 187–197
13 Brown, M. J. F., Gordon, D. M. (2000). How resources and encounters affect the distribution of foraging activity in a seed-harvesting ants. Behav.Ecol.Sociobiol. , 47, 195-203.
14 Rowan Hooper (2007-12-03). "Chimps outperform humans at memory task" (http://www.newscientist.com/article/dn12993-chimps-outperform-humans-at-memory-task.html). New Scientist (http://www.revleft.org/wiki/New_Scientist). http://www.newscientist.com/article/dn12993-chimps-outperform-humans-at-memory-task.html (http://www.newscientist.com/article/dn12993-chimps-outperform-humans-at-memory-task.html). Retrieved 2008-03-24.
15 doi (http://www.revleft.org/wiki/Digital_object_identifier):10.1037/a0017703 (http://dx.doi.org/10.1037%2Fa0017703)

Rosa Lichtenstein

22nd February 2011, 21:17

CM:

Well I am afraid a lot of scientific opinion is against you.

So what? A awful "lot of scientific opinion" was against Galileo -- and is still against Marx.

Someone has to innovate or we'd still think the earth is at the centre of the universe.

It seems they can actually pick each other out too, apparently.

I'm sorry but what does that mean? Pick who or what out?

One might argue that humans can only count based on what they recognise in nature, albeit in a more sophisticated form- afterall, we are only able to subitise numerosities of five basically.

Sure, human beings have to be able to discriminate to be able to count, but what does that prove?

However the ability to subitise and estimate numerosities is well-known in many animals.

I've already covered that response in my last reply.

And thanks for the link, but I have been reading bold claims like this (that turned out to be wishful thinking) for longer than most RevLefters have been alive.

What they all do is make the same pre-Fregean mistakes about numbers -- you know, the sort of points you ignored from an earlier post of mine -- my answer to Mr A above (escept, where you see the word "concept" substitute "count noun (http://en.wikipedia.org/wiki/Count_noun)", and the argument will be more up-to-date).

ComradeMan

22nd February 2011, 21:56

CM:So what? A awful "lot of scientific opinion" was against Galileo -- and is still against Marx. Someone has to innovate or we'd still think the earth is at the centre of the universe. I'm sorry but what does that mean? Pick who or what out? Sure, human beings have to be able to discriminate to be able to count, but what does that prove? I've already covered that response in my last reply.

And thanks for the link, but I have been reading bold claims like this (that turned out to be wishful thinking) for longer than most RevLefters have been alive.

What they all do is make the same pre-Fregean mistakes about numbers -- you know, the sort of points you ignored from an earlier post of mine -- my answer to Mr A above (escept, where you see the word "concept" substitute "count noun (http://en.wikipedia.org/wiki/Count_noun)", and the argument will be more up-to-date).

Hang on a minute, you are not prepared to read the scientific arguments based on experimentation and observation before you discount them?

Come on Rosa, that's not very "empirical" of you!!! :lol:

As for Frege on mathematics, well- far be it from me to ridicule a great and important figure such as Frege but we are talking about the same Frege who proved that 2+2=5 in Die Kleine Begriffsschrift until Russell demolished his argument showing that he had actually proven that 2+2=4 in Grundbeefen der Mathematik :) at which point he retired from mathematics! ;) *

More seriously: the trouble with Frege...

Frege saw arithmetic as being reducible to logic whereas Kant held the opposite view that it is not reducible to logic. However what is this logic and did Kant and Frege both have the same starting points or definitions of logic? This is fundamental otherwise things begin to collapse. The problem with this logicism of Frege is that although it is true that a syllogism such as A=A is as true as 1=1 and is self-evident and true in form as opposed merely to what we perceive its meaning to be, i.e. A=A is true regardless of whatever meaning we ascribe to A and is thus an analytical truth, Frege's objective to show that all of arithmetic is the logical consequence of analytical truth has never beem reached, The fundamental problem is that in seeking to axiomitise arithmetic some axioms that are not analytical truths are inevitably involved. A major obstacle in this is the mathematical induction. No one would deny the importance of Frege and mathematical logicism in proof theory or the theory of computability however it fails to address areas such as the whole problem of mathematical philosophy, the ontological status of mathematical "objects" and so on- bringing everything back to the philosophy of logic. On the other hand induction alone is not considered to be strong proof and one shouldn't discard deduction either- considering that most hard sciences are based on deduction based on observation it brings us back to the problem of what mathematics fundamentally is. As for all of these attempts at formalism, futile- simce Godel! :)

I also would like to point out that is not an argument of the logical and philosophical meaning of what it is "to count" rather a biological and cognitive-science theory of numerosity in non-human sentient beings/lifeforms.

Anyway, back to numerosity in animals:-

http://www.cogs.indiana.edu/spackled/2010readings/Chittka_Big%20brains_2009.pdf

http://www.uv.es/fon/Carazo_etal2009.pdf

The ability to estimate, use and relay numerical concepts as well as the ability to solve basic "problems" with/by the application of "numerical" knowledge, i.e. numerical cognition is what is being discussed here and so far you have not provided any information, research or arguments to back up your assertion that the claims being made are erroneous.

Here's an interesting article on ants
http://www.chd.ucsd.edu/seminar/documents/Dornhaus.2008.MN.pdf

I also did my own ant experiments as a boy with an ant-farm, but that's another story....

* This is a joke! ;)

Rosa Lichtenstein

23rd February 2011, 02:08

CM:

Hang on a minute, you are not prepared to read the scientific arguments based on experimentation and observation before you discount them?

Read what I said again and tell me where it says I won't read it.

As for Frege on mathematics, well- far be it from me to ridicule a great and important figure such as Frege but we are talking about the same Frege who proved that 2+2=5 in Die Kleine Begriffsschrift until Russell demolished his argument showing that he had actually proven that 2+2=4 in Grundbeefen der Mathematik at which point he retired from mathematics!

1) Frege's early work (in the Grundlagen), criticising previous theories of number, is not in fact affected by his later writings.

2) The work you quote was not written by Frege and only appears online in joke/spoof pages -- it was made up, and you either fell for this, or you thought I would. I invite you to find a copy of it in any library on the planet, or in any Bibliography of his work. [You can, perhaps, begin here (http://plato.stanford.edu/entries/frege/catalog.html#Cat).]

And either you have made the following up, too, or you have completed some rather dodgy 'research' on the internet:

Russell demolished his argument showing that he had actually proven that 2+2=4 in Grundbeefen der Mathematik

Russell wrote no such work; he did not in fact publish anything in German -- the name itself "Grundbeefen" should have clued you in to the fact that this is a spoof title, too!

What Russell showed (in a letter to Frege) was that Frege's naive set theory (although Frege would not have called it that) implied a contradiction, but more recent Fregeans have managed to show that Frege's system can be repaired -- although this is still controversial.

But, it is now quite clear that Frege's Logicism is not as defective as we once thought; check these out:

Dummett, M. (1991), [I]Frege. Philosophy Of Mathematics (Duckworth).

--------, (1998b), 'Neo-Fregeans In Bad Company', in Schirn (1998), pp.369-87.

Wright, C. (1983), Frege's Conception Of Numbers As Objects (Aberdeen University Press).

--------, (1998a), 'On The Harmless Impredicativity Of N= ("Hume's Principle")', in Schirn (1998), pp.339-68.

--------, (1998b), 'Response To Dummett', in Schirn (1998), pp.389-405.

Hale, R., and Wright, C. (2001), The Reason's Proper Study. Essays Towards A Neo-Fregean Philosophy Of Mathematics (Oxford University Press).

--------, (2003), 'Responses To Commentators', Philosophical Books 44, 3, pp.245-63.

Hale, R. (1987), Abstract Objects (Blackwell).

MacBride, F. (2003), 'Speaking With Shadows: A Study Of Neo-Logicism', British Journal for the Philosophy of Science 54, 1, pp.103-63.

Rumfitt, I. (2003), 'Singular Terms And Arithmetical Logicism', Philosophical Books 44, 3, pp.193-219.

Demopoulos, W. (2003), 'On The Philosophical Interest Of Frege's Arithmetic', Philosophical Books 44, 3, pp.220-28.

Rosen, G. (2003), 'Platonism, SemiPlatonism And The Caesar Problem', Philosophical Books 44, 3, pp.229-44.

Schirn, M. (1998) (ed.), The Philosophy Of Mathematics Today (Oxford University Press).

Burgess, J. (2005), Fixing Frege (Princeton University Press).

Burgess, J., and Rosen, G. (1997), A Subject With No Object. Strategies For Nominalistic Interpretation Of Mathematics (Oxford University Press).

Noonan, H. (2001), Frege. A Critical Introduction (Polity Press).

And:

http://plato.stanford.edu/entries/frege-logic/

Frege saw arithmetic as being reducible to logic whereas Kant held the opposite view that it is not reducible to logic. However what is this logic and did Kant and Frege both have the same starting points or definitions of logic? This is fundamental otherwise things begin to collapse. The problem with this logicism of Frege is that although it is true that a syllogism such as A=A is as true as 1=1 and is self-evident and true in form as opposed merely to what we perceive its meaning to be, i.e. A=A is true regardless of whatever meaning we ascribe to A and is thus an analytical truth, Frege's objective to show that all of arithmetic is the logical consequence of analytical truth has never been reached, The fundamental problem is that in seeking to [axiomatise] arithmetic some axioms that are not analytical truths are inevitably involved. A major obstacle in this is the mathematical induction. No one would deny the importance of Frege and mathematical logicism in proof theory or the theory of computability however it fails to address areas such as the whole problem of mathematical philosophy, the ontological status of mathematical "objects" and so on- bringing everything back to the philosophy of logic. On the other hand induction alone is not considered to be strong proof and one shouldn't discard deduction either- considering that most hard sciences are based on deduction based on observation it brings us back to the problem of what mathematics fundamentally is. As for all of these attempts at formalism, futile- since Gödel!

Thank you for this novice's guide to Frege, with which I take exception for the distortions and gross errors it contains.

Here is a small selection of your screw-ups:

syllogism such as A=A

This is not a syllogism, it's a simple identity proposition (if we ignore the fact that "=" is the sign for equality not identity!).

A syllogism is a three proposition argument (http://plato.stanford.edu/entries/aristotle-logic/), two of which are premisses and one the conclusion. And the propositions themselves must be quantified according to strict rules.

Frege's objective to show that all of arithmetic is the logical consequence of analytical truth has never been reached

As you will be able to see if you consult the books and papers I have listed above, this is no longer the case.

A=A is true regardless of whatever meaning we ascribe to A and is thus an analytical truth

I defy you to find "A=A" in Frege's work on the definition of number, except perhaps where he criticises this useless sentence.

the ontological status of mathematical "objects" and so on

While I personally reject 'ontology' as non-sensical (http://www.revleft.com/vb/all-philosophical-theories-t148537/index.html), it is just not true that Logicists have failed to address this. Check out Bob Hale's book on Abtract Objects above to see this, for example. But many other Logicists have addressed this question, too, since Frege's day, including Frege himself (and Russell!).

As for all of these attempts at formalism, futile- since Gödel!

Not so. Quite apart from the replies above to this application of Gödel's infamous 'proof', I have shown earlier in this thread that his 'proof' is worthless since it is based on the defective diagonalisation argument which he lifted from Cantor.

I also would like to point out that is not an argument of the logical and philosophical meaning of what it is "to count" rather a biological and cognitive-science theory of numerosity in non-human sentient beings/lifeforms.

In that case, all you will have shown (or all these scientists will have shown) is that the animals you mention can 'count', not that they can count.

And then you will face an uphill task explaining what this new word "'count'" means without using the old word "count", which would then only succeed in making my neo-Fregean counter-arguments apposite once more.

The ability to estimate, use and relay numerical concepts as well as the ability to solve basic "problems" with/by the application of "numerical" knowledge, i.e. numerical cognition is what is being discussed here and so far you have not provided any information, research or arguments to back up your assertion that the claims being made are erroneous.

Well, what I have questioned is what you mean by "count", and up to now you have ducked this serious problem, which confronts both you and these researchers -- all of whom use pre-Fregean notions of number and counting.

So, it's no use quoting 'research' if that 'research' is riddled with conceptual confusion.

ComradeMan

23rd February 2011, 10:15

CM:
1) Frege's early work (in the Grundlagen), criticising previous theories of number, is not in fact affected by his later writings.

2) The work you quote was not written by Frege and only appears online in joke/spoof pages -- it was made up, and you either fell for this, or you thought I would. I invite you to find a copy of it in any library on the planet, or in any Bibliography of his work. [You can, perhaps, begin here (http://plato.stanford.edu/entries/frege/catalog.html#Cat).]

And either you have made the following up, too, or you have completed some rather dodgy 'research' on the internet:.

Rosa, you need to get out more! It was a joke- hence the smiley face!!!! I don't think you need the reference to know that Russell's paradox caused Frege's ideas a big, big problem just before he was about to publish his work! ;)

Mamma mia,- if a=a and b=c thus a=c is not an Aristotle syllogism? I didn't think we had to write everything out all the time.... ;)

On Frege's basis, applying some kind of iron formalism and logicism you could argue that no one can count but only "count" couldn't you? Or perhaps that counting doesn't exist. But that doesn't explain how cicadas use prime numbers as a survival mechanism nor the cognitive research that uses the same criteria for humans as for animals that has shown that indeed some species have similar abilities and uses of numerosity as we do. We have other problems too as some of Euclid's axioms go out of the window.

So, it's no use quoting 'research' if that 'research' is riddled with conceptual confusion.

Rosa, you can't turn every debate into a debate of logic otherwise a lot of scientific research would go out the window so to speak. Fundamentally you are applying a system of logic which is linguistic to a non-linguistic issue. This is NOT a debate about what the philosophy is of what is meant by counting. The research is not debating what is meant by counting or "counting". I have already clarified these points anyway:-

recognising and estimating numerosities
using estimates of numerosities to make decisions/solve problems
relaying numerical information based on those estimates
The problem is this, you are arguing logicism and formalism on a subject which is only narrowly related to the matter. This is not a debate about what the ant or wasp in question instanziates when "estimating numerosities" ;)

You made some bold statements before ridiculing the idea and when presented with scientific evidence you cunningly, as all "logicists" do, start with logical and linguistic juggling of theories and terms to prove that you were not wrong despite the fact that the answers to Hilber's second problem is negative.

Don't take this as personal attack, despite your high and mighty tone, your arguments are valid and stong but I often think you are in danger of trying to over-axiomitise things and an axiom in itself may be seen as subjective. I prefer a more structuralist approach based on epistemological realities and instead of wasting so much time on ontological debates. The fact that in biology certain animals have been shown to be numerically cognisant is not part of the debate of the three crises in mathematics and your rather negative stance towards Godel.

Logicism is not concerned with formalisability the discovery or application of mathematical truths are discovered or applied and since no one is trying to demonstrate a specific theorem's truth in this debate I don't see what your "issue" is to be honest.

You'll have us all speaking E-prime soon.... :)

Mr.Awesome

23rd February 2011, 10:44

Rosa, I disagree :p

If I have an apple and I get another, I will have more. The concepts of 'more' or 'less' are more or less what maths is ultimately based on. :D

Exakt

23rd February 2011, 10:54

Was language & grammar invented or discovered? :blink:

To me, it seems the same question and the Platonic view just as flawed...

The problem I have with the idea that certain organisms 'count' (and its interesting that in this context we have to use apostrophes), is that it applies an anthromorphic perspective to what is essentially a human invention and activity...

hatzel

23rd February 2011, 11:05

The problem I have with the idea that certain organisms 'count' (and its interesting that in this context we have to use apostrophes), is that it applies an anthromorphic perspective to what is essentially a human invention and activity...

But the entire point of all this is that it isn't an exclusively human invention and activity. Your suggestion is based on the supposed maxim that counting is a human invention and activity, which cannot be debated. Which means that if we then provide evidence of non-human animals counting, you'll say 'they're not counting, we just think they are because they're doing the same thing as us when we count, but only we count', which isn't the strongest argument going...

ComradeMan

23rd February 2011, 11:09

But the entire point of all this is that it isn't an exclusively human invention and activity. Your suggestion is based on the supposed maxim that counting is a human invention and activity, which cannot be debated. Which means that if we then provide evidence of non-human animals counting, you'll say 'they're not counting, we just think they are because they're doing the same thing as us when we count, but only we count', which isn't the strongest argument going...

On that basis when the "mathematical" information was put on the Voyager satellite it was a complete waste of time. Like my point about the "superior intelligence sentient being"- who could equally argue that despite what is perceived to be human mathematical intelligence/knowledge it was just a causal similarity. :laugh:

Exakt

23rd February 2011, 11:15

ComradeMan

23rd February 2011, 11:21

Well, counting seems to be the application of concept to an unlimited amount of situations; we can count bottles of milk, cars on the road, hairs on your head etc. I don't think any animal counts in this manner, i.e. that they've developed a number system which can be applied to any particular situation - they don't separate the 'number' from the 'object(s).' Does that make sense? What do you think?

If you read the research you might see that there is a growing body of evidence to suggest they do.

But suppose the ants had their own number system to recognise objective numerosities as we have our number systems to do the same? Then we could argue that counting is species-subjective but conveniently ignore the numerosities and estimations thereof that are being observed.

If we can count bottles of milk that we may need to buy from the shop based on an "numerical" piece of data we have stored in our memory such as we need x bottles of milk per x day then the wasp that collects 5 and 10 caterpillars respectively for each (1) egg layed is not doing the same thing?

http://www.guardian.co.uk/world/2010/oct/24/bees-route-finding-problems

Rosa Lichtenstein

23rd February 2011, 13:34

CM:

Rosa, you need to get out more! It was a joke- hence the smiley face!!!! I don't think you need the reference to know that Russell's paradox caused Frege's ideas a big, big problem just before he was about to publish his work!

Others might not have known it was a joke, so the points I made needed making.

I don't think you need the reference to know that Russell's paradox caused Frege's ideas a big, big problem just before he was about to publish his work!

Indeed they did, but logicians are well on the way toward repairing his system.

Mamma mia,- if a=a and b=c thus a=c is not an Aristotle syllogism? I didn't think we had to write everything out all the time....

A. No it's not, it's a conditionalised proposition.

B. It's hypothetical, and syllogisms are categorical.

C. Syllogisms, as I told you, have to comprise nothing but quantified propositions, like this:

1. All As are Bs.
2. Some As are Cs.
3. Therefore, some Cs are Bs.

On Frege's basis, applying some kind of iron formalism and logicism you could argue that no one can count but only "count" couldn't you? Or perhaps that counting doesn't exist.

How did you work that one out? in fact, his later Logicism does not affect his earlier arguments about number.

But, let us suppose you are right -- even then -- Wittgenstein's criticisms of Frege, where he takes counting as basic, but which accepts Frege's demolition of earlier theories of number, and which I call the 'Neo-Fregean account of number', still stand.

And that is the version I am defending here, not Frege's later Logicism.

But that doesn't explain how cicadas use prime numbers as a survival mechanism nor the cognitive research that uses the same criteria for humans as for animals that has shown that indeed some species have similar abilities and uses of numerosity as we do. We have other problems too as some of Euclid's axioms go out of the window.

I have already been over this. May I suggest you re-read my earlier reply, and respond to my argument, as opposed to just ignoring it.

Rosa, you can't turn every debate into a debate of logic otherwise a lot of scientific research would go out the window so to speak. Fundamentally you are applying a system of logic which is linguistic to a non-linguistic issue. This is NOT a debate about what the philosophy is of what is meant by counting. The research is not debating what is meant by counting or "counting". I have already clarified these points anyway:-

This is just another way of admitting what I alleged earlier, that this 'research' is riddled with conceptual confusion, which, of course, means that the conclusions drawn are scientifically worthless.

The problem is this, you are arguing logicism and formalism on a subject which is only narrowly related to the matter. This is not a debate about what the ant or wasp in question instanziates when "estimating numerosities"

No I'm not.

I am not a Logicist or a Formalist (these two doctrines are not the same, you seem to think they are -- check out Sections 2.2 and 2.3 at this link (http://en.wikipedia.org/wiki/Philosophy_of_mathematics) for the difference). I just object to misleading things said about them, compounded by some sub-Aristotelian logic thrown in for good measure.

I am in fact a 'nothing-at-all-ist' when it comes to the philosophy of mathematics (do not confuse that with nihilism) -- and that is because I reject all philosophical theories as non-sensical.

You made some bold statements before ridiculing the idea and when presented with scientific evidence you cunningly, as all "logicists" do, start with logical and linguistic juggling of theories and terms to prove that you were not wrong despite the fact that the answers to Hilbert's second problem is negative.

Once again I am not a Logicist; I just know what the English verb "to count" means, which, it seems, some 'researchers' do not when it comes to observing animals.

Don't take this as personal attack, despite your high and mighty tone, your arguments are valid and strong but I often think you are in danger of trying to over-axiomitise things and an axiom in itself may be seen as subjective.

This is plainly another of your 'jokes' since I have in fact 'axiomatised' nothing.

I prefer a more structuralist approach based on epistemological realities and instead of wasting so much time on ontological debates.

And where have I entered into an 'ontological debate'? I specifically said I reject all ontology as non-sense.

The fact that in biology certain animals have been shown to be numerically cognisant is not part of the debate of the three crises in mathematics and your rather negative stance towards Gödel.

You are the one who introduced these 'crises' and mentioned Gödel (in this exchange between me and you), not me!

Logicism is not concerned with formalisability the discovery or application of mathematical truths are discovered or applied and since no one is trying to demonstrate a specific theorem's truth in this debate I don't see what your "issue" is to be honest.

And what relevance has this comment of yours got to do with anything I have argued, or implied?

Answer: none whatsoever.

My arguments have not only not been formalised, they do not need to be.

I don't see what your "issue" is to be honest

And that is hardly surprising is it if you keep reading into what I have in fact said what you would like me to have said, but didn't?

Rosa Lichtenstein

23rd February 2011, 13:42

Mr A:

If I have an apple and I get another, I will have more. The concepts of 'more' or 'less' are more or less what maths is ultimately based on.

In fact, this supports what I argued, since in order to count (anything, not just apples) you have to use a concept expression (a count noun (http://en.wikipedia.org/wiki/Count_noun), in this case "apple") not a name or singular expression.

And that was Frege's point -- which all previous theorist had missed, and which most commentators since his day still miss.:)

Rosa Lichtenstein

23rd February 2011, 13:45

Krimskrams:

But the entire point of all this is that it isn't an exclusively human invention and activity. Your suggestion is based on the supposed maxim that counting is a human invention and activity, which cannot be debated. Which means that if we then provide evidence of non-human animals counting, you'll say 'they're not counting, we just think they are because they're doing the same thing as us when we count, but only we count', which isn't the strongest argument going...

Well, as I have shown, unless these animals can use count nouns (http://en.wikipedia.org/wiki/Count_noun), they aren't counting, whatever else they are doing.

Rosa Lichtenstein

23rd February 2011, 13:47

CM:

If you read the research you might see that there is a growing body of evidence to suggest they do.

But suppose the ants had their own number system to recognise objective numerosities as we have our number systems to do the same? Then we could argue that counting is species-subjective but conveniently ignore the numerosities and estimations thereof that are being observed.

If we can count bottles of milk that we may need to buy from the shop based on an "numerical" piece of data we have stored in our memory such as we need x bottles of milk per x day then the wasp that collects 5 and 10 caterpillars respectively for each (1) egg layed is not doing the same thing?

Well, as we have seen, this 'research' is based on conceptual confusion, so whatever else it shows, it does not show animals can count.

Meridian

23rd February 2011, 14:11

Animals, plants and other things do often act or form in ways which we can count. But this does not mean that the animals or things themselves can count. A species of trees, for example, could be imagined to have an average amount of branching. We can find a multitude of reasons as to why this number happens to be the average, perhaps relating to survivability and reproduction, but the trees being able to count is not one of them. In my opinion, in any case, the patterns we happen to find in observable phenomena are still interesting.

ComradeMan

23rd February 2011, 17:12

Indeed they did, but logicians are well on the way toward repairing his system.

Well on the way to repairing his system- thus using a broken system to attack other systems? Hmmm....;)

A. No it's not, it's a conditionalised proposition..

It's a syllogism describing a transitive property, aka a categorical syllogism in which each part is categorical proposition.

Men are all mortal, Socrates is a man, thus Socrates is mortal.

There are many kinds of syllogism and I am not trying to extoll the virtues of Aristotle however to say that is not a syllogism when it is, is rather bizarre. I have seen it argued that it is rather a Peripatetic syllogism- but a syllogism it remains in either case. ;)

Rosa, all of this metamathematics has nothing to do with the fact that science through observation and experimentation have shown several species of animals to be numerically cognisant. I did point out earlier that no one was saying an ant had written some Principia Mathematica Formica or solved Fermat's last theorem! The logic and philosophy of mathematics is not connected to the observation and application of mathematics.

But I think I see where the misunderstanding or problem is-

What you are saying is that counting implies counting nouns such as 1, 2, 3, 4 and using these to describe quantities. Counting for you then is reduced merely to the ability to demonstrate numerical knowledge "out loud" as such.

By the way, since when did mathematics fundamentally depend on theories of sets in order to function?

What I am saying is that these species, to varying degrees, are numerically cognisant and are able to estimate numerosities and process that data in order to solve problems and futhermore are, in some cases, able to relay that information to other members of the species.

If animals are finding, as to their needs, "bijections" which are being observed such as the wasp example. Thus I think a fair argument can be made that they are counting- although by what "logic" and how they perceive this we might never know. What is the difference between the bottle of milk example and the wasp example? If the wasp had no concept of numerosity how come it always gets 5 and 10 respectively and never 4,11 or 5.5? Or on the other hand if I say that today I have drunk four espressi you could argue that someone who spoke a different language, or my "alien" or perhaps the wasp could argue I was not counting because it could not be proven that what I was saying corresponded to their notions of numerical estimation.

The research is not based on confusion because the research is based on clearly defined axioms of estimating numerosity that I do, you do and so it seems a whole myriad of other lifeforms do subjective, of course, to needs.

PS- Glad you got the other joke this time.;)

Rosa Lichtenstein

23rd February 2011, 20:03

CM:

Well on the way to repairing his system- thus using a broken system to attack other systems? Hmmm....

No, his Logicist definition of number, which appears in the Grudgezetse long after the Grundlagen, has absolutely nothing to do with his demolition of older theories of number in the latter book, as you have been told several times.

It's a syllogism describing a transitive property, aka a categorical syllogism in which each part is categorical proposition.

No, the sentence you used is called a conditionalised proposition, and the fact that you used an "if...then" connective means its is hypothetical not categorical.

In addition, it's not a set of three quantified propositions, so it can't be a syllogism (check out the link I added in my last but one reply to you -- but here (http://plato.stanford.edu/entries/aristotle-logic/) it is again).

There are many kinds of syllogism and I am not trying to extoll the virtues of Aristotle however to say that is not a syllogism when it is, is rather bizarre. I have seen it argued that it is rather a Peripatetic syllogism- but a syllogism it remains in either case

Of course, you can alter the meaning of the word "syllogism" in order to bale yourself out, but we can all do that.

To that end, what would you say if I re-defined "counting" or "number" to include a clause such as this "...which animals cannot master"?

Well, we all know what you'd say...

Men are all mortal, Socrates is a man, thus Socrates is mortal.

Not even this is a syllogism (but it is closer to being one than your earlier "A=A"!), despite what bad logic books will tell you. Once more, if you read Aristotle, each proposition in a syllogism has to be quantified, so a name such as "Socrates" cannot feature in one, except perhaps like this:

1 All men are mortal.
2. Some Socrates is a man.
3. Ergo: Some Socrates is mortal.

But 2. and 3. are syntactically ill-formed.

Rosa, all of this metamathematics has nothing to do with the fact that science through observation and experimentation have shown several species of animals to be numerically cognisant. I did point out earlier that no one was saying an ant had written some Principia Mathematica Formica or solved Fermat's last theorem! The logic and philosophy of mathematics is not connected to the observation and application of mathematics.

No "metamathematics" at all in my arguments. You really must stop inventing things to attribute to me.

The point is that animals do not use count nouns so they can't count.

That would still be true had Frege, Hilbert, Cantor, Gödel, Peano, Russell, Tarski, Skolem, Löwenheim, Church, Gödel, von Neumann, and Wittgenstein (etc.) all died in infancy.

What you are saying is that counting implies counting nouns such as 1, 2, 3, 4 and using these to describe quantities. Counting for you then is reduced merely to the ability to demonstrate numerical knowledge "out loud" as such.

No, the counting numbers you refer to aren't count nouns (http://en.wikipedia.org/wiki/Count_noun). I posted a link for you to familiarise yourself with this phrase. May I suggest you avail yourself of it?

By the way, since when did mathematics fundamentally depend on theories of sets in order to function?

Probably since Dirichlet (http://en.wikipedia.org/wiki/Johann_Peter_Gustav_Lejeune_Dirichlet) invented his odd idea of a function, but what has that got to do with anything?

I have gone on record here saying I do not like set theory since it has nothing to do with mathematics, but represents some sort of Super-Science fiction.

So, why mention it?

What I am saying is that these species, to varying degrees, are numerically cognisant and are able to estimate numerosities and process that data in order to solve problems and furthermore are, in some cases, able to relay that information to other members of the species.

If animals are finding, as to their needs, "bijections" which are being observed such as the wasp example. Thus I think a fair argument can be made that they are counting- although by what "logic" and how they perceive this we might never know. What is the difference between the bottle of milk example and the wasp example? If the wasp had no concept of numerosity how come it always gets 5 and 10 respectively and never 4,11 or 5.5? Or on the other hand if I say that today I have drunk four espressi you could argue that someone who spoke a different language, or my "alien" or perhaps the wasp could argue I was not counting because it could not be proven that what I was saying corresponded to their notions of numerical estimation.

The research is not based on confusion because the research is based on clearly defined axioms of estimating numerosity that I do, you do and so it seems a whole myriad of other lifeforms do subjective, of course, to needs.

Thanks for that, but since this work is based on obsolete ideas about number and counting, it's a waste of time and effort.

Or on the other hand if I say that today I have drunk four espressi you could argue that someone who spoke a different language, or my "alien" or perhaps the wasp could argue I was not counting because it could not be proven that what I was saying corresponded to their notions of numerical estimation.

It would be a change of meaning if there were a language that did not use count nouns in relation to the employment of number words and counting.

Fortunately, there isn't.

Revolution starts with U

23rd February 2011, 20:14

Ive learned one thing here. The amount of things I don't know is ASTOUNDING. :lol:
Well, I already knew that. But it's been heartily reinforced :thumbup1:

ComradeMan

23rd February 2011, 20:26

Ive learned one thing here. The amount of things I don't know is ASTOUNDING. :lol:
Well, I already knew that. But it's been heartily reinforced :thumbup1:

Well- the wise man admits he knows very little--- the fool boasts of his intelligence!

ComradeMan

23rd February 2011, 20:27

Rosa- you don't actually state why these theories are not valid in your opinion other than quibble over the philosophical meaning of what it means to "count" and whereas I have stated quite clearly- estimating, using and relaying numerosities and evidently using numerical information as being what I mean you haven't actually stated what you mean.

Furthermore your insistance that a well know syllogism is not in actual fact a syllogism is bizarre in the least. Denying that set theory, an important branch of mathematics is not part of mathematics because there are some objections to it from some quarters seems a bit like you're being deliberately iconoclastic.

You have failed to address the actual matter at hand, i.e. why you say these animals are not numerically cognisant. All you have to say is that you don't like the theory basically but you don't seem to want to say why or answer the questions.

I also do not understand what you mean when you say count-nouns? The English definitions are all talking about something entirely different connected to English grammar so I presume you mean mathematical objects. If you don't mean mathematical objects and intend count-nouns as linked by you in your answer then I am taken aback really- because that has absolutely nothing to do with this debate at all and is a purely linguistic matter of the English language!

However, if you do mean mathematical objects then you have a problem here because fundamentally mathematical objects do not exist in reality but are abstract objects anyway. So what logic can be based on an abstract object? We would have to agree, axiomatically, on what that abstract object was and would that not pose a problem then for our claims of objectivity and logical truth?

If we want to be really pedantic about terminology, okay- do you deny that these researches show that the species in question are numerically cognisant and possess the ability to subitise numerical information, solve problems based on that information and relay that information in some cases- as............ humans do as well!

Rosa Lichtenstein

23rd February 2011, 21:22

CM:

Rosa- you don't actually state why these theories are not valid in your opinion other than quibble over the philosophical meaning of what it means to "count" and whereas I have stated quite clearly- estimating, using and relaying numerosities and evidently using numerical information as being what I mean you haven't actually stated what you mean.

In fact I have done so several times; here's the latest:

Thanks for that, but since this work is based on obsolete ideas about number and counting, it's a waste of time and effort.

And I am not raising 'philosophical' quibbles about counting; not even you could count without the use of/comprehension of count nouns (on that, see below). So, this is about what we do in ordinary language and every day life, and it would still be the case had philosophy never been invented.

Furthermore your insistence that a well know syllogism is not in actual fact a syllogism is bizarre in the least. Denying that set theory, an important branch of mathematics is not part of mathematics because there are some objections to it from some quarters seems a bit like you're being deliberately iconoclastic.

The 'well known syllogism' you refer to isn't a syllogism to begin with, but as I said before:

Of course, you can alter the meaning of the word "syllogism" in order to bale yourself out, but we can all do that.

To that end, what would you say if I re-defined "counting" or "number" to include a clause such as this "...which animals cannot master"?

Well, we all know what you'd say...

You:

Denying that set theory, an important branch of mathematics is not part of mathematics because there are some objections to it from some quarters seems a bit like you're being deliberately iconoclastic

And there were those who criticised Bolyai, Lobachevsky and Riemann when they denied the validity of Euclid's parallel postulate (which had been accepted as 'part of mathematics' for nigh on 2000 years).

Someone has to say this Emperor is without clothes. [And I'm not the only one -- Poincare for example argued this way, as have others.]

But, the last two points have nothing to do with Frege's demolition of obsolete theories of number.

So, you can bang your head against this brick wall for another couple of weeks/months, if you like.

I'm game...:)

You have failed to address the actual matter at hand, i.e. why you say these animals are not numerically cognisant. All you have to say is that you don't like the theory basically but you don't seem to want to say why or answer the questions.

I have, several times, you just seem to want to ignore what I had to say.

And, it's not that I do not 'like' this theory; it's based on conceptual confusion whether I like it or not.

I also do not understand what you mean when you say count-nouns?

Then follow that link.

The English definitions are all talking about something entirely different connected to English grammar so I presume you mean mathematical objects. If you don't mean mathematical objects and intend count-nouns as linked by you in your answer then I am taken aback really- because that has absolutely nothing to do with this debate at all and is a purely linguistic matter of the English language!

No they feature in all known languages where people can count.

[Or, if you know of one where they don't, I'd be interested to hear about it.]

No human being on the planet would or could do the following if asked to fetch 5 red apples (assuming, of course, they understand the request):

1. Look for sets/collections of five things.
2. Look for sets/collections of red things.
3. Look for apples in either of the latter two sets/collections.

In that order.

Every single person on the planet, who understood this request in their own language, would do this:

4. Look for apples -- and 'apple' is a count noun.
5. Look for red apples in a collection of apples -- or just look for red apples, and count them.

[This example has been adapted from Wittgenstein.]

And they'd do that even if they had never heard of 'count nouns' (as you seem not to have), but what they did would show they understood this logical/grammatical point. Anyone who did not would show they had not grasped the practical skill of counting, or our concept of number (in practical situations).

Now, try that with your ants...:lol:

However, if you do mean mathematical objects then you have a problem here because fundamentally mathematical objects do not exist in reality but are abstract objects anyway. So what logic can be based on an abstract object? We would have to agree, axiomatically, on what that abstract object was and would that not pose a problem then for our claims of objectivity and logical truth?

Yet another red herring, since I nowhere referred to 'mathematical objects', nor would I in such a context.

If we want to be really pedantic about terminology, okay- do you deny that these researches show that the species in question are numerically cognisant and possess the ability to subitise [???] numerical information, solve problems based on that information and relay that information in some cases- as............ humans do as well!

Well, until these 'researchers' show they have abandoned obsolete theories of number and counting, all their work is a sad waste of time and effort.

And, finally, information is only something human beings can appropriate -- unless, of course, you mean 'information' and not information.

ComradeMan

24th February 2011, 00:04

And I am not raising 'philosophical' quibbles about counting; not even you could count without the use of/comprehension of count nouns (on that, see below). So, this is about what we do in ordinary language and every day life, and it would still be the case had philosophy never been invented..

Rubbish. The ability to comprehend the abstract objects develops before the ability to develop the system- a bit like language. The fact that I can perceive, as may other species, numerosities, and then relate them in linguistic form is secondary.

The 'well known syllogism' you refer to isn't a syllogism to begin with, but as I said before:..

Despite the fact that everyone else in the known world seems to say it is....:rolleyes:

And there were those who criticised Bolyai, Lobachevsky and Riemann when they denied the validity of Euclid's parallel postulate (which had been accepted as 'part of mathematics' for nigh on 2000 years).

Someone has to say this Emperor is without clothes. [And I'm not the only one -- Poincare for example argued this way, as have others.].[/QUOTE]
And your point is.... show me one scholar, academic, philosopher who has not been criticised and/or criticised- are you drawing proof from criticism alone- I notice you don't actually explain what the criticism is or why you agree/disagree with it.... Come on... let's have some proofs.

But, the last two points have nothing to do with Frege's demolition of obsolete theories of number.So, you can bang your head against this brick wall for another couple of weeks/months, if you like.

I'm game...:)

And err.... none of your points have anything to do with numerical cognisance in non-human species.... :lol:

I have, several times, you just seem to want to ignore what I had to say. And, it's not that I do not 'like' this theory; it's based on conceptual confusion whether I like it or not.

But you haven't- you've just said what someone else says and used that as an argument.

No they feature in all known languages where people can count.

What are you talking about? The concept of countable and uncountable is pretty damn alien to Italian to start with- and something which is pretty weird in English given that some things can be "countable" and something "uncountable".... but wait, some can be both and some have not always been the same.... dan dan daaan. You can't use features of English language grammar to prove some kind of mathematical universal. This is just ridiculous- and very anglo-centric.

In Italian I can ask for "un'informazione" i.e. an information or "delle informazioni"- some informations or I can do "una ricerca" or "due ricerche" a research or two researches and so on.....

You're mixing up linguistic analysis and logic connected to set theory with NUMERICAL COGNISANCE- they are not the same.

Thanks for the example from Wittgenstein.

Let me ask you, if someone in a crowded bar points at me and indicates with gesture how many beers I want (let's imagine it's very noisy) and then I hold up three fingers back- has any counting happened? :lol:

Or how do you deal with Japanese that has different systems of "number" and "count nouns" depending on what is being counted- untranslatable in other languages? Or there is a South American tribe that basically has no concept of number in their language and culture. Or perhaps Chinese with its unique system?

Now, try that with your ants...:lol:.

Well for a start we were talking about estimating numerosities, ask your human to bring back a grub to hive whatever at x distance based on the chemical relaying of "facts"- or perhaps solve the travelling salesman problem as quick as a bee.....and fly there :lol:- you're using false equivalencies.

Yet another red herring, since I nowhere referred to 'mathematical objects', nor would I in such a context..

Well that's what a number is in mathematics.... ooops, I forgot we were trying to discuss....mathematics and not pseudo-linguistic hocus pocus.

Well, until these 'researchers' show they have abandoned obsolete theories of number and counting, all their work is a sad waste of time and effort...

But you haven't actually shown why it is other than circular arguments based on the fact that you say it is due to your upholding a particular philsophy of mathematics that does not have anything to do with application in the field or observation.

And, finally, information is only something human beings can appropriate -- unless, of course, you mean 'information' and not information.

Can you prove that assertion?

Seeing as information works in biology on the sensory input/output of an organism I think your argumentation is even weaker here, see how bees navigate and provide information on where to find nectar etc- let alone "higher" forms of organisms such as dolphins and the like. But I know where you're going to go with this... okay, so a software program that was designed by a software program and sends a code to a machine- entirely without human interference- would then not be relaying information? Or is a human neuron not relaying information? Or is perhaps DNA not information encoded?

Furthermore, if only humans can attain information then how do animals learn behaviours? What are all those millions of neurons and sensory organs doing.... are you suggesting they are just automatons?

This narrow adherence to a very narrow definition of what is permissable in logic is all well and good in debates on logic but it completely without validity in this argument.

I know where your arguments are coming from but you make the mistake of playing your game in the wrong field.

Nothing you have said so far has refuted the evidence of numerical cognisance in animal species. Given that is probably this same numerical cognisane in the human "animal" that combined with the development of a recorded language etc led to the arguments you put forwards I think the ground is slipping from beneath you.

Rosa Lichtenstein

24th February 2011, 03:25

CM:

Rubbish.

Yes, I wondered how long it would take before you became abusive.

The ability to comprehend the abstract objects develops before the ability to develop the system- a bit like language. The fact that I can perceive, as may other species, numerosities, and then relate them in linguistic form is secondary.

And what 'abstract objects' are these, then? The same as the ones you told us do not exist?

But, even if you are right, the count noun here would be 'abstract object', which means you have inadvertently made my point for me!:lol:

Despite the fact that everyone else in the known world seems to say it is....

In that case, you won't mind posting the original data sheets from the survey I am sure you must have carried out (on a random sample of denizens of this planet) that supports this latest bold claim of yours, will you? :)

And your point is.... show me one scholar, academic, philosopher who has not been criticised and/or criticised- are you drawing proof from criticism alone- I notice you don't actually explain what the criticism is or why you agree/disagree with it.... Come on... let's have some proofs.

Of what?

And may I remind you that you are the one who wanted to keep formalism out of this.

And may I also remind you that you said this not too long ago:

Don't take this as personal attack, despite your high and mighty tone, your arguments are valid and st[r]ong

http://www.revleft.com/vb/showpost.php?p=2030455&postcount=50

Perhaps you have changed your mind and have decided to become abusive since you are losing the argument... :(

you've just said what someone else says and used that as an argument.

Even if that were true, you have yet to respond to it.

But, it isn't true. I defy you to find my arguments anywhere else.

Sure parts have been adapted from Frege and Wittgenstein (and one or two others), but the final form is original to me.

You are welcome to try to show otherwise.:)

And err.... none of your points have anything to do with numerical cognisance in non-human species....

Indeed they have, since they are based on the fact that you (and these 'researchers') have adopted an obsolete theory of number (and thus of something you keep calling 'numerosity'), and of counting.

What are you talking about? The concept of countable and uncountable is pretty damn alien to Italian to start with- and something which is pretty weird in English given that some things can be "countable" and something "uncountable".... but wait, some can be both and some have not always been the same.... dan dan daaan. You can't use features of English language grammar to prove some kind of mathematical universal. This is just ridiculous- and very anglo-centric.

Every known language in which human beings count there are count nouns. I did challenge you to show otherwise, but you seem to have failed miserably

In Italian I can ask for "un 'informazione" i.e. an information or "delle informazioni"- some informations or I can do "una ricerca" or "due ricerche" a research or two researches and so on.....

If the noun in question is capable of receiving a number answer (not a quantity, or else it becomes a mass noun (http://en.wikipedia.org/wiki/Mass_noun)), or is qualified by a number word, then it's a count noun.

And typographically the same word (noun) can flip between the two -- your Italian examples seem to fit that bill, but there are many in English too.

You're mixing up linguistic analysis and logic connected to set theory with NUMERICAL COGNISANCE- they are not the same.

Not so, you are simply ignoring a simple fact about how number words are used in every day life across the globe.

Let me ask you, if someone in a crowded bar points at me and indicates with gesture how many beers I want (let's imagine it's very noisy) and then I hold up three fingers back- has any counting happened?

Your three fingers only make sense to you and your interlocutor since they relate to the count noun "beers".

To see this, if your friend comes across with three dollars instead, you could only clear up the confusion by saying "I meant three beers." You'd have to use the count noun that was implicit all along.

Or how do you deal with Japanese that has different systems of "number" and "count nouns" depending on what is being counted- untranslatable in other languages? Or there is a South American tribe that basically has no concept of number in their language and culture. Or perhaps Chinese with its unique system?

No problem, they are still count nouns if they are used in this way -- no matter what language they appear in.

As for that S American tribe (which you do not name, so we will just have to trust you are not making stuff up again), I did say this:

No they feature in all known languages where people can count.

If they can't count, then my comments do not apply to them -- but we will just have to wait until you provide us with more information, won't we? :)

Well for a start we were talking about estimating numerosities, ask your human to bring back a grub to hive whatever at x distance based on the chemical relaying of "facts"- or perhaps solve the travelling salesman problem as quick as a bee.....and fly there - you're using false equivalencies.

1. I note you have to put "facts" in quotation marks since as far as the ants are concerned they aren't facts. On the other hand, as far as human observers are concerned they might well be.

2. We have been over this many times; the ants can't have a concept of number since they can't use or understand count nouns. Now you can try to bamboozle us with neologisms like "numerosity" and "numerical cognisance", but until you can show these ants use/understand count nouns, then these neologisms are no more substantive than the histrionic hand gestures of stage magicians (who, of course, do this, too, in order to distract and fool the easily fooled).

Too bad for you I have exposed your failed magic trick.

Well that's what a number is in mathematics....

Not so; in mathematics numbers typically feature as number names (often abbreviated by conventionalised figures like "87" or "128665") which they are then used to complete number functions, or they form part of number word rules --, or, with respect to children, they form part of the litany they have to lean off by heart (a bit like they have to learn the alphabet, except these number names are rule-governed).

In more advanced number theory, they are often replaced by algebraic or group theoretical terms, which are expressed on the page, or on your screen, in a highly visible form.

So, there are no 'abstract objects' anywhere in sight here.

Hence, they are very material beings these number names.

ooops, I forgot we were trying to discuss....mathematics and not pseudo-linguistic hocus pocus.

May I suggest you stop doing it then?:)

But you haven't actually shown why it is other than circular arguments based on the fact that you say it is due to your upholding a particular philosophy of mathematics that does not have anything to do with application in the field or observation.

It's not a 'philosophy' of mathematics, it's based on how even you use number words in every day life, that is, when you are not trying to sell someone conceptually confused theories or defend obsolete ideas about numbers.

And what precisely is 'circular' about my argument? You failed to say.

Can you prove that assertion?

No need to; as soon as I informed you, and you were informed by me, and showed that by responding, you proved it for yourself.

Of course, if you can do the same to a bat, or an ant, and tell it something, and get it to respond in a language you or someone else can understand, I will be happy to withdraw my assertion.

Until then, the information that passes between us here only serves to strengthen my case all the time.

So, more please...:)

[Not that it needs strengthening; it is based on how we already use the word "information" in every day life, before some fast talking 'theorist' tries to sell us an oddball 'theory' about animal 'numerical cognisance', and the like.]

Seeing as information works in biology on the sensory input/output of an organism I think your argumentation is even weaker here, see how bees navigate and provide information on where to find nectar etc- let alone "higher" forms of organisms such as dolphins and the like. But I know where you're going to go with this... okay, so a software program that was designed by a software program and sends a code to a machine- entirely without human interference- would then not be relaying information? Or is a human neuron not relaying information? Or is perhaps DNA not information encoded?

I have no problem with the use this word in such areas, but it relates to 'information' not information, and that is because the latter is conveyed by language, and neurons have no language.

I'm sorry if this is news to you.

And software languages, designed by humans who have a language already, is merely a code which can convey information in that sense.

So, once again we see information is solely language based, and thus only humans can disseminate, appropriate it and understand it.

If you have information to the contrary, please share it since, as I noted above, the more you do this, the more you strengthen my case (always assuming you are human, of course).

Furthermore, if only humans can attain information then how do animals learn behaviours? What are all those millions of neurons and sensory organs doing.... are you suggesting they are just automatons?

Well, they certainly do not do so by means of information.

Of course, if you think neurons have a language, please tell us what it is, and how you manage to talk to brain cells.

This narrow adherence to a very narrow definition of what is permissible in logic is all well and good in debates on logic but it completely without validity in this argument.

1. Where have I argued about what is 'permissible' in logic (in relation to information, which is what I assume you mean here)?

2. And where have I even so much as mentioned a definition? In fact, you'd have to understand the word "information" before a definition of it were any use to you (and then it wouldn't be any use, would it?), in view of the fact that definitions contain information. ["Information" is almost unique in this respect. The word "definition" and the word "word" are also constrained in the same way.]

I know where your arguments are coming from but you make the mistake of playing your game in the wrong field.

Apparently not, since you keep making stuff up about them. :lol:

Nothing you have said so far has refuted the evidence of numerical cognisance in animal species. Given that is probably this same numerical cognisance in the human "animal" that combined with the development of a recorded language etc led to the arguments you put forwards I think the ground is slipping from beneath you.

So you say, but we already know you are conceptually confused...

ComradeMan

24th February 2011, 09:33

Rosa-

To start with- no one is being abusive. Saying "rubbish" is not an attack on you, we can disagree strongly without it being a personal attack- however I do find it rich from someone who is so condescending and deliberately facetious at times- albeit it masked in the garb of discussion;) :lol:

You are not conducting a mathematical argument here or an argument based on science. Your basic argument is to go round in circles with linguistics games.

The fact that you insist on denying:
a) that a well-known syllogism is indeed a syllogism (it's not whether you like it or not);
b) that numbers are mathematical objects used to describe an abstract concept- your concept of numbers is a linguistic concept and by all means valid but by no meals all encompassing. Your "real" numbers, i.e. nouns are no more real than anything else seeing as they refer to abstracts- if we want to go down that road that is;

is unhelpful.

Estimating numerosity, i.e. being numerically cognisant does not depend on linguistic ability. This is an incredibly superficial and naive way of looking at things. It is the ability to perceive those abstract concepts, enumerate, if you so prefer, and make real life decisions/solve problems that is being discussed here.

The scientific evidence goes a long way in showing that this is not solely a human trait. Scientific researches suggest that there is a biological and domain specific determined concept of number in both humans and animals- this includes estimation, distinguishing and calculation abilities in organisms that are- as far as we know, non-verbal.
http://www.unicog.org/publications/Dehaene_ReviewNumbersAnimalsInfants_TINS1998.pdf (http://www.unicog.org/publications/Dehaene_ReviewNumbersAnimalsInfants_TINS1998.pdf)

See: Trends Neurosci. (1998) 21, 355–361

Ooops.....:blushing:

Your arguments are circular because you just repeat the same things over again saying that commonly held notions are wrong because you say they are quoting from all over the place in what appears to be random fashion and secondly your insistence on "fringe" theories is irritating at times. One could argue that no one can truly count because all numbers are uncountable--- lol... Cantor.

What you are doing is derailing what was a scientifc sub-debate about mathematical ability into a linguistic debate which is completely invalid here. Your whole argument is that counting and mathematical ability only count in a linguistic sense- and sure if you apply that narrow point-of-view you can win your argument but if you actually bother to read what what is being said and think out of the box, i.e. note that we were talking about being numerically cognisant and having mathematical ability, you'll have to admit being wrong. The inane comparison of Fibonacci sequences in sunflowers to active mathematical decision making in animals is all the more evidence for that.

No one is making up anything, in a negative sense you are making up an argument by falling into the trap of using facts to confirm your opinion/conclusion rather than drawing your conclusions from the facts.

As for the South American tribe, they are called the Pirarrã- and are quite well known to anyone who has studied linguistics. The whole issue of count- and non-count is by no means universal and if you bothered to look at other languages you might find that it is far from universal- as an Italian speaker I have already shown you how this is problematic in the Italian language to start with too.

Your problem is that you can't actually discuss the science here, or the results, can you? So you are going to try and derail things into quibbling about definitions and philosophical arguments that could go on forever about what it actually means "to count" etc. You can deny it all you like but your arguments are within the field of logic and metamathematics and they would be fine in a discussion on those topics but unfortunately this sub-thread, if you like, is not about logic and metamathematics.

So, if all of this human etc etc- and we are going to become anal about information as opposed to "information" etc, I suppose it was completely pointless to send out the Voyager Satellite with information and mathematical codes etc etc on it because even if it is found/receieved by another intelligent sentient being there is no way it could understand it because it would not be human?
:lol:

Well that was a waste of money!

I suggest you stick to philosophy and linguistics (after doing some more fieldwork/research outside of your anglo-centric box).

PS- There will be the day in which software/computers are not designed by humans at all- in which case we will have "machines" designed by "machines" with no human involvement and there are already developments underway to this effect.

ChrisK

24th February 2011, 10:23

Furthermore your insistance that a well know syllogism is not in actual fact a syllogism is bizarre in the least.

Its not a syllogism. According to Quine's Methods of Logic, the only way that what you say can be a syllogism is if it is rendered

All men are mortal.
All things identical with Socrates are men.
Therefore all things identical with Socrates are mortal.

Syllogism require that the propositions be quantified with with "all", "no", "some" or "some...are not..."

ComradeMan

24th February 2011, 12:40

Its not a syllogism. According to Quine's Methods of Logic, the only way that what you say can be a syllogism is if it is rendered

All men are mortal.
All things identical with Socrates are men.
Therefore all things identical with Socrates are mortal.

Syllogism require that the propositions be quantified with with "all", "no", "some" or "some...are not..."

It is the famous syllogism which I translated from the form I know it in- pick it at the translated form is just Rosa's form of being "smart". Of course if I could write it in Italian I would say:-

Tutti gli uomni sono mortali, Socrate è un uomo e quindi Socrate è mortale.

Apologies for bad translations! ;) However this particular syllogism is so well-known I didn't think it would be so necessary to translate it as such. Of course we could get into a debate as to whether the use of "Men" plural- collective infers "all men" or not. :lol:

However leaving this aside, Rosa still has to explain what her theory of number and counting is in a mathematical context and not a linguistic sense and she is full aware that when the references were made to numerical ability in non-human species no one dreamt that insects/ants/dolphins etc were sitting there or swimming around saying numbers out aloud! :lol:

It seems as though Rosa only considers the superficial ability to name and use words as opposed to the deep neuro-cognitive abilities to perceive, manipulate and apply when it comes to numerical cognisance.

She still has not said why her "theories" disprove the assertions made about numerical cognisance in non-human species and she has avoided the hypothetical alien argument too.

Rosa Lichtenstein

24th February 2011, 14:44

CM:

To start with- no one is being abusive. Saying "rubbish" is not an attack on you, we can disagree strongly without it being a personal attack- however I do find it rich from someone who is so condescending and deliberately facetious at times- albeit it masked in the garb of discussion

I'm glad to hear it.

[But you began the facetious remarks.]

You are not conducting a mathematical argument here or an argument based on science. Your basic argument is to go round in circles with linguistics games.

Well you are the one who wants you use ordinary words in odd ways, so I rather think you are the one playing games. [Remember that 'joke' of yours about Frege and Russell?]

The fact that you insist on denying:

a) that a well-known syllogism is indeed a syllogism (it's not whether you like it or not);

1. Who said I liked it? Not me.

2. I did say you can re-define words if you want, but then so can I.

b) that numbers are mathematical objects used to describe an abstract concept- your concept of numbers is a linguistic concept and by all means valid but by no mea[n]s all encompassing. Your "real" numbers, i.e. nouns are no more real than anything else seeing as they refer to abstracts- if we want to go down that road that is;

This is part of the obsolete theory that has you in its grip -- of course, if you do not want me to help extricate you from that quagmire, so be it.

And, may I remind you that human beings were using numbers, and counting, long before philosophers (like Plato) came along and decided "that numbers are mathematical objects used to describe an abstract concept", so it is you who are denying ordinary usage, not me.

Your "real" numbers, i.e. nouns are no more real than anything else seeing as they refer to abstracts- if we want to go down that road that is

Well, as I have pointed out already, I am merely reminding you how even you use number words in every day life, and how you were taught to count, long before the odd ideas you now have invaded your thinking. Which means, of course, that I am talking about numbers, whereas you are talking about 'numbers'.

And it's surely your right to continue to do so; far be it from me to help extricate you from confusion.

Estimating numerosity, i.e. being numerically cognisant does not depend on linguistic ability. This is an incredibly superficial and naive way of looking at things. It is the ability to perceive those abstract concepts, enumerate, if you so prefer, and make real life decisions/solve problems that is being discussed here.

Fine, but recall, these neologisms are based on conceptual confusion.

the ability to perceive those abstract concepts

And how do you do that? Do you go into a trance-like state? Use meditation? Receive messages from on high?

Even worse, how do you know you have 'perceived' the same 'abstract concepts' as anyone else who wants to play this quasi-religious game, or even that you have counted them the same?

As Frege pointed out, this obsolete Platonic theory you are now trying to sell us would destroy mathematics, since no one would be able to check anyone else's 'perceptions', and no one would know that they had 'perceived' the same 'abstractions' as anyone else. So, for instance, you might mean something different by "three" to anyone else.

This is quite apart from the fact, as I have already pointed out, even if you are right, you would still have to use a count noun, namely 'abstract object', to make this ramshackle theory seem to work.

So, in criticising me, you actually end up agreeing with me.:)

Anyway, how do ants 'perceive' these abstractions?

Do we have here meditative ants? Philosophical ants? Was there once an ant version of Plato?

The scientific evidence goes a long way in showing that this is not solely a human trait. Scientific researches suggest that there is a biological and domain specific determined concept of number in both humans and animals- this includes estimation, distinguishing and calculation abilities in organisms that are- as far as we know, non-verbal.

So you keep saying, but 'scientific evidence' was once used to show that the earth was immobile, that there is such a thing as Caloric, and that the continents do not move.

And you are in an even worse position than the above scientists were, since you are conceptually confused, as are the researchers involved in studying 'numerosity' and 'numerical cognisance'.

And it can't be non-verbal, since number words are inextricably connected with count nouns. Even you have to use them.

Your arguments are circular because you just repeat the same things over again saying that commonly held notions are wrong because you say they are quoting from all over the place in what appears to be random fashion and secondly your insistence on "fringe" theories is irritating at times. One could argue that no one can truly count because all numbers are uncountable--- lol... Cantor.

1. You keep repeating yourself, too. I have lost count of the number of times you have told us about 'numerosity', 'numerical cognisance' and these ant versions of Plato.

2. I'm not sure you know what a circular argument is. It has nothing to do with repeating oneself.

3. Criticising 'commonly held notions' isn't either. If that were so, Copernicus was arguing in a circle when he challenged the idea that the earth was stationary.:lol:

4. Neither is referring to 'fringe' theories arguing in a circle.

It seems your grasp of the phrase 'circular argument' is even less secure than your original grasp of 'syllogism' (recall, you tried to tell us that "A=A" was a syllogism!).

What you are doing is derailing what was a scientific sub-debate about mathematical ability into a linguistic debate which is completely invalid here.

Not so; it is central to the point, since these obsolete theories should be challenged.

Your whole argument is that counting and mathematical ability only count in a linguistic sense- and sure if you apply that narrow point-of-view you can win your argument

Well, even you have to use the phrase/count noun 'abstract object' to make your own point. And last I checked you used language to do so, too. So, the more you do this, the more you make my case for me.:)

but if you actually bother to read what is being said and think out of the box,

But, it is yours truly who is thinking 'out of the box', and it is you who is wedded to ancient and obsolete philosophical ideas about number and counting.

i.e. note that we were talking about being numerically cognisant and having mathematical ability, you'll have to admit being wrong.

Not so, since, as I have shown, these ideas are based on conceptual confusion.

The inane comparison of Fibonacci sequences in sunflowers to active mathematical decision making in animals is all the more evidence for that.

Then how do plants know how to count? They must be just as adept little Platonists as your ants are, if you are right.

No one is making up anything,

Well, you made up the idea that I was a Logicist, and then tried to saddle me with your own obsolete theory that numbers are abstract objects, and then you tried to suggest I was not prepared to read stuff:

Hang on a minute, you are not prepared to read the scientific arguments based on experimentation and observation before you discount them?

Then you made stuff up about syllogisms (you tried to argue that "A=A" was a syllogism), then you alleged I had an ontology, or was interested in the subject, and then you asserted Formalism was the same a Logicism (or implied it), and now you are making stuff up about making stuff up!

in a negative sense you are making up an argument by falling into the trap of using facts to confirm your opinion/conclusion rather than drawing your conclusions from the facts.

But you are the one who wants to impose an obsolete theory on the facts, whereas I have merely reminded you how you (and billions of others) use number words in every day life.

As for the South American tribe, they are called the Pirarrã- and are quite well known to anyone who has studied linguistics.

Thanks for that, but as I noted earlier:

No they feature in all known languages where people can count.

So, why you mentioned them is still obscure.

The whole issue of count- and non-count is by no means universal and if you bothered to look at other languages you might find that it is far from universal- as an Italian speaker I have already shown you how this is problematic in the Italian language to start with too.

No, you just showed that Italians have a wider range of count nouns than we do. You also failed to note that when a noun is attached to a number word it automatically becomes a count noun.

The clue is in the phrase "[I]count noun".

Even those Platonic ants of yours should be able to spot that one.

Your problem is that you can't actually discuss the science here, or the results, can you?

What is there to discuss if it's not science to begin with, but a farrago of conceptual confusion?

So you are going to try and derail things into quibbling about definitions and philosophical arguments that could go on forever about what it actually means "to count" etc. You can deny it all you like but your arguments are within the field of logic and metamathematics and they would be fine in a discussion on those topics but unfortunately this sub-thread, if you like, is not about logic and metamathematics.

May I remind you that this thread is entitled:

"Philosophical Question -- Maths Invented or Discovered?"

So, it is you, my fine friend, who is derailing it with these Pythagorean insects of yours.

You can deny it all you like but your arguments are within the field of logic and metamathematics and they would be fine in a discussion on those topics but unfortunately this sub-thread, if you like, is not about logic and metamathematics

Well, until you show my arguments belong to logic and metamathematics, of course I will deny it. It's up to you to substantiate that allegation or withdraw it.

You earlier alleged I was arguing philosophically, failing to note that this thread is about Philosophy. So, you are rather cavalier with the facts, as we can see.

So, if all of this human etc etc- and we are going to become anal about information as opposed to "information" etc, I suppose it was completely pointless to send out the Voyager Satellite with information and mathematical codes etc etc on it because even if it is found/received by another intelligent sentient being there is no way it could understand it because it would not be human?

Not so, since that satellite was programmed by human beings, which general point I have already covered.

because even if it is found/received by another intelligent sentient being there is no way it could understand it because it would not be human?

Well, if they have a language that is translatable into a human language, no problem.

If they do not, then it's not a language, but a 'language', and my point still stands.

Well that was a waste of money!

Indeed, and a waste of your time into the bargain.:(

I suggest you stick to philosophy and linguistics (after doing some more fieldwork/research outside of your anglo-centric box).

Thanks, but I am not a linguist, and I am an anti-philosopher.

May I counter suggest you allow yourself to be extricated from conceptual confusion, even if only to prevent you from wasting any more time and effort on these Hilbertian Hymenoptera?

PS- There will be the day in which software/computers are not designed by humans at all- in which case we will have "machines" designed by "machines" with no human involvement and there are already developments underway to this effect.

Just as there will be a day when seemingly intelligent interlocutors stop confusing science fiction with proof.:)

[Don't tell me, but are these 'developments' being conducted by human beings?]

Rosa Lichtenstein

24th February 2011, 14:49

CM:

However leaving this aside, Rosa still has to explain what her theory of number and counting is in a mathematical context and not a linguistic sense and she is full aware that when the references were made to numerical ability in non-human species no one dreamt that insects/ants/dolphins etc were sitting there or swimming around saying numbers out aloud!

I do not have a theory, nor do I want one. Yet another invention.

It seems as though Rosa only considers the superficial ability to name and use words as opposed to the deep neuro-cognitive abilities to perceive, manipulate and apply when it comes to numerical cognisance.

In which case, and once more, you are talking about 'numbers' and 'counting', not numbers and counting.

She still has not said why her "theories" disprove the assertions made about numerical cognisance in non-human species and she has avoided the hypothetical alien argument too.

Once more, I do not have a theory, and I have shown that you and these 'researchers' are gripped by conceptual confusion, so that's not so much a 'disproof' as it is a demolition.

ChrisK

24th February 2011, 21:03

It is the famous syllogism which I translated from the form I know it in- pick it at the translated form is just Rosa's form of being "smart". Of course if I could write it in Italian I would say:-

Tutti gli uomni sono mortali, Socrate è un uomo e quindi Socrate è mortale.

Apologies for bad translations! ;) However this particular syllogism is so well-known I didn't think it would be so necessary to translate it as such. Of course we could get into a debate as to whether the use of "Men" plural- collective infers "all men" or not. :lol:

Except that it is not a syllogism unless it is quantified. That argument is always given as an example of a valid deductive argument, but it is not called a syllogism.

However leaving this aside, Rosa still has to explain what her theory of number and counting is in a mathematical context and not a linguistic sense and she is full aware that when the references were made to numerical ability in non-human species no one dreamt that insects/ants/dolphins etc were sitting there or swimming around saying numbers out aloud! :lol:

It seems as though Rosa only considers the superficial ability to name and use words as opposed to the deep neuro-cognitive abilities to perceive, manipulate and apply when it comes to numerical cognisance.

She still has not said why her "theories" disprove the assertions made about numerical cognisance in non-human species and she has avoided the hypothetical alien argument too.

You haven't been paying attention to what she's been saying have you?

ComradeMan

24th February 2011, 21:26

This is part of the obsolete theory that has you in its grip -- of course, if you do not want me to help extricate you from that quagmire, so be it. And, may I remind you that human beings were using numbers, and counting, long before philosophers (like Plato) came along and decided "that numbers are mathematical objects used to describe an abstract concept", so it is you who are denying ordinary usage, not me.

And your point? May I remind you that all the philosophers did was find a way of expressing/describing what was already going on. People had language before writing, long before- all writing does is find a means to express and record. Were the Greeks not using grammar before Aristarchus' Τέχνη Γραμματική? In fact many things existed long before the terminology for them was developed or the means of recording them etc. This is not an argument that either invalidates the existence of the item in question nor the terminology to describe it.

Well, as I have pointed out already, I am merely reminding you how even you use number words in every day life, and how you were taught to count, long before the odd ideas you now have invaded your thinking. Which means, of course, that I am talking about numbers, whereas you are talking about 'numbers'.

So what? And who taught the person who taught me? And take it back right to the beginning, damn- who taught the original teacher? The same could be said of language, okay it is acquired in a superficial sense but without and inbuilt, or hardwired system them to be programmed it wouldn't work. If someone, a child, did not already have the "instinct" and the basic ability to estimate numerosities "one" more than "one" etc the whole process would fail. This seems to be further suggested by the fact that some species seem to have non-verbal mathematical ability and others do not, which further suggests that it's a natural product of evolution in social animals- which we happen to be too.

The next points are just sophistry- you may as well argue that one has to prove that Manchester United play in red- what is red? How do I know your red is my red etc etc? It's being intellectually silly. Seeing as you hate abstractions so much, your very language is in itself an abstraction- words are not the things they represent- merely labels. I have haven't seen a dog before I still see something which I then learn is labelled a dog- otherwise how would children acquire their first language?

What happens is that there is recognition of something and we learn the labels. Are you telling me then that if a child sees two apples it does not see what we call two apples on the basis of the fact it might not yet know the word for two? :lol:

Do we have here meditative ants? Philosophical ants? Was there once an ant version of Plato?

Strawman. All we are saying is that some species have numerical cognisance (for the millionth time!!!!)

So you keep saying, but 'scientific evidence' was once used to show that the earth was immobile, that there is such a thing as Caloric, and that the continents do not move.

Yes sure and knew scientific evidence showed that those theories were wrong-but ever the master of perspective here aren't we. There is a slight difference.

And it can't be non-verbal, since number words are inextricably connected with count nouns. Even you have to use them.

Number words are- but not numerosities. When two ants fell into a drop of tree amber millions of years ago- there were two ants, despite no one ever having mentioned the word two. What about if I hold four fingers up? I haven't used a noun.... have I not indicated * * * * ? :lol:

The numerosity, i.e. the ability to estimate and subitise precedes the labelling.

It seems your grasp of the phrase 'circular argument' is even less secure than your original grasp of 'syllogism' (recall, you tried to tell us that "A=A" was a syllogism!).

And I also corrected the bad translation in order to satisify the pedants, like you, and you still don't acknowledge that it is a syllogism. Like I said before, I didn't realise we had to write everything out and the fact that you keep picking at this one small matter instead of looking at the more important issues.

Your circular reasoning is all over the place. You have proved something or do not need to prove something because it is already proven or perhaps not worth proving- because you say so.:thumbup: You constantly "insult" scholars, philosophers and theories- deriding them and claiming they have been demolished because... you say so.

Not so; it is central to the point, since these obsolete theories should be challenged.

Indeed they should- but you haven't actually challenged them at all- in fact you haven't really explained how your ideas work or why they are wrong other than saying that you think they are- I suppose in an existentialist sense they are wrong for you. :lol:

Well, even you have to use the phrase/count noun 'abstract object' to make your own point. And last I checked you used language to do so, too. So, the more you do this, the more you make my case for me.:)

Because I am writing this in a linguistic medium that relies on writing. How about if I held up * * * * fingers.... ;)

Or ** ** -> * * * *

:lol:

Then how do plants know how to count? They must be just as adept little Platonists as your ants are, if you are right.

Strawman- no one was talking about plants- did I say plants were numerically cognisant? -seeing as very little evidence suggests that there is much cognisance to be measured, let alone numerical cognisance.

Well, you made up the idea that I was a Logicist, and then tried to saddle me with your own obsolete theory that numbers are abstract objects, and then you tried to suggest I was not prepared to read stuff:

Well you keep using arguments drawn from logic.

Why is it obsolete? Show me where this definition is considered obsolete and by whom.

"Philosophical Question -- Maths Invented or Discovered?"

Yes and your point... I took the idea from a book I have finished reading by Mario Livio the astrophysicist and mathematician. There are no clear answers to this and so it's a philosophical question in order to encourage discussion. No one was presenting a "proof" or a theorem. Anyway, the thread has evolved since then...

Well, until you show my arguments belong to logic and metamathematics, of course I will deny it. It's up to you to substantiate that allegation or withdraw it.

Well seeing as you keep using nominalist argumentation that belong to the realm of philosophy of mathematics and metamathematics and applying logical arguments drawn from the likes of Wittgenstein then what do you expect? Since when is this worthy of "allegation"- I didn't think it was a crime to be logicist. :lol: But of course you have techincally admitted they are anyway in that sentence. If your arguments were not then you would deny the "allegation" no matter what. ;)

You earlier alleged I was arguing philosophically, failing to note that this thread is about Philosophy. So, you are rather cavalier with the facts, as we can see.

No, you because you are not arguing philosophically about whether mathematics was invented or discovered but trying to refute scientific evidence based on notions which you refuse to explain. Your basic tactic when challenged to discuss the material is just to write it off because it must be wrong etc etc- you obviously haven't even bothered to read it.

You are the one who is accusing me of Aristotleanism or perhaps Plato's Heaven arguments. I would also refer you to Quine-Putnam and perhaps Penelope Maddy. :lol: :p

Not so, since that satellite was programmed by human beings, which general point I have already covered.

:lol:We are talking about the message and information on the satellite destined for alien lifeforms in the case they might find it. If nothing that is human can have information then there is, by your argument, no way they could comprehend it.

Well, if they have a language that is translatable into a human language, no problem. If they do not, then it's not a language, but a 'language', and my point still stands.

What a ridiculous point of view. You may as well say that some species of birds cannot see blue or yellow, but "blue" or "yellow" because they haven't got a word for it. :lol: Of course the fact that a spectrum of light exists and has existed since before humans at varying wavelengths is I suppose irrelevent.

Thanks, but I am not a linguist, and I am an anti-philosopher.

WTF is that supposed to mean? Therefore your existence as an anti-philosopher depends on the existence of that which you are against. LOL!!! Whether you are a linguist or not you are basing your objections on a linguistic argument.

May I counter suggest that you actually demonstrate your theories and defend your points of view without all of this sesquipedalian smokescreen accusing others' arguments of bryophitic aggregation:lol:.

You cannot seem to separate the word for something and that which it labels- be at an object abstract or non-abstract.

As Wittgenstein might remind you- perhaps you should stop applying language outside of its domain of significance.

ComradeMan

24th February 2011, 21:37

Except that it is not a syllogism unless it is quantified. That argument is always given as an example of a valid deductive argument, but it is not called a syllogism.

Well Sextus Empiricus referred to it as a Peripatetic syllogism- it's quoted everywhere as a syllogism περι τŵν κατηγορικν καλουμέν συλλογισμω (syllogismo) in Sextus Empiricus, Hyp. Pyrrh. ii. 164 see also Ernst Kapp, Greek Foundations of Traditional Logic, New York ( 1942), pg 11; Frederick S. J. Copleston, A History of Philosophy, vol. i: Greece and Rome ( 1946), p. 277; Bertrand Russell, History of Western Philosophy, London ( 1946), p. 218.

Here's a paper that discusses it:-
http://www.questia.com/read/54588624?title=Chapter+I%3A+Elements+of+the+System

Rosa Lichtenstein

25th February 2011, 00:13

CM:

And your point?

Read what I said again, only more carefully.

May I remind you that all the philosophers did was find a way of expressing/describing what was already going on. People had language before writing, long before- all writing does is find a means to express and record. Were the Greeks not using grammar before Aristarchus' Τέχνη Γραμματική? In fact many things existed long before the terminology for them was developed or the means of recording them etc. This is not an argument that either invalidates the existence of the item in question nor the terminology to describe it.

Well, this is what I told you a while back, in order to make the point that the obsolete Platonic theory that has you in its grip bears no relation to ordinary usage.

I also pointed out that my argument does not depend on people knowing any grammar; that was why I related that example from Wittgenstein.

No one --, not those who know grammar, not those who do not -- when asked to fetch five red apples will do this:

1. Look for collections of five objects.

2. Look for collections of red objects.

2. Look for apples in 1. or 2.

Not one single person on the planet, now or ever will do this in that order. Not even you will try to do this. [Nor will you try to access the 'abstract mathematical objects' to help you out.]

They (and you) will simply look for apples (count noun, as we now call them), and then sort the red ones out.

So, why you are retailing these homilies about the time before Aristarchus is something of a mystery.

Human beings (including you) show by their practice that have mastered their comprehension of what we now call count nouns.

Or do you think that people only started using/understanding terms like, say, nouns and verbs when grammarians classified these expressions as such?

So what? And who taught the person who taught me?

Whoever did, had to master count nouns in practice, or you'd not be able to count.

And take it back right to the beginning, damn- who taught the original teacher?

Someone, or some group of people, discovered the use of count nouns, and then counting. We can speculate all day long about this, but that does not alter the fact that once discovered, count nouns, numbers and counting go hand-in-hand.

The same could be said of language, okay it is acquired in a superficial sense but without and inbuilt, or hardwired system them to be programmed it wouldn't work. If someone, a child, did not already have the "instinct" and the basic ability to estimate numerosities "one" more than "one" etc the whole process would fail. This seems to be further suggested by the fact that some species seem to have non-verbal mathematical ability and others do not, which further suggests that it's a natural product of evolution in social animals- which we happen to be too.

Well, this will remain controversial until you show that these animals can use and understand count nouns.

The next points are just sophistry- you may as well argue that one has to prove that Manchester United play in red- what is red? How do I know your red is my red etc It's being intellectually silly. Seeing as you hate abstractions so much, your very language is in itself an abstraction- words are not the things they represent- merely labels. I have haven't seen a dog before I still see something which I then learn is labelled a dog- otherwise how would children acquire their first language?

You will note that you had to use a public language to make these points, so the answer, wherever it lies, will be found in the ordinary use of language, not in speculations about unknowable 'abstractions'.

The point is that in the public domain, we can check that we all agree on what certain colours are. You can't do that with these 'abstractions'.

And I'd like to see the argument that shows that language is an abstraction. Until then it remains very material -- you have to speak it (using vibrations in the air), or write it down using ink molecules (and the like) or pixels on a screen. These do not look like abstractions to me.

But you seem to see them everywhere.

What happens is that there is recognition of something and we learn the labels. Are you telling me then that if a child sees two apples it does not see what we call two apples on the basis of the fact it might not yet know the word for two?

Well, I doubt that they use labels, but even if they do, they learn to label things already sorted by means of these count nouns. Even you had to refer to "two apples" using an adjective ("two") and a count noun ("apple").

So, thanks again for making my point for me.:)

Strawman.

Yet another count noun. You see, you are getting the point.

All we are saying is that some species have numerical cognisance (for the millionth time!!!!)

One of which was these Analytic Ants, I believe.

Yes sure and new scientific evidence showed that those theories were wrong-but ever the master of perspective here aren't we. There is a slight difference.

Well, in fact, it was Galileo who showed that the old Aristotelian Physics no longer made sense. Read his Dialogue Concerning Two Chief World Systems and his Dialogues Concerning Two New Sciences, where he uses common sense arguments (and little evidence) -- a bit like me, then -- to show that those ancient Greek theories were obsolete -- again, a bit like me in relation to your obsolete Platonic ideas about number.

Number words are- but not numerosities. When two ants fell into a drop of tree amber millions of years ago- there were two ants, despite no one ever having mentioned the word two. What about if I hold four fingers up? I haven't used a noun.... have I not indicated * * * * ?

Indeed, and when an amoeba splits into two, no doubt you will argue that it understands fractions!

And I note again, you can only make this point by using yet more of those pesky count nouns -- as in "Two ants".

The numerosity, i.e. the ability to estimate and subitise precedes the labelling.

Not so, since no numbers can be attributed to anything without the use of count nouns -- even you find you have to use them.

So, whatever an individual -- or an ant -- is doing when it 'subitizes', he/she/it isn't using numbers. So, the neologism "numerosity" is a misnomer.

What about if I hold four fingers up?

Oops, yet another count noun.

I haven't used a noun....

You just did, in telling me.

And if I see your display of fingers, I can see four fingers -- and so can you -- which is yet another use of a count noun.

Anyway, this is just a variation on your 'beers' example, which I have already covered.

have I not indicated * * * * ?

Well, I can see four asterisks, which you can see, too.

Guess what..., "asterisk" is a count noun.:)

And I also corrected the bad translation in order to satisfy the pedants, like you, and you still don't acknowledge that it is a syllogism. Like I said before, I didn't realise we had to write everything out and the fact that you keep picking at this one small matter instead of looking at the more important issues.

In fact, you asserted that "A=A" was a syllogism! So, we should, I think, look to others for lectures on this subject.

Perhaps your Aristotelian Ants can do better?

Your circular reasoning is all over the place.

Well, we already know -- since you very kindly demonstrated this in your last reply -- you have a rather shaky understanding of what constitutes a circular argument. So, we do not need any more defective lectures from you on this topic, thank you very much.

You have proved something or do not need to prove something because it is already proven or perhaps not worth proving- because you say so.

That is just repetition, it's not a circular argument.

You constantly "insult" scholars, philosophers and theories- deriding them and claiming they have been demolished because... you say so.

Nope, sorry, not circular either.:(

At this point, may I commend your impressive consistency in failing, once again, to grasp the simple concept of a circular argument?

You constantly "insult" scholars, philosophers and theories- deriding them and claiming they have been demolished because... you say so.

Well, you have yet to show I haven't demolished this obsolete theory of theirs/yours.

Perhaps you should concentrate on that and stop trying to lecture us on the nature of the syllogism, which you get wrong, or on the concept of a circular argument, which you can't quite grasp.

Just a thought...

Indeed they should- but you haven't actually challenged them at all- in fact you haven't really explained how your ideas work or why they are wrong other than saying that you think they are- I suppose in an existentialist sense they are wrong for you.

I do not need to explain how 'my ideas work' -- you already know. Every time you use numbers (in this thread, and in every day life), you find you are forced to employ count nouns. So, pick a fight with yourself, not me.

Because I am writing this in a linguistic medium that relies on writing. How about if I held up * * * * fingers....

Oops, you used another count noun here!

Or ** ** -> * * * *

That's at least ten symbols.

Oh, did you not mean that?

Well, what did you mean?

Strawman-

You're getting quite good at these count nouns, aren't you?

There's hope for you yet...

no one was talking about plants- did I say plants were numerically cognisant? -seeing as very little evidence suggests that there is much cognisance to be measured, let alone numerical cognisance.

I didn't mention S American tribes, but you did.

Why are you allowed to introduce new examples and I'm not?

So, according to your obsolete theory, plants must be experts with Fibonacci numbers, and amoebae must be dab hands with fractions.

Well you keep using arguments drawn from logic.

My only arguments drawn from logic were in relation to your odd ideas about syllogisms and to correct your misinformation about Frege.

My arguments against your obsolete theory were not drawn from logic, but depend on how we, and you, use number language and how we, and you, count.

Why is it obsolete?

It's based on ancient ideas about the nature of numbers -- that they are abstract objects of some sort

Show me where this definition is considered obsolete and by whom.

Already done -- it's in Frege's Grundlagen. You should read it some time.

[You are rather like someone who clings onto the idea that the earth is stationary long after the work of Copernicus, Galileo and Newton.]

Yes and your point...

I explained my point; you need to read more carefully. Here it is again:

You earlier alleged I was arguing philosophically, failing to note that this thread is about Philosophy.

You

Well seeing as you keep using nominalist argumentation that belong to the realm of philosophy of mathematics and metamathematics and applying logical arguments drawn from the likes of Wittgenstein then what do you expect? Since when is this worthy of "allegation"- I didn't think it was a crime to be logicist.

Nothing nominalist about my arguments; I fully accept abstractions -- I just balk at the use of philosophical abstractions. I am perfectly OK with abstract common nouns -- I have even used many myself in this thread. No Nominalist would say that.

philosophy of mathematics and metamathematics and applying logical arguments drawn from the likes of Wittgenstein then what do you expect?

1. Does this mean you prefer illogical arguments?

2. As I have pointed out already:

My only arguments drawn from logic were in relation to your odd ideas about syllogisms and to correct your misinformation about Frege.

3. This thread, may I remind you once again, is about philosophy. So why complain if you think I am using 'philosophical arguments'. You should complain if I didn't!

4. Wherever my arguments are from, you can't respond effectively to them, hence these diversionary tactics of yours.

5. Not one of my arguments against your obsolete theory is metamathematical. I'm beginning to think you are as insecure with this word as you were with 'circular argument' and 'syllogism'.

Metamathematics is another word for proof theory.

The branch of logic dealing with the study of the combination and application of mathematical symbols is also sometimes called metamathematics or metalogic.

http://mathworld.wolfram.com/Metamathematics.html

If you think otherwise, be kind enough to show the good people here where I have used 'proof theory (http://plato.stanford.edu/entries/proof-theory-development/)' or 'metalogic (http://en.wikipedia.org/wiki/Metalogic)'.

But, let us suppose you are right, what is so evil about metamathematics?

If you can refer to obscure S American tribes, why can't I refer to proof theory (not that I have)?

I didn't think it was a crime to be logicist. But of course you have technically admitted they are anyway in that sentence. If your arguments were not then you would deny the "allegation" no matter what.

Indeed, it isn't a crime, but do I have to deny I am all manner of things just to stop you alleging I am one anyway? On that basis, I could claim you are a Tibetan Head-hunter since you haven't denied you are one.

Anyway, I did deny it. In earlier in this thread I said this:

I am not a Logicist or a Formalist (these two doctrines are not the same, you seem to think they are -- check out Sections 2.2 and 2.3 at this link (http://en.wikipedia.org/wiki/Philosophy_of_mathematics) for the difference). I just object to misleading things said about them, compounded by some sub-Aristotelian logic thrown in for good measure.

I am in fact a 'nothing-at-all-ist' when it comes to the philosophy of mathematics (do not confuse that with nihilism) -- and that is because I reject all philosophical theories as non-sensical

http://www.revleft.com/vb/showpost.php?p=2030583&postcount=57

So, it looks like you are still trying to make stuff up.

If I were in your parlous state, I think I might do so, too.

No, you because you are not arguing philosophically about whether mathematics was invented or discovered but trying to refute scientific evidence based on notions which you refuse to explain. Your basic tactic when challenged to discuss the material is just to write it off because it must be wrong etc you obviously haven't even bothered to read it.

Make your mind up! One minute I am arguing philosophically, the next I'm not, according to you.

Your basic tactic when challenged to discuss the material is just to write it off because it must be wrong etc you obviously haven't even bothered to read it.

1. You haven't bothered to read Frege on this. That's like not bothering to read Newton or Galileo in this area, all the while urging others to re-read the old Ptolemaic textbooks.

2. I will read them. Until then, and unless you can show where my arguments go wrong, my case still stands.

You are the one who is accusing me of Aristotelianism or perhaps Plato's Heaven arguments. I would also refer you to Quine-Putnam and perhaps Penelope Maddy.

I have read and studied them, and many more besides. [Putnam has since changed his mind, and is now more of a Wittgensteinian]. But, what have they go to do with how we use number words in every day life and how we count?

Nothing, that's what.

So, you can stop name-dropping.

We are talking about the message and information on the satellite destined for alien lifeforms in the case they might find it. If nothing that is human can have information then there is, by your argument, no way they could comprehend it.

I already covered that; here it is again:

Well, if they have a language that is translatable into a human language, no problem.

If they do not, then it's not a language, but a 'language', and my point still stands.

And I note that you use the word 'comprehend', which is an English word, not a term taken from an alien 'language'.

So, even you have to use human language to make yourself understood. And understood even to aliens, who, if they can translate your words into their tongue, no problem.

If they can't, the point falls by default, since they will not then be able to understand this information, or you.

What a ridiculous point of view.

Ah, yet more abuse. I feel right at home now.

You may as well say that some species of birds cannot see blue or yellow, but "blue" or "yellow" because they haven't got a word for it. Of course the fact that a spectrum of light exists and has existed since before humans at varying wavelengths is I suppose irrelevant.

Where did I say birds could not see colours? But, try talking to a bird using colour language and see how far you get.

Same with aliens. If you try to communicate with them and they can't translate what you say into their language, you will be wasting your time -- just as much in fact as you would be chatting to birds.

WTF is that supposed to mean?

Which word don't you understand? [Perhaps if you obtained a dictionary, it might help.]

Therefore your existence as an anti-philosopher depends on the existence of that which you are against.

The same is true of those who, say, fight disease: the fact that they do so does not mean they have to catch one. Same with philosophy.

LOL!!! Whether you are a linguist or not you are basing your objections on a linguistic argument.

Not so; I am basing it on how you and I both use number language, and how humans did so before Linguistics and Grammar were invented.

But, even if I were using Linguistics, you have yet to reply adequately to my arguments.

May I counter suggest that you actually demonstrate your theories

Once more, I do not have theory, nor do I want one.

and defend your points of view without all of this sesquipedalian smokescreen accusing others' arguments of bryophitic aggregation

Where exactly have I failed to defend my allegations? Point out where and I will rectify the situation.

You cannot seem to separate the word for something and that which it labels- be at an object abstract or non-abstract

Well, words aren't labels, we have covered that point here many times. I can re-direct you to those discussions if you like.

The basic idea is that if all words were labels, then they would all be names. That would turn every sentence into a list, and lists say nothing. As Prof Lowe made the point:

"What is the problem of predication? In a nutshell, it is this. Consider any simple subject-predicate sentence, such as..., 'Theaetetus sits'. How are we to understand the different roles of the subject and the predicate in this sentence, 'Theaetetus' and 'sits' respectively? The role of 'Theaetetus' seems straightforward enough: it serves to name, and thereby to refer to or stand for, a certain particular human being. But what about 'sits'? Many philosophers have been tempted to say that this also refers to or stands for something, namely, a property or universal that Theaetetus possesses or exemplifies: the property of sitting. This is said to be a universal, rather than a particular, because it can be possessed by many different individuals.

"But now we have a problem, for this view of the matter seems to turn the sentence 'Theaetetus sits' into a mere list of (two) names, each naming something different, one a particular and one a universal: 'Theaetetus, sits.' But a list of names is not a sentence because it is not the sort of thing that can be said to be true or false, in the way that 'Theaetetus sits' clearly can. The temptation now is to say that reference to something else must be involved in addition to Theaetetus and the property of sitting, namely, the relation of possessing that Theaetetus has to that property. But it should be evident that this way of proceeding will simply generate the same problem, for now we have just turned the original sentence into a list of three names, 'Theaetetus, possessing, sits.'

"Indeed, we are now setting out on a vicious infinite regress, which is commonly known as 'Bradley's regress', in recognition of its modern discoverer, the British idealist philosopher F. H. Bradley. Bradley used the regress to argue in favour of absolute idealism...." [Lowe (2006).]

Lowe, E. (2006), 'Take A Seat, Then Consider This Simple Sentence (http://www.timeshighereducation.co.uk/story.asp?storyCode=202436&sectioncode=39)', Times Higher Education Supplement, 07/04/06.

This is an ancient idea, found in Plato's Cratylus. It's no surprise, therefore, to find it re-surfacing in support of your other obsolete theory of numbers.

As Wittgenstein might remind you- perhaps you should stop applying language outside of its domain of significance

1. But you try to do that when you talk about ants and their 'numerosity', or do you suppose you are not using language to do this?

2. You might like to consult Wittgenstein's arguments that words are not labels while you are at it.

But, what do these label: Nothing, all, but, or, if, everything, Hermite Polynomial, nowhere, gap, Abelian Group, something, when, today, Centre of Mass of the Galaxy, yesterday, pi, the average woman, surface, hole, label, not a label, word...?

Rosa Lichtenstein

25th February 2011, 00:14

CM:

Well Sextus Empiricus referred to it as a Peripatetic syllogism- it's quoted everywhere as a syllogism περι τŵν κατηγορικν καλουμέν συλλογισμω (syllogismo) in Sextus Empiricus, Hyp. Pyrrh. ii. 164 see also Ernst Kapp, Greek Foundations of Traditional Logic, New York ( 1942), pg 11; Frederick S. J. Copleston, A History of Philosophy, vol. i: Greece and Rome ( 1946), p. 277; Bertrand Russell, History of Western Philosophy, London ( 1946), p. 218.

Nice piece of hurried, cut and paste research on the internet, from someone who tried to tell us that "A=A" is a syllogism.:lol:

Rosa Lichtenstein

25th February 2011, 01:10

Moreover your link is to Jan Lukasiewicz's book Aristotle's Syllogistic, which I venture to suggest you did not read too carefully before you posted that link, for he says the following:

IN three recently published philosophical works the following is
given as an example of the Aristotelian syllogism:

(1) All men are mortal,
Socrates is a man,
therefore
Socrates is mortal.

This example seems to be very old. With a slight modification --
'animal' instead of 'mortal' -- it is quoted already by Sextus
Empiricus as a 'Peripatetic' syllogism. But a Peripatetic syllo-
gism need not be an Aristotelian one. As a matter of fact the
example given above differs in two logically important points
from the Aristotelian syllogism.

First, the premiss ' Socrates is a man' is a singular proposition,
as its subject ' Socrates' is a singular term. Now Aristotle does not
introduce singular terms or premisses into his system. The follow-
ing syllogism would therefore be more Aristotelian:

(2) All men are mortal,
All Greeks are men,
therefore
All Greeks are mortal.

Bold added.

Which is what I have been saying all along.

And you are right. The skeptic Sextus Empiricus (nearly 500 years after Aristotle died) began to use singular terms (I even hinted at such in an earlier thread), calling these 'Peripatetic Syllogisms', but you did not use the phrase 'Peripatetic Syllogisms' from the start, you just mentioned 'Syllogisms', which were, of course, invented by Aristotle.

Moreover, not even "A=A" is one of your 'Peripatetic Syllogisms'.

ComradeMan

25th February 2011, 01:37

CM:Nice piece of hurried and cut and paste research on the internet, from someone who tried to tell us that "A=A" is a syllogism.:lol:

Is it wrong? I notice this tactic of yours that conveniently avoids the point. You said the, probably most, famous syllogism that was mentioned in passing was not a syllogism (presumably by your definition:lol:) and when presented with sources you proceed to attack the idea of giving a source. Fundamentally it does not matter if it was quoted on the back of a chocolate bar wrapper- as long as it's right/truthful. ;)

What have you offered other than "cut and pasted" ideas. Seeing as most of my books are in Italian- would you prefer me to write in Italian- or rather try to do you the courtesy of finding things in your language?

Your reduction of mathematics to linguistic tokens- i.e. count nouns seems more like nominalism than anything else.

All your facetious points here are rather stupid because you are attacking my use of language while ignoring the fact that this medium requires both of us to use it. On the other hand if I am alone in a place with no other people and find two apples, I can pick them up and know I have two apples- estimating their numerosities by placing one in each pocket without ever breathing a word, thinking a count noun as you so choose to view it or even thinking of the words "two apples, one in each pocket"- I have done a basic mathematical operation without recourse to language.

Over and over and over again- you fail to see the point, which strikes me as rather obtuse- in order for one to be able to use your count-nouns the ability to deal with numerical estimation must be "hardwired" into the brain or any such count-nouns etc etc could not follow.

You seem to swing from one viewpoint to the other with vague references and denials and anti-statements and yet you actually fail time and time again to come up with an argument that refutes the---

numerical cognisance of non-human species

:lol:

There are differing philosophies of mathematics and also differing views within these "sets" :lol: and no one theory holds absolute sway so your all or nothing type approach writing off everything in the name of something or other you cannot even define is ridiculous.

Quite frankly I don't care what Wittgenstein's arguments about words and labels is- I am not writing a treatise here. Seeing as a "label" is something attached to something in order to identify it or its content etc is not an unreasonable use in a light debate.

Your other tactic it seems is to rely on strawmen- where have I promoted the idea of a Platonic Heaven for you to start with all this nonsense about Platonic ideas.

I would prefer the ideas of Maddy to be honest- but that's not what we're discussing here.

So if x number of apples exists in a box that no one can see then there isn't x number of apples until someone opens the box and counts them? And what if a humble ant or bee were trapped in the box and could enumerate them- estimate their numerosity as such, would it not count for mathematical/numerical cognisance because the said insect could not shout out "Hey there are x number of apples in here and please let me out?".....

When "bees" communicate angles and directions in their bee dance in order to provide a navigational "map" to a food source to their co-hive bees, i.e. providing distance information and angular direction and numbers up to four (indicating the estimation of the numerosity of landmarks etc) this is not mathematical? Not numerical? Has no validity in science?

Stop being disingenuous and deliberately obtuse because you can't distinguish between when certain arguments are appropriate and when they are not. However I suppose you'll just insist you're right and everyone else is wrong yet fail to show why.

There is also a problem with the fact that if an apple didn't exist, we wouldn't couldn't have a word for apple- or we would have to imagine an apple to give it a name, just like unicorns or other imaginary things that exist in the mind so to speak.

Now, if numbers didn't exist in a certain sense there would be no count-nouns or numerals.

Another interesting thing is that if I say for example 2:2=1 the numeral two or the sound "two" has nothing that indicates * * therefore I am capable of doing an operation without having to have two things in front of me as such, only 1 could be argued to represent 1 and what does the number 0 represent? Because if zero is nothing then 0 is exactly what?:lol:

But at the end of the day no amount of intellectual masturbation changes the fact that animal species use their numerical cognisance to solve problems of calculation and arithmetic in the natural world and entirely independently of human intervention.

Rosa Lichtenstein

25th February 2011, 06:08

CM:

Is it wrong?

Read my second post on this.

I notice this tactic of yours that conveniently avoids the point. You said the, probably most, famous syllogism that was mentioned in passing was not a syllogism (presumably by your definition) and when presented with sources you proceed to attack the idea of giving a source. Fundamentally it does not matter if it was quoted on the back of a chocolate bar wrapper- as long as it's right/truthful.

Where did I "attack the idea of giving a source"?

You just can't resist making stuff up, can you?

You said the, probably most, famous syllogism that was mentioned in passing was not a syllogism

And, indeed it isn't. Sextus Empiricus re-defined the word, which I have already told you, or anyone can do.

But, if so I can do it, too.

So, here's my 're-definition' of 'number' and 'counting': "Animals can't count, nor do they have numerical cognisance".

Are you forced to accept this? Of course not. Same with 'Syllogism'. No one is forced to accept Sextus Empiricus's re-definition of 'syllogism' so it can't be the definition.

Moreover, as I have pointed out several times, but you choose to avert your tender eyes, your very first example of a syllogism was "A=A". I invite you now to try to find that given as an example of a syllogism in Sextus Empiricus, in Aristotle, or in any logic text you can find on the internet, or in a library, published in the last 2000+ years.

And good luck with that one!

What have you offered other than "cut and pasted" ideas. Seeing as most of my books are in Italian- would you prefer me to write in Italian- or rather try to do you the courtesy of finding things in your language?

Other than re-quote earlier posts of mine in this thread, I have in fact only cut and pasted one item, my quotation of Professor Lowe, and that wasn't done after hasty 'research' on the internet, like you, since I have copy of the original review in my possession (I used to subscribe to The London Review of Books), which I read four years ago. Moreover, it appeared at my site in one of my essays soon after. In addition, I have quoted it at RevLeft many times over the last few years.

Your reduction of mathematics to linguistic tokens- i.e. count nouns seems more like nominalism than anything else.

Not so, as I have pointed out already, I am quite happy to accept abstract ideas in relation to mathematics; where I draw the line is over the philosophical use of abstractions.

But, let us suppose you are right, [I]even then, you have no effective answer to even to this, and that is because in your every day practice this is precisely what you do too -- that is, you use number words associated with count nouns -- as does the rest of humanity, now and in the past.

All your facetious points here are rather stupid because you are attacking my use of language while ignoring the fact that this medium requires both of us to use it.

Well, you are the one who began the use of facetious remarks, so you can hardly point any fingers at me.

On the other hand if I am alone in a place with no other people and find two apples, I can pick them up and know I have two apples- estimating their numerosities by placing one in each pocket without ever breathing a word, thinking a count noun as you so choose to view it or even thinking of the words "two apples, one in each pocket"- I have done a basic mathematical operation without recourse to language.

And once again, you have to use count nouns to make this point.

I have done a basic mathematical operation without recourse to language

Not so, all you have done is put something in your pocket. You might as well say that when two apples fall off a tree, the tree has done some mathematics, too.

But, what if I interjected, and said "Ah, there are four items here, not two." How would you clear that up?

So, you are confusing the perception of distinct objects with the apprehension of number words. To see that, I could pick up a hundred marbles, not appreciate there are a hundred there, and put them in one pocket. But to know what I had in fact done, I'd have to count them, and that would involve the implicit use of count nouns.

Over and over and over again- you fail to see the point, which strikes me as rather obtuse- in order for one to be able to use your count-nouns the ability to deal with numerical estimation must be "hardwired" into the brain or any such count-nouns etc could not follow.

[I]You are resorting to science fiction again.

If these things are 'hard-wired' in the brain, and it actions 'numerical estimation' for us, that implies that little human beings (who also use count nouns) live in your head. And those little human beings must likewise have even smaller humans in their heads, and so on...

If not, then you must be using 'numerical' in a new and-as-yet-unexplained sense. If so what is it?

You seem to swing from one viewpoint to the other with vague references and denials and anti-statements and yet you actually fail time and time again to come up with an argument that refutes the---

I note you do not give any examples, which suggest you are back to making stuff up again.

numerical cognisance of non-human species

Well, as I have shown this idea is based on conceptual confusion,-- either that or, once again, you must be using 'numerical' in a new and-as-yet-unexplained sense.

There are differing philosophies of mathematics and also differing views within these "sets" and no one theory holds absolute sway so your all or nothing type approach writing off everything in the name of something or other you cannot even define is ridiculous.

I thought you did not want to introduce such considerations into this thread? You need to make your mind up.

And sure there are different theories, but since I do not have a theory, nor do I want one, it's not too clear why raised this point.

None of my arguments against your obsolete ideas depends on set theory, or upon anyone's theory of number -- as you have been told several times.

Any chance you can stick to the point, then?

Quite frankly I don't care what Wittgenstein's arguments about words and labels is- I am not writing a treatise here. Seeing as a "label" is something attached to something in order to identify it or its content etc is not an unreasonable use in a light debate.

Fine, stay ignorant, and remain super-glued to ancient and unworkable ideas about the nature of language -- ideas even Plato rejected.

On the other hand, if you are right, all your sentences would be lists, and they'd say nothing.

That's OK with me...:)

Your other tactic it seems is to rely on strawmen-

Nice use of yet another count noun.

where have I promoted the idea of a Platonic Heaven for you to start with all this nonsense about Platonic ideas.

You promoted the idea that numbers were abstract objects. If they do not live in Platonic heaven, where then do they reside?

I would prefer the ideas of Maddy to be honest- but that's not what we're discussing here.

Fine, but as I have already noted, nothing she has to say impacts on how we already use number words, and how we count -- so why mention her work?

So if x number of apples exists in a box that no one can see then there isn't x number of apples until someone opens the box and counts them?

Certainly there is an unknown number of apples in the box, but so what? There are apples in the box too that we can't see. Does that make them abstract apples?

And, I note once more you have to use the count noun "apple" to make your point -- which is my point too.

If you really believed your own theory you'd say something like this:

So if x number exists in a box that no one can see inside, there isn't x number until someone opens the box and counts?

But number of what? Apples, pips, peels, cores, piths, blemishes on the skins of each apple, apple molecules, carbon atoms, trace elements, elementary particles...? Until you say which count noun applies, the attribution of number plainly cannot gain a grip. There is no number as such in the box, on a number of apples, of cores, of pips, of...

And what if a humble ant or bee were trapped in the box and could enumerate them- estimate their numerosity as such, would it not count for mathematical/numerical cognisance because the said insect could not shout out "Hey there are x number of apples in here and please let me out?".....

Well, if you can show that these Hilbertian Hymenoptera have a grasp of count nouns, then sure they will be able to count.

But can you?

Otherwise this intrepid Pythagoras of the insect world will not know what to count: Apples, pips, peels, cores, piths, blemishes on the skins of each apple, apple molecules, carbon atoms, trace elements, elementary particles...?

And it's little use you telling us it will count the apples, since that is to bias the question with your own use of a count noun -- which you have yet to show this Archimedean Ant can grasp.

When "bees" communicate angles and directions in their bee dance in order to provide a navigational "map" to a food source to their co-hive bees, i.e. providing distance information and angular direction and numbers up to four (indicating the estimation of the numerosity of landmarks etc) this is not mathematical? Not numerical? Has no validity in science?

No maths involved here -- unless these Boolean Bees have a grasp of count nouns. So, whatever they are doing, it's "not mathematical. Not numerical" -- unless, of course, you are using these words in a new and-as-yet-unexplained sense.

But, let us suppose that you are right, in that case, when a pea is planted upside down in the ground, and has to reverse itself and turn through 180 degrees to grow toward the surface, it too must be using mathematics. Are you prepared to countenance the existence of these Poincarés of the Pea World?

And when amoebae divide into two, they must surely understand fractions.

And if I throw a ball at an angle to the horizontal, and it follows a path of least action (http://en.wikipedia.org/wiki/Principle_of_least_action) (a parabola, of we ignore air resistance), then it too must understand advanced projectile mathematics. After all, how could a ball possibly understand this complex principle and know exactly where to go, and how to get there? Methinks we have a Brouwerian (http://en.wikipedia.org/wiki/Luitzen_Egbertus_Jan_Brouwer) Ball here.

Stop being disingenuous and deliberately obtuse because you can't distinguish between when certain arguments are appropriate and when they are not. However I suppose you'll just insist you're right and everyone else is wrong yet fail to show why

No disingenuousness from me. And you are the one who keeps introducing irrelevances here not me.

There is also a problem with the fact that if an apple didn't exist, we wouldn't couldn't have a word for apple- or we would have to imagine an apple to give it a name, just like unicorns or other imaginary things that exist in the mind so to speak.

Even so, 'imaginary apple' is a count noun, as is 'unicorn'. If you can count them, then they have already been discriminated by count nouns.

And there is no escaping from this -- since, as we have seen many times, even you have to use them to make yourself understood.

If you find you can kick the habit, and still make yourself comprehensible, then I might have to revise my ideas. But can you?

Give it a go...:)

Now, if numbers didn't exist in a certain sense there would be no count-nouns or numerals.

No, it's the other way round, as you have seen -- since even you just can't kick the habit of using those pesky count nouns.

Or, can you?

Once more, go for it. We're all rooting for you: Tell us a tale about counting, or the use of numbers, where there are no count nouns anywhere in sight, either as used by you or anyone else -- and make your intentions clear so we can all follow you without using any count nouns to help you out.

Another interesting thing is that if I say for example 2:2=1 the numeral two or the sound "two" has nothing that indicates * * therefore I am capable of doing an operation without having to have two things in front of me as such, only 1 could be argued to represent 1 and what does the number 0 represent? Because if zero is nothing then 0 is exactly what?

I covered this 'objection' in an earlier post.

But, it's you, not me, who has a problem with zero. Which 'abstract object' does it refer to? As soon as you tell us, then that 'object' will be one in number, not zero!

If you want me to tell you how I can easily cope with zero, you only have to ask...:)

But at the end of the day no amount of intellectual masturbation

Yes, I wondered what was making you blind...

changes the fact that animal species use their numerical cognisance to solve problems of calculation and arithmetic in the natural world and entirely independently of human intervention.

Alas for you, until you show otherwise, this obsolete idea is still based on conceptual confusion.

ComradeMan

25th February 2011, 09:41

CM:Where did I "attack the idea of giving a source"? You just can't resist making stuff up, can you?

Stop being disingenuous, if I am to be accused of being "abusive" for saying "rubbish" then your sarcasm, sniping and little comments are "attacks"- I gave a source, a respected source and also an original source along with Russell- intstead of discussing it, you jump to straight to saying it was "copied" and "pasted"... so what? Sorry... that's a fail.

And, indeed it isn't. Sextus Empiricus re-defined the word, which I have already told you, or anyone can do.

So, here's my 're-definition' of 'number' and 'counting': "Animals can't count, nor do they have numerical cognisance".Are you forced to accept this? Of course not. Same with 'Syllogism'. No one is forced to accept Sextus Empiricus's re-definition of 'syllogism' so it can't be the definition.

But this silly ontological debate gets us exactly where? Because if we start on that line of thinking then what is a definition? What logic did the definer use to define the definition? Who judges the judge? I suppose a physicist only studies "physics" then and not physics because of the risk of incompleteness or error in any of his or her work.:lol:

Moreover, as I have pointed out several times, but you choose to avert your tender eyes, your very first example of a syllogism was "A=A"......

And I admitted that I put it up in haste and corrected it accordingly- now move on.... Picking out one bad example or miswording, dwelling on it and trying to use this to "win" your argument is which fallacy?....:lol:

Other than re-quote earlier posts of mine in this thread, I have in fact only cut and pasted one item, my quotation of Professor Lowe, and that wasn't done after hasty 'research' on the internet, like you, since I have copy of the original review in my possession (I used to subscribe to The London Review of Books), which I read four years ago. Moreover, it appeared at my site in one of my essays soon after. In addition, I have quoted it at RevLeft many times over the last few years.

You're not really attacking the argument are you? All of this "unlike you" and all the heroic deeds you have done at RevLeft etc... irrelevant smokesecreen--

Not so, as I have pointed out already, I am quite happy to accept abstract ideas in relation to mathematics; where I draw the line is over the philosophical use of abstractions.But, let us suppose you are right, even then, you have no effective answer to even to this, and that is because in your every day practice this is precisely what you do too -- that is, you use number words associated with count nouns -- as does the rest of humanity, now and in the past.

I use number words or count-nouns to express numerosities that I (can) perceive within the limits of my sensory and cognitive evolution as an organism. Perhaps a "bee" by buzzing using its wings and angling its body- (as a person would do holding up four fingers in a foreign country to indicate "four" "quattro" or whatever else would do.

If there were no numerosity, no concept and recognition of one in terms of singularity and two in terms of two ones etc etc etc there could be no development of your definition of counting. Just like if there were no yellow "wavelength" on the spectrum my eyes could not see it, or evolve to see it.

If I say that 1 + 1 = 2 just like if i say "This apple is red" it is either true or untrue therefore for 1 + 1 = 2 to be true both 1 and 2 must exist. If I say "count-noun one plus count-noun one equals count-noun two" in a purely linguistic sense I could also say it doesn't equal two merely by "redefining" things, and who has the definition?:lol:

When it comes to arithmetic numbers exist that successfully refer to numeroisities and it is the perception of these numerosities that is interesting in terms of numerical cognisanse in non-human species. No one is saying you can "touch 2" or trying to materialise a number of waiting for it to incarnate like some numerical avatar from Plato's Heaven!

None of my arguments against your obsolete ideas depends on set theory, or upon anyone's theory of number -- as you have been told several times.

Prove that the ideas are obsolete.

Fine, stay ignorant, and remain super-glued to ancient and unworkable ideas about the nature of language -- [I]ideas even Plato rejected.

But, but.... we were talking about numerical cognisance in animals until you came along and said it can't exist because they don't have count-nouns. :thumbup:

On the other hand, if you are right, all your sentences would be lists, and they'd say nothing.That's OK with me...:)

Linguistics---- linguistics..... alert alert- we weren't actually talking about the meaning of number in human language.

Do you know what numerically cognisant means? :lol:

You promoted the idea that numbers were abstract objects. If they do not live in Platonic heaven, where then do they reside?

No I didn't, that's a strawman you have built up because you refuse to accept any "definition" and pick at wording. Arithmetic is neither wholly sythetic nor is it entirely analytical.

Your argument is basically silly in this context and you confuse numerical cognisance with the linguistic ability to name things.

You don't seem to be able to "process" the idea that numerosity could exist without there being a name for it. So if I see something I have never seen before and do not know what it is, i.e. what the name for it should or would be it only "exists" and doesn't exist.

Now, it would be nice if. instead of your usual tactic, you could explain succintly why you feel that non-human lifeforms cannot be numerically cognisant, estimate numerosities, subitise and use this "information" or information to solve problems in the real world.

Can you do that?

Rosa Lichtenstein

25th February 2011, 11:58

CM, I am going into hospital in a few days time, so I can't spend much time here.

I'll reply to you when, or if, I am discharged.

ZeroNowhere

25th February 2011, 12:02

It's not clear that this discussion is not somewhat off-topic.

Exakt

25th February 2011, 12:04

CM, I am going into hospital in a few days time, so I can't spend much time here.

I'll reply to you when, or if, I am discharged.I hope everything goes well and I look forward to you coming back.

ComradeMan

25th February 2011, 12:06

CM, I am going into hospital in a few days time, so I can't spend much time here.

I'll reply to you when, or if, I am discharged.

Oh well, good luck and I hope everything works out.

ComradeMan

25th February 2011, 20:49

This whole controversy seems to be a case of mathematical realism vs nominalism and seeimingly, not wanting to accept the possibility of "other" mathematical systems.

But I posit a question-

Is the number 2 in:-

2+2=4

The same as the number 2 in :-

2 apples?

In the first 2 is just 2 whereas in the second example 2 is describing a quantity, numerosity.

:confused:

What if I say that there is an "appleness of two" or a "twoness of applation"?
;)

The dispute between nominalism and realism in mathematics is ongoing.

Rosa Lichtenstein

11th March 2011, 16:30

Apologies for my delay in replying; I will do so some time next week.

Revolution starts with U

11th March 2011, 18:42

Good to see you back :D

Rosa Lichtenstein

17th March 2011, 16:55

Ok, here is my delayed response.

[However, CM, there are several places in your last post where you quote me, but fail to put all my words in quotation boxes. This only creates confusion, as I am sure you appreciate.]

CM:

Stop being disingenuous, if I am to be accused of being "abusive" for saying "rubbish" then your sarcasm, sniping and little comments are "attacks"- I gave a source, a respected source and also an original source along with Russell- instead of discussing it, you jump to straight to saying it was "copied" and "pasted"... so what? Sorry... that's a fail.

So, you can't show where I attacked "the idea of giving a source", as you alleged. Which means that you did make it up, as I said.

And we already know that by "respected source" you mean "source which supports my argument".

But this silly ontological debate gets us exactly where? Because if we start on that line of thinking then what is a definition? What logic did the definer use to define the definition? Who judges the judge? I suppose a physicist only studies "physics" then and not physics because of the risk of incompleteness or error in any of his or her work.

And yet, it wasn't 'ontological' until you introduced that term. Moreover, I have pointed out several times that I reject all ontological questions as non-sensical -- so perhaps you are coming round to my view?

And I admitted that I put it up in haste and corrected it accordingly- now move on.... Picking out one bad example or miswording, dwelling on it and trying to use this to "win" your argument is which fallacy?

No doubt you'll try to re-define that fallacy, too.:)

You're not really attacking the argument are you? All of this "unlike you" and all the heroic deeds you have done at RevLeft etc... irrelevant smokescreen--

I was in fact responding to your baseless assertion that I cut and paste my arguments. So, the only 'smokescreen' seems to be coming from your direction.

I use number words or count-nouns to express numerosities that I (can) perceive within the limits of my sensory and cognitive evolution as an organism. Perhaps a "bee" by buzzing using its wings and angling its body- (as a person would do holding up four fingers in a foreign country to indicate "four" "quattro" or whatever else would do.

Which only serves to make my point for me, since it is your use of count nouns that lends any sense to your neologism "numerosity", not the other way round.

I'd comment on the rest of the above quotation from your last post, but sadly it does not seem to make much sense.

If there were no numerosity, no concept and recognition of one in terms of singularity and two in terms of two ones etc etc etc there could be no development of your definition of counting. Just like if there were no yellow "wavelength" on the spectrum my eyes could not see it, or evolve to see it.

Well, as we have seen, since you can only try to make sense of your own theory by the use of count nouns (on your own admission), we can now see that the above is as misguided as anything else you have posted in this thread.

Of course, that is quite apart from the fact that you have yet to show this is true:

If there were no numerosity, no concept and recognition of one in terms of singularity and two in terms of two ones etc etc etc there could be no development of your definition of counting.

And this analogy is no use either:

Just like if there were no yellow "wavelength" on the spectrum my eyes could not see it, or evolve to see it

The reason for saying this is that light exists in nature, and did so before any sentient life evolved; 'numerosity' (even if we could make sense of this neologism) does not exist in non-sentient nature, even for you.

If I say that 1 + 1 = 2 just like if i say "This apple is red" it is either true or untrue therefore for 1 + 1 = 2 to be true both 1 and 2 must exist. If I say "count-noun one plus count-noun one equals count-noun two" in a purely linguistic sense I could also say it doesn't equal two merely by "redefining" things, and who has the definition?

But, "1 + 1 = 2" cannot fail to be true -- and it cannot be false, either, for if it were, the meaning of these symbols will have changed. That shows that your comparison with "This apple is red" is defective, since this can be false without that affecting the meaning of 'apple' or of 'red'.

I have explained in detail why that is so here:

http://www.revleft.com/vb/showpost.php?p=1995528&postcount=1

1 + 1 = 2 to be true both 1 and 2 must exist

So, now you have returned to consider to 'ontological' issues, which you earlier declared were: "silly".

Anyway, where do these numbers exist?

If I say "count-noun one plus count-noun one equals count-noun two" in a purely linguistic sense I could also say it doesn't equal two merely by "redefining" things, and who has the definition?

Well, you can say such odd things if you like, but it would have nothing to do with anything I have posted here, nor with anything that could reasonably be inferred from it.

When it comes to arithmetic numbers exist that successfully refer to numerosities and it is the perception of these numerosities that is interesting in terms of numerical cognisance in non-human species. No one is saying you can "touch 2" or trying to materialise a number of waiting for it to incarnate like some numerical avatar from Plato's Heaven!

But, you have yet to show that these 'numerosities' exist.

Nor have you explained what 'numerosities' the following numbers refer to: 0, 1/2, 0.0009, -2.3 x 10^99, the square root of two, pi, e, i...

And good luck with that one...

Prove that the ideas are obsolete.

Already done it.

But, but.... we were talking about numerical cognisance in animals until you came along and said it can't exist because they don't have count-nouns.

And you have yet to show that they have 'numerical cognisance' -- or that this idea makes any sense.

Linguistics---- linguistics..... alert alert- we weren't actually talking about the meaning of number in human language.

Then you aren't talking about number, but 'number', a term you have yet to explain.

[And, as I have told you several times, there is no linguistics in my argument. Philosophy of language, perhaps, but no linguistics.]

Do you know what numerically cognisant means?

Well, if I don't, I'm in good company, since you have yet to explain it.

No I didn't, that's a strawman you have built up because you refuse to accept any "definition" and pick at wording. Arithmetic is neither wholly synthetic nor is it entirely analytical.

Yes you did assert they were abstract objects:

However, if you do mean mathematical objects then you have a problem here because fundamentally mathematical objects do not exist in reality but are abstract objects anyway. So what logic can be based on an abstract object? We would have to agree, axiomatically, on what that abstract object was and would that not pose a problem then for our claims of objectivity and logical truth?

Bold added.

http://www.revleft.com/vb/showpost.php?p=2030941&postcount=66

you refuse to accept any "definition" and pick at wording

1. Yet another invention; where did I refuse to accept a definition? What I said was this if you can re-define things, then so can I.

2. Anyway, we have yet to see your definition of number -- or even of 'numerosity' and 'numerically cognisant'.

Your argument is basically silly in this context and you confuse numerical cognisance with the linguistic ability to name things.

Where have I even mentioned "the linguistic ability to name things"?

As I have said several times: [i]you just can't resist making stuff up, can you?

And, the use of count nouns has nothing to do with naming things. We name things with proper nouns not count nouns.

See what confusion results from your sloppy approach to language?

You don't seem to be able to "process" the idea that numerosity could exist without there being a name for it. So if I see something I have never seen before and do not know what it is, i.e. what the name for it should or would be it only "exists" and doesn't exist.

Well, we have yet to be told what 'numerosity' is. Until you do that, you might just as well have said the following for all the good it does:

You don't seem to be able to "process" the idea that schnumerosity could exist without there being a name for it.

You:

So if I see something I have never seen before and do not know what it is, i.e. what the name for it should or would be it only "exists" and doesn't exist.

Nice argument, except for one minor detail -- hardly worth mentioning in fact since it's so insignificant -- this has nothing to do with anything I have argued.

Any chance you can stick to what I have said, rather than make stuff up as you go along?

[Now that is a "silly" question; we have already seen several times you can't.]

Now, it would be nice if. instead of your usual tactic, you could explain succinctly why you feel that non-human lifeforms cannot be numerically cognisant, estimate numerosities, subitise and use this "information" or information to solve problems in the real world.

As I have already pointed out, until you tell us what 'numerosity' is (without the use of count nouns, of course), you might just as well have posted:

Now, it would be nice if. instead of your usual tactic, you could explain succinctly why you feel that non-human lifeforms cannot be numerically cognisant, estimate schnumerosities, subitise and use this "information" or information to solve problems in the real world.

Bold added.

And animals do not use "information", or even information, as I have already established -- just 'information'.

Can you do that?

Even better: can you?

ComradeMan

18th March 2011, 10:34

Boolean algebraic logic 1 = true 0 = false. 1 is not always 1 and 0 is not always 0.

Numerosities are simply the evaluation of the quantiy of a given object or substance.

Previously I stated that I was not making some claim that animals had solved Fermat's last theorem, I won't take that away from Wiles! Primitive man probably had no more ability than this, to do basic arithmetic so arguing about the square root of 2 and pi etc is being silly. You may as well say that Newton was not a physicist only a "physicist".

On your basis what proof do you have that any two humans share the same information and that it is not "information"?

You keep avoiding the Voyager Satellite I see. There was mathematical information encoded on the satellite if I remember correctly- now, why was that?

As far as numerical cognisance is concerned- well, if you refuse outright to look at the studies that have been presented because you have already decided that they are flawed a priori, then what can be done?:rolleyes:

I'm sorry but you keep begging the question and most of your argument rests on "inverted commas"..... :lol:

Rosa Lichtenstein

18th March 2011, 13:40

CM:

Boolean algebraic logic 1 = true 0 = false. 1 is not always 1 and 0 is not always 0.

Yes, so?

Numerosities are simply the evaluation of the quantity of a given object or substance.

Bold added

Then numerosities are mass terms (http://en.wikipedia.org/wiki/Mass_noun), not count terms, and thus have nothing to do with counting.

Previously I stated that I was not making some claim that animals had solved Fermat's last theorem, I won't take that away from Wiles! Primitive man probably had no more ability than this, to do basic arithmetic....

I'm not too sure what this has got to do with anything I have argued, but it is reassuring to see you are still finding it difficult to stick to the point.

so arguing about the square root of 2 and pi etc is being silly. You may as well say that Newton was not a physicist only a "physicist"

Well, you were the one who said this:

When it comes to arithmetic numbers exist that successfully refer to numerosities and it is the perception of these numerosities that is interesting in terms of numerical cognisance in non-human species.

Bold added.

In which case it is apposite to ask where numbers like 0, -6, 1/2 and 0.00076, pi and e, etc. exist, or to what these numerals refer.

On your basis what proof do you have that any two humans share the same information and that it is not "information"?

1) The fact that you understood the information in my claim about which this question of yours is directed.

2) Of course, if I am wrong, and you do not understand the point I was making, then there is little I can do to assist you, is there?

3) Moreover, if you do not understand the information in sentence 2), then you will not be able to raise an objection to it, will you?

On the other hand, if you object to the above three sentences, then that will imply you perfectly well understand my use of the word "information" and are merely asking a time-wasting question.

And the same can be said if you object to the above sentence..., and so on.

You keep avoiding the Voyager Satellite I see.

I'm surprised you haven't mentioned Icelandic Pottery, Tibetan Head-hunters and the Adhedral Triangle -- they too are equally irrelevant to anything I have argued -- about information or even "information".

Of course, it you respond to the above sentence, by agreeing or disagreeing with it, accepting or challenging its veracity, that too will imply you use the word "information" in the same way as yours truly and the rest of the English speaking community do.

There was mathematical information encoded on the satellite if I remember correctly- now, why was that?

Of course, this information was put there by human beings.

You need to find an example of information not put there by human beings.

As far as numerical cognisance is concerned- well, if you refuse outright to look at the studies that have been presented because you have already decided that they are flawed a priori, then what can be done?

Until we are told what 'numerical cognisance' is, you might just as well have posted this for all the good it does:

As far as schnumerical cognisance is concerned- well, if you refuse outright to look at the studies that have been presented because you have already decided that they are flawed a priori, then what can be done?

I'm sorry but you keep begging the question and most of your argument rests on "inverted commas".....

In fact, I have used very few double quotes in my posts.

Perhaps you can't count?:(

ComradeMan

19th March 2011, 13:37

CM: Yes, so?

You fail to distinguish between number and numeral.

Then numerosities are mass terms (http://en.wikipedia.org/wiki/Mass_noun), not count terms, and thus have nothing to do with counting.

You just can't seem to get away from the linguistic definitions of things, can you? This is not a debate how some sentient species may or may not percieve number nor what their philosophy of number may or may not be! :lol: The point is that some species are apparently able to evaluate numerosities, which has been explained ad nauseam, and have been observed to make decisions that rely on these evaluations- call it enumeration if you like, call it the ability to evaluate and process the cardinalities of a set if you like- yet you refuse to acknowledge this.

In which case it is apposite to ask where numbers like 0, -6, 1/2 and 0.00076, pi and e, etc. exist, or to what these numerals refer.

Hang on a second, you are now being uncharacteristically unpedantic. You are mixing natural numbers, integers, rational numbers, real numbers and irrational numbers all in one. You also seem to be confusing numerals with numbers.

1) The fact that you understood the information in my claim about which this question of yours is directed.

How do you know I understood the information? I wasn't aware that understanding was so easily definable. All you are doing is projecting philosophical points of view onto a scientific argument.

Your definition of information is also rather bizarre- to be honest and also completely irrelevant in a discussion about cognisance in non-human species. The point about the Voyager Satellite is quite simple, according to your definition of information as human it was completely pointless to put any information on the satellite for non-human species. More specifically, the mathematical information would be even more pointless as you seem to see this as an exlusively human ability and one would presume that anyone/anything that came across the satellite in the future would be non-human.

You also fail to remember that the Voyager Satellite was sending information out wasn't it? Secondly, by your argumentation if indeed we did find information put somewhere or represented/relayed/recorded in some for by a non-human species we would not be able to process it as information but only "information". :thumbup1:

Of course, it you respond to the above sentence, by agreeing or disagreeing with it, accepting or challenging its veracity, that too will imply you use the word "information" in the same way as yours truly and the rest of the English speaking community do. .

You're not actually discussing the argument but trying to pick at the wording of the argument, aren't you? Clever tactic to avoid positive debate. By the way, since when was this about the English speaking community? Okay, we are discussing this in English but is it perhaps that some of your presumed language universals are not so universal when you consider things outside the Anglophone sphere?

Until we are told what 'numerical cognisance' is, you might just as well have posted this for all the good it does..

Dehaene, S. (1997), The number sense: How the mind creates mathematics, New York: Oxford University Press,

Non-verbal numericalcognition: from reals to integers
C.R. Gallistel and Rochel Gelman
http://eebweb.arizona.edu/faculty/dornhaus/courses/materials/papers/Gallistel%20Gelman%20numbers%20counting%20cognitio n.pdf

The Concept of Number in Animals
http://www.fbk.eu/node/1313

etc

etc

In fact, I have used very few double quotes in my posts. Perhaps you can't count?:(

I wasn't talking about how many you used, perhaps you can't understand? :lol:

The problem with your argument is that whereas you attack the definitions and pick holes at the definitions and words of others you do not actually offer any of your own other than a vague notion of some kind of difference between information and "information" which you are either unable or reluctant to give.

Rosa Lichtenstein

19th March 2011, 15:12

CM:

You fail to distinguish between number and numeral.

And on what do you base this latest invention of yours?

You just can't seem to get away from the linguistic definitions of things, can you?

1. Well, you are the one who confuses quantities with amounts.

2. In fact, I haven't given a definition yet.

3. When you can explain yourself without using any language at all, I'll stop referring to such linguistic niceties. Deal?

This is not a debate how some sentient species may or may not perceive number nor what their philosophy of number may or may not be!

Then you can't be talking about "number", as us human beings use that term, but something else. Maybe Alien Arithmetic? Immaterial Integers? Otherworldly Ordinals?

The point is that some species are apparently able to evaluate numerosities,

As I have already told you, until you can tell us in comprehensible terms what a "numerosity" is, you might just as well have posted this:

The point is that some species are apparently able to evaluate schnumerosities,

You:

which has been explained ad nauseam, and have been observed to make decisions that rely on these evaluations- call it enumeration if you like, call it the ability to evaluate and process the cardinalities of a set if you like- yet you refuse to acknowledge this.

You have certainly thrown a load of words at us, but I don't think we can dignify any of it with the term "explanation".

Hang on a second, you are now being uncharacteristically unpedantic. You are mixing natural numbers, integers, rational numbers, real numbers and irrational numbers all in one. You also seem to be confusing numerals with numbers.

1. Not me; all mathematicians call these numbers.

2. And in what way am I doing the following?

You also seem to be confusing numerals with numbers

3. Don't tell me you have caught the bug, and you too are concerned with the careful use of language?

In which case, these wise words from an authority on the subject should put you straight:

You just can't seem to get away from the linguistic definitions of things, can you?

You:

How do you know I understood the information?

I covered this response in my earlier reply:

2) Of course, if I am wrong, and you do not understand the point I was making, then there is little I can do to assist you, is there?

And then I added this afterthought:

3) Moreover, if you do not understand the information in sentence 2), then you will not be able to raise an objection to it, will you?

Ooops, you fell right into that trap didn't you?

I wasn't aware that understanding was so easily definable.

Well, thanks for being open about your ignorance here, but where did I try to define anything?

[Of course, if you do not understand the information in that reply, you'll just repeat your error won't you?]

All you are doing is projecting philosophical points of view onto a scientific argument.

I haven't seen a 'scientific argument' yet, just a series of linguistic confusions.

Your definition of information is also rather bizarre- to be honest and also completely irrelevant in a discussion about cognisance in non-human species.

Once more, find me where I have even so much as tried to define "information".

Still making stuff up, I see.

The point about the Voyager Satellite is quite simple, according to your definition of information as human it was completely pointless to put any information on the satellite for non-human species.

Once more, this was programmed by a human being (or a group of humans) -- or do you think it programmed itself?

More specifically, the mathematical information would be even more pointless as you seem to see this as an exclusively human ability and one would presume that anyone/anything that came across the satellite in the future would be non-human.

I see, you now want to switch to science fiction?

In fact, I covered this weeks ago: if this information is expressed in a language that we can translate into a human language, then no problem. If it isn't then it will just be meaningless noises, blips or symbols, won't it? You can call that "information" if you want, but then it might more accurately be called "gibberish".

You also fail to remember that the Voyager Satellite was sending information out wasn't it?

Where did I 'forget' this?

Secondly, by your argumentation if indeed we did find information put somewhere or represented/relayed/recorded in some for by a non-human species we would not be able to process it as information but only "information".

Already covered.

You're not actually discussing the argument but trying to pick at the wording of the argument, aren't you?

You mean like you tried to claim I was confusing two words: "number" and "numeral"?

If you can raise questions about the use of language, why can't I?

Clever tactic to avoid positive debate.

If so -- but I deny it is so -- then you use this 'tactic', too, as we have just seen.

By the way, since when was this about the English speaking community?

As soon as you made the fatal mistake of posting in English. Had you posted in, say, Arabic, then not only would that have involved the Arabic speaking community, but I would not have been able to understand you.

Okay, we are discussing this in English but is it perhaps that some of your presumed language universals are not so universal when you consider things outside the Anglophone sphere?

Where did I refer to 'language universals', or even hint at them?

Yet more invention.

You should think of getting a job with Fox News.

Dehaene, S. (1997), The number sense: How the mind creates mathematics, New York: Oxford University Press,

Ooops, bad start, since there is no such thing as 'the mind'.

And human beings created language, not 'minds'.

Non-verbal numerical cognition: from reals to integers C.R. Gallistel and Rochel Gelman

The Concept of Number in Animals

Thanks, but you have already tried this ploy, and it failed to work the last time.

What makes you think I'd fall for it this time when I rumbled it weeks ago?

You, in your last post, before you were rumbled this time round:

I'm sorry but you keep begging the question and most of your argument rests on "inverted commas".....

You after you were rumbled:

I wasn't talking about how many you used, perhaps you can't understand?

Perhaps you can tell us how you determined that "most" of my argument rests on "inverted commas" if you did no counting?

Are you psychic?

The problem with your argument is that whereas you attack the definitions and pick holes at the definitions and words of others you do not actually offer any of your own other than a vague notion of some kind of difference between information and "information" which you are either unable or reluctant to give.

Well, you have only given us one definition, as far as I can see, and in that 'definition' you switched from number to quantities, undermining that 'definition', as I pointed out in my last post.

and words of others you do not actually offer any of your own other than a vague notion of some kind of difference between information and "information" which you are either unable or reluctant to give

Unfortunately, it is you who wants to introduce a new term here, namely 'information', not me, so it's up to you to tell is what you mean by it, not me.

[If you understand the information in that sentence then you can count yourself as a paid up member of the English language community, who already understands the difference. Of course, if you do not, then the only thing I can suggest is a crash course in English.

And once more, if you understand the information in that sentence then you already know the difference..., and so on ad infinitem...]

ComradeMan

20th March 2011, 15:18

Rosa, is it necessary to multi-quote an entire post line for line that makes replying more arduous than it seems worthwhile? Or is it that you are, yet again, not coming up with an argument at all but picking at words- BECAUSE YOU HAVE NO MATHEMATICAL OR SCIENTIFIC ARGUMENT. :laugh:

Anyone with the basics of mathematical knowledge would know not to confuse numerals with numbers and that they should be distinguished. A numeral may represent a number as some kind of symbol but it is not in itself that number in any more sense than you are your name. Furthermore the words that we use to describe many numbers are not autological- one may be one words but zero becomes an impossibility and in no way is seven, seven. :laugh:

Can't you differentiate between the value, i.e. number and the digit/numerical system(s) etc used to express it?

And can you actually write out the numeral for pi? See you at the end of the universe. :laugh: By your argument then pi can't exist only "pi".

"Well, you are the one who confuses quantities with amounts."

quanity -

n., pl., -ti·ties

A specified or indefinite number or amount.
A considerable amount or number: sells drugs wholesale and in quantity.
An exact amount or number.

American Heritage Dictionary: (http://www.revleft.org/library/Dictionary-cid-66464)

http://www.answers.com/topic/quantity

In fact they offer (5) definitions.... However it is derived from the Latin quantitas- deriving itself from quantus "how much" i.e. an amount- this is still the case in Italian, quanto (how much) quantità (amount). :rolleyes:

"2. In fact, I haven't given a definition yet."

You never do give exact definitions but just orbit around vague anti-definitions....

"3. When you can explain yourself without using any language at all, I'll stop referring to such linguistic niceties. Deal?"

What a ridiculous argument! You don't see the difference between discussing something and the means of discussion? On that basis you could apply principles of linguistics to quantum physics and then seek to invalidate counter-arguments on the mere basis that they are being expressed linguistically....

"Then you can't be talking about "number", as us human beings use that term, but something else. Maybe Alien Arithmetic? Immaterial Integers? Otherworldly Ordinals? "

Your argument is degenerating here. You may as well say that certain species of animals can't see colours but only "colours". The fact stands that if an intelligent sentient form of life exists out there somewhere that has developed a civilisation then they will use mathematics as we do and presuming that we are talking about the same universe their right-angled triangles with have 90 degree right angles just as much as ours do- whether they call it /(&()&, or ABBBZEDKHAK (-----------) or communicate with chemical messages likes ants or whistles or whatever else.

"As I have already told you, until you can tell us in comprehensible terms what a "numerosity" is, you might just as well have posted this:"

You are the only one who seems to have any problem with the definition so you can leave out the "us" part. A standard type of definition would be state or condition of being numerous and/or the extent to which that said state or condition is numerous.

"All mathematicians call these numbers. "

All mathematicians indeed do call these numbers but they also recognise the little details that you conveniently leave out of the argument and do not treat them as being the same.

"Don't tell me you have caught the bug, and you too are concerned with the careful use of language?"

But you are only careful about the use of language when it's your use of language and your rather subjective points of view. On the other hand you conveniently ignore the other bits. Like the point about the Voyager Satellite, it's not about who put it up into space but who or what may receive it and whether they would be able to understand the information recorded on it, especially the mathematical information- according to you the answer would be no.

You have no argument here other than making facetious comments and infantile remarks due to the lack of an argument.

You can't actually debate the science involved so you will derail the debate by picking at definitions and applying whichever fits your idea in a given moment.

As for that ridiculous comment about the mind- :rolleyes: We certainly can't see or touch the mind but through conceptual logic and observation we deduce its existence. In the words of a philosopher, perhaps it's about time you started to look with your intellect and not only with your eyes.

Touché!

Rosa Lichtenstein

20th March 2011, 16:48

CM:

Rosa, is it necessary to multi-quote an entire post line for line that makes replying more arduous than it seems worthwhile?

Yes.

Or is it that you are, yet again, not coming up with an argument at all but picking at words- BECAUSE YOU HAVE NO MATHEMATICAL OR SCIENTIFIC ARGUMENT.

That's a bit rich coming from someone who has yet to do either.

Anyone with the basics of mathematical knowledge

In fact I have a mathematics degree.

would know not to confuse numerals with numbers and that they should be distinguished.

Once more, and I have asked this several times, where have I done this?

Or is this just another of those things you prefer to make up about me?

A numeral may represent a number as some kind of symbol but it is not in itself that number in any more sense than you are your name.

And how does a numeral represent a number?

[Now, let's see you try to escape from that Platonic trap...]

Furthermore the words that we use to describe many numbers are not autological- one may be one words but zero becomes an impossibility and in no way is seven, seven.

Eh? This does not seem to make much sense.

And you have still to tell us what zero refers to.

Once more, if it refers to one abstract object, then zero in fact refers to one, not zero.

On the other hand, as Blaise Pascal noted, if it refers to nothing, then we should, for instance, write 10,001 as 11, since those three zeros are the same as nothing. In which case nothing should stand between those two ones, which thus changes 10,001 into 11!

Can't you differentiate between the value, i.e. number and the digit/numerical system(s) etc used to express it?

In fact, I'm far more worried about your propensity to invent.

And can you actually write out the numeral for pi? See you at the end of the universe. By your argument then pi can't exist only "pi".

But, this has nothing whatsoever to do with my argument.

Once more, this presents you with problems, not me -- which 'abstract object' does pi stand for?

And thanks for the material from that dictionary entry for "quantity":

A specified or indefinite number or amount.
A considerable amount or number: sells drugs wholesale and in quantity.
An exact amount or number.

In fact they offer (5) definitions.... However it is derived from the Latin quantitas- deriving itself from quantus "how much" i.e. an amount - this is still the case in Italian, quanto (how much) quantità (amount).

But, once you ask how we come by these numbers, my point is underlined, for we use number scales to ascertain them, which scales depend on the use of yet more of those pesky count nouns.

So, a weighing scale, for instance, is marked off in kilograms, or grams, or..., and each of these is a count noun. That's how we turn mass noun terms into count noun terms, so that we can apply numbers to mass term items.

You just run these together.

You never do give exact definitions but just orbit around vague anti-definitions....

And those vague definitions we can always rely on you to supply.

What a ridiculous argument!

Not so; it was aimed at showing you that not even you can get away from the use of language if you want to explain anything. And if that is the case, it's important to point out when words are being employed in odd ways -- as you seem to want to do.

You don't see the difference between discussing something and the means of discussion?

I certainly do, but you do not, apparently, since you seem to think that by just using any old language you have somehow 'explained' something, rather than express your own confusion.

On that basis you could apply principles of linguistics to quantum physics and then seek to invalidate counter-arguments on the mere basis that they are being expressed linguistically....

In which case, you'll like this:

"It hasn't been a great couple of years for theoretical physics. Books such as Lee Smolin's The Trouble with Physics and Peter Woit's Not Even Wrong embody the frustration felt across the field that string theory, the brightest hope for formulating a theory that would explain the universe in one beautiful equation, has been getting nowhere. It's quite a comedown from the late 1980s and 1990s, when a grand unified theory seemed just around the corner and physicists believed they would soon, to use Stephen Hawking's words, 'know the mind of God'. New Scientist even ran an article called 'The end of physics'.

"So what went wrong? Why are physicists finding it so hard to make that final step? I believe part of the answer was hinted at by the great physicist Niels Bohr, when he wrote: 'It is wrong to think that the task of physics is to find out about nature. Physics concerns what we can say about nature.'

"At first sight that seems strange. What has language got to do with it? After all, we see physics as about solving equations relating to facts about the world -- predicting a comet's path, or working out how fast heat flows along an iron bar. The language we choose to convey question or answer is not supposed to fundamentally affect the nature of the result.

"Nonetheless, that assumption started to unravel one night in the spring of 1925, when the young Werner Heisenberg worked out the basic equations of what became known as quantum mechanics. One of the immediate consequences of these equations was that they did not permit us to know with total accuracy both the position and the velocity of an electron: there would always be a degree of irreducible uncertainty in these two values.

"Heisenberg needed an explanation for this. He reasoned thus: suppose a very delicate (hypothetical) microscope is used to observe the electron, one so refined that it uses only a single photon of energy to make its measurement. First it measures the electron's position, then it uses a second photon to measure the speed, or velocity. But in making this latter observation, the second photon has imparted a little kick to the electron and in the process has shifted its position. Try to measure the position again and we disturb the velocity. Uncertainty arises, Heisenberg argued, because every time we observe the universe we disturb its intrinsic properties.

"However, when Heisenberg showed his results to Bohr, his mentor, he had the ground cut from under his feet. Bohr argued that Heisenberg had made the unwarranted assumption that an electron is like a billiard ball in that it has a 'position' and possesses a 'speed'. These are classical notions, said Bohr, and do not make sense at the quantum level. The electron does not necessarily have an intrinsic position or speed, or even a particular path. Rather, when we try to make measurements, quantum nature replies in a way we interpret using these familiar concepts.

"This is where language comes in. While Heisenberg argued that 'the meaning of quantum theory is in the equations', Bohr pointed out that physicists still have to stand around the blackboard and discuss them in German, French or English. Whatever the language, it contains deep assumptions about space, time and causality -- assumptions that do not apply to the quantum world. Hence, wrote Bohr, 'we are suspended in language such that we don't know what is up and what is down'. Trying to talk about quantum reality generates only confusion and paradox.

"Unfortunately Bohr's arguments are often put aside today as some physicists discuss ever more elaborate mathematics, believing their theories to truly reflect subatomic reality. I remember a conversation with string theorist Michael Green a few years after he and John Schwartz published a paper in 1984 that was instrumental in making string theory mainstream. Green remarked that when Einstein was formulating the theory of relativity he had thought deeply about the philosophical problems involved, such as the nature of the categories of space and time. Many of the great physicists of Einstein's generation read deeply in philosophy.

"In contrast, Green felt, string theorists had come up with a mathematical formulation that did not have the same deep underpinning and philosophical inevitability. Although superstrings were for a time an exciting new approach, they did not break conceptual boundaries in the way that the findings of Bohr, Heisenberg and Einstein had done.

"The American quantum theorist David Bohm embraced Bohr's views on language, believing that at the root of Green's problem is the structure of the languages we speak. European languages, he noted, perfectly mirror the classical world of Newtonian physics. When we say 'the cat chases the mouse' we are dealing with well-defined objects (nouns), which are connected via verbs. Likewise, classical physics deals with objects that are well located in space and time, which interact via forces and fields. But if the world doesn't work the way our language does, advances are inevitably hindered.

"Bohm pointed out that quantum effects are much more process-based, so to describe them accurately requires a process-based language rich in verbs, and in which nouns play only a secondary role...." [Peat (2008), pp.41-43. Bold emphases added; quotation marks altered to conform to the conventions adopted here.]

Peat, D. (2008), 'Trapped In A World View', New Scientist 197, 2637, 05/01/08, pp.42-43.

The only thing I would add is that I do not want to bring the "principles of linguistics" to anything, as you have been told many times.

Your argument is degenerating here. You may as well say that certain species of animals can't see colours but only "colours".

You have tried this ploy before, and I responded to it.

Here we go again: Colours exist in nature, and they did so before sentient life evolved. But, numbers did not. [Or if you think they did, where then did they exist?]

So, if someone tells me animals see colours, I would not think to refer to these as 'colours'.

But, if someone tells me animals can 'cognise' numbers, I immediately ask if animals can use count nouns. If they can't (and you have yet to show they can) then that person must be referring to 'numbers' -- a term that has yet to be explained -- not numbers.

Same with you.

The fact stands that if an intelligent sentient form of life exists out there somewhere that has developed a civilisation then they will use mathematics as we do and presuming that we are talking about the same universe their right-angled triangles with have 90 degree right angles just as much as ours do- whether they call it /(&()&, or ABBBZEDKHAK (-----------) or communicate with chemical messages likes ants or whistles or whatever else.

Are you suggesting that ants have names for things? A sort of Ant Alphabet, perhaps?

And there are no such things as 'chemical messages', since chemicals aren't human beings, nor do they have a language.

Moreover, noises can only convey information if they are passed between those who already have a language -- and ants do not.

Of course, you might be using "message", or "information", in a new, and-as-yet-unexplained sense; if so what is it?

You are the only one who seems to have any problem with the definition so you can leave out the "us" part. A standard type of definition would be state or condition of being numerous and/or the extent to which that said state or condition is numerous.

Not so, you have a problem with it if you can't explain yourself.

A standard type of definition would be state or condition of being numerous and/or the extent to which that said state or condition is numerous

That's little use since you employ the word to be defined in the definition.

After all I could define 'schnumerosity' in the following way:

A standard type of definition would be state or condition of being schnumerous and/or the extent to which that said state or condition is schnumerous

What's that I hear? "A useless definition", you say?

Don't tell me "you are the only one who seems to have [a] problem with [my] definition"!?

All mathematicians indeed do call these numbers but they also recognise the little details that you conveniently leave out of the argument and do not treat them as being the same.

In which case, you will find it easy to say in what way these "little details" prevent you from telling us what abstract object(s) they refer to.

But you are only careful about the use of language when it's your use of language and your rather subjective points of view. On the other hand you conveniently ignore the other bits. Like the point about the Voyager Satellite, it's not about who put it up into space but who or what may receive it and whether they would be able to understand the information recorded on it, especially the mathematical information- according to you the answer would be no.

But, your only example of my alleged confused use of language was over "numeral" and "number", which you have yet to show I committed.

Like the point about the Voyager Satellite, it's not about who put it up into space but who or what may receive it and whether they would be able to understand the information recorded on it, especially the mathematical information- according to you the answer would be no

In which case, you really do think the computers in this satellite programmed themselves!

You have no argument here other than making facetious comments and infantile remarks due to the lack of an argument.

That's a bit rich coming from someone who began by posting a joke about Frege.

You can't actually debate the science involved so you will derail the debate by picking at definitions and applying whichever fits your idea in a given moment.

1. You need to post some science first; all we have seen up to now from you are confused musing and neologisms, which you don't seem to be able to explain.

2. Your 'definitions' (what few you have given) in fact "pick" at themselves -- the circular 'definition' of 'numerosity' being just the latest example.

As for that ridiculous comment about the mind- We certainly can't see or touch the mind but through conceptual logic and observation we deduce its existence.

Ok, smarty pants: deduce it's existence with a valid argument then...

In the words of a philosopher, perhaps it's about time you started to look with your intellect and not only with your eyes

So, you think the intellect has eyes now?

Human Anatomists will be interested to hear from you.

Or, at least, from your intellect's mouth.

ComradeMan

20th March 2011, 19:09

Rosa- in that massive wall of nothing and tu quoque you've typed and pasted you haven't actually presented an argument whatsoever

You're failing miserably because you are venturing into a field which you haven't researched.

Ant communicate with codes of pheromones, the fact that we don't (yet) understand what they are communicating does not stop us from observing their communication anymore than the first explorers who encountered unknown peoples could observe their language despite not understanding it.

On your basis someone who did not understand a word of Italian could not deduce that "ciao" means "hi" and not that the Italian in question is sneezing!

You've made basic mathematical errors throughout- including the fatal mistake of confusing numerals with numbers and different kinds of numbers.

You cannot actually present one coherent paragraph, succinctly, stating what is wrong with the research etc. Furthermore you reject or manipulate definitions of words/terms to suit your own distorted argument and the best you can come up with is picking at typos and quibbling details here and there.

So far you have been wrong on
1) Numerals vs numbers
2) Quantities & amounts
3) The logical non-existence of the mind+
4) The biology of animal species

Moreover, your rather human-centric view of things like "information" and "numbers" etc has no place in a discussion about the numerical/mathematical/whatever abilities of certain non-human species.

I suppose you'll be arguing next that a male lion does not recognise a female lion as female but only "female" because lions don't have any verbal language and a word for "Ciao, bella!" :laugh:

I know what has happened. You waded in on this thread thinking it was about some weird metaphysical stuff about the Fibonacci sequences showing nature's divine consciousness etc... which it wasn't, found yourself in difficult seas with the argument- because you didn't bother to research it even and just rejected them outright and now you are quibbling at words and definitions as a way out.

Rosa Lichtenstein

20th March 2011, 20:11

CM:

Rosa- in that massive wall of nothing and tu quoque you've typed and pasted you haven't actually presented an argument whatsoever

Depends what you mean by "argument" -- but we already know you are struggling to cope with "number".

You're failing miserably because you are venturing into a field which you haven't researched.

In that case, it's up to you to help me out; but all you do is post confused ideas, obscure neologisms and obsolete claims about 'numbers'.

Ant communicate with codes of pheromones, the fact that we don't (yet) understand what they are communicating does not stop us from observing their communication anymore than the first explorers who encountered unknown peoples could observe their language despite not understanding it.

Well, a code is something that requires an object language, a translation manual, a de-coding manual, and a target language to translate into.

Do these Ant Secret Agents, these 007s of the Hymenopterian universe, possess any of these?

No.

In that case, you must be using "code" in a new, and as-yet-unexplained sense. If so, what is it?

And, is this Ant Dialect capable of being translated into a human tongue?

No?

Then you must mean they have a 'language' not a language.

On your basis someone who did not understand a word of Italian could not deduce that "ciao" means "hi" and not that the Italian in question is sneezing!

Well, I'm not sure what you are trying to say here. If you mean that those who do not know a certain language could misconstrue a word for something that is not a word, then I agree -- but nothing I have argued is affected by this. That is because, there are others who understand Italian who can clear this up for the individual concerned.

Now, unless you can point us in the direction of Ant Interpreters, this can't work with ants.

On the other hand, if you mean that ants makes noises that we might misconstrue for Italian words, or the other way round, then I'd like to know where these Italian-speaking ants are to be found.

Antarctica perhaps? Maybe Antwerp?

You've made basic mathematical errors throughout- including the fatal mistake of confusing numerals with numbers and different kinds of numbers.

You keep saying this, but when asked you repeatedly fail to say where I have done this.

In that case, I can only conclude you are either being mendacious or you are getting desperate.

Anyway, this is a bit rich coming from someone who said that A=A is a syllogism and that numbers are abstract objects.

You cannot actually present one coherent paragraph, succinctly, stating what is wrong with the research etc.

Again, you keep saying things like this, but when it comes to substantiating such allegations, you go suspiciously quiet.

Furthermore you reject or manipulate definitions of words/terms to suit your own distorted argument and the best you can come up with is picking at typos and quibbling details here and there.

Well, you were the one who posted a circular 'definition' of 'numerosity' -- a term we still do not understand.

And which typo have I picked up on?

Yet another fib -- you don't half know how to tell 'em, do you?

So far you have been wrong on

1) Numerals vs numbers

Once more, you have yet to show where I was 'wrong' on this.

2) Quantities & amounts

In fact, as I was able to show, it's you who is struggling with these words.

3) The logical non-existence of the mind

Where did I say that the mind did not exist, or even this: "The logical non-existence of the mind"?

What I in fact said was that there is no such thing as the mind.

You really must learn to read more carefully.

And we are still waiting for your 'logical' proof there is such a thing as 'the mind'.

4) The biology of animal species

Which biological facts did I get wrong?

You failed to say.

No surprise there then...

Moreover, your rather human-centric view of things like "information" and "numbers" etc has no place in a discussion about the numerical/mathematical/whatever abilities of certain non-human species.

Well, I'm a human being, and I'm reasonably sure you are. In which case, perhaps you should try to tell us what your new use of 'information' is in a non-human language so that it isn't biased by such irrelevances.

I suppose you'll be arguing next that a male lion does not recognise a female lion as female but only "female" because lions don't have any verbal language and a word for "Ciao, bella!"

You'd be far better occupied responding to what I have argued rather than making stuff up about what you think I might argue. Or even better: with trying to tell us with some clarity what you mean by 'numerosity'.

[We are beginning to suspect that not even you know!]

May I therefore suggest you persuade your loquacious chums in the ant world to help you out?

Now, if you can find a lion that is able to use the word "female", get back to me -- until then, there is no way I'd argue this way -- or anything like it.

I know what has happened. You waded in on this thread thinking it was about some weird metaphysical stuff about the Fibonacci sequences showing nature's divine consciousness etc... which it wasn't, found yourself in difficult seas with the argument- because you didn't bother to research it even and just rejected them outright and now you are quibbling at words and definitions as a way out.

Think what you like; you seem to prefer life in a fantasy world all of your own making, anyway. Until you snap out of it, and respond effectively without making stuff up, my arguments still stand.

ComradeMan

21st March 2011, 11:27

Rosa, no one is making up anything and these constant accusations of people making up stuff do not support your argument or rather lack of argument.

Yet again in that great wall of a post in which you pick at things "but you said this" but "that is not the case" etc etc YOU don't actually say much.

Whether some animals are numerically cognisant or not does not depend on their linguistic abilities any more than a person depends on his or her name or an apple on being called an apple.

The point you miss about this is that in order to count there must be something to count and the debate is about that something and how it is processed by non human species. Your human centric views have no place in biology or biological arguments as they would exclude a great deal of research out of hand because of a rather intellectually silly application of human logic.

Yet again, take the example of pi. It is impossible for us to write out the complete numerical form of pi, so therefore we only have "pi" and not pi? :D On that basis how can we call pi, pi. or even know it is pi seeing as we have never seen all of it nor could we possibly say all of it either, so to speak?

*"And which typo have I picked up on?"

schnumerosity

Fib?

Rosa Lichtenstein

21st March 2011, 13:10

CM:

Rosa, no one is making up anything and these constant accusations of people making up stuff do not support your argument or rather lack of argument.

Well, you made up these accusations (among others): that I thought numbers were abstract objects, that I was using linguistics, that I had confused numbers with numerals (we are still waiting for you to cite a single quotation from my posts that even so much as hints at this), that I had used definitions when I haven't, that I had defined "information" when I haven't even tried to do so, that I had an ontology when you had been told several times I reject all ontologies as non-sensical (and then it turned out you were trying to foist one on us), that I had referred to 'language universals' when I hadn't, that I had made certain allegations about "the logical non-existence of the mind" when I hadn't, and then that "most" of my argument rests on "inverted commas", when it doesn't (and you failed to say how you had arrived at that fabrication), and so on. [Links provided on request.]

In which case, we must now add the phrase "making up anything" to the words "number" and "language" with which you seem to be struggling.

yet again in that great wall of a post in which you pick at things "but you said this" but "that is not the case" etc etc YOU don't actually say much.

Is it my fault that there is not much to say about your fibs, confusions, obscure neologisms and circular definitions? It's like trying to punch a cloud.

Whether some animals are numerically cognisant or not does not depend on their linguistic abilities any more than a person depends on his or her name or an apple on being called an apple.

Once more, until you tell us with some clarity what "numerically cognisant" means, you might just as well have posted this, for all the good it does:

Whether some animals are schnumerically cognisant or not does not depend on their linguistic abilities any more than a person depends on his or her name or an apple on being called an apple.

And, you have been asked before to explain to us in a non-human language just how animals can count -- for it if is true what you say that the use of numbers (what I think you call 'numerical cognisance') "does not depend on...linguistic abilities" then you should be able to show us how this is so in just such a non-human language.

And we are still waiting for your proof that animals do/can use count nouns.

[As I have already pointed out several times, if they can't use such nouns, then you must mean that they use 'numbers' not numbers -- and we are still waiting for you to explain what these interesting 'numbers' are -- without the use of count nouns, that is.]

The point you miss about this is that in order to count there must be something to count

Where have I 'missed' this? What do you think my reference to count nouns was all about -- as in two apples, three books, at least ten fabrications by CM, etc.?

and the debate is about that something and how it is processed by non human species.

Are you suggesting that these animals have factories or offices? That's where we process things.

Or are you using the word "processed" in a new and-as-yet-unexplained sense?

If so, what is it?

[Silly question, I know. You never explain your odd use of English, do you?]

Your human centric views have no place in biology or biological arguments as they would exclude a great deal of research out of hand because of a rather intellectually silly application of human logic.

I have already covered this; here it is again:

Well, I'm a human being, and I'm reasonably sure you are. In which case, perhaps you should try to tell us what your new use of 'information' [or the words used in "biological arguments"] is in a non-human language so that it isn't biased by such ["human centric"] irrelevances.

Since you have failed to do so, I can only conclude that not even you believe this, you just like to argue.

Moreover, I'm not excluding "a great deal of research", merely questioning your idiosyncratic use of language.

Yet again, take the example of pi. It is impossible for us to write out the complete numerical form of pi, so therefore we only have "pi" and not pi? On that basis how can we call pi, pi. or even know it is pi seeing as we have never seen all of it nor could we possibly say all of it either, so to speak?

Then why did you say numbers are abstract objects? If the decimal expansion of pi can't be written down, then there is no abstract object that it could be, or that "pi" could refer to, is there?

But, if you find pi impossible to comprehend given your odd ontology, then what about zero? To what does zero refer?

May I remind you what I said earlier about your 'theory' (that numbers are abstract objects) in relation to zero:

Once more, if it refers to one abstract object, then zero in fact refers to one, not zero.

On the other hand, as Blaise Pascal noted, if it refers to nothing, then we should, for instance, write 10,001 as 11, since those three zeros are the same as nothing. In which case nothing should stand between those two ones, which thus changes 10,001 into 11!

And I couldn't follow this:

so therefore we only have "pi" and not pi? On that basis how can we call pi, pi. or even know it is pi seeing as we have never seen all of it nor could we possibly say all of it either, so to speak?

Perhaps if you translated it into Ant-speak it might become a little clearer?

Just a thought...

"And which typo have I picked up on?"

schnumerosity

Oh dear. You clearly do not know what "typo" means. It refers to a typing error. Since I have referred to none of your typing errors, then I haven't been "picking at typos", as you alleged in an earlier post.

"Schnumerosity" was made up, so it can't be a typo.

Fib?

No thanks, I think we've already had quite enough from you as it is.

---------------------------------------------

Oh, and we're still waiting for your logical proof that there is such a thing as 'the mind'.

And good luck with that one!

Even Descartes failed.

Revolution starts with U

21st March 2011, 18:58

I just have one question Rosa... cuz I agree with most of what you're saying here. Especially Bohr on creating a verb heavy language in order to better understand the phsyical processes of a never static world.

It seems you're saying animals could not "count" because that relies upon certain simplifications of complex schemes that can only be understood in the context of language (and it's social nature); count nouns. (I may be completely wrong, but that's how it read to me)
But, could an animal not be able to cognisize the difference between what we call 1 gazelle, from two? Surely he doesn't need language to understand that?
Of course just having numbers is not arithmetic. But I still don't see how an animal could not have its own version of count nouns it understands personally.

Rosa Lichtenstein

21st March 2011, 19:06

RSWU:

It seems you're saying animals could not "count" because that relies upon certain simplifications of complex schemes that can only be understood in the context of language (and it's social nature); count nouns. (I may be completely wrong, but that's how it read to me)

But, could an animal not be able to cognisize the difference between what we call 1 gazelle, from two? Surely he doesn't need language to understand that?

In fact, I admitted this quite early on, even though I'd not put it the way you do.

The ability to tell the difference between one animal and two animals is not the same as being able to count, anymore than being able to tell the difference between music and a cacophony implies a comprehension of music. Or the ability to throw stones implies a knowledge of ballistics.

ComradeMan

22nd March 2011, 10:52

RSWU:
In fact, I admitted this quite early on, even though I'd not put it the way you do.

The ability to tell the difference between one animal and two animals is not the same as being able to count, anymore than being able to tell the difference between music and a cacophony implies a comprehension of music. Or the ability to throw stones implies a knowledge of ballistics.

This just shows how you haven't even bothered to read the research. No one would argue that the mere difference to distinguish between two animals was the ability to count... but there was just a little more going on there with the various animals observed wasn't there?

How does a bee solve the travelling salesman problem if it is not able to evaluate or measure energy consumption and distance?
http://www.sciencedaily.com/releases/2010/10/101025090020.htm

As for your other comments. Well, you never do actually come out and say directlty "numbers are the same as numerals" but it is clear through your confused use of terminology and concepts that you don't make the distinction.

As for the mind vs body argument, and excluding Cartesian dualism, this is a very old philosophical debate that has NEVER been resolved and probably cannot be in a scientific sense. However, your body can only touch/feel/hear/go etc to something that exists in the material world yet your mind can imagine something that does not exist. Franz Brentano made the statement about being able to imagine a unicorn etc- this intentionality therefore cannot be part of the material world.

Yet again, other than trying to twist things into a linguistic logical debate you have no mathematical or scientific arguments to challenge the research.

Your argument is also ambiguous to say the least.

If the mind does not exist then what processes information? What are numbers if not products of the human mind- which seems to be your argument against numerical ability in non-human species and yet you now state that the mind does not exist?

What is your logic if it is not a product of the human mind? :laugh: If we want to argue in your way?

I suggest you buy a good dictionary and work on your Latin too because your quibbiling about the definitions of words such as "process", apart from being bizarre, leaves you open to criticism- especially seeing as you like to pick at words all the time.

As for your comments about pi, well back in 1882 Ferdinand Lindemann proved its transcendence. Pi can only be expressed through abstract symbols and represented incompletely- it cannot be expressed through a finite series or any operation. So pi, according to your apparent view on things does not exist it only "exists"? :rolleyes:

Your argument is entirely lame.

"May I remind you what I said earlier about your 'theory' (that numbers are abstract objects) in relation to zero:"

"Is it my fault that there is not much to say about your fibs, confusions, obscure neologisms and circular definitions? It's like trying to punch a cloud."

Wrong- I said numbers were abstract mathematical objects expressed/represented by, but distinct from, numerals and used to decribe quantities.
This is a fairly standard definition of what numbers are- no neologisms, falsehoods or made up stuff here.

Your problem is that you cannot separate the description from that which is being described. This is a rather typical and dilettante misconception. An apple exists regardless of people perceiving the apple, i.e. it is not a problem of the mind- the existence versus the non-existence is not dependent on being perceived as such- that is to say if we accept the idea of a primordial reality.

The accusation of not knowing what a typo is really does hit rock bottom in the levels of silliness to which you unashamedly aspire- so now someone makes a typing error, but it's not a typing error because you say so? Please, stop being infantile.

The fact of the matter is that you cannot entirely reduce mathematics to logic, these attempts have failed- this is not write off the value of logic, but one might ask which logic? Brouwer's logic? Frege's logic etc? Wasn't it Russel who compared logic to a boy and mathematics to a man? :laugh:

Can you demonstrate how empirical your logic itself is? :laugh:

Rosa Lichtenstein

22nd March 2011, 13:58

CM:

This just shows how you haven't even bothered to read the research. No one would argue that the mere difference to distinguish between two animals was the ability to count... but there was just a little more going on there with the various animals observed wasn't there?

Well, I wasn't addressing anything you had posted, confused as it was, but responding to a particular point raised by RSWU

How does a bee solve the travelling salesman problem if it is not able to evaluate or measure energy consumption and distance?
http://www.sciencedaily.com/releases...1025090020.htm

Maybe the bee has an advanced degree in mathematics? After all we need one to be able to solve this problem. So why not bees?

An even better question: How does a projectile solve the problem of following the path of least action (http://en.wikipedia.org/wiki/Principle_of_least_action) as it travels along its trajectory -- a much more difficult 'problem'? Perhaps rocks and stones understand 'numerosity' -- which is more than you seem to be able to manage, since you have yet to explain it.

On a side issue, your question reminds me of a cartoon I once saw. It involved two fish [note the count noun] conversing in a fish tank. The first fish says to the second "Well if god doesn't feed us, who does?"

You seem to want to solve all such 'scientific problems' by anthropomorphising animals, which is no more of a solution than the one the above fish proposed.

As for your other comments. Well, you never do actually come out and say directly "numbers are the same as numerals" but it is clear through your confused use of terminology and concepts that you don't make the distinction.

Fine, so you made it up then.

Now, perhaps you can quote the passages from my posts which suggest this is the case:

it is clear through your confused use of terminology and concepts that you don't make the distinction

In fact, as we will see below, you seem to confuse the numerals used to refer to pi with that number itself.

You:

As for the mind vs body argument, and excluding Cartesian dualism, this is a very old philosophical debate that has NEVER been resolved and probably cannot be in a scientific sense. However, your body can only touch/feel/hear/go etc to something that exists in the material world yet your mind can imagine something that does not exist. Franz Brentano made the statement about being able to imagine a unicorn etc- this intentionality therefore cannot be part of the material world.

Let me get this straight: this is your 'logical proof' that there is such a thing as 'the mind'?

May I point out that you assume what you want to prove:

Your mind can imagine something that does not exist

Once more, where is your 'logical proof' that there is such a thing as 'the mind'? If you don't have one (a proof, that is), perhaps then you will have the humility to admit it.

Yet again, other than trying to twist things into a linguistic logical debate you have no mathematical or scientific arguments to challenge the research.

We have been over this several times: If you object to such 'linguistic' issues, then maybe you should try to argue without using any language at all.

Or, if you find you have to use language, perhaps you will tell us what the special meanings of the neologisms you employ (and the other ordinary words you misuse) are.

Until you do, it's not easy to make sense of anything you say.

Your argument is also ambiguous to say the least.

That's a bit rich coming from someone who still can't tell us with any clarity what 'numerosity' is and who seems to have problems with words like "information" and "number".

If the mind does not exist then what processes information? What are numbers if not products of the human mind- which seems to be your argument against numerical ability in non-human species and yet you now state that the mind does not exist?

I do not know who the above comment is directed at, but it can't be me since I have never argued that 'the mind' does not exist -- as you have been told several times -- only that there is no such thing as 'the mind'. If you are not too sure of the difference between these two questions, then maybe you need to retake Philosophy 101.

And I note that you seem to think that 'the mind' (whatever it is) is some sort of factory, or office, otherwise why say this:

then what processes information?

Unless, of course, you are using the word "processes" in a new and-as-yet-unexplained sense. If so what is it?

And 'the mind', whatever it is, can't 'process' information, since only human beings can do that. Unless, of course, you think 'the mind' is run by an homunculus of some sort (http://en.wikipedia.org/wiki/Homunculus_argument)?

What is your logic if it is not a product of the human mind?

[I]Ah, the fish argument again.

I suggest you buy a good dictionary and work on your Latin too because your quibbling about the definitions of words such as "process", apart from being bizarre, leaves you open to criticism- especially seeing as you like to pick at words all the time.

I rather think that this would be good advice for you to take, since you not only seem to be having problems with words like "number" and "information", you can't even tell us what your own neologisms mean!

As for your silly comments about pi, well back in 1882 Ferdinand Lindemann proved its transcendence. Pi can only be expressed through abstract symbols and represented incompletely- it cannot be expressed through a finite series or any operation. So pi, according to your apparent view on things does not exist it only "exists"?

So, "symbols" are abstract now! I'm afraid they look pretty material and concrete to me on the screen and the page. [Ooops! I suspect you have confused numerals with numbers here.]

And, of course, we represent pi by means of infinite series (I prefer to call these "rules", since no series can be infinite), but you have yet to tell us to what this series refers? If all numbers are abstract objects, as you earlier claimed, then to what abstract object does pi, or the series you mention, refer?

And we are still waiting for you to tell us to what zero refers.

ComradeMan

22nd March 2011, 14:24

CM: Well, I wasn't addressing anything you had posted, confused as it was, but responding to a particular point raised by RSWU.

Well more than two people can participate in a discussion can't they?:rolleyes:

Maybe the bee has an advanced degree in mathematics? After all we need one to be able to solve this problem. So why not bees?.

Why? Is it a prerequisite of the ability to estimate and evaluate distances? :lol: In which case most people would not qualify by your standard.

An even better question: How does a projectile solve the problem of following the path of least action (http://en.wikipedia.org/wiki/Principle_of_least_action) as it travels along its trajectory -- a much more difficult 'problem'? Perhaps rocks and stones understand 'numerosity' -- which is more than you seem to be able to manage, since you have yet to explain it.

Because bees are living creatures with a brain and are capable of independent decision on their movement within the laws of physics- of course- which rocks, bullets and stones are not. Next question....

You seem to want to solve all such 'scientific problems' by anthropomorphising animals, which is no more of a solution than the one the above fish proposed.

No, anthropomorphisis would be if I claimed that bees had also solved Fermat's Last theorem.

Fine, so you made it up then..

No, it was one of the first things I learned at high school mathematics... LOL!!! I thought it wouldn't need an advanced degree in mathematics to no what the difference is between numbers and numerals and also between different kinds of numbers- hence the use of terms like real numbers, integers, transcendental numbers and....oh wait.... imaginary numbers.

In fact, as we will see below, you seem to confuse the numerals used to refer to pi with that number itself...

Err.... sorry, the confusion arises because you seem to lack the power to differentiate. The problem with pi is a theoretical problem of your making, not mine.

Let me get this straight: this is your 'logical proof' that there is such a thing as 'the mind'?

"Cogito ergo sum"- albeit problematical. Can you smell, hear, taste, touch or feel a thought? In which case a thought cannot be deduced through the senses therefore some things may exist outside of the senses. Now if we are bundles of perceptions. :lol:, provide the logical proof that the material or rational world exists without resorting to axioms that could be questioned?:thumbup1:

We have been over this several times: If you object to such 'linguistic' issues, then maybe you should try to argue without using any language at all....[/QUOTE]

Yawn... it's the application of linguistic logic to neurobiology etc that is the problem. Prove to me logically that garlic does not go well with milk, you can't but you aren't going to do well in cookery class or become a top chef are you? :lol:

That's a bit rich coming from someone who still can't tell us with any clarity what 'numerosity' is and who seems to have problems with words like "information" and "number".....

FFS stop saying "us" all the time as it's presumptious. Secondly, tell "us" what clarity means and what "is" is and perhaps your use of the verb to be is also dubious if we take things to logical extremes with e-prime etc. The only person who has a problem is YOU- and numerosity is not a neologism nor an invented term- look it up in a dictionary, why don't you?

All you do is take one specific meaning or definition of a word and try to say that is the only meaning or definition of it in arguments that would go on and on ad infinitum. It's intellectually childish.

Not one of my uses of the word process, information, abstract is out-of-line and I suggest you look up the meanings, definitions etc. For example, in English mind has approximately twenty; process has a fair few too.

You have some serious issues with vocabulary.

Rosa Lichtenstein

22nd March 2011, 15:15

CM (once again, your odd use of the quote function has mixed some of my words up with your own):

Well more than two people can participate in a discussion can't they?

You see, even you know how to use count nouns...

Why? Is it a prerequisite of the ability to estimate and evaluate distances? In which case most people would not qualify by your standard.

Well, you referred to their mathematical skills:

How does a bee solve the travelling salesman problem if it is not able to evaluate or measure energy consumption and distance?

So, I assumed you meant they had been to university. Or are they all self-taught? Is each one a sort of Bee Ramanujan (http://en.wikipedia.org/wiki/Srinivasa_Ramanujan)? Perhaps, too, you think bees have metre rulers or laser measuring equipment in their hives, if they can "measure" things?

Or were you using terms like "solve" and "measure" in a new and-as-yet-unexplained sense? If so, what is it?

Because bees are living creatures with a brain and are capable of independent decision on their movement within the laws of physics- of course- which rocks, bullets and stones are not. Next question....

And yet how do rocks manage to do this?

Why can't I anthropomorphise a rock, just like you anthropomorphise bees?

No, anthropomorphism would be if I claimed that bees had also solved Fermat's Last theorem.

But you asked this rhetorical question:

How does a bee solve the travelling salesman problem if it is not able to evaluate or measure energy consumption and distance?

This is an advanced problem in Discrete Mathematics (http://en.wikipedia.org/wiki/Discrete_mathematics). I do not see the difference between the claim that bees can 'solve' this one but can't 'solve' Fermat's Last Theorem.

No, it was one of the first things I learned at high school mathematics... LOL!!!

Did you really learn to make stuff up about my alleged confusion between numbers and numerals at high school? For that is what I meant when I posted this comment:

Fine, so you made it up then.

By this, I was referring to you making up the allegation that I had confused numbers with numerals, since you have yet to quote a single passage where I do this, or even imply it.

I thought it wouldn't need an advanced degree in mathematics to no what the difference is between numbers and numerals and also between different kinds of numbers- hence the use of terms like real numbers, integers, transcendental numbers and....oh wait.... imaginary numbers.

As we can now see, you misconstrued my comment. So, this fine example of sarcasm was all wasted effort, impressive though it is.

Err.... sorry, the confusion arises because you seem to lack the power to differentiate. The problem with pi is a theoretical problem of your making, not mine.

Well, you were the one who confused pi with 'abstract symbols':

Pi can only be expressed through abstract symbols and represented incompletely- it cannot be expressed through a finite series or any operation.

And yet the symbols mathematicians use are eminently concrete. [Anyway, what is an 'abstract symbol'?]

"Cogito ergo sum"- albeit problematical. Can you smell, hear, taste, touch or feel a thought? In which case a thought cannot be deduced through the senses therefore some things may exist outside of the senses. Now if we are bundles of perceptions, provide the logical proof that the material or rational world exists without resorting to axioms that could be questioned

The cogito is in fact an invalid argument.

On top of that, even Descartes found he had to appeal to 'god' to make it work (in order to guarantee that his 'clear and distinct ideas, like the cogito, did not always lead him astray).

But, thanks again for demonstrating that you have in fact no 'logical proof' that there is such a thing as 'the mind', just a few vague ruminations about thoughts and feelings.

Yawn... it's the application of linguistic logic to neurobiology etc that is the problem.

But, all you seem to do is use words in odd ways, and ways that not even you can explain, despite being asked several times to do so..

Prove to me logically that garlic does not go well with milk, you can't but you aren't going to do well in cookery class or become a top chef are you?

Er, what has that got to do with anything have argued?

May I suggest you reach for that dictionary of yours and check out the meaning of the word "relevant"?

FFS stop saying "us" all the time as it's presumptuous.

1. No.

2. It's my way of reminding you that you are using language differently from the rest of us -- and in ways that not even you can explain.

Secondly, tell "us" what clarity means and what "is" is and perhaps your use of the verb to be is also dubious if we take things to logical extremes with e-prime etc.

Well, if you don't know what "clarity" means no wonder you can't explain yourself with any clarity. [Same comment over the use of "is".]

The only person who has a problem is YOU- and numerosity is not a neologism nor an invented term- look it up in a dictionary, why don't you?

Not so, as I have explained before; you are the one who wants to use perfectly ordinary words in odd ways, so it's up to you to help us out here. It's not my fault if you now blame me for your own failings.

All you do is take one specific meaning or definition of a word and try to say that is the only meaning or definition of it in arguments that would go on and on ad infinitum. It's intellectually childish.

Well, if I were to copy you and use words in odd ways, I'd try to explain what I meant -- you seem to think we can all follow you. Well, we can't. And you won't even help us out!

All you do is take one specific meaning or definition of a word and try to say that is the only meaning or definition of it in arguments that would go on and on ad infinitum. It's intellectually childish.

Not so; you can mean whatever you like by any of the words you use. All I ask, and I have done repeatedly, is that you tell us what the new senses of your words are. You seem to think it some sort of affront to be asked to explain yourself, and then you blame me for even asking!

You have some serious issues with vocabulary.

Maybe so, maybe not, but you are the one who now seems to have problems with the word "is", so you have no room to point any fingers at me, chummy.

--------------------------------

I've noticed that you have added a few comments to your last post, which I have missed, so I will return to it and respond to them.

Rosa Lichtenstein

22nd March 2011, 15:40

CM:

Wrong- I said numbers were abstract mathematical objects expressed/represented by, but distinct from, numerals and used to describe quantities.

Then they are still abstract objects, according to you.

Anyway, what 'abstract mathematical object' does zero refer to?

It can't be a single 'abstract mathematical object', for if it were, then zero would refer to one 'abstract mathematical object', and zero would be the same as one! [And it can't refer to nothing for reasons I have set out already.]

This is a fairly standard definition of what numbers are- no neologisms, falsehoods or made up stuff here.

Sure, and that is why I said that your ideas are based on obsolete theories of number -- we can see that since you still can't tell us what 'abstract mathematical object' zero refers to. [Or even what one refers to, come to that!]

Your problem is that you cannot separate the description from that which is being described.

Well, until you tell us what you mean, we do not even know what you are trying to describe.

This is a rather typical and dilettante misconception. An apple exists regardless of people perceiving the apple, i.e. it is not a problem of the mind- the existence versus the non-existence is not dependent on being perceived as such- that is to say if we accept the idea of a primordial reality.

So, you think that numbers exist like apples, eh?

If not, what is the point of your analogy?

The accusation of not knowing what a typo is really does hit rock bottom in the levels of silliness to which you unashamedly aspire- so now someone makes a typing error, but it's not a typing error because you say so?

Well, do you or do you not know what a typo is?

Please, stop being infantile.

In what way is asking you to explain your odd use of language 'infantile'?

Of course, you might be using "infantile" in a new, and-as-yet-unexplained sense. If so, what is it?

The fact of the matter is that you cannot entirely reduce mathematics to logic,

Oh dear, you seem to have returned to an earlier false accusation. Where have I tried to do this?

We went over this weeks ago!

these attempts have failed- this is not write off the value of logic, but one might ask which logic? Brouwer's logic? Frege's logic etc? Wasn't it Russell who compared logic to a boy and mathematics to a man?

Fine words, but they only serve to confirm that you are still having problems with the word "relevant".

Can you demonstrate how empirical your logic itself is?

Even better: Can you demonstrate this has got anything to do with anything I have posted here, or anywhere else, for that matter?

Revolution starts with U

22nd March 2011, 20:41

Imo Descartes theroem should be amended to say "I am thinking, and other thinkers think I am thinking, therefore we are." :thumbup1:

But I am in the camp that the mind, at least as it describes a so-called metaphysical phenomenon, does not exist. But the mind, describing physical process of neuronal memory and forsight exists, and is physical

Rosa Lichtenstein

22nd March 2011, 20:49

RSWU:

But I am in the camp that the mind, at least as it describes a so-called metaphysical phenomenon, does not exist. But the mind, describing physical process of neuronal memory and forsight exists, and is physical

That view is, I'm afraid, a left-over from the ancient Platonic/Christian/Cartesian idea that there are two substances, mind and matter. The only difference is that you have an explanation of the one in terms of the other. But, in order to free yourself from this ancient world-view, you need to reject the dichotomy itself, and the idea that there is something called 'the mind' that needs explaining.

I have said more about this in the following threads and posts:

http://www.revleft.com/vb/consciousness-and-passage-t100438/index.html

http://www.revleft.com/vb/why-do-we-t98047/index.html

http://www.revleft.com/vb/self-t105849/index.html

http://www.revleft.com/vb/consciousness-t135419/index.html

http://www.revleft.com/vb/showpost.php?p=2041282&postcount=17

http://www.revleft.com/vb/showpost.php?p=1750114&postcount=20

http://www.revleft.com/vb/meridian-disagreeing-noxion-t146733/index.html

http://www.revleft.com/vb/showpost.php?p=1962485&postcount=18

http://www.revleft.com/vb/showpost.php?p=1962582&postcount=21

Revolution starts with U

22nd March 2011, 20:56

That view is, I'm afraid, a left-over from the ancient Platonic/Christian/Cartesian idea that there are two substances, mind and matter. The only difference is that you have an explanation of the one in terms of the other. But, in order to free yourself from this ancient world-view, you need to reject the dichotomy itself, and the idea that there is something called 'the mind' that needs explaining.

Perhaps I didn't phrase myself correctly, I agree completely. I don't think there is any such thing as "the mind" other than the physical phenomenon that make up the brain and neural network. Perhaps the whole is greater than the sum of it's parts, but that is as far as I am willing to go.

I think the meta-physical only arises because our language is to want of identification in an ever-changing reality.

ComradeMan

22nd March 2011, 21:44

Rosa, I implore you to keep your answers coherent, or is this a ploy?

Well, you referred to their mathematical skills

Rocks and bees... think about the difference.:lol:

It's only anthropomorphisis if you insist that being numerical cognisant is de facto an exclusively human trait- the point that was being debated and for which you have provided no evidence based on scientific observation or any logical proofs- so far at least. If you can't see the difference between a rock and a bee then you do have problems. The rest of your comment is just being facetious in its worst sense. Do you need to go to university to have mathematical ability? If you didn't have the ability in the first place no amount of learning would make any difference.

Here we go again: Colours exist in nature, and they did so before sentient life evolved. But, numbers did not. [Or if you think they did, where then did they exist?]

What is a colour? A colour only exists if you can perceive it or its wavelength and how can your prove your assertion that colours existed before sentient life evolved (not all of which can perceive/perceives colour in the same way)?

Godel demonstrated that and mathematical concepts are communicated communicated by equations, symbols and so on but do not exist merely or exclusively because of them, i.e. the point about the description and that which is being described. All of this logical positivism of yours should have been thrown on the waste dump of history years ago. There are true statements that are not provable and not all statements that are known to be true can be demonstrated through the manipulation of mathematical symbols.

Once more, if it refers to one abstract object, then zero in fact refers to one, not zero.

Since when do the words we use for numbers have to be autological? The etymology of the word, through Italian from Arabic means "a void" or "an emptiness".

Even better: Can you demonstrate this has got anything to do with anything I have posted here, or anywhere else, for that matter?

I am asking you to demonstrate how logic is anything in actual fact materially tangible, empirical or materialistic.

The cogito is in fact an invalid argument

Because.... ? Has it been convincingly refuted and furthermore is that agreed upon the same way in which most people agree the world isn't flat? I did say "problematic".

Show me where I have used one of the words you have picked at in an unacceptable or at least unique way? By the way an object does not have to be a thing- as you should know. ;) Your denial of the mind is all well and good but then explain imagination?

@RVSU
This cogito ergo sum thing- well, Descartes wrote the original quote in French Je pense donc je suis which does not distinguish between a simple or continuous/progressive form as English does and Italian partially does- so it could be argued that "I think" or "I am thinking" etc the full and later Latin quote is "Ac proinde haec cognitio, ego cogito, ergo sum, est omnium prima et certissima, quae cuilibet ordine philosophanti occurrat"

Rosa Lichtenstein

22nd March 2011, 23:55

CM:

Rosa, I implore you to keep your answers coherent, or is this a ploy?

Yes, I think it is a ploy on your part.

Rocks and bees... think about the difference.

Human beings and bees... think about the difference.

It's only anthropomorphism if you insist that being numerical cognisant is de facto an exclusively human trait

1. You have yet to tell us what 'numerically cognisant' means -- without, that is, a use of count nouns.

2. You are assuming that which is to be proved: that other organisms can use numbers, when the only ones that do are us human beings. After all, we are the only ones who use count nouns. Of course, if you can show that animals can and do use count nouns, I will be happy to concede the point. On the other hand, if you still claim that they can use numbers (or that they can count), but they can't or don't use count nouns, then you must be speaking about 'numbers' and not numbers, or 'counting' and not counting. And we are still waiting for you to explain these interesting 'numbers' to us.

the point that was being debated and for which you have provided no evidence based on scientific observation or any logical proofs- so far at least.

Once more, you have yet to present us with a comprehensible possibility, and that will remain so until you explain what 'numerical cognisance', 'numerosity' and 'numbers' are.

If you can't see the difference between a rock and a bee then you do have problems.

But you are the one who can't see the difference between a bee and human being.

The rest of your comment is just being facetious in its worst sense.

May I remind you that you are the one who began with a facetious joke about Frege, so you have no room to talk.

Do you need to go to university to have mathematical ability?

Unless you are a mathematical genius, then yes you have to go to university to be able to understand the solution to the travelling salesman problem.

If you didn't have the ability in the first place no amount of learning would make any difference.

Dah.

What is a colour? A colour only exists if you can perceive it or its wavelength and how can your prove your assertion that colours existed before sentient life evolved (not all of which can perceive/perceives colour in the same way)?

But what colour is a particular wavelength of light associated with? In order to know the answer to that one, we'd already have to understand the language colour. So, it's our knowledge of the vocabulary of colour that informs our knowledge of the science of colour, not the other way round.

And, are you really committed to the idea that there are no colours in nature? That it is totally colourless?

Godel demonstrated that and mathematical concepts are communicated by equations, symbols and so on but do not exist merely or exclusively because of them, i.e. the point about the description and that which is being described.

1. Where did he 'demonstrate' this?

2. How did he demonstrate this?

3. If we did not already know this (i.e., "that and mathematical concepts are communicated by equations"), what could he possibly have communicated to us if he was the first to realise this? In other words, we should already have to know this (i.e., "that and mathematical concepts are communicated by equations") for us to be able to understand his 'demonstration' in the first place. In which case, he was wasting his time since we already knew this (i.e., "that and mathematical concepts are communicated by equations")!

All of this logical positivism of yours should have been thrown on the waste dump of history years ago.

Ah, yet another invention.

I am not, nor have I ever been a logical positivist, and nothing I have said even so much as suggests I am or that I agree with anything they ever said.

Where do you get these odd ideas from?

There are true statements that are not provable and not all statements that are known to be true can be demonstrated through the manipulation of mathematical symbols.

Even if that were so, which I deny anyway, what has it got to do with this thread?

You really must look up the meaning of the word "relevant" as a matter of some urgency.

Since when do the words we use for numbers have to be autological? The etymology of the word, through Italian from Arabic means "a void" or "an emptiness".

I have already covered this in an earlier thread. Here it is again (slightly modified to take account of this latest claim of yours):

Once more, if it refers to one abstract object, then zero in fact refers to one, not zero.

On the other hand, as Blaise Pascal noted, if it refers to nothing, a void or an emptiness, then we should, for instance, write 10,001 as 11, since those three zeros are the same as nothing, or a void. In which case nothing or a void should stand between those two ones, which would thus change 10,001 into 11 -- or into 1 1!

And sure the etymology of words is important but it can't really help decide what mathematical symbols mean. If it did then when we spoke about the "roots" of an equation, for example, we would have to conclude that equations were like plants, and grew in the soil!

I am asking you to demonstrate how logic is anything in actual fact materially tangible, empirical or materialistic.

Which I will be happy to do just as soon as you show what this has got to do with anything I have argued in this thread -- or anywhere else for that matter.

Because.... ? Has it been convincingly refuted

1. The "cogito" bit does not imply the "sum" bit.

2. Yes it has been refuted.

and furthermore is that agreed upon the same way in which most people agree the world isn't flat? I did say "problematic".

Eh?

Show me where I have used one of the words you have picked at in an unacceptable or at least unique way?

Where did I say you had? What I said was that you are using them in odd ways -- ways you consistently refuse to explain. [Which suggests that not even you understand them.]

I am beginning to suspect that your predilection for using words in such odd ways might be connected with your incapacity to read with due care anything I have posted.

By the way an object does not have to be a thing- as you should know.

Perhaps then you can tell us what a "thing" is?

Your denial of the mind is all well and good but then explain imagination?

Where did I "deny the mind"?

Yet another invention.

A successful career at Fox News beckons you, I think.

And why do I need to 'explain' imagination? Where have I denied we are capable of exercising it?

[However, I'd like to see you explain it! Ha -- some hope.]

Rosa Lichtenstein

22nd March 2011, 23:57

RSWU:

Perhaps I didn't phrase myself correctly, I agree completely. I don't think there is any such thing as "the mind" other than the physical phenomenon that make up the brain and neural network. Perhaps the whole is greater than the sum of it's parts, but that is as far as I am willing to go

Ok, but this is in fact little different from what you said earlier.

Never mind, it's not worth arguing over in this thread.:)

ComradeMan

23rd March 2011, 12:00

CM: Yes, I think it is a ploy on your part.

Tu quoque

Human beings and bees... think about the difference..

Err.... well seeing as both are living organisms with brains and the capacity for decision making and organisation and rocks....err, are not sentient minerals/conglomerates of minerals etc.... I think your making stupid analogies and using false equivalencies for lack of an actual argument.

1. You have yet to tell us what 'numerically cognisant' means -- without, that is, a use of count nouns.

It has been gone over again and again. Look up the words/phrases subitise/enumerate/estimate numerosities etc etc etc....

2. You are assuming that which is to be proved: that other organisms can use numbers, when the only ones that do are us human beings. After all, we are the only ones who use count nouns. Of course, if you can show that animals can and do use count nouns, I will be happy to concede the point. On the other hand, if you still claim that they can use numbers (or that they can count), but they can't or don't use count nouns, then you must be speaking about 'numbers' and not numbers, or 'counting' and not counting. And we are still waiting for you to explain these interesting 'numbers' to us..

Children who don't use count nouns and have not been taught to count or any form of arithmetic have shown the ability to subitise. This has been shown to be an innate/inborn biological ability and demonstrated in new born babies of as little as 3 weeks of age. Non-human species have also been shown to have this ability. Without the ability to subitise it is doubtful whether any kind of mathematical ability could/would develop. Furthermore, non-human species have also been shown to have abilities of enumeration too.

Here's an extract from this paper- my highlighting.

Representation of the Numerosities 1-9 by
Rhesus Macaques (Macaca mulatto)
Elizabeth M. Brannon and Herbert

"It is often assumed that numerical thought is beyond the reach of animals because all human numerical systems use arbitrary symbols, (e.g., Hurford, 1987). That assumption can be questioned on both theoretical and empirical grounds (Carey, 1998; Dehaene & Changeux, 1993; Meek & Church, 1983). Recent experiments on species as diverse as pigeons, rats, raccoons, ferrets, dolphins, and monkeys provide evidence that animals have numerical abilities that do not require knowledge of symbols (see Boysen & Capaldi, 1993; Davis & Perusse, 1988; Dehaene, 1997; Dehaene, Dehaene-Lambertz, & Cohen, 1998; Gallistel & Gelman, 1992, for reviews"

http://www.columbia.edu/cu/psychology/primatecognitionlab/References/BrannonTerrace2000.pdf

Unless you are a mathematical genius, then yes you have to go to university to be able to understand the solution to the travelling salesman problem...

Or a bee it seems.

But what colour is a particular wavelength of light associated with? In order to know the answer to that one, we'd already have to understand the language colour. So, it's our knowledge of the vocabulary of colour that informs our knowledge of the science of colour, not the other way round....

So that's why red is so often a warning colour in nature to other organisms, which of course have no word for red- yet need to recognise this colour.....

But what is a wavelength? Is it a wave and is it long? And what is a wave unless we call it a wave? So it doesn't exist if we don't have a name for it? :lol:

A rose by any other name would be.....?

If we did not already know this (i.e., "that and mathematical concepts are communicated by equations"), what could he possibly have communicated to us if he was the first to realise this? In other words, we should already have to know this (i.e., "that and mathematical concepts are communicated by equations") for us to be able to understand his 'demonstration' in the first place. In which case, he was wasting his time since we already knew this (i.e., "that and mathematical concepts are communicated by equations")!

Yet again avoiding the points by asking a question. ;)

I am not, nor have I ever been a logical positivist, and nothing I have said even so much as suggests I am or that I agree with anything they ever said.

If you use arguments that come from that side of the playing field then so be it.

For the rest of your tu quoque, lack of argument and answering a question
or "refuting" a point by merely asking a question there is little to be said.

The old "cogito ergo sum" debate is ongoing- but it has not been refuted outright. Problems have been highlighted and discussed but there is no consensus on the matter. You are the person who seems to feel the mind does not exist, that would be pretty much a denial of the mind, wouldn't it?

Ooops, bad start, since there is no such thing as 'the mind'.

And human beings created language, not 'minds'.

Yet strangely in another thread here at RevLeft you were talking about inner minds etc....

But let's await your responses in which a) you'll suddenly move the goalposts again b) quibble about words or come up with some reason why a perfectly normal use of a word is "made up" or an invention or c) skip over a point by asking a question. :lol:

Rosa Lichtenstein

23rd March 2011, 14:05

CM:

Err.... well seeing as both are living organisms with brains and the capacity for decision making

Well, you must be using the word "decision" here in a new and-as-yet-unexplained sense; if so, what is it?

and organisation and rocks....err, are not sentient minerals/conglomerates of minerals etc....

But, humans can and do use count nouns whereas bees can't. So, when it comes to numbers, this is just as significant a difference.

I think your making stupid analogies and using false equivalencies for lack of an actual argument.

Whereas you seem to think bees went to university!

It has been gone over again and again. Look up the words/phrases subitise/enumerate/estimate numerosities etc

Well, you gave us a circular 'definition' of 'numerosity', but that's about all.

Now, I'm not interested in how others use these odd words of yours; they aren't party to this discussion. What we want to know is what you mean by them. Of course, if you don't know, just admit it.

Children who don't use count nouns and have not been taught to count or any form of arithmetic have shown the ability to subitise.

Then those children can't count yet -- unless of course you want to use "count" in a new and-as-yet-unexplained sense; if so, what is it?

This has been shown to be an innate/inborn biological ability and demonstrated in new born babies of as little as 3 weeks of age. Non-human species have also been shown to have this ability. Without the ability to subitise it is doubtful whether any kind of mathematical ability could/would develop.

Same point

Furthermore, non-human species have also been shown to have abilities of enumeration too.

Not so, unless they can use count nouns. Well, can they? If so, where's the evidence? If not, then, whatever else this is, it has nothing to do with what we call numbers and counting.

And thanks for the references, but it seems those authors are happy to make the same mistakes as you -- or they are using the relevant words in new and-as-yet-unexplained senses. If so, what are they?

You keep forgetting to tell us.

Or a bee it seems.

And a stone has 'solved' the path of least action, too.

So that's why red is so often a warning colour in nature to other organisms, which of course have no word for red- yet need to recognise this colour.....

I'm sorry, but you seem to be suffering from that recurring affliction of yours -- that is, over the meaning of the word "relevant" -- and I fear this will continue until you refresh your memory by looking it up in that cob-web covered dictionary of yours.

Anyway, what has this got to do with numbers, or counting?

Are you suggesting that numbers exist like colours do? If so, what wavelength of light represents the number 4,567,734? Or -34,567?

But what is a wavelength? Is it a wave and is it long? And what is a wave unless we call it a wave? So it doesn't exist if we don't have a name for it?

I'm sorry, but what is the point of these rhetorical questions? Are you suggesting that numbers existed before the human race invented words to express them? If so, where did they exist before this happened?

You keep refusing to say.

I suspect you do not know.

A rose by any other name would be.....?

"Nothing like a number...", so why quote this hackneyed phrase?

Yet again avoiding the points by asking a question.

Like you never ask questions; here are just a few of yours from your last five posts in this thread:

But what is a wavelength? Is it a wave and is it long? And what is a wave unless we call it a wave? So it doesn't exist if we don't have a name for it?

A rose by any other name would be.....?

Do you need to go to university to have mathematical ability?

What is a colour?

Since when do the words we use for numbers have to be autological?

these attempts have failed- this is not write off the value of logic, but one might ask which logic? Brouwer's logic? Frege's logic etc? Wasn't it Russell who compared logic to a boy and mathematics to a man?

Can you demonstrate how empirical your logic itself is?

How does a bee solve the travelling salesman problem if it is not able to evaluate or measure energy consumption and distance?

Can you smell, hear, taste, touch or feel a thought?

Why? Is it a prerequisite of the ability to estimate and evaluate distances?

If the mind does not exist then what processes information? What are numbers if not products of the human mind- which seems to be your argument against numerical ability in non-human species and yet you now state that the mind does not exist?

What is your logic if it is not a product of the human mind?

[There's another question of yours, below, too!]

The difference is, I try to answer your questions, whereas you, in general, just ignore mine.

If you use arguments that come from that side of the playing field then so be it

But which arguments of mine "come from that side of the playing field" -- that is, from the logical positivist side?

You have failed to say -- so this is yet another baseless allegation/fib of yours.

For the rest of your tu quoque, lack of argument and answering a question or "refuting" a point by merely asking a question there is little to be said.

But, which questions you can't answer. For example: what 'abstract mathematical object' does zero refer to? What's your 'logical proof' there is such a thing as 'the mind'? What is 'numerosity', and what is the meaning of 'number' and 'counting'?

The old "cogito ergo sum" debate is ongoing- but it has not been refuted outright.

Oh yes it has.

Problems have been highlighted and discussed but there is no consensus on the matter.

In that case, I am sure you will be able to tell us all about those 'problems', who has 'discussed' them, and who is involved in that lack of 'consensus', won't you?

You are the person who seems to feel the mind does not exist, that would be pretty much a denial of the mind, wouldn't it?

For the tenth time, where have I denied the existence of 'the mind'? And where have I been involved in a "denial of the mind"?

Yet more fibs.

Yet strangely in another thread here at RevLeft you were talking about inner minds etc....

Where did I do this? I note, yet again, you neglected to provide the link.

One more fib to add to the growing list.

But let's await your responses in which a) you'll suddenly move the goalposts again b) quibble about words or come up with some reason why a perfectly normal use of a word is "made up" or an invention or c) skip over a point by asking a question.

Once more, there is nothing for me to respond to if you insist on using words in odd ways, and which you refuse to explain. How can I answer a question if it contains words that only you seem to comprehend? You refuse even to help us out, too!

And how come you expect me to answer questions, when you rarely answer mine?

ComradeMan

23rd March 2011, 14:47

CM:Well, you must be using the word "decision" here in a new and-as-yet-unexplained sense; if so, what is it?

So decide cannot mean to choose or select etc and when a bee, for instances, chooses the nearest source of nectar it hasn't made a decision? Please... stop with all your sophistry.

But, humans can and do use count nouns whereas bees can't. So, when it comes to numbers, this is just as significant a difference.

But the ability to subitise and enumerate are not dependent on count nouns either in newborn humans or non-human species- as has been shown.

Whereas you seem to think bees went to university!

Whereas you have no argument and have to resort to mockery and putting words in people's mouths...

Well, you gave us a circular 'definition' of 'numerosity', but that's about all.

Latin- numerositas the condition/state/being numerous.
Numerosità - un'entità numerica più o meno grande- a numerical entity more or less great/large.

Now, I'm not interested in how others use these odd words of yours; they aren't party to this discussion. What we want to know is what you mean by them. Of course, if you don't know, just admit it.

Then those children can't count yet -- unless of course you want to use "count" in a new and-as-yet-unexplained sense; if so, what is it?

But we are talking about possible innate and biological mathematical abilities. Do you now deny that subitising and enumerating are not mathematical in any sense, in no way connected to mathematics? :lol:
Do you deny that without those abilities nothing else, as far as we know, could have developed/been developed in the field of mathematics? Ooops....

And thanks for the references, but it seems those authors are happy to make the same mistakes as you -- or they are using the relevant words in new and-as-yet-unexplained senses. If so, what are they?

And a stone has 'solved' the path of least action, too.

More nonsense and sophistry. Seeing as "to solve" i.e. work out the solution to a problem requires a cognitive process, which as far as we know is dependent on the presence of a brain, which both humans and bees as well as many other organisms have, your rock analogy is just, well- completely irrelevant to the debate- i.e. it has nothing to do with the matter at hand.

What has this got to do with numbers, or counting? Are you suggesting that numbers exist like colours do? If so, what wavelength of light represents the number 4,567,734? Or -34,567?

This is a philosophical debate that has never been answered and probably cannot be answered- not even Nobel winning mathematicians have an answer and usually concede that it is unanswerable or that no answer is satisfactory- but it does not invalidate the research into numerical ability in non-human species.

I am not suggesting that numbers existed before the human race anymore than I would suggest that chairs existed in some platonic cave waiting to be discovered. However numerosities, quantities and the biological ability to subitise and evaluate/estimate numerosities is not exclusively human and neurobiological research has demonstrated this- nor is it dependent on abstract symbols, count nouns or anything else.

What wavelength of light represents the number? Well what geological characteristic represents a bowl of spaghetti? :laugh: Where is the logical proof that Mr Rossi prefers chocolate ice-cream?

Like you never ask questions; here are just a few of yours from your last five posts in this thread:

Tu quoque
Tu quoque
Tu quoque
Tu quoque
Tu quoque
Tu quoque

The difference is, I try to answer your questions, whereas you, in general, just ignore mine.

What have you answered? Nothing. You have not stated your position nor have you presented anything much other than arguing over semantics and reducing everything into some weird and distorted ontological/metaphysical/pseudo-scientific debate.

But, which questions you can't answer. For example: what 'abstract mathematical object' does zero refer to? What's your 'logical proof' there is such a thing as 'the mind'? What is 'numerosity', and what is the meaning of 'number' and 'counting'?

Zero is both ordinal and cardinal, and refers to the absense of quantity.

Oh yes it has.

In that case, I am sure you will be able to tell us all about those "refutations", who has 'refuted" them, and who is involved in that "consensus" of refutation, won't you?
:thumbup1:

For the tenth time, where have I denied the existence of 'the mind'? And where have I been involved in a "denial of the mind"?
Yet more fibs.

*cough

Ooops, bad start, since there is no such thing as 'the mind'.

Rosa Lichtenstein

23rd March 2011, 17:28

CM (Once again, your cavalier use of the quote function has mixed some of my comments up with your own. You really are the non-existent deity's gift to confusion aren't you?):

So decide cannot mean to choose or select etc and when a bee, for instances, chooses the nearest source of nectar it hasn't made a decision? .

I am denying nothing, except, when you use the words "choose" and "select" in relation to a what a bee does, you must mean them in a new and-as-yet-unexplained sense.

Please... stop with all your sophistry

No 'sophistry' -- unless you mean by "stop with all your sophistry" "stop asking me to explain my odd use of words". And it is entirely possible you do mean this since you are an expert in the idiosyncratic use of language.

But the ability to subitise and enumerate are not dependent on count nouns either in newborn humans or non-human species- as has been shown.

Then they have nothing to do with what we call numbers and counting, do they?

Whereas you have no argument and have to resort to mockery and putting words in people's mouths...

That's a bit rich coming from someone who does little other than fib and make stuff up about my ideas. Here is a shortened list of your inventions from earlier:

Well, you made up these accusations (among others): that I thought numbers were abstract objects, that I was using linguistics, that I had confused numbers with numerals (we are still waiting for you to cite a single quotation from my posts that even so much as hints at this), that I had used definitions when I haven't, that I had defined "information" when I haven't even tried to do so, that I had an ontology when you had been told several times I reject all ontologies as non-sensical (and then it turned out [i]you were trying to foist one on us), that I had referred to 'language universals' when I hadn't, that I had made certain allegations about "the logical non-existence of the mind" when I hadn't, and then that "most" of my argument rests on "inverted commas", when it doesn't (and you failed to say how you had arrived at that fabrication), and so on. [Links provided on request.]

In which case, we must now add the phrase "making up anything" to the words "number" and "language" with which you seem to be struggling.

And you have continued to make then since; here is the latest batch from your last but one post:

If you use arguments that come from that side of the playing field then so be it

But which arguments of mine "come from that side of the playing field" -- that is, from the logical positivist side?

You have failed to say -- so this is yet another baseless allegation/fib of yours.

You are the person who seems to feel the mind does not exist, that would be pretty much a denial of the mind, wouldn't it?

For the tenth time, where have I denied the existence of 'the mind'? And where have I been involved in a "denial of the mind"?

Yet more fibs.

Yet strangely in another thread here at RevLeft you were talking about inner minds etc....

Where did I do this? I note, yet again, you neglected to provide the link.

One more fib to add to the growing list.

And there's another near the end.

You:

Latin- numerositas the condition/state/being numerous.
Numerosità - un'entità numerica più o meno grande- a numerical entity more or less great/large.

Two more circular definitions! Well done, twice as good as before.

But we are talking about possible innate and biological mathematical abilities. Do you now deny that subitising and enumerating are not mathematical in any sense, in no way connected to mathematics?

Well, unless you can show they are connected with the use of count nouns and the construction of proofs, then, yes, I am denying this.

Do you deny that without those abilities nothing else, as far as we know, could have developed/been developed in the field of mathematics?

The ability to hold a pencil is connected with our capacity to do mathematics, but it has nothing to do with mathematics itself. Same with these alleged 'innate' capacities you mention, but still can't explain. Or, better: it would in fact be possible to say whether or not they had anything to do with mathematics if you'd at least try to be clear about what you mean. [Ha, some hope!]

More nonsense and sophistry.

No thanks -- but we are grateful for your kind offer.

Seeing as "to solve" i.e. work out the solution to a problem requires a cognitive process, which as far as we know is dependent on the presence of a brain, which both humans and bees as well as many other organisms have, your rock analogy is just, well- completely irrelevant to the debate- i.e. it has nothing to do with the matter at hand.

Don't tell me you are using an appeal to allegedly 'linguistic' issues to reply to a comment of mine!

If you can do it, why complain when I do it?

which as far as we know is dependent on the presence of a brain, which both humans and bees as well as many other organisms have, your rock analogy is just, well- completely irrelevant to the debate- i.e. it has nothing to do with the matter at hand

However, the chemical and electrical processes in a bee's brain that allegedly 'solve' this problem are lifeless, too. Chemicals and electrical processes do not have a brain, but they are the ones that in the end allegedly 'solve' this 'problem'. Hence a bee is just a more complex version of a stone. So, a stone must have 'numerical cognisance' if a bee's chemicals do.

If not, then neither have bees.

This is a philosophical debate that has never been answered and probably cannot be answered- not even Nobel winning mathematicians have an answer and usually concede that it is unanswerable or that no answer is satisfactory- but it does not invalidate the research into numerical ability in non-human species.

So, why did you so confidently claim that numbers are 'abstract mathematical objects' if you can't tell us a single one that is the reference of a mathematical symbol?

And, of course, this question can't be answered by those who are super-glued to obsolete ideas about numbers, and other mathematical concepts. No wonder then that you are struggling.

I am not suggesting that numbers existed before the human race anymore than I would suggest that chairs existed in some platonic cave waiting to be discovered.

1. Then bees knew nothing of numbers before we evolved, unless, of course, you think the evolution of bees post-dated that of us humans.

2. In which case, mathematics is invented, not discovered.

However numerosities, quantities and the biological ability to subitise and evaluate/estimate numerosities is not exclusively human and neurobiological research has demonstrated this- nor is it dependent on abstract symbols, count nouns or anything else.

Unfortunately, until you tell us what 'numerosities' (and the other words you use in odd ways) are, without the use of yet another circular 'definition', you might just as well have posted this for all the use it is:

However schnumerosities, schquantities and the biological ability to schubitise and schevaluate/schestimate schnumerosities is not exclusively human and neurobiological research has demonstrated this- nor is it dependent on abstract symbols, count nouns or anything else.

You:

What wavelength of light represents the number? Well what geological characteristic represents a bowl of spaghetti? Where is the logical proof that Mr Rossi prefers chocolate ice-cream?

And you have the cheek to accuse me of posting nonsense! :lol:

What have you answered? Nothing.

Well, we already know you are having problems with simple numbers, so we can safely conclude that you counted my replies incorrectly too.

You have not stated your position

I don't have one -- as you have been told -- nor do I want one.

nor have you presented anything much other than arguing over semantics

Which you did above, repeated here:

Seeing as "to solve" i.e. work out the solution to a problem requires a cognitive process, which as far as we know is dependent on the presence of a brain, which both humans and bees as well as many other organisms have, your rock analogy is just, well- completely irrelevant to the debate- i.e. it has nothing to do with the matter at hand.

Once more, if you can do it, why can't I?

and reducing everything into some weird and distorted ontological/metaphysical/pseudo-scientific debate.

Where have I reduced anything to an "ontological/metaphysical/pseudo-scientific debate"?

Yet another fib to add to the list I compiled earlier.

In fact, you are the one who keeps referring us to those obscure 'abstract mathematical objects' (the nature and location of which you refuse to reveal), which, may I remind you, is as good an example of an "ontological/metaphysical" question as one could wish to find.

Zero is both ordinal and cardinal, and refers to the absence of quantity.

So, it's not an 'abstract mathematical object' as you alleged.

In that case, I am sure you will be able to tell us all about those "refutations", who has 'refuted" them, and who is involved in that "consensus" of refutation, won't you?

Well, I asked first.

Finally, in response to this question of mine:

For the tenth time, where have I denied the existence of 'the mind'? And where have I been involved in a "denial of the mind"?
Yet more fibs.

You added this 'reply':

*cough

Originally Posted by Rosa Lichtenstein

Ooops, bad start, since there is no such thing as 'the mind'.

In other words, I haven't denied the existence of 'the mind', since the assertion that there is no such thing as 'the mind' is not the same as denying 'it' exists.

As you have had pointed out to you already.

I also offered to explain the difference, but you prefer to stay ignorant.

Oh, and we are still waiting for your 'logical proof' that there is such a thing as 'the mind'.

ComradeMan

23rd March 2011, 18:13

Rosa, you really are at rock bottom with your facetious arguments and pseudo-intellectual trolling tactics now. :D

If you deny nothing then you must assert something? But, what do you assert? Your constant refuting of the meanings of words is completely ridiculous and also anti-scientific because we would thus arrive at a situation in which most of biology/zoology/botany etc would be invalidated through the use of human language which we, as humans, use to describe them. I suppose you are going to tell me that a cheetah can't run fast, it can only "run" because it does not have a word for running. :laugh: When a bee hovers over one flower and then changes course to hover over another flower and then takes the pollen from that flower and not the first one it has made a selection/choice/decision. I don't see what's unreasonable nor bizarre about that assertion. No one is saying that we can tell what the bee might actually be thinking in that moment but from our observation we can deduce this reasonably.

Then they have nothing to do with what we call numbers and counting, do they?

Oops...

The ability to hold a pencil is connected with our capacity to do mathematics, but it has nothing to do with mathematics itself.

So that rules out Stephen Hawkins.

I was actually speaking to a Professor of Mathematics today and we discussed this issue for over an hour.

If a mathematical object is not abstract then what is it? Apart from this being the generally accepted definition of a number. And if something is not abstract then it must be concrete or tangible in which case allow me to touch a seven, or smell it, or hear it etc! :D

In other words, I haven't denied the existence of 'the mind', since the assertion that there is no such thing as 'the mind' is not the same as denying 'it' exists.

More sophistry- so saying that there is no such thing is not the same as saying it doesn't exist which is not the same as denying it's existence. :laugh:

I also offered to explain the difference, but you prefer to stay ignorant.

Says the Nobel Prize winning mathematician.... stop being arrogant and stop patronising people.

Your views are interesting and there are things there to be considered but your rather childish and zealoutlike insistance that you are right and everyone else in the world, including leading mathematicians, scientists and consensus knowledge is wrong is completely silly. When you can come up with more than semantics and sophistry you might have an argument- your positions with regard to biology are ridiculous in the least.

However, the chemical and electrical processes in a bee's brain that allegedly 'solve' this problem are lifeless, too. Chemicals and electrical processes do not have a brain, but they are the ones that in the end allegedly 'solve' this 'problem'. Hence a bee is just a more complex version of a stone. So, a stone must have 'numerical cognisance' if a bee's chemicals do.

But... but.... the chemical and electrical processes (I see we can now use the word process) in a human's brain that allegedly "solve" problems are lifeless, too. Therefore humans AND bees are just miore complex versions of stones. So if a stone and a bee can't do mathematics in anyway shape or form then neither can a human? :laugh:

Well done Rosa, you've just proven that people are the same as rocks fundamentally which might lend Judaism some support seeing as the first man Adam, was basically "earth". ;)

Revolution starts with U

23rd March 2011, 22:40

Human beings ARE basically just rocks... that's the whole point of being on the "there is no mind" naturalist side of the debate.

Rosa Lichtenstein

23rd March 2011, 22:48

CM:

Rosa, you really are at rock bottom with your facetious arguments and pseudo-intellectual trolling tactics now.

1. As we now know, from your way of looking at the world, rocks are able to solve the path of least action problem, so that's a compliment.

2. Quite apart from this, you have some cheek to talk about 'trolling'; you began with a bad joke about Frege, you regularly tell fibs, and you constantly raise totally irrelevant issues.

If you deny nothing then you must assert something?

Not necessarily; I might refuse to do both. After all, if you refuse to ask a question, does that imply you have to answer one? [Well, we already know you rarely do.]

But, what do you assert?

Nothing substantive, except you seem to have a predilection for using words in odd ways, compounded by the fact that you refuse to explain yourself.

Your constant refuting of the meanings of words is completely ridiculous and also anti-scientific because we would thus arrive at a situation in which most of biology/zoology/botany etc would be invalidated through the use of human language which we, as humans, use to describe them.

Yet another invention: Where do I "refute...the meanings of words"? All I have done is ask you what you mean by your odd use of terms -- like "number", "counting", "decision" and "process" --, as well as ask you to explain neologisms like 'numerosity'. And all you have done is refuse to help us out -- or you post circular 'definitions'.

I suppose you are going to tell me that a cheetah can't run fast, it can only "run" because it does not have a word for running.

1. As I have told you several times, you'd be far better occupying your time here explaining your odd use of the words I have mentioned above, rather than trying to guess what I might say about large cats.

2. Quite apart from that, why on earth do you think I'd say anything quite so brainless? A cheetah does not have to understand a single world to run fast, but in order to count or to understand numbers, a comprehension of count nouns is essential -- unless of course, you intend to use words like "number" and "count" in a new and-as-yet-unexplained sense. If so, what is it? [But, we all know you'll refuse to tell us once more.]

When a bee hovers over one flower and then changes course to hover over another flower and then takes the pollen from that flower and not the first one it has made a selection/choice/decision.

So, you are still determined to use "choice" and "decision" in an odd way. No problem with that, but what do you mean by this new use of language? [But, we all know you'll refuse to tell us once more.]

I don't see what's unreasonable nor bizarre about that assertion.

Well, it would be entirely reasonable if you'd explain what these ordinary words mean in these odd contexts.

No one is saying that we can tell what the bee might actually be thinking in that moment but from our observation we can deduce this reasonably.

Then a bee cannot make a choice and cannot decide. So what do you mean then?

Oops...

That was your considered reply to this:

Then they have nothing to do with what we call numbers and counting, do they?

[Your underlining added.]

Well we have already seen that even you have to use count nouns when explaining what numbers and counting are, so even you agree with the rest of us.

That is, you do so until you start to appeal to obsolete theories of number -- then you seem to forget what you yourself (and not just me) do whenever you use number words.

So, this "Ooops" can only apply to you, not me.

So that rules out Stephen Hawkins.

Do you mean Stephen Hawking?

Anyway, read again what I said, except with more care this time:

The ability to hold a pencil is connected with our capacity to do mathematics, but it has nothing to do with mathematics itself.

Notice, I did not say:

The ability to hold a pencil is necessarily connected with our capacity to do mathematics, but it has nothing to do with mathematics itself.

I could have listed all the other things that are connected with the ability to do mathematics (such as the devices Hawking uses), but I didn't. I suppose I foolishly expected you to be able to read with due care.

I was actually speaking to a Professor of Mathematics today and we discussed this issue for over an hour.

Good for you.

If a mathematical object is not abstract then what is it? Apart from this being the generally accepted definition of a number. And if something is not abstract then it must be concrete or tangible in which case allow me to touch a seven, or smell it, or hear it etc!

Depends on what you mean by "mathematical object"; they vary from rules to items of mathematical grammar. So, you'll need to be more specific.

Notice: I try to answer your questions, you just ignore mine.

So, what 'abstract mathematical object' does zero, or i (the square root of minus one) refer to? You keep refusing to say.

More sophistry

No thanks: I've already told you we have had quite enough from you as it is.

so saying that there is no such thing is not the same as saying it doesn't exist which is not the same as denying it's existence.

In other words, you don't know the difference. Once more, if you ask real nice, I'll explain it to you.

Says the Nobel Prize winning mathematician

There is no Nobel prize for mathematics.

http://nobelprizes.com/nobel/why_no_math.html

stop being arrogant and stop patronising people.

It's all the same to me if you want to stay ignorant.

Your views are interesting and there are things there to be considered but your rather childish and zealot-like insistence that you are right and everyone else in the world, including leading mathematicians, scientists and consensus knowledge is wrong is completely silly.

Well, if you read up on this (I can give you a reading list, or post links), everything written about the nature of mathematics and number was rendered obsolete overnight by Frege's work, and then that was further revolutionised by the even more radical ideas of Wittgenstein. So, it's not my fault if the majority want to cling to such out-dated theories, ideas that in their everyday use of number words they refute anyway.

Furthermore, most people used to think the earth was at the centre of the universe. In that case I can just imagine a 17th century version of you saying this to, say, Galileo:

but your rather childish and zealot-like insistence that you are right and everyone else in the world, including leading mathematicians, scientists and consensus knowledge is wrong is completely silly.

Human progress would have ground to a halt if everyone were like you.

When you can come up with more than semantics and sophistry you might have an argument- your positions with regard to biology are ridiculous in the least.

Once more, I don't have any 'positions' -- as you have been told many times -- nor do I want any.

But... but.... the chemical and electrical processes (I see we can now use the word process) in a human's brain that allegedly "solve" problems are lifeless, too. Therefore humans AND bees are just more complex versions of stones. So if a stone and a bee can't do mathematics in anyway shape or form then neither can a human?

Yet another invention: I have never said you can't use the word "process"; all I asked was that you explain this odd use of that word. I can explain my use of this word, and if you ask real nice, I'll explain it to you. [But we already know you prefer to remain ignorant.]

But what about the following?

the chemical and electrical processes (I see we can now use the word process) in a human's brain that allegedly "solve" problems are lifeless, too. Therefore humans AND bees are just more complex versions of stones.

I have already said that brains do not solve problems, human beings do.

Therefore humans AND bees are just more complex versions of stones

Not so; we have a language; stones and bees do not. We also have a complex culture, bees and stones do not.

Well done Rosa, you've just proven that people are the same as rocks fundamentally which might lend Judaism some support seeing as the first man Adam, was basically "earth".

In fact, all you have done is show that your head is full of rocks.

And we are still waiting for your 'logical proof' that there is such a thing as 'the mind'.

ComradeMan

24th March 2011, 10:43

:laugh:
Have you seen any of those flying rocks yet....? Ooops.... I meant bees.

We don't need language to subitise/enumerate as has been shown. Seeing as this are very basic, dare I say primitive, numerical abilities your argument that numerical ability is entirely depdendent on language is flawed.

As for the rest of your tu quoque, word picking, little typos etc and sophistry- dare I say nonsese... :laugh:

There is no Nobel prize for mathematics.

Do you mean Nobel Prize? OMG OMG you made a mistake... let's quote that and make a big deal about it. Hawkings/Hawkins? I am sorry, but I do have difficulty spelling English names at times, with that most logical spelling system it has..... ;) On a side note- please abandon those silly "gh" things that are annoying too! :laugh: Interestingly though, despite an error in the "symbols" used to represent this person's name you still knew to whom I was referring? Interesting eh?

Indeed there is no Nobel prize for mathematics but I did not say that.... I said Nobel Prize winning mathematician... and there have been quite a few,.... Feymann, Nash, Planck etc... usually, although not always, the prizes have been awarded for Physics.

This just shows how you misunderstand or deliberately minsinterpret what people say to suit your own hollow arguments.

Well, if you read up on this (I can give you a reading list, or post links), everything written about the nature of mathematics and number was rendered obsolete overnight by Frege's work, and then that was further revolutionised by the even more radical ideas of Wittgenstein. So, it's not my fault if the majority want to cling to such out-dated theories, ideas that in their everyday use of number words they refute anyway.

Frege's work was rather trashed by Russell and what remained of this attempt to reduce mathematics to logic was demolished by Godel.... There are many theories and no one theory really has the upperhand. For a discussion of this see Mario Livio. Wittgenstein too is not without his critics. Unlike you who seems to take this all or nothing approach I am prepared to see the validity of the work of all of these great minds and yet not adhere to them like some kind of pseudo-religion. This kind of mentality produces "ideologically" closed minds and narrow thinking.

I have already said that brains do not solve problems, human beings do.

And human beings have brains that dominate their thought processes and central nervous system... go back to biology class. My hair does not solve a problem does it? It just grows and gets cut. Without a brain all of your theories of language would be meaningless because there would be no language, and no count nouns either! LOL!!! So does my toenail solve problems in its "being" part of a human being in the same way as my brain can? Does my pancreas recieve and store information through my sensory system and does it think to itself, "I'd like a coffee" and thus send messages to my motor system so as I go to the bar and order an espresso?

What is a human being by the way? If we want to play with words? And if there were only one human being left on the entire planet would he or she still be a human or just a "human"- and if a tree falls in a forest with no one present does it make a sound?

Please try more than this silly undergraduate level sophistry.

Human progress would have ground to a halt if everyone were like you.

Tu quoque- but let's see. The person who refuses to read scientific papers because she knows they are flawed anyway because, despite being from an entirely different field in many senses, they must be based on flawed views because they don't agree to a certain philosophical/ontological school? The person who refuses outright to consider material based on empirical research, peer review and so on... The person who abuses semantics and logic to undermine every discussion and claims to have refuted major theories of mathematics and philosophy without actually providing any information or proofs and also the person whose debating style rests on a) refusing to state their position b) constantly shifting their position c) claiming they have no position d) patronising and mockey, facetious humour e) attacking the poster and not the post e) dishonest/disingenuous (mis-)use of language.

Stop claiming to have answered questions. Your only answers are basically "this is not so because I say so" or "I don't have to explain this because this has already been discussed elsewhere".

Now, show me a "proof" that non-human species are not able to subitise/enumerate etc. .

Rosa Lichtenstein

24th March 2011, 13:52

CM:

Have you seen any of those flying rocks yet....? Ooops.... I meant bees.

You see, you can explain yourself when you try.

We don't need language to subitise/enumerate as has been shown.

Only by those who adhere to obsolete theories of number and counting.

Seeing as this are very basic, dare I say primitive, numerical abilities your argument that numerical ability is entirely dependent on language is flawed.

Well, unless you can show these "primitive...abilities" are associated with the use of count nouns, then you might as well have posted this for all the use it was:

Seeing as this are very basic, dare I say primitive, schnumerical abilities your argument that numerical ability is entirely dependent on language is flawed.

You:

As for the rest of your tu quoque, word picking, little typos etc and sophistry- dare I say nonsense

Unfortunately for you we already know you do not know what a typo is.

Do you mean Nobel Prize? OMG OMG you made a mistake

Er..., what mistake? You posted the following:

Says the Nobel Prize winning mathematician

I merely pointed out that there is no such thing as a Nobel prize for mathematics. So, where's my mistake?

let's quote that and make a big deal about it.

What big deal? You really do need to try to get a grip.

Hawkings/Hawkins? I am sorry, but I do have difficulty spelling English names at times, with that most logical spelling system it has.

No problem, but I always check before I post anything that I'm not 100% sure of; you should do the same. Like when you forgot to do so when you told us that A=A is a syllogism and that there is a Nobel prize for mathematics.

On a side note- please abandon those silly "gh" things that are annoying too!

Eh? What are you on about now?

Interestingly though, despite an error in the "symbols" used to represent this person's name you still knew to whom I was referring? Interesting eh?

Indeed, I tend to suffer fools gladly.

I thought you might have been referring to this astronomer:

Hawkins, M. (1997), Hunting Down The Universe (Abacus).

Indeed there is no Nobel prize for mathematics but I did not say that.... I said Nobel Prize winning mathematician

And there are none of these either.

and there have been quite a few,.... Fey[nman], Nash, Planck etc... usually, although not always, the prizes have been awarded for Physics

In other words, they did not receive Nobel prizes for mathematics.

Here is what the Noble Prize website says:

Six Nobel Prizes are awarded each year, one in each of the following categories: literature, physics, chemistry, peace, economics, and physiology & medicine. Notably absent from this list is an award for Mathematics. The reason for this conspicuous omission has been subject of extensive speculations, some of which are discussed below.

http://www.almaz.com/nobel/why_no_math.html

The equivalent prize in mathematics is called The Field's Medal:

http://en.wikipedia.org/wiki/Fields_Medal

This just shows how you misunderstand or deliberately misinterpret what people say to suit your own hollow arguments.

You've got some cheek; here are just a few of your fibs and misrepresentations from the last handful of posts of yours:

Well, you made up these accusations (among others): that I thought numbers were abstract objects, that I was using linguistics, that I had confused numbers with numerals (we are still waiting for you to cite a single quotation from my posts that even so much as hints at this), that I had used definitions when I haven't, that I had defined "information" when I haven't even tried to do so, that I had an ontology when you had been told several times I reject all ontologies as non-sensical (and then it turned out you were trying to foist one on us), that I had referred to 'language universals' when I hadn't, that I had made certain allegations about "the logical non-existence of the mind" when I hadn't, and then that "most" of my argument rests on "inverted commas", when it doesn't (and you failed to say how you had arrived at that fabrication), and so on. [Links provided on request.]

In which case, we must now add the phrase "making up anything" to the words "number" and "language" with which you seem to be struggling.

And you have continued to make then since; here is the latest batch from your last but one post:

If you use arguments that come from that side of the playing field then so be it

But which arguments of mine "come from that side of the playing field" -- that is, from the logical positivist side?

You have failed to say -- so this is yet another baseless allegation/fib of yours.

You are the person who seems to feel the mind does not exist, that would be pretty much a denial of the mind, wouldn't it?

For the tenth time, where have I denied the existence of 'the mind'? And where have I been involved in a "denial of the mind"?

Yet more fibs.

Yet strangely in another thread here at RevLeft you were talking about inner minds etc....

Where did I do this? I note, yet again, you neglected to provide the link.

One more fib to add to the growing list.

There are at least another half dozen below, at the end of this post.

Now, all I did was point out a minor error on your part and you then accuse me of "misunderstand or deliberately misinterpret[ing] what people say to suit your own hollow arguments" -- when you are a serial offender in this regard yourself.

Frege's work was rather trashed by Russell and what remained of this attempt to reduce mathematics to logic was demolished by Gödel....

We have been over this, near the beginning of this thread. In fact, Russell tried to rescue Frege's theory with his Theory of Types; he in no way "trashed" Frege's work. As I pointed out to you, Frege's criticisms of earlier theories of number are not affected by this, nor by Gödel's work.

And, I have also shown in this thread that Gödel's own work was vitiated by his reliance on Cantor's Diagonal Argument.

But, none of this, as I have just said, affects the fact that overnight Frege's work rendered all previous theories of number obsolete. It is as important an event in the Philosophy of Mathematics as the Copernican Revolution was in Physics; if anything, more important. Unfortunately for you, the scientists working on non-human 'mathematicians', to which you refer us, seem to be locked into the equivalent of pre-Copernican theories of number -- which helps explain why you are struggling to explain any of your ideas with any clarity or consistency.

There are many theories and no one theory really has the upper hand.

Maybe so, but that does not alter the fact that Frege's criticism of earlier theories of number (which include yours, it seems) rendered them all obsolete. Frege's positive theory of number has nothing to do with this, whatever its own flaws happen to be.

For a discussion of this see Mario Livio.

Eh? Do you mean I have to go and see this guy?

Wittgenstein too is not without his critics.

I know, my PhD was on Wittgenstein; but unless you tell us who these 'critics' are, and what they have to say, that comment was a simple waste of space.

Unlike you who seems to take this all or nothing approach I am prepared to see the validity of the work of all of these great minds and yet not adhere to them like some kind of pseudo-religion. This kind of mentality produces "ideologically" closed minds and narrow thinking.

In that case, I presume you are "prepared to see the validity" in Ptolemy's theory of the solar system, in Galen's theory of the heart, Aristotle's theory of the four elements, Plato's theory that all of us pre-existed in heaven with 'god' and 'the Forms' before we were born?

[i]If not, then even you have an "all or nothing approach" when it suits you -- except in this case, you do not even know what Frege's criticisms of previous theories of mathematics are.

[We can see that from the many mistakes about his work you keep making, and the fact that you are still committing the errors he highlighted.]

So, your 'open-minded' approach is informed by little other than ignorance, at least in this regard.

And human beings have brains that dominate their thought processes and central nervous system...

How can the brain "dominate" thought? Are you really committed to the idea that we have thoughts independently of the brain, which the brain then has to dominate? If not, how can the brain do what you say?

Anyway, and quite independently of that, the brain has nothing to do with thought -- unless, of course, you are using "thought" in a new and-as-yet-unexplained sense. If so, what is it? [Ha, some hope of an answer to that from you!]

go back to biology class.

What is the point of that comment? Human beings were using words associated with thought long before there were biology classes; so the meaning of our words for thought has nothing to do with what can be learnt there. You really are strange.

My hair does not solve a problem does it? It just grows and gets cut.

Who can say what you believe in the odd universe you inhabit -- where we have bees that go to university, Nobel prizes that do not exist, syllogisms that no one has heard of before, and a 'theory' that implies stones can solve advanced problems from projectile physics!***

Without a brain all of your theories of language would be meaningless because there would be no language, and no count nouns either! LOL!!!

All that shows is a human brain is a necessary biological pre-requisite for an individual to be able to learn to think, but it is no more associated with thought than you are associated with a telephone when you use it to contact your friends, or those university graduate bees.

So does my toenail solve problems in its "being" part of a human being in the same way as my brain can? Does my pancreas receive and store information through my sensory system and does it think to itself, "I'd like a coffee" and thus send messages to my motor system so as I go to the bar and order an espresso?

Same comment as earlier.***

What is a human being by the way?

Next time you look in the mirror, I strongly suspect one might be looking back at you.

If not, get back to me.

If we want to play with words?

Well, you are the one who wants to 'play with words' -- like your odd use of "decide", "number" and "count", and your even odder neologisms, like 'numerosity' -- all of which you repeatedly fail to explain, despite being asked to do so many times.

And if there were only one human being left on the entire planet would he or she still be a human or just a "human"

Oh dear, your insecure grasp of the word "relevant" is beginning to show again.

and if a tree falls in a forest with no one present does it make a sound?

Why don't you go and check? [At least you'd be doing something useful for a change.]

Please try more than this silly undergraduate level sophistry.

Indeed, I always try harder than you.

Tu quoque- but let's see. The person who refuses to read scientific papers because she knows they are flawed anyway because, despite being from an entirely different field in many senses, they must be based on flawed views because they don't agree to a certain philosophical/ontological school?

Yet another invention on your part; where have I refused to read these papers?

The person who refuses outright to consider material based on empirical research, peer review and so on...

Yet another invention on your part; where have I refused to consider this material?

The person who abuses semantics and logic

Yet another invention on your part; quote me one passage where I have done this.

claims to have refuted major theories of mathematics and philosophy

Yet another invention on your part; quote me one passage in this thread where I have claimed to have done this.

the person whose debating style rests on a) refusing to state their position

How is it possible to "state [my] position" if I not only do not have one, but I don't want one?

b) constantly shifting their position

Yet another invention on your part; how can I shift my position if I do not have one?

c) claiming they have no position

And what is so wrong with that?

d) patronising and mocke[r]y, facetious humour

You have some cheek; may I remind you of the facetious joke you posted about Frege right back at the beginning, the fibs and inventions you continually inflict on us in this thread (see above)?

e) attacking the poster and not the post

Which is something you do all the time.

e) dishonest/disingenuous (mis-)use of language.

What language have I mis-used? In fact, as we can see from your posts (details given in practically every one of my posts in this thread), it is you who inflicts on words like "decide", "choice", "number" and "count" your own idiosyncratic use (which you refuse to explain).

Stop claiming to have answered questions.

No.

Your only answers are basically "this is not so because I say so" or "I don't have to explain this because this has already been discussed elsewhere".

In fact, I have not done any of these in this thread -- except, with respect to the latter allegation, perhaps once or twice in reference to my refutation of metaphysics and ontology (and I could not repeat that refutation here, since it's approximately 5000 words long!).

But, where have I ever said anything like this: "this is not so because I say so"?

Yet another fib.

ComradeMan

25th March 2011, 01:17

tldr

The fact that you are practically quoting and picking at every word just goes all the more to prove my point and it completely ruins the thread for others.

Hey, watch out for those flying rocks.

Rosa Lichtenstein

25th March 2011, 01:44

CM:

The fact that you are practically quoting and picking at every word just goes all the more to prove my point and it completely ruins the thread for others.

See, I knew you had problems counting, since I have 'picked' at only a few words, like "counting", "number", "choice", "process", and one or two others.

But, true to form you failed to support this latest fib of yours with any evidence.

Hey, watch out for those flying rocks.

What? Has someone thrown your head?:ohmy:

ComradeMan

25th March 2011, 12:57

CM: See, I knew you had problems counting, since I have 'picked' at only a few words, like "counting", "number", "choice", "process", and one or two others.

But, true to form you failed to support this latest fib of yours with any evidence.

What? Has someone thrown your head?:ohmy:

Well you seem to be a great person for demonstrating your own truths and praising your own "victories".

The fact of the matter is that you haven't actually refuted one of those uses of words with anything but sophistry and over-contextualisation in order to twist things round to your argument. I challenge you to actually show, i.e. scientifically with a demonstration/proof/source etc where words have been used outside of a generally accepted norm rendering discussion unreasonable.

As for numbers:-

Un numero è una entità astratta usata per descrivere una quantità (http://it.wikipedia.org/wiki/Quantit%C3%A0).
A number is an abstract entity used to describe a quantity.

Mathematical objects, such as numbers, are abstract objects in that they are not situated within time and space- abstracta are thus opposed to concreta- crudely put as a physical object.

What you seem to confuse is the following.

Whereas "7" is an abstractum in terms of a number "Seven cats" is a concretum in terms of being a physical realtity located in time and space etc.

The debate on the abstract nature of mathematics and its relation to the physical world in terms of its "unreasonable effectiveness" is ongoing.

There is no resolution of this debate, no consensus and no one accepted theory and it would make an interesting argument if you did not insist in your rather aggressive and patronising way that there were, i.e. yours.

Why do you keep avoiding the words subitise and enumerate? Ooops.....

So tell me, if I say that "3 is prime", is that true or false?

Rosa Lichtenstein

25th March 2011, 15:24

CM:

Well you seem to be a great person for demonstrating your own truths and praising your own "victories".

And you, for your part, seem well placed to help secure even more of them for me. Cheers!

The fact of the matter is that you haven't actually refuted one of those uses of words with anything but sophistry and over-contextualisation in order to twist things round to your argument.

Well, done -- yet another invention!

Where have I tried to 'refute' your odd use of language? All I have asked is for you to explain the meaning of the ordinary words you insist on using in such odd ways (and the neologisms you keep inflicting on us).

Even if I wanted to, which I do not, it's not possible to refute the ideas of someone who will not explain why he/she insists on imposing on language their own idiosyncratic meaning.

I challenge you to actually show, i.e. scientifically with a demonstration/proof/source etc where words have been used outside of a generally accepted norm rendering discussion unreasonable.

No problem -- I will produce such a proof the moment you provide (1) the proof that ants and bees can use count nouns and have been to university, and (2) your 'logical proof' that there is such a thing as 'the mind'.

After all, I asked first. :)

As for numbers:-

Un numero è una entità astratta usata per descrivere una quantità.
A number is an abstract entity used to describe a quantity.

Mathematical objects, such as numbers, are abstract objects in that they are not situated within time and space- abstracta are thus opposed to concreta- crudely put as a physical object.

Thanks for reminding us of that obsolete 'theory' of numbers that holds you in its grip.

But, since you are so knowledgeable in this area, perhaps you can explain where these 'abstract entities' reside, how us humans (and bees and ants) gain knowledge of them, and to which 'abstract entity' zero, -345 and i (the square root of minus one), for example, refer.

Ah, but you have an 'answer':

What you seem to confuse is the following.

Whereas "7" is an abstractum in terms of a number "Seven cats" is a concretum in terms of being a physical reality located in time and space etc.

What a disappointment! That's no help at all!

Among other things, it fails to tell us the answer to any of the questions I asked above. Nor does it explain how bees and ants can access 'abstract mathematical objects'.

The debate on the abstract nature of mathematics and its relation to the physical world in terms of its "unreasonable effectiveness" is ongoing.

There is no resolution of this debate, no consensus and no one accepted theory and it would make an interesting argument if you did not insist in your rather aggressive and patronising way that there were, i.e. yours.

Sure it will continue, and sure there's no 'resolution', since you, and the others to whom you look for inspiration, are locked in the equivalent of a pre-Copernican mathematical universe.

In fact, you are rather like a 15th century astronomer who, when asked how the angels manage to push the planets around in their orbit of the earth, scratches his head and says:

The debate on the nature of these angels and their relation to the physical world is ongoing.

You:

and it would make an interesting argument if you did not insist in your rather aggressive and patronising way that there were, i.e. yours

Well, it's not just my view, it's yours too, since, as we have seen, even you have to use count nouns when using number language and when attempting to explain what numbers are.

We have also seen that when you forget the common sense you usually bring to your everyday use of number words (and their associated count nouns), and attempt to substitute for it an obsolete theory, you begin to flounder.

That alone should tell you that you have taken a wrong turn.

Why do you keep avoiding the words subitise and enumerate?

Why do you keep avoiding the words "Adhedral" and "Comiplexium"?

You see, we can all ask irrelevant questions; it's not your sole area of expertise, you know.

So tell me, if I say that "3 is prime", is that true or false?

Neither; it's a rule for the use of certain symbols.

Now, let's see the long lost 'logical proof' that there is such a thing as 'the mind'.

We can't wait...

ComradeMan

25th March 2011, 18:28

If the best you can come up with is strawmen- Where did I make claims for ants going to university? Where did I suggest that non-human species we know about have higher maths? I pointed to simple scientific research that suggests that some numerical ability is not solely human.

You keep saying things are obsolete and no longer valid etc.... But it seems only according to you- but then according to you there is fundamentally no difference between a bee and a rock! :laugh:

This rather circular argumentation of yours is very unhelpful- things are wrong/obsolete/etc because YOU say they are.... Even those mathematicians and philosophers that fall into various camps and dispute the others don't make such claims for absolute veracity or having the last word as you do.

No, why can't some animals have the ablity to subitise?

even you have to use count nouns when using number language and when attempting to explain what numbers are.

Yes but whether I use that language or not doesn't change what I am describing does it? If I suddenly start to call a goat a cat, apart from being a bit strange does the goat metamorphose into a cat? :laugh: You can't separate the word from that which it describes- but that has nothing to do with the ability to subitise, which is non-verbal, in non-human species! ;)

Rosa Lichtenstein

25th March 2011, 21:18

CM:

If the best you can come up with is strawmen- Where did I make claims for ants going to university? Where did I suggest that non-human species we know about have higher maths?

Well, I thought that since you make stuff up all the time, it would be Ok for me to do so too.

Anyway, your idea that bees have solved the Travelling Salesman Problem implies that they have got degrees in mathematics.

I pointed to simple scientific research that suggests that some numerical ability is not solely human.

Yes, you have been saying odd things like this for weeks, which is why I have had to spoil the fun by reminding you that such ideas are based on obsolete theories of mathematics -- unless, that is, you really mean the following:

I pointed to simple scientific research that suggests that some 'numerical' ability is not solely human.

Given the additional fact that such non-humans do not and cannot use count nouns. And then, despite being asked to do so many times, you refuse to tell us what 'numerical' means.

You keep saying things are obsolete and no longer valid etc....

Yes, it seems you need to be told several times before it sinks in.

But it seems only according to you- but then according to you there is fundamentally no difference between a bee and a rock!

Alas for you, I was merely working out the logical consequences of that obsolete theory of yours.

Oh dear! I said it again.

This rather circular argumentation of yours is very unhelpful-

Perhaps I learnt too much from your circular definitions.

things are wrong/obsolete/etc because YOU say they are....

I covered this in my last reply. Here it is again for you to ignore some more:

Well, it's not just my view, it's yours too, since, as we have seen, even you have to use count nouns when using number language and when attempting to explain what numbers are.

We have also seen that when you forget the common sense you usually bring to your everyday use of number words (and their associated count nouns), and attempt to substitute for it an obsolete theory, you begin to flounder.

That alone should tell you that you have taken a wrong turn.

But, what the hell; if you refuse to be helped...

Even those mathematicians and philosophers that fall into various camps and dispute the others don't make such claims for absolute veracity or having the last word as you do.

Except, in their everyday lives, they, like you, use count nouns -- so they, and you, agree with me.

No, why can't some animals have the ability to subitise?

Maybe you should ask those postgrad bees of yours?

Yes but whether I use that language or not doesn't change what I am describing does it?

Indeed, and your use of such everyday language tells us that you agree with me; the use of number words is necessarily connected with the use of count nouns.

Once more, it's only when you lose sight of that simple fact that you begin to go astray.

If I suddenly start to call a goat a cat, apart from being a bit strange does the goat metamorphose into a cat?

No, but if you began to tell us that cats were members of the plant kingdom, that would show you had made yet another wrong turn -- which is the same kind of error you make when you think that numbers are 'abstract mathematical objects' -- and then you wonder why begin to flounder when you can't tell us what zero, -235 and i (the square root of minus one) refer to.

You can't separate the word from that which it describes

But, you do it all the time when you try to separate number words from count nouns, etc.

but that has nothing to do with the ability to subitise, which is non-verbal, in non-human species!

Well, it's only that obsolete theory of yours that makes you say such odd things.

Oh dear, I said it again!

Somebody stop me...

-----------------------------------------

Oh, and by the way: we are still waiting for that long lost 'logical proof' of yours that there is such a thing as 'the mind'.

ComradeMan

25th March 2011, 23:58

CM: Well, I thought that since you make stuff up all the time, it would be Ok for me to do so too..

Oh shut up with all this silly hyperbole- No one is making anything up. I love the way you accuse anyone who disagrees with YOU as making things up... You do not have the last word on these matters, nor do I, but I don't presume to as you seem to do.

Anyway, your idea that bees have solved the Travelling Salesman Problem implies that they have got degrees in mathematics. ..

No, it doesn't. Euclid didn't have a degree in mathematics... LOL!!! :lol: Neither did Einstein or many others...

Yes, you have been saying odd things like this for weeks, which is why I have had to spoil the fun by reminding you that such ideas are based on obsolete theories of mathematics -- unless, that is, you really mean the following:..

They are not odd and the theories are not obsolete... I didn't realise one camp had won, so to speak. But I am sure you'll be able to provide a source and evidence in this case..... or perhaps you'll just link to your own posts making these claims as usual....

Given the additional fact that such non-humans do not and cannot use count nouns. And then, despite being asked to do so many times, you refuse to tell us what 'numerical' means..

But... but.... you don't need count nouns to subitise or enumerate? " it seems you need to be told several times before it sinks in".:lol: I suppose you'll say that this is irrelevant or find some semantic way to get out of the fix you are in...

No, but if you began to tell us that cats were members of the plant kingdom, that would show you had made yet another wrong turn -- which is the same kind of error you make when you think that numbers are 'abstract mathematical objects' -- and then you wonder why begin to flounder when you can't tell us what zero, -235 and i (the square root of minus one) refer to...

Not really, afterall you were the one saying that bees and rocks were basically the same... so really...

Oh dear- the square root of minus one is an imaginary number (i)--- Ooops.
i2 = − 1.

All numbers are fundamentally abstractions but are you telling me that if they are not abstractions then they are concrete? You're going to have trouble with that....

But, you do it all the time when you try to separate number words from count nouns, etc....

Well, when we are talking about this it's obvious but when I do a calculation on paper or digit keys on a calculator- what count nouns am I using? :thumbup1:

I think the onus is on you to tell "us" what numbers are if they are not abstract mathematical objects?

Please from your Olympian heights do tell us......

But you won't!;)

Rosa Lichtenstein

26th March 2011, 00:42

CM:

Oh shut up with all this silly hyperbole

In other words, you are the only one who is allowed to make stuff up.

No one is making anything up. I love the way you accuse anyone who disagrees with YOU as making things up...

Here is that earlier list of just a few of your more recent fibs (to which we can add the new fib that you never make stuff up):

Well, you made up these accusations (among others): that I thought numbers were abstract objects, that I was using linguistics, that I had confused numbers with numerals (we are still waiting for you to cite a single quotation from my posts that even so much as hints at this), that I had used definitions when I haven't, that I had defined "information" when I haven't even tried to do so, that I had an ontology when you had been told several times I reject all ontologies as non-sensical (and then it turned out you were trying to foist one on us), that I had referred to 'language universals' when I hadn't, that I had made certain allegations about "the logical non-existence of the mind" when I hadn't, and then that "most" of my argument rests on "inverted commas", when it doesn't (and you failed to say how you had arrived at that fabrication), and so on. [Links provided on request.]

In which case, we must now add the phrase "making up anything" to the words "number" and "language" with which you seem to be struggling.

And you have continued to make then since; here is the latest batch from your last but one post:

If you use arguments that come from that side of the playing field then so be it

But which arguments of mine "come from that side of the playing field" -- that is, from the logical positivist side?

You have failed to say -- so this is yet another baseless allegation/fib of yours.

You are the person who seems to feel the mind does not exist, that would be pretty much a denial of the mind, wouldn't it?

For the tenth time, where have I denied the existence of 'the mind'? And where have I been involved in a "denial of the mind"?

Yet more fibs.

Yet strangely in another thread here at RevLeft you were talking about inner minds etc....

Where did I do this? I note, yet again, you neglected to provide the link.

One more fib to add to the growing list.

You:

You do not have the last word on these matters, nor do I, but I don't presume to as you seem to do.

So, you deny you made the above stuff up, eh? [I can provide the links.]

No, it doesn't. Euclid didn't have a degree in mathematics... Neither did Einstein or many others...

1. They did not solve the Travelling Salesman Problem like your postgrad bees have.

2. They could use count nouns, just like you can, whereas your post-doctorate bees can't. Unless, of course, you think they can...

They are not odd and the theories are not obsolete...

Unfortunately, they are until you can show that count nouns are not necessarily associated with number words.

I didn't realise one camp had won, so to speak.

And can we thank you once again for openly advertising your own ignorance? It's rather refreshing.

But I am sure you'll be able to provide a source and evidence in this case..... or perhaps you'll just link to your own posts making these claims as usual....

Don't need to; each time you use number words in every day life you show your own 'theory' is obsolete. So, you are the only proof I need in this thread.

But... but.... you don't need count nouns to subitise or enumerate?

Then you must be using 'enumerate', a term you have yet to explain.

" it seems you need to be told several times before it sinks in"

No problem; as many times as it takes before you realise that your everyday use of number language shows your 'theory' is obsolete.

I suppose you'll say that this is irrelevant or find some semantic way to get out of the fix you are in...

In fact, the only fix I am in is having to tell you the obvious over and over when, as I have noted several times, you already agree with me; your everyday use of number language gives you away.

Not really, after all you were the one saying that bees and rocks were basically the same... so really...

According to your 'theory' they are.

Oh dear- the square root of minus one is an imaginary number (i)--- Ooops.

i2 = − 1.

That is a popular mistake. They were called imaginary numbers until the Argand Diagram was invented to represent them, and rules were developed to manipulate them. Now they are called Complex Numbers. They are no longer imaginary, and are used in Physics and Electronics all the time.

http://mathworld.wolfram.com/ComplexNumber.html

http://mathworld.wolfram.com/ArgandDiagram.html

Anyway, according to your 'theory' all numbers are imaginary.

So what 'abstract mathematical object' do complex numbers refer to? And what about zero, and -234?

All numbers are fundamentally abstractions

Abstracted from what? And where do they exist?

but are you telling me that if they are not abstractions then they are concrete?

They are neither. I have already told you what I think they are. You really must learn to pay attention.

You're going to have trouble with that....

But, you are the one who can't tell us what 'abstract mathematical object' numbers like zero, the complex numbers and -234 refer to.

Well, when we are talking about this it's obvious but when I do a calculation on paper or digit keys on a calculator- what count nouns am I using?

They are part of a formal system. In order to interpret them you have to use count nouns. [In fact, you fall back on the general count noun, "object", all the time.]

I think the onus is on you to tell "us" what numbers are if they are not abstract mathematical objects?

In fact I have already told "you"; when "you" asked whether "3 is a prime" was true or false. Do "you" want me to repeat it?

Please from your Olympian heights do tell us.....

No publicity please. You know what will happen if that gets out!

But you won't!

Already have.:)

Revolution starts with U

26th March 2011, 04:34

If the best you can come up with is strawmen- Where did I make claims for ants going to university? Where did I suggest that non-human species we know about have higher maths? I pointed to simple scientific research that suggests that some numerical ability is not solely human.

Technically it's a red herring, but either way :lol:
A straw man is creating an argument to destroy. A red herring is making bold mischaracterizations of a position and then proceeding ridicule them.

You keep saying things are obsolete and no longer valid etc.... But it seems only according to you- but then according to you there is fundamentally no difference between a bee and a rock! :laugh:

Of all people, you with your new age christian mysticism, I would have thought would agree with this statement.
What IS the difference between a bee and a rock? Said "fundamental difference" exists only if you assume the existence of mind/spirit as seperate from matter.

I think you guys are really just talking over each other's heads, as I can see it reasonable to agree with parts of both.
I think Rosa's expose of language, count nouns, and the limitations of explainability are spot on.
But I also see no reason why that rules out animals not being able to recognize, and possibly even combine, differences in quantity.
... tho Im pretty sure Rosa would agree with that as well.

Ã‘Ã³ẊÃ®Ã¶ŉ

26th March 2011, 04:59

Human beings ARE basically just rocks... that's the whole point of being on the "there is no mind" naturalist side of the debate.

Umm, no. While I understand that the thrust of the argument is that humans and rocks are both made of atoms and are thus similar on that level, what's also relevant is the nature of those atoms and how they are arranged. So far as we can tell, a rock is incapable of producing the kind of phenomena we associate with a particular type of material arrangement, namely living brains. Thus it is misleadingly simplistic to just baldly assert that "humans are rocks".

Humans are no more "just rocks" than computers are.

Revolution starts with U

26th March 2011, 07:48

Umm, no. While I understand that the thrust of the argument is that humans and rocks are both made of atoms and are thus similar on that level, what's also relevant is the nature of those atoms and how they are arranged. So far as we can tell, a rock is incapable of producing the kind of phenomena we associate with a particular type of material arrangement, namely living brains. Thus it is misleadingly simplistic to just baldly assert that "humans are rocks

What you're talking about here is a matter of degree. There are 118 fundamental possibliities of arranging these atoms (that show up regularly in nature) and really you can take that down to >30. Through our perception we can say "me" and "rock" and "human." But nature no more cares about your definitions than a rabbit does.
It is simplistic. But nowhere did I assert humans are just rocks. Rather that they were "basically," meaning at the most basic level, no different than rocks.
When you eat an apple, does it just disappear, or do you just poop out whole apples? Otherwise where do you now draw the line between you and the apple?

RATM-Eubie

26th March 2011, 08:02

Math sucks :p

Rosa Lichtenstein

26th March 2011, 08:42

Noxion:

While I understand that the thrust of the argument is that humans and rocks are both made of atoms and are thus similar on that level, what's also relevant is the nature of those atoms and how they are arranged. So far as we can tell, a rock is incapable of producing the kind of phenomena we associate with a particular type of material arrangement, namely living brains. Thus it is misleadingly simplistic to just baldly assert that "humans are rocks".

I agree, but then that is a consequence of CM's theory.

ComradeMan

26th March 2011, 12:18

CM:That is a popular mistake. They were called imaginary numbers until the Argand Diagram was invented to represent them, and rules were developed to manipulate them. Now they are called Complex Numbers. They are no longer imaginary, and are used in Physics and Electronics all the time.

Err... Rosa... I am not sure you're quite right with this.....

Imaginary numbers are not exactly the same as complex numbers although they are undoubtedly linked.

A complex number is the combination of both a real and an imaginary part. Thus the square root of minus one is imaginary- i2 = − 1

Complex numbers- the fictitious numbers of Gerolamo Cardano- are represented by z whereas imaginary numbers are represented by the unit i.

E.g.

a +bi

An example of a complex number would be

z= x+iy

x and y are real numbers whereas i is imaginary and z is the complex.

The two are connected but not the same. Whereas i can have no real part z does have a real part- there is a difference- unless of course you are using the Cartesian idea that complex numbers are imaginary. :confused:

Although z requires i, i does not require z.

Now, the term imaginary is, in my opinion a bad term and if we look at Bombelli we will see that the complex and imaginary numbers are inextricably connected however z is not (just) i, although i is undoubtedly connected to z.

But that's not really what we were talking about, is it? Seeing as those Italian mathematicians and algebraists "imagined" numbers to solve their quadratic problems it is not unreasonable to say we are in the real of abstracta here. The wonderful thing about this is, and the "magic" of mathematics, is that we can put such abstracta to good use in our physical world- concretum.

However, if i and z etc are not abstracta to what concretum do they refer?

Rosa Lichtenstein

26th March 2011, 13:39

CM:

Err... Rosa... I am not sure you're quite right with this.....

Imaginary numbers are not exactly the same as complex numbers although they are undoubtedly linked.

Well, as I pointed out, what used to be called Imaginary Numbers (by 16th century mathematicians) are now called Complex Numbers, which are comprised of an 'imaginary' part and a 'real' part.

But, you must not be mislead by the word 'imaginary' any more than by the word 'real'. 'Real' refers to the location of that part of the number on the x axis, while 'imaginary' refers to its location on the y-axis. Both parts are as real as one another, as the Argand Diagram shows.

But, even if you are right, and it is 'imaginary' in the usual sense of that word, to what does it refer?

You failed to say.

And thanks for the rushed research you did on the internet, but I do have a degree in mathematics.

Whereas i can have no real part z does have a real part- there is a difference- unless of course you are using the Cartesian idea that complex numbers are imaginary.

Not at all. But you have still not told us what this 'imaginary' number refers to. After all, all numbers, according to you, are 'abstract; and are thus imaginary. So, it is just as much a problem (for you) explaining the reference of i as it is that of zero or -234, which you have also yet to inform us about.

Although z requires i, i does not require z.

Oh dear, that just shows what rushed 'research' on the internet leads to! All complex numbers are designated by "z", whose general form is given by this rule "z = a + bi", where "a" and "b" are real numbers.

In that case when a = 0 and b = 1, z = i.

However, if i and z etc are not abstracta to what concretum do they refer?

They aren't referring expressions to begin with. They feature in rules that enable us to manipulate symbols in order to solve problems or prove things.

Anyway, on your 'theory', what does zero refer to?

[It can't be referring to one 'abstract mathematical object' otherwise it would be equal to one. And it can't be referring to nothing for reasons I have set out in an earlier thread.]

And: we are still waiting for that long lost 'logical proof' of yours that there is such a thing as 'the mind'.

Ã‘Ã³ẊÃ®Ã¶ŉ

26th March 2011, 14:19

What you're talking about here is a matter of degree. There are 118 fundamental possibliities of arranging these atoms (that show up regularly in nature) and really you can take that down to >30.

If you're referring to the chemical elements, then that is merely one set of possibilities: you also have to consider the spatial arrangements of atoms as well. If you were to take a human apart, atom by atom, and then rejoin those atoms in one of any number of possible configurations, only a extremely tiny proportion of those new arrangements would constitute a viable organism, let alone a viable human. There are vastly many more ways of being dead than alive.

Even then, one has to remember that living things aren't just specifically arranged collections of atoms, they are also dense and head-spinningly complex, multi-layered integrated networks of processes; just think of all the major systems (http://en.wikipedia.org/wiki/Biological_system) in a typical vertebrate body, the various and wonderous functions of tissues and organs, and the astounding array of functions and active structures found within a single cell (http://en.wikipedia.org/wiki/Cellular_biology).

Through our perception we can say "me" and "rock" and "human." But nature no more cares about your definitions than a rabbit does.
It is simplistic. But nowhere did I assert humans are just rocks. Rather that they were "basically," meaning at the most basic level, no different than rocks.

Even so, that ignores a huge difference between humans (or any other organism) and other objects known in the universe - rocks aren't subject to evolution via natural selection. Pointing out that both humans and rocks are made of atoms adds nothing new to the discussion.

When you eat an apple, does it just disappear, or do you just poop out whole apples? Otherwise where do you now draw the line between you and the apple?

When an apple is eaten, it is digested and is no more - the atoms that previously made it up may become part of the organism that eats it, or they may be dispersed into the environment.

It seems rather obvious to me, rather than some kind of great ontological mystery that philosophers are uniquely qualified to answer.

ComradeMan

26th March 2011, 15:19

CM: Well, as I pointed out, what used to be called Imaginary Numbers (by 16th century mathematicians) are now called Complex Numbers, which are comprised of an 'imaginary' part and a 'real' part..

Rosa you are implying that they are not called imaginary numbers by anyone- that the term imaginary numbers is some obsolete relic of the Renaissance which it isn't- absolute nonsense on your part.

http://www.algebra.com/cgi-bin/wiki-image.mpl?image=http%3A%2F%2Fupload.wikimedia.org% 2Fmath%2Fa%2F5%2Fb%2Fa5b080e63a3b527f4e751f51a4977 f75.png&site=wikibook&host=http://en.wikibooks.org/

I suppose you will tell us next you have a solution to this? I am fully aware of the relationship between imaginary and complex numbers and your rather silly red-herrings thrown into the argument to divert the discussion do not help. At the same time you can say that z=i.

But, you must not be mislead by the word 'imaginary' any more than by the word 'real'. 'Real' refers to the location of that part of the number on the x axis, while 'imaginary' refers to its location on the y-axis. Both parts are as real as one another, as the Argand Diagram shows..

Thanks... I did point out that the terminology is misleading or bad- the real numbers are no more real than the imaginary numbers- in either case we are dealing with abstracta.:thumbup1:

But, even if you are right, and it is 'imaginary' in the usual sense of that word, to what does it refer?

You failed to say...

But... but.... I asked you the question. What is the usual sense of imaginary by the way?

And thanks for the rushed research you did on the internet, but I do have a degree in mathematics.

This is rich from someone who actually does not usually explain their positions/points ever and uses links to "mathworld" etc.:laugh:

Great appeal to authority too.... "I'm write because I have a degree in mathematics".... LOL!!!! Therefore no one with a degree in mathematics and/or mathematicians can ever make a mistake?

[QUOTE=Rosa Lichtenstein;2059119]Not at all. But you have still not told us what this 'imaginary' number refers to. After all, all numbers, according to you, are 'abstract; and are thus imaginary. So, it is just as much a problem (for you) explaining the reference of i as it is that of zero or -234, which you have also yet to inform us about

http://staff.jccc.edu/swilson/complex/images/defi1.gif

Oh dear, that just shows what rushed 'research' on the internet leads to! All complex numbers are designated by "z", whose general form is given by this rule "z = a + bi", where "a" and "b" are real numbers.

In that case when a = 0 and b = 1, z = i.

Where did I say that complex numbers were not designated by z?

But what does the imaginary unit i stand for? If we want to get pedantic- I notice you are pedantic when it suits you- then we should talk about the imaginary unit i representing an imaginary number, e.g. http://www.algebra.com/cgi-bin/wiki-image.mpl?image=http%3A%2F%2Fupload.wikimedia.org% 2Fmath%2F5%2F0%2Fc%2F50c87172e13d308c2c7d3f5433533 833.png&site=wikibook&host=http://en.wikibooks.org/

The exact definition of i depends on the method of its extension. Now, I don't know the exactness of what you say in English but this i is called a unità immaginaria in Italian: a complex number- numero complesso- may be represented by the sum of a real number R and a pure imaginary number, i.e. a multiple of the imaginary unit. Like I said- they are inextricably linked but you can't just say they are exactly the same- note I did say, not quite the same.

Why do you keep asking questions but not actually answering questions?

If any of these numbers are not abstracta then to what concreta do they refer? You are the one who rejects a reasonable definition in mathematics and yet although you feel free to trash it you can't actually say what it is yourself.

Another interesting thing I have noticed, since I have to do research on Internet to find the English equivalents etc, is that there seems to be no general consensus and a rather large discrepancy in definitions. Yet again you divert attention from the original matter however, because you CAN'T actually answer the questions but choose rather to snipe at others all the time....

and....

How does this disprove the ability to subitise or enumerate in non-human species?

Rosa Lichtenstein

26th March 2011, 17:17

CM:

Rosa you are implying that they are not called imaginary numbers by anyone- that the term imaginary numbers is some obsolete relic of the Renaissance which it isn't- absolute nonsense on your part.

Well, they had to call them this for fear that the Catholic Church would accuse them of heresy -- after all, the Church fought tooth and nail against the introduction of zero and negative numbers centuries earlier, as the work of the 'devil'.

But, it doesn't matter what we call them, they are no more nor no less imaginary than any other numbers are. Have you ever bumped into a negative number?

I suppose you will tell us next you have a solution to this?

Er..., to what?

"i equals the square root of minus one" is not a puzzle, it's a definition/rule.

I am fully aware of the relationship between imaginary and complex numbers and your rather silly red-herrings thrown into the argument to divert the discussion do not help. At the same time you can say that z=i.

Complain all you like but your hasty internet 'research' led you astray.

At the same time you can say that z=i.

Only when a = 0 and b = 1.

What's the problem with that?

I did point out that the terminology is misleading or bad- the real numbers are no more real than the imaginary numbers- in either case we are dealing with abstracta.

Except, when asked to explain these 'abstracta' you go mysteriously quiet.

But... but.... I asked you the question. What is the usual sense of imaginary by the way?

Look it up.

This is rich from someone who actually does not usually explain their positions/points ever and uses links to "mathworld" etc

I'd post references to mathematics textbooks, but what would be the point of that? Unless you had access to them, they'd be of no use to you. So, I'm forced to post links. [And 'mathworld' is run by University Mathematics Lecturers.]

Great appeal to authority too.... "I'm write because I have a degree in mathematics".... LOL!!!!

Yet more invention. Where did I say that?

I reminded you of the fact that I have a degree in mathematics in order to let you know I do not need lectures on the subject from a novice like you.

Therefore no one with a degree in mathematics and/or mathematicians can ever make a mistake?

Eh? Where is that part of my argument? Yet more invention.

Where did I say that complex numbers were not designated by z?

Where did I say you did?

But what does the imaginary unit i stand for?

And, once more, you failed to tell us.

If we want to get pedantic- I notice you are pedantic when it suits you-

Just as you are hopelessly vague, and post circular definitions, when you run out of ideas.

then we should talk about the imaginary unit i representing an imaginary number, e.g.

But, it is a problem for you (hence the acres of waffle you post, to hide this fact), not me. I have already told you what these symbols express.

The exact definition of i depends on the method of its extension.

Where did you copy that odd idea from?

Now, I don't know the exactness of what you say in English but this i is called a unità immaginaria in Italian: a complex number- numero complesso- may be represented by the sum of a real number R and a pure imaginary number, i.e. a multiple of the imaginary unit. Like I said- they are inextricably linked but you can't just say they are exactly the same- note I did say, not quite the same.

Well, it's not too clear what you did say.

Why do you keep asking questions but not actually answering questions?

I answer far more than you do.

If any of these numbers are not abstracta then to what concreta do they refer?

In your haste to stagger from error to error, you clearly missed this answer from my last post***:

They aren't referring expressions to begin with. They feature in rules that enable us to manipulate symbols in order to solve problems or prove things.

You:

You are the one who rejects a reasonable definition in mathematics and yet although you feel free to trash it you can't actually say what it is yourself.

We have yet to have one from you -- other than those circular definitions you tried to palm us off with a while back, of course.

you can't actually say what it is yourself

See my answer above.***

Another interesting thing I have noticed, since I have to do research on Internet to find the English equivalents etc, is that there seems to be no general consensus and a rather large discrepancy in definitions. Yet again you divert attention from the original matter however, because you CAN'T actually answer the questions but choose rather to snipe at others all the time....

I think psychologists call this 'transference', i.e., when you attribute to me your own errors and omissions.

How does this disprove the ability to subitise or enumerate in non-human species?

When you tell us how these non-humans can use count nouns, I'll be happy to answer you -- unless, of course, you are using "enumerate" in a new and as-yet-unexplained sense. If so, what is it? [Some hope you'll tell us!]

And we are still waiting for you to tell us what 'abstract mathematical objects' zero and -234 refer to.

Just as we wait with baited breath for that long lost 'logical proof' of yours that there is such a thing as 'the mind'.

ComradeMan

26th March 2011, 19:37

CM:
Well, they had to call them this for fear that the Catholic Church would accuse them of heresy -- after all, the Church fought tooth and nail against the introduction of zero and negative numbers centuries earlier, as the work of the 'devil'..

Err.... not really seeing as the 0 and the 0-9 system we use in Europe owes much of it's diffusion mostly to Leonardo di Pisa, Fibonacci, and the Liber Abaci. I wasn't aware of any issues with him. Of course earlier works had broached the subject, including the earlier work of Pope Sylvester II- the "mathematician pope"- he did have issues but these were more connected to ideas surrounding astrology and the time spent in Islamic centres, of course he also spoilt a lot of business by eradicating simony too. It's not really about the maths.

But, it doesn't matter what we call them, they are no more nor no less imaginary than any other numbers are. Have you ever bumped into a negative number?..

I don't think I have ever bumped into 1, 7, pi or the Golden Section etc... You are the one saying they are not abstracta but yet you can't seem to explain what numbers are- other than repeat this somewhat dubious idea of yours about count nouns over and over again. The reason why they are imaginary numbers is that we know that the square root of -1 cannot be a real number.

"i equals the square root of minus one" is not a puzzle, it's a definition/rule.

If I say let x be the square root of 16 then the answer is quite simply x=4, (or -4 as we know that is also possible).

But if I ask you what is the square root of minus 1 then we have to say i.

That's the difference.

So what does i refer to? In hardcore materialist terms?

"Except, when asked to explain these 'abstracta' you go mysteriously quiet..

But I am not the one who is making all the assertions against commonly and generally held ideas in mathematics- you are.

"Look it up...

So you don't know. I notice you do this a lot- when posed a direct question you avoid the issue, say it's already been dealt with somewhere else or deride it as being obsolute, mystic or any of the other pejoratives you like to use in your accusations. It's only a simple question- would it kill you to answer it?

"I'd post references to mathematics textbooks, but what would be the point of that? Unless you had access to them, they'd be of no use to you. So, I'm forced to post links. [And 'mathworld' is run by University Mathematics Lecturers.]...

And I'd have this conversation in Italian if you want but most of my books and references are in Italian so that would not be very useful here? So you have no right to accuse others in a mocking fashion of using the Internet to find references, especially considering language and translations issues when you yourself do the same thing. Whether mathworld is run by University Mathematics Lecturers is of no interest to me, the books I have are also written by mathematics professors emeritus, astrophysicists and the like.

They seldom agree on such matters. ;)

"Yet more invention. Where did I say that? I reminded you of the fact that I have a degree in mathematics in order to let you know I do not need lectures on the subject from a novice like you.

Firstly I didn't say you said that, I pointed out a flaw in your appeal to authority. Secondly, you resort to yet another appeal to authority.

A "novice like you".... that comment is really beneath contempt. :rolleyes:

If I were you I'd burn my maths degree.... :lol:

All you have to offer is tu quoque, appeals to authority and begging the question- or your other trick of taking a word used in a general sense in the course of a discussion, applying your own narrow definition or definition of choice and turning things into an enthymemic debate, which conveniently avoids the issues. ;)

Why will you not answer the simple question being posited- If indeed numbers are not mathematical objects, i.e. not abstracta- then please, with your maths degree tell a humble novice like me what they are?

But you can't.

So burn your maths degree.:lol: Once you've finished counting the set of real numbers.... Cantor... * cough!

Rosa Lichtenstein

26th March 2011, 20:40

CM:

Err.... not really seeing as the 0 and the 0-9 system we use in Europe owes much of it's diffusion mostly to Leonardo di Pisa, Fibonacci, and the Liber Abaci. I wasn't aware of any issues with him.

You seem to be unaware of the opposition mounted by the Catholic Church to the introduction of zero, and negative numbers. Sure, they were later accepted because of the pressure exerted mainly by Italian merchants, which explains why the characters you mention could get away with what they got away with.

On that, see:

Seife, C. (2000), Zero, The Biography Of A Dangerous Idea (Souvenir Press).

Ifrah, G. (2000), The Universal History Of Numbers, Three Volumes (Harvill) -- Volume Two (notice the count noun?), chapter 26 (notice the count noun?), pp.1139-1167 -- 'The Slow Progress of Indo-Arabic Numerals in Western Europe'.

I don't think I have ever bumped into 1, 7, pi or the Golden Section etc...

Which shows, as I pointed out, that these are just as imaginary as i.

You are the one saying they are not abstracta but yet you can't seem to explain what numbers are

But, I have, when you asked whether "3 is prime" is true or false.

other than repeat this somewhat dubious idea of yours about count nouns over and over again.

Well, it's so 'dubious' that even you find you have you employ such nouns when you use number language.

The reason why they are imaginary numbers is that we know that the square root of -1 cannot be a real number.

Well, I warned you not to get confused over the use of these words. Real numbers are just as imaginary as 'imaginary numbers' are. It's just that they can be represented on the real number line, whereas the complex numbers can only be represented on the Complex Plane. Next time you meet that mathematics professor you mentioned a few days ago, try telling him/her that i is imaginary, whereas 1 is real.

If I say let x be the square root of 16 then the answer is quite simply x=4, (or -4 as we know that is also possible).

But if I ask you what is the square root of minus 1 then we have to say i.

That's the difference.

So what does i refer to? In hardcore materialist terms?

Well, you need to tell us.

I have told you what I think, but we have yet to hear you tell us what i refers to.

But I am not the one who is making all the assertions against commonly and generally held ideas in mathematics- you are.

Like what?

So you don't know.

I can't be expected to do all your thinking for you.

I notice you do this a lot

In fact, that is the first time I have done this.

Yet another fib of yours.

when posed a direct question you avoid the issue, say it's already been dealt with somewhere else

And, invariably it has.

or deride it as being obsolete

Well, is it my fault if your 'theory' is obsolete?

mystic or any of the other pejoratives you like to use in your accusations. It's only a simple question- would it kill you to answer it?

Would it kill you to tell us what 'abstract mathematical object' zero or -234 refer to? After all, I have been asking this of you for the last few days. All we get from you is a deafening silence.

And I'd have this conversation in Italian if you want but most of my books and references are in Italian so that would not be very useful here? So you have no right to accuse others in a mocking fashion of using the Internet to find references, especially considering language and translations issues when you yourself do the same thing. Whether mathworld is run by University Mathematics Lecturers is of no interest to me, the books I have are also written by mathematics professors emeritus, astrophysicists and the like.

That does not explain the basic mathematical errors you keep making (such as the muddle you got yourself into over z). And you keep doing this sort of thing. After all, it was you who tried to palm us off with the idea that 'A=A' is a syllogism.

Firstly I didn't say you said that, I pointed out a flaw in your appeal to authority. Secondly, you resort to yet another appeal to authority.

Not so; once more my reference to my degree was to remind you that I do not need lectures from you on basic mathematics -- that's not an appeal to authority, but a reminder that I already know all this stuff, so you do not need to post it here.

A "novice like you".... that comment is really beneath contempt.

But you have been saying such things to me all through this thread -- about my alleged ignorance of science.

Once more, we see that you are somehow allowed to spread fibs and accuse me of ignorance, by as soon as I allegedly do it, you throw your toys out of the pram.

If I were you I'd burn my maths degree....

You need to get one first, then I'll think about burning it.

All you have to offer is tu quoque, appeals to authority and begging the question.

What 'question' have I 'begged'?

And the point of 'tu quoque' posts of mine is quite clear: to point out to you that you indulge in the very things you falsely accuse me of doing. If you want them to stop, you need to resist the temptation to fib and invent.

Why will you not answer the simple question being posited- If indeed numbers are not mathematical objects, i.e. not abstracta- then please, with your maths degree tell a humble novice like me what they are?

Already done it. You need to pay attention.

But you can't.

Yet another fib. Are you going for the European record by any chance?

So burn your maths degree.

Already done it. :)

ComradeMan

26th March 2011, 21:08

CM: You seem to be unaware of the opposition mounted by the Catholic Church to the introduction of zero, and negative numbers. Sure, they were later accepted because of the pressure exerted mainly by Italian merchants, which explains why the characters you mention could get away with what they got away with.

Hardly the stuff of Crusades and witchhunts though is it? :thumbup1:

Which shows, as I pointed out, that these are just as imaginary as i..

You're abusing terminology here- predictably at least. A unicorn is also imaginary it does not make it an imaginary number.

You seem to think for some reason that we may no longer use the term- which is also used on your mathworld link. You claimed that this was an obsolete term and it isn't. Who's making stuff up?:lol:

Well, it's so 'dubious' that even you find you have you use such nouns when you use number language...

For a start when I checked this idea for which I could find no reference in Italian sources I found the English definitions that are talking about number as used in Grammar and not numbers and also to the idea of countability and uncountability derived thereof and not anything to do with numbers or mathematics as such, nor necessarily to do with the actual meaning of the words. Money is uncountable. :lol: That is why I say it is dubious.

Secondly, you make no distinction between "3" and "Three chairs"- in the former an abstractum and in the latter a concretum.

Well, I warned you not to get confused over the use of these words. Real numbers are just as imaginary as 'imaginary numbers' are. It's just that they can be represented on the real number line, whereas the complex numbers can only be represented on the Complex Plane. Next time you meet that mathematics professor you mentioned a few days ago, try telling him/her that i is imaginary, whereas 1 is real....

You are the one who seems to be confused and in your arrogance don't realise that probably most other people interested know why real numbers are called real and imaginary numbers are called imaginary, the same goes for irrational numbers and ratios. ;) Your also trying to project confusion that does sometimes arise over the nomenclature of mathematical objects and units etc.

So i is not an imaginary unit and the square root of minus -1 is not called an imaginary number? Please.....

I can't be expected to do all your thinking for you.....

Just like you can be expected to answer questions honestly.... this is one of your tactics I mentioned in the previous post.

Would it kill you to tell us what 'abstract mathematical object' zero or -234 refer to? After all, I have been asking this of you for the last few days. All we get from you is a deafening silence......

Please shut up. Zero is an integer, perhaps also a natural number depending on theory and thus as a NUMBER is a mathematical object, and in turn an abstract object like many others.

What does pi refer to? Do perfect circles really exist in the material world?

More sophistry.

That does not explain the basic mathematical errors you keep making (such as the muddle you got yourself into over z). And you keep doing this sort of thing. After all, it was you who tried to palm us off with the idea that 'A=A' is a syllogism.

An error which I admitted due to a hasty translation and which I also corrected.

Nor did I get into any error or muddle about "z"- despite your trying to build that trap. For someone who is so obsessive about "careful use of language" you should actually try to note when people use words like "not exactly the same" and "quite" etc.... ;)

Not so; once more my reference to my degree was to remind you that I do not need lectures from you on basic mathematics -- that's not an appeal to authority, but a reminder that I already know all this stuff, so you do not need to post it here..

:lol: It seems to me you are feeling a bit insecure because you are being challenged and making a terrible job of defending your points. So what? You have a degree in mathematics, according to you and in spite of copying and pasting hastily from "mathworld" and "mathmadefun" type sites etc etc you seem to have issues with some very basic ideas and concepts in mathematics. How embarassing is that? :blushing:

But you have been saying such things to me all through this thread -- about my alleged ignorance of science...

Well if you go around saying that bees and rocks are basically the same it doesn't help your case, does it?

Once more, we see that you allowed to spread fibs and accuse me of ignorance, by as soon as I allegedly do it, you throw your toys out of the pram. ...

More tu quoque-- grow up? Throughout this discussion and generally in most threads in which you are involved, you do nothing but accuse people of lying, insult them, patronise them and mock them because they dare disagree with your position on matters which are by no means settled whatsoever. You then have the gall to complain when you receive a lighthearted and nowhere near as insulting taste of your own medicine?

The lady protests too much, methinks.

You need to get one first, then I'll think about burning it....

No I am quite happy with the degrees I have and of course an open mind. Furthermore I would never be so arrogant and crass, and I believe no truly intellectual person would be, as to use my own qualifications as a means of silencing others- which is fundamentally what all that is about.

Now, stop crying and stick to the point.

If numbers are not abstract objects then what are they?

Revolution starts with U

26th March 2011, 21:14

If you're referring to the chemical elements, then that is merely one set of possibilities: you also have to consider the spatial arrangements of atoms as well. If you were to take a human apart, atom by atom, and then rejoin those atoms in one of any number of possible configurations, only a extremely tiny proportion of those new arrangements would constitute a viable organism, let alone a viable human. There are vastly many more ways of being dead than alive.

Im not going to disagree with any of this.

Even then, one has to remember that living things aren't just specifically arranged collections of atoms, they are also dense and head-spinningly complex, multi-layered integrated networks of processes; just think of all the major systems (http://en.wikipedia.org/wiki/Biological_system) in a typical vertebrate body, the various and wonderous functions of tissues and organs, and the astounding array of functions and active structures found within a single cell (http://en.wikipedia.org/wiki/Cellular_biology).

Yes, but there's nothing magical about it. It's merely a natural process and a part of nature. To say there was any fundamental difference would be akin to saying there is a such thing as "spirit." Surely you are not a spiritist?
Life/consciousness is a beautiful, but still natural thing.

Even so, that ignores a huge difference between humans (or any other organism) and other objects known in the universe - rocks aren't subject to evolution via natural selection. Pointing out that both humans and rocks are made of atoms adds nothing new to the discussion.

It takes the debate out of anthropomorphising everything.

When an apple is eaten, it is digested and is no more - the atoms that previously made it up may become part of the organism that eats it, or they may be dispersed into the environment.

It seems rather obvious to me, rather than some kind of great ontological mystery that philosophers are uniquely qualified to answer.

That's the beauty of it, it is simple, and obvious. You need no great degree in math or philosophy, or even physics. I don't know why you would refer it to white tower intellectualism, when it is blatantly pop philosophy anyone can understand.

Rosa Lichtenstein

26th March 2011, 22:19

CM:

Hardly the stuff of Crusades and witchhunts though is it?

In fact, it could get you killed.

You're abusing terminology here- predictably at least. A unicorn is also imaginary it does not make it an imaginary number.

Fine words from someone who abuses words like "number", "counting" and "decision".

You seem to think for some reason that we may no longer use the term- which is also used on your mathworld link. You claimed that this was an obsolete term and it isn't. Who's making stuff up?

I claimed no such thing -- yet another lie. [Or if you think I did, let's see you quote me to that effect.]

For a start when I checked this idea for which I could find no reference in Italian sources I found the English definitions that are talking about number as used in Grammar and not numbers and also to the idea of countability and uncountability derived thereof and not anything to do with numbers or mathematics as such, nor necessarily to do with the actual meaning of the words. Money is uncountable.

In that case, it's a mass noun.

But, last I checked, I could count the money in my pocket. Perhaps you don't know how to count?

That is why I say it is dubious.

Another word you seem to be having difficulties with.

Secondly, you make no distinction between "3" and "Three chairs"- in the former an abstractum and in the latter a concretum

1. That shows you do know I answered your question about numbers.

2. I did not mention 'three chairs'.

3. If it's an 'abstractum' to what does it refer? You do not seem to know.

You are the one who

Is that a 'childish' tu quoque of yours?

seems to be confused and in your arrogance don't realise that probably most other people interested know why real numbers are called real and imaginary numbers are called imaginary, the same goes for irrational numbers and ratios. Your also trying to project confusion that does sometimes arise over the nomenclature of mathematical objects and units etc.

In that case, if I am so confused, you should be able to help me out: to what does the real number zero refer? Or, -234, or 0.000123? Or, indeed, i?

So i is not an imaginary unit and the square root of minus -1 is not called an imaginary number? Please.....

It's just a real as the Real Numbers are -- or, just as 'imaginary' as the Reals are, too. Take your pick. But, whatever it is, you certainly do not know what it refers to.

Just like you can be expected to answer questions honestly.... this is one of your tactics I mentioned in the previous post.

And lied about, too.

Please shut up. Zero is an integer, perhaps also a natural number depending on theory and thus as a NUMBER is a mathematical object, and in turn an abstract object like many others.

You said this weeks ago, and then I asked: so where does this 'abstract object' reside? You have yet to reply.

But, if zero is an 'abstract object' then it's one, not zero.

What does pi refer to?

I have already told you that number words are not referring expressions. We can see the mess you get into when you think they are.

In that case, you tell us what you think pi refers to?

Can't say?

No surprise there then.

Do perfect circles really exist in the material world?

What makes you think I think they do?

But, you will find it impossible to explain where they do exist. If they do not, then on your 'theory' pi can't relate to anything, either.

By way of contrast, if, on my account, mathematical 'objects' are rules, or feature in the grammar of rules, then they do not have to exist anywhere, they just need to be followed or used to solve problems, or construct proofs.

2500 years of philosophical speculation goes out of the window...

More sophistry.

That's very kind of you. But, you have already offered; so, no thanks.

An error which I admitted due to a hasty translation and which I also corrected.

In fact, I corrected you.

Nor did I get into any error or muddle about "z"- despite your trying to build that trap.

In fact, you trapped yourself.

For someone who is so obsessive about "careful use of language" you should actually try to note when people use words like "not exactly the same" and "quite" etc...

In fact, you posted this howler:

Although z requires i, i does not require z.

Tell that to the maths professor you mentioned, and watch him/her cringe.

It seems to me you are feeling a bit insecure

Well, you are the novice who is manifestly out of 'his' depth.

because you are being challenged and making a terrible job of defending your points.

Small point, hardy worth mentioning, in fact -- except, you can't quite show where I fail to do this.

So what? You have a degree in mathematics,

Methinks the novice doth protest too much.

according to you and in spite of copying and pasting hastily from "mathworld" and "mathmadefun" type sites etc you seem to have issues with some very basic ideas and concepts in mathematics.

Where did I copy anything from "mathmadefun"?

Yet another lie.

How embar[r]assing is that?

No lie of yours is embarrassing.

Well if you go around saying that bees and rocks are basically the same it doesn't help your case, does it?

Good job I don't, then -- I merely draw the consequences of your obsolete 'theory'.

More tu quoque-- grow up?

As I pointed out in my last post:

And the point of 'tu quoque' posts of mine is quite clear: to point out to you that you indulge in the very things you falsely accuse me of doing. If you want them to stop, you need to resist the temptation to fib and invent.

You:

Throughout this discussion and generally in most threads in which you are involved, you do nothing but accuse people of lying,

Well, and once again, here is a list of some of your more recent lies:

Well, you made up these accusations (among others): that I thought numbers were abstract objects, that I was using linguistics, that I had confused numbers with numerals (we are still waiting for you to cite a single quotation from my posts that even so much as hints at this), that I had used definitions when I haven't, that I had defined "information" when I haven't even tried to do so, that I had an ontology when you had been told several times I reject all ontologies as non-sensical (and then it turned out you were trying to foist one on us), that I had referred to 'language universals' when I hadn't, that I had made certain allegations about "the logical non-existence of the mind" when I hadn't, and then that "most" of my argument rests on "inverted commas", when it doesn't (and you failed to say how you had arrived at that fabrication), and so on. [Links provided on request.]

In which case, we must now add the phrase "making up anything" to the words "number" and "language" with which you seem to be struggling.

And you have continued to make then since; here is the latest batch from your last but one post:

If you use arguments that come from that side of the playing field then so be it

But which arguments of mine "come from that side of the playing field" -- that is, from the logical positivist side?

You have failed to say -- so this is yet another baseless allegation/fib of yours.

You are the person who seems to feel the mind does not exist, that would be pretty much a denial of the mind, wouldn't it?

For the tenth time, where have I denied the existence of 'the mind'? And where have I been involved in a "denial of the mind"?

Yet more fibs.

Yet strangely in another thread here at RevLeft you were talking about inner minds etc....

Where did I do this? I note, yet again, you neglected to provide the link.

One more fib to add to the growing list.

You:

insult them, patronise them and mock them because they dare disagree with your position on matters which are by no means settled whatsoever.

Once more, you make a series of accusations, which you fail to support with any evidence.

You then have the gall to complain when you receive a lighthearted and nowhere near as insulting taste of your own medicine?

I complain about your serial lying, in fact.

The lady protests too much, methinks.

The novice lies too much, I think.

No I am quite happy with the degrees I have

In Tibetan pottery?

and of course an open mind.

Into which any old obsolete idea finds easy access.

Furthermore I would never be so arrogant and crass,

Just more arrogant and crass.

and I believe no truly intellectual person would be, as to use my own qualifications as a means of silencing others- which is fundamentally what all that is about.

Except you have been trying to do that to me all through this thread.

Now, stop crying and stick to the point.

Yet more invention.

If numbers are not abstract objects then what are they?

I have already told you, as you admitted above.

ComradeMan

26th March 2011, 22:57

Rosa, I really can't be bothered with your stupidity in this matter anymore.

All you have to offer is the most ridiculous and fallacious arguments based on tu quoque, enthymemes and blatant intellectual dishonesty.

It's quite sad really.

There's nothing wrong with holding certain views in these matters but your insistance that only your view is the right one, when it is not even by any means a general consensus, your insistance that everyone else is wrong and you're right despite the fact that no one much seems to agree with your views from any field- and you wonder why?

Perfectly contemporary and accepted definitions are obsolete? Confined to the dustbin of history because of... oops.... because you say they are? :laugh:

For someone who claims to have a degree in mathematics it's odd how you avoid mathematical arguments and don't seem to accept any basic definitions. All of this hyperbole and exaggeration as well as accusing people of lying all the time... I wonder, feeling a bit insecure? Can't understand why they rejected some thesis of yours?

After all of this sophistry, you have not:

1) stated what numbers are if they are not mathematical objects and thus abstract objects.

"Thus it is universally acknowledged that numbers and the other objects of pure mathematics are abstract.."
http://plato.stanford.edu/entries/abstract-objects/

Natural Numbers and Natural Cardinals as
Abstract Objects: A Partial Reconstruction
of Frege’s Grundgesetze in Object Theory
http://mally.stanford.edu/Papers/numbers.pdf

2) disproven the scientific research that shows non-human species can subitise.

3) shown why it is obsolete to speak of imaginary numbers.

4) explained what exactly you mean by count nouns or number names.

5) Explained what abstracta are if they are not abstracta.

Owned-

by a novice at that!
:laugh:

You seem to confuse the way that mathematical objects in general, in this case numbers, are treated in maths. If I am working with a calculation or something I treat them as "real" however this does not mean I need to get into some pseudo-philosophical struggle because I can't actually see, hear, touch or smell the number. There is no problem with abstract objects but if you want to apply some strange kind of materialistic realism to numbers you're going to get into a mess.

Ã‘Ã³ẊÃ®Ã¶ŉ

27th March 2011, 00:40

Yes, but there's nothing magical about it. It's merely a natural process and a part of nature. To say there was any fundamental difference would be akin to saying there is a such thing as "spirit." Surely you are not a spiritist?
Life/consciousness is a beautiful, but still natural thing.

That complexity of interacting systems is what makes life special, not what it's made of. There's no need to posit anything like a soul or elan vital now that we know that intricate flows of matter and energy can achieve the same results, so to speak.

It takes the debate out of anthropomorphising everything.

No it doesn't. In fact, I have seen it seriously argued that the fact that one's atoms continue to exist after death (or that energy cannot be created or destroyed) is evidence for life after death.

That's the beauty of it, it is simple, and obvious. You need no great degree in math or philosophy, or even physics. I don't know why you would refer it to white tower intellectualism, when it is blatantly pop philosophy anyone can understand.

True, but what should be simple is frequently obfuscated by third-rate philosophers, who have had a hard time justifying their existence since modern science came along and soundly answered many questions that they previously would have attempted to answer.

Rosa Lichtenstein

27th March 2011, 14:37

CM:

Rosa, I really can't be bothered with your stupidity in this matter anymore.

That's OK, since there is none.:)

[Your additional comments are, of course, further proof of that!]

All you have to offer is the most ridiculous and fallacious arguments based on tu quoque, enthymemes and blatant intellectual dishonesty.

Ah, showing off your novice knowledge of logic now, I see.

It's quite sad really.

No need to be sad that you're a novice.

There's nothing wrong with holding certain views in these matters

Where have I said otherwise?

but your insistence that only your view is the right one, when it is not even by any means a general consensus,

Once more, it's not my fault if you have latched onto an obsolete theory.

your insistence that everyone else is wrong and you're right despite the fact that no one much seems to agree with your views from any field- and you wonder why?

You have tried this one on before; here is a repeat of my earlier reply to it: The vast majority of 'informed opinion' used to think the earth was at the centre of the universe. So, popularity is no guarantee of truth, as you seem to think. Now, you are trapped in the equivalent of a pre-Copernican theory of numbers. You can stay trapped there if you want; who am I to try to protect you from your own folly? But, you should no more point fingers at me than the Ptolemaists had any right to point fingers at, say, Galileo.

Someone has to innovate -- too bad for you its little old me.:)

Anyway, there are plenty of others who agree with me. You can find some of their ideas outlined here:

http://plato.stanford.edu/entries/wittgenstein-mathematics/

Perfectly contemporary and accepted definitions are obsolete?

1. Well, you haven't offered any definitions -- except, of course, for the two circular definitions you tried to palm us off with a few days ago.

2. But even if you had, it's quite plain that whoever is feeding you these ideas is also trapped in that pre-Copernican world.

Confined to the dustbin of history because of... oops.... because you say they are?

Well, you have yet to defend this ailing 'theory' of yours. In fact, if this were a trial, I think you'd be advised to plead guilty and throw yourself on the mercy of the court.

For someone who claims to have a degree in mathematics it's odd how you avoid mathematical arguments

Yet another lie -- so you are going for the European record.

Where have I 'avoided mathematical arguments'?

and don't seem to accept any basic definitions.

Well, all the definitions you have offered so far were circular. Now, you might be happy with circular definitions, but I think even those who agree with your 'theory' won't be. Try one out on that maths professor you mentioned the other day.

All of this hyperbole

What 'hyperbole'?

and exaggeration

What 'exaggeration'?

Yet more baseless allegations. For someone who claims to be science-friendly, you don't seem to believe in evidence.

as well as accusing people of lying all the time

So, do you deny you said the following?

Well, you made up these accusations (among others): that I thought numbers were abstract objects, that I was using linguistics, that I had confused numbers with numerals (we are still waiting for you to cite a single quotation from my posts that even so much as hints at this), that I had used definitions when I haven't, that I had defined "information" when I haven't even tried to do so, that I had an ontology when you had been told several times I reject all ontologies as non-sensical (and then it turned out you were trying to foist one on us), that I had referred to 'language universals' when I hadn't, that I had made certain allegations about "the logical non-existence of the mind" when I hadn't, and then that "most" of my argument rests on "inverted commas", when it doesn't (and you failed to say how you had arrived at that fabrication), and so on. [Links provided on request.]

In which case, we must now add the phrase "making up anything" to the words "number" and "language" with which you seem to be struggling.

And you have continued to make then since; here is the latest batch from your last but one post:

If you use arguments that come from that side of the playing field then so be it

But which arguments of mine "come from that side of the playing field" -- that is, from the logical positivist side?

You have failed to say -- so this is yet another baseless allegation/fib of yours.

You are the person who seems to feel the mind does not exist, that would be pretty much a denial of the mind, wouldn't it?

For the tenth time, where have I denied the existence of 'the mind'? And where have I been involved in a "denial of the mind"?

Yet more fibs.

Yet strangely in another thread here at RevLeft you were talking about inner minds etc....

Where did I do this? I note, yet again, you neglected to provide the link.

One more fib to add to the growing list.

The above a shortened list of your most recent lies.

... I wonder, feeling a bit insecure?

So you should. All your ideas have crumbled to dust.

Can't understand why they rejected some thesis of yours?

Indeed, I do understand -- they, like you, can't defend their ideas, while I can.

After all of this sophistry, you have not:

1) stated what numbers are if they are not mathematical objects and thus abstract objects.

Yes I have -- in fact, in earlier posts, after you commented on what I have said they are, you now have the cheek to repeat the lie that I haven't!

More importantly, you have yet to tell us where these 'abstract objects' are to be found -- or even what they are -- and what 'abstract object' zero, for example, refers to.

"Thus it is universally acknowledged that numbers and the other objects of pure mathematics are abstract.."

It's not 'generally accepted'; check out nominalist theories of mathematics. Begin here:

Field, H. (1989), Realism, Mathematics And Modality (Blackwell).

--------, (1998), 'Mathematical Objectivity And Mathematical Objects', in Laurence and Macdonald (1998), pp.387-403; reprinted in Field (2001), pp.315-31.

--------, (2001), [/i]Truth And Absence Of Fact[/i] (Oxford University Press).

Laurence, S., and Macdonald, C. (1998) (eds.), Contemporary Readings In The Foundations Of Metaphysics (Blackwell).

Burgess, J., and Rosen, G. (1997), A Subject With No Object. Strategies For Nominalistic Interpretation of Mathematics (Oxford University Press).

And check out the following section in the same Encyclopedia you quoted (which shows that that article you referenced is in error):

Mathematics Without Abstract Entities

You can find that here:

http://plato.stanford.edu/entries/philosophy-mathematics/

Go to section 4, and then section 4.3

Now, I do not agree with the above theory, I only mention it to show that your superficial knowledge in this area means you can't tell truth from error.

You will find an outline of other approaches to mathematic, much closer to my own, which do not postulate such 'abstract objects', here, again:

http://plato.stanford.edu/entries/wittgenstein-mathematics/

So, may I suggest you learn a little more about the philosophy of mathematics before you expose your ignorance in public again?

2) disproven the scientific research that shows non-human species can subitise.

Yet another lie to add to the ever-lengthening list. I haven't even tried to 'disprove' this, since it makes no sense -- unless, of course, you can show that these post-graduate 'non-humans' can use count nouns.

3) shown why it is obsolete to speak of imaginary numbers.

Yet another lie. I have never said this of 'imaginary numbers'.

4) explained what exactly you mean by count nouns or number names.

Don't need to, you already know -- I think, but I am beginning to suspect you might not -- since you use them every day of your life. That is, until this obsolete 'theory' grips your brain, and you start to flounder.

5) Explained what abstracta are if they are not abstracta.

That's like asking me to explain this poem:

JABBERWOCKY

Lewis Carroll

(from Through the Looking-Glass and What Alice Found There, 1872)

'Twas brillig, and the slithy toves
Did gyre and gimble in the wabe:
All mimsy were the borogoves,
And the mome raths outgrabe.

"Beware the Jabberwock, my son!
The jaws that bite, the claws that catch!
Beware the Jubjub bird, and shun
The frumious Bandersnatch!"

He took his vorpal sword in hand:
Long time the manxome foe he sought --
So rested he by the Tumtum tree,
And stood awhile in thought.

And, as in uffish thought he stood,
The Jabberwock, with eyes of flame,
Came whiffling through the tulgey wood,
And burbled as it came!

One, two! One, two! And through and through
The vorpal blade went snicker-snack!
He left it dead, and with its head
He went galumphing back.

"And, has thou slain the Jabberwock?
Come to my arms, my beamish boy!
O frabjous day! Callooh! Callay!'
He chortled in his joy.

'Twas brillig, and the slithy toves
Did gyre and gimble in the wabe;
All mimsy were the borogoves,
And the mome raths outgrabe.
If you won't tell us what (and where) these 'abstracta' are, how am I expected to help you out of your difficulties? I can't possibly be expected to unravel the knots in your thinking if you refuse to come clean.

Owned

More like: you have merely held yourself up for derision.

by a novice at that!

And, believe me, it shows.

You seem to confuse the way that mathematical objects in general, in this case numbers, are treated in maths.

You just can't help yourself can you?

Where have I done this?

If I am working with a calculation or something I treat them as "real" however this does not mean I need to get into some pseudo-philosophical struggle because I can't actually see, hear, touch or smell the number.

In fact, what you actually do is manipulate symbols. Nothing 'abstract' (whatever that means) about them -- and you use well-known rules to do so.

There is no problem with abstract objects

Except no one (literally no one -- check it out -- certainly not you) seems to know what they are (or where they are). Other than that, we appear to have a pretty good handle on the subject.:rolleyes:

but if you want to apply some strange kind of materialistic realism to numbers you're going to get into a mess.

Yet more fiction from our very own god-father of invention.

Where have I even mentioned 'materialistic realism'?

And we are still waiting for your earth-shattering 'logical proof' that there is such a thing as 'the mind'.

ComradeMan

27th March 2011, 15:40

Rosa you are being shot down in flames faster than a Libyan jet.

Now you are beginning to backtrack- you don't agree with theories... so they're not necessarily inventions and lies as you have been implying throughout. They are theories and there is no one consensus.

What it comes down to is that when you disagree with a theory you give yourself some self-ordained right to mock, ridicule and be intellectually dishonest.

The fact that you can point to a source is not evidence of a proof- especially when we are talking about the philosophy of mathematics. :lol:

Now- the onus is on you who reject to state why- which you can't. That very same Stanford source also gave me a neat little definition of abstract objects which I included above.

And please... is the best thing you have to offer ad hominems? Not very scientific.... but then I suppose when bees are rocks what can one expect.

You are like some kind of resurrected Lysenko. :laugh:

The whole motive behind this, I suspect, is that you can't stand the idea of a connection between abstracta and concreta, i.e. how mathematical objects, i.e. abstract objects can lead to solutions in the physical world or the "concretum". This in turn undermines your rather controversial positions on Lenin doesn't it? So fundamentally this is not about maths or philosophical debate but about your political crusade against DM and the other rocks in your bonnet.
:laugh:

Exposed!

Rosa Lichtenstein

27th March 2011, 16:31

CM, who earlier said this:

Rosa, I really can't be bothered with your stupidity in this matter anymore.

So, you even lie to yourself.:lol:

Rosa you are being shot down in flames faster than a Libyan jet.

If I am, the fire hasn't been coming from you. You do not seem to know what simple words like "counting" and "decision" mean.

Now you are beginning to backtrack

Yet another baseless allegation not supported by any evidence.

- you don't agree with theories... so they're not necessarily inventions and lies as you have been implying throughout.

What are you blathering on about? Where have I ever said such a stupid thing? Or even implied it?

They are theories and there is no one consensus.

You'll be telling us grass is green next.:lol:

What it comes down to is that when you disagree with a theory you give yourself some self-ordained right to mock, ridicule and be intellectually dishonest.

Like you never mock.

The fact that you can point to a source is not evidence of a proof- especially when we are talking about the philosophy of mathematics.

Proof of what, for goodness sake? We're not all psychic like you, you know.

Now- the onus is on you who reject to state why- which you can't.

Why what?

Are you being deliberately enigmatic?

That very same Stanford source also gave me a neat little definition of abstract objects which I included above.

In fact -- small point really, hardly worth mentioning -- it doesn't actually tell us what they are, or where they are.

And please... is the best thing you have to offer ad hominems?

Which is an ad hominem itself. Nice one!

Anyway, there's nothing inherently wrong with ad hominems -- which you appear to have confused with abuse.

On that, check this out:

The ad hominem fallacy fallacy

-------------------------------------------------------------------------

One of the most widely misused terms on the Net is "ad hominem". It is most often introduced into a discussion by certain delicate types, delicate of personality and mind, whenever their opponents resort to a bit of sarcasm. As soon as the suspicion of an insult appears, they summon the angels of ad hominem to smite down their foes, before ascending to argument heaven in a blaze of sanctimonious glory. They may not have much up top, but by God, they don't need it when they've got ad hominem on their side. It's the secret weapon that delivers them from any argument unscathed.

In reality, ad hominem is unrelated to sarcasm or personal abuse. Argumentum ad hominem is the logical fallacy of attempting to undermine a speaker's argument by attacking the speaker instead of addressing the argument. The mere presence of a personal attack does not indicate ad hominem: the attack must be used for the purpose of undermining the argument, or otherwise the logical fallacy isn't there. It is not a logical fallacy to attack someone; the fallacy comes from assuming that a personal attack is also necessarily an attack on that person's arguments.

Therefore, if you can't demonstrate that your opponent is trying to counter your argument by attacking you, you can't demonstrate that he is resorting to ad hominem. If your opponent's sarcasm is not an attempt to counter your argument, but merely an attempt to insult you (or amuse the bystanders), then it is not part of an ad hominem argument.

Actual instances of argumentum ad hominem are relatively rare. Ironically, the fallacy is most often committed by those who accuse their opponents of ad hominem, since they try to dismiss the opposition not by engaging with their arguments, but by claiming that they resort to personal attacks. Those who are quick to squeal "ad hominem" are often guilty of several other logical fallacies, including one of the worst of all: the fallacious belief that introducing an impressive-sounding Latin term somehow gives one the decisive edge in an argument.

But enough vagueness. The point of this article is to bury the reader under an avalanche of examples of correct and incorrect usage of ad hominem, in the hope that once the avalanche has passed, the term will never be used incorrectly again. I will begin with some invented examples, before dealing with some real-life misuses of the term at the end.

--------------------------------------------------------------------------------

A: "All rodents are mammals, but a weasel isn't a rodent, so it can't be a mammal."
B: "This does not logically follow. By your own argument, the set of rodents is a subset of the set of mammals; and therefore, a weasel can be outside the set of rodents and still be in the set of mammals."
Hopefully it should be clear that neither A's argument nor B's argument is ad hominem. Perhaps there are some people who think that any disagreement is an ad hominem argument, but these people shouldn't be allowed out of fairyland.

A: "All rodents are mammals, but a weasel isn't a rodent, so it can't be a mammal."
B: "This does not logically follow."
B's argument is less comprehensive, but still not ad hominem.

A: "All rodents are mammals, but a weasel isn't a rodent, so it can't be a mammal."
B: "This does not logically follow. You evidently know nothing about logic."
B's argument is still not ad hominem. Note that B directly engages A's argument: he is not attacking the person A instead of his argument. There is no indication that B thinks his subsequent attack on A strengthens his argument, or is a substitute for engaging with A's argument. Unless we have a good reason for thinking otherwise, we should assume it is just a sarcastic flourish.

A: "All rodents are mammals, but a weasel isn't a rodent, so it can't be a mammal."
B: "You evidently know nothing about logic. This does not logically follow."
B's argument is still not ad hominem. B does not imply that A's sentence does not logically follow because A knows nothing about logic. B is still addressing the substance of A's argument.

A: "All rodents are mammals, but a weasel isn't a rodent, so it can't be a mammal."
B: "You evidently know nothing about logic."
B's argument is, most probably, still not ad hominem. The word "evidently" indicates that B is basing his opinion of A's logical skills on the evidence of A's statement. Therefore, B's sentence is a sarcastic way of saying that A's argument is logically unsound: B is attacking A's argument. He is not attacking the person instead of the argument.

A: "All rodents are mammals, but a weasel isn't a rodent, so it can't be a mammal."
B: "You know nothing about logic."
Even now, we can't conclude that B's reply is ad hominem. It could well be, and probably is, the case that B is basing his reply on A's argument. He is not saying that A's argument is flawed because A knows nothing about logic; instead, he is using A's fallacious argument as evidence to present a new argument: that A knows nothing about logic.

Put briefly, ad hominem is "You are an ignorant person, therefore your arguments are wrong", and not "Your arguments are wrong, therefore you are an ignorant person." The latter statement may be fallacious, but it's not an ad hominem fallacy.

A: "All rodents are mammals, but a weasel isn't a rodent, so it can't be a mammal."
B: "This does not logically follow. And you're an asshole."
B is abusive, but his argument is still not ad hominem. He engages with A's argument. There is no reason to conclude that the personal abuse of A is part of B's argument, or that B thinks it undermines A's argument.

A: "All rodents are mammals, but a weasel isn't a rodent, so it can't be a mammal."
B: "You're an asshole."
B's reply is not necessarily ad hominem. There is no evidence that's his abusive statement is intended as a counter-argument. If it's not an argument, it's not an ad hominem argument.

A: "All rodents are mammals, but a weasel isn't a rodent, so it can't be a mammal."
B: "You evidently know nothing about logic. And you're an asshole."
Again, B's reply is not necessarily ad hominem.

A: "All rodents are mammals, but a weasel isn't a rodent, so it can't be a mammal."
B: "Fuck you."
Not ad hominem. B's abuse is not a counter-argument, but a request for A to cease the discussion.

A: "All rodents are mammals, but a weasel isn't a rodent, so it can't be a mammal."
B: "Well, you've never had a good grasp of logic, so this can't be true."
B's argument here is ad hominem. He concludes that A is wrong not by addressing A's argument, but by appealing to the negative image of A the person.

A: "All rodents are mammals, but a weasel isn't a rodent, so it can't be a mammal."
B: "Well, you're a moron and an asshole, so there goes your argument."
B's reply here is ad hominem and abusive.

A: "All rodents are mammals, but a weasel isn't a rodent, so it can't be a mammal."
B: "Well, you're a rodent and a weasel, so there goes your argument."
B's argument here might appear on superficial inspection to be sound, but it is in fact ad hominem. He is using the terms "rodent" and "weasel" in different senses to those used by A. Although he tries to make it appear that he is countering A's argument by invalidating one of the premises, he is in fact trying to counter A's argument by heaping abuse on A. (This might also be an example of an ad homonym argument.)

A: "All murderers are criminals, but a thief isn't a murderer, and so can't be a criminal."
B: "Well, you're a thief and a criminal, so there goes your argument."
Harder to call this one. B is addressing A's argument, but perhaps unwittingly.

A: "All rodents are mammals, but a weasel isn't a rodent, so it can't be a mammal."
B: "Wrong! If a weasel isn't a rodent, then it must be an insectivore! What an asshole!"
B's argument is logically fallacious, and he concludes with some gratuitous abuse, but nothing here is ad hominem.

A: "All rodents are mammals, but a weasel isn't a rodent, so it can't be a mammal."
B: "I'm sorry, but I'd prefer to trust the opinion of a trained zoologist on this one."
B's argument is ad hominem: he is attempting to counter A not by addressing his argument, but by casting doubt on A's credentials. Note that B is polite and not at all insulting.

A: "Listen up, asshole. All rodents are mammals, but a weasel isn't a rodent, so it can't be a mammal."
B: "Yet another ad hominem argument. Ignore this one, folks."
A is abusive, and his argument is fallacious, but it's not ad hominem. B's reply, ironically, is ad hominem; while he pretends to deal with A's argument, in using the term "ad hominem" incorrectly, B is in fact trying to dismiss the argument by imputing that A is resorting to personal attacks.

A: "Listen up, asshole. All rodents are mammals, and a lizard isn't a mammal, so it can't be a rodent."
B: "Yet another ad hominem argument. Ignore this one, folks."
A's argument is sound, and not ad hominem. B's reply is again ad hominem.

A: "B is a convicted criminal and his arguments are not to be trusted."
B: "Yet another ad hominem argument. Ignore this one, folks."
A's argument is ad hominem, since it attempts to undermine all of B's (hypothetical) arguments by a personal attack. B's reply is not ad hominem, since it directly addresses A's argument (correctly characterising it as ad hominem).

A: "All politicians are assholes, and you're just another politician. Therefore, you're an asshole."
B: "Yet another ad hominem argument."
If you accept the premises, A's argument is sound. Either way, from the given context, we cannot conclude that it is ad hominem: it's not an attempt to undermine B's (hypothetical) arguments by abusing him, but instead an attempt to establish that B is an asshole. B's reply is ad hominem, since by incorrectly using the term "ad hominem", he is trying to undermine A's argument by claiming that A is resorting to personal attacks.

A: "All politicians are liars, and you're just another politician. Therefore, you're a liar and your arguments are not to be trusted."
B: "Yet another ad hominem argument."
If you accept the premises, A's argument is sound; but I think most of us would sympathise with B and class it as fallacious, and ad hominem. This is because we do not accept the premise that all politicians are liars. There is a false premise that lies behind all ad hominem arguments: the notion that all people of type X make bad arguments. A has just made this premise explicit.

A: "All rodents are mammals, but a weasel isn't a rodent, so it can't be a mammal."
B: "That does not logically follow."
A: "*Sigh* Do I have to spell it out for you? All rodents are mammals, right, but a weasel isn't a rodent, so it can't be a mammal! What's so hard to understand???!?"
B: "I'm afraid you're mistaken. Look at it logically. If p implies q, then it does not follow that not-p implies not-q."
A: "I don't care about so-called logic and Ps and Qs and that stuff, I'm talking COMMON SENSE. A weasel ISN'T a mammal."
B: "Okay, this guy's an idiot. Ignore this one, folks."
A: "AD HOMINEM!!!! I WIN!!!!!"
Although the last line of B, taken out of context, might look ad hominem (and was seized upon as such by A), it should be clear that taken as a whole, B's argument is not ad hominem. B engaged thoroughly with A's argument. He is not countering A's argument by saying A is an idiot; on the contrary, having logically countered A's argument, and having seen A's reaction, he is arguing that A is an idiot.

--------------------------------------------------------------------------------

Some real-life examples:

A: "I agree that the writing is first class, but I am left with the distinct impression that the author is using the game as a vehicle for self-aggrandizement rather than to entertain the player. "
B: "... let's refrain from ad hominem arguments, and accept that we have different tastes, shall we?"
A's argument was not ad hominem. "The author is using the game as a vehicle for self-aggrandizement" is the conclusion of his argument, not an attempt to undermine the said author's (unseen) arguments by casting aspersions on him.

A: "I can even handle misplaced apostrophes every now and then. Not excessive amounts of them, [...]"
B: "Perhaps double-check your grammar before you write a grammar rant that refers to 'amounts of apostrophes'."
C: " ...the ad hominem nature of [B's reply] takes the sanctimonious angle that any who criticize must be without stain."
B's reply was not ad hominem. It was not a counter-argument to A, but an attempt to point out what B saw as A's hypocrisy. C's use of language, by the way, demonstrates that he is clearly out of his depth.

A: "Can someone please direct me to the ad hominem attacks in the TADS competition game "Futz Mutz"?"
There are no ad hominem attacks in Futz Mutz. Just a lot of stupid abuse.

A: "OK, I've been following this thread for a while, and I hate to say it, but you're being an asshole. You're really taking this whole thing too personally, and seriously misconstruing everyone else's arguments. Nobody here is arguing that copyright infringement is ethically, morally, legally, or otherwise justifiable. They're simply arguing that equating it with theft is simplistic and inaccurate."
B: "...calling me an asshole is called an ad hominem attack, which does not show me wrong."
No, calling you an asshole is just abuse. A's argument is not ad hominem. A has carefully pointed out what he sees as the flaws in B's argument, and based on B's failure to acknowledge them and general behaviour, has concluded that B is an asshole. This conclusion is quite independent of A's treatment of B's arguments.

A: "But the capability is, of course, there, and if you 'fail to see' how any of the standard systems can handle realtime then you clearly have zero understanding of virtual machines."
B: "...your over-reaching ad hominim[sic] judgements about what people do and do not know..."
A's argument is not ad hominem: he is not attempting to undermine B's arguments by claiming that B knows nothing about VMs. Instead, based on B's arguments about VMs, he has reached the conclusion that B has no understanding of them, and presented this as a new argument. (B later even had the nerve to direct A to the Wikipedia page on ad hominem, which he clearly didn't understand.)

-------------------------------------------------------------------

From here:

http://plover.net/~bonds/adhominem.html

It's also worth adding that this is not a formal fallacy (such as Affirming the Consequent (http://en.wikipedia.org/wiki/Affirming_the_consequent)), but an informal one.

Finally, arguing ad hominem can be a valid form of argument, for example, if it is used to expose inconsistency in an opponent's argument.

Not very scientific.... but then I suppose when bees are rocks what can one expect.

That's odd, why on earth do you think they are?

You are like some kind of resurrected Lysenko.

I'm nothing like you! Cheek!

The whole motive behind this, I suspect, is that you can't stand the idea of a connection between abstracta and concreta, i.e. how mathematical objects, i.e. abstract objects can lead to solutions in the physical world or the "concretum". This in turn undermines your rather controversial positions on Lenin doesn't it? So fundamentally this is not about maths or philosophical debate but about your political crusade against DM and the other rocks in your bonnet.

I'd like to be able to respond to this but it contains terms which you have yet to explain -- namely 'abstracta' and 'concreta'.

And we are still waiting for your pioneering 'logical proof' that there is such a thing as 'the mind'.

ComradeMan

27th March 2011, 16:56

^^^^^^^^^ Nothing to do with the topic being discussed.

:laugh:

By the way, numbers, in language, can also be adjectives.
:rolleyes:

Revolution starts with U

27th March 2011, 17:02

I think you're still misunderstanding what a "count noun" is.

Rosa Lichtenstein

27th March 2011, 17:38

CM:

Nothing to do with the topic being discussed.

Then the only thing I can suggest is you try to focus a little more.

By the way, numbers, in language, can also be adjectives.

And adjectives qualify nouns, and in this case, count nouns.

Glad to see you are getting the point.:)

ComradeMan

27th March 2011, 21:06

CM: And adjectives qualify nouns, and in this case, count nouns.

Glad to see you are getting the point.

And definite articles are also used with nouns that does not make them nouns.

The problem is that I find no definition anywhere that says numbers are count nouns- I find numbers as number names, as nouns, as adjectives and as abstracta and concreta- but nowhere can I find your use of count nouns. The only use of count nouns I can find is to do with the grammatical number of nouns and not "number names". Unlike you, I try to give the benefit of the doubt that perhaps there is some difference in nomenclature between languages but I am not convinced by your argument to be honest.

Count nouns are, from everything I have found, mereley the countable (in contrast to uncountable/mass) nouns found in languages but particularly so in English.

Furthermore a count noun is a count noun in that it may be modified by a "numeral" i.e. number name- but these number names are not count nouns themselves.

In addition to this these number names with little modification or none in English also serve as adjectives.

So, Rosa- please explain your theory and the terms you are using that underpin your argument yet don't seem to correspond to anything that can, as of yet, be verified.

Rosa Lichtenstein

28th March 2011, 01:01

CM:

And definite articles are also used with nouns that does not make them nouns.

Eh, what are you on about now?
The point is that these number words, which you rightly call adjectives, qualify nouns -- and that makes those nouns (not those adjectives!) into count nouns. This is quite simple, even for a novice to grasp.

The problem is that I find no definition anywhere that says numbers are count nouns-

Where did I say they were!

I find numbers as number names, as nouns, as adjectives and as abstracta and concreta- but nowhere can I find your use of count nouns. The only use of count nouns I can find is to do with the grammatical number of nouns and not "number names". Unlike you, I try to give the benefit of the doubt that perhaps there is some difference in nomenclature between languages but I am not convinced by your argument to be honest.

All wasted effort since you plainly can't read.

Count nouns are, from everything I have found, merely the countable (in contrast to uncountable/mass) nouns found in languages but particularly so in English.

Who counts count nouns? Have you ever counted nouns? No, and neither have I.

But, you use count nouns (explicitly, or implicitly) when you count things, as I have explained several times (looks like I might as well have been talking to the cat, for all the good it did!), as in one (adjective) apple (count noun), two apples, three apples, etc.

Furthermore a count noun is a count noun in that it may be modified by a "numeral" i.e. number name- but these number names are not count nouns themselves.

Again, who said they were?

In addition to this these number names with little modification or none in English also serve as adjectives.

Indeed.

So, Rosa- please explain your theory

I don't have a theory, nor do I want one, as you have been told many times -- here Kitty, Kitty... http://serve.mysmiley.net/animals/animal0048.gif

and the terms you are using that underpin your argument yet don't seem to correspond to anything that can, as of yet, be verified.

That's because you just don't pay attention.

ComradeMan

28th March 2011, 01:19

CM:
Eh, what are you on about now?
The point is that these number words, which you rightly call adjectives, qualify nouns -- and that makes those nouns (not those adjectives!) into count nouns. This is quite simple, even for a novice to grasp..

But.... numbers are also nouns in their own right without being adjectives.

I'm not sure either about your interpretation either. So what? If I say "two cats" there's nothing strange here at all- we have the adjective two describing how many, i.e. quantity, of cats.

Cat(s) is a count noun anyway- even if I say "Look at that cat!"- cat remains a count noun despite the absence of number adjectives.

As for the rest of your bullshit...

"countable" and "uncountable" are grammatical terms- it seems now you can suddenly apply one of your many interpretations of definitions- unlike of course imaginary numbers and real numbers. The same person who can talk about "anti-philosphers" and "empty" words.

In linguistics (http://www.revleft.org/wiki/Linguistics), a count noun (also countable noun) is a common noun (http://www.revleft.org/wiki/Common_noun) that can be modified by a numeral (http://www.revleft.org/wiki/Number_names) and that occurs in both singular (http://www.revleft.org/wiki/Grammatical_number) and plural (http://www.revleft.org/wiki/Plural) form, as well as co-occurring with quantificational determiners (http://www.revleft.org/wiki/Determiner_(linguistics)) like every, each, several, etc. A mass noun (http://www.revleft.org/wiki/Mass_noun) has none of these properties. It can't be modified by a numeral, occur in singular/plural or co-occur with the relevant kind of determiner.
http://en.wikipedia.org/wiki/Count_noun

http://grammar.ccc.commnet.edu/grammar/noncount.htm

And you have the gall to accuse others of being mystics.

Your whole argument depends not on the actual content or factual material of your ideas but rather third-rate undergraduate sophistry and picking at words- with which you are not consistant.

Now, all I can gather from your bizarre notions is that you seem to think that words are somehow autological per se, that count nouns/countable nouns, de facto refer to some quality of that which they describe- well that seems to be a rather dilettante error. Money is a non-count/mass noun.... Have you never counted money? :laugh: Your confusing grammatical terminology and guilty of what you falsely accused me of doing regarding mathematical terms.

It still doesn't change the fact that number names are nouns, not count nouns as far as I can see, and also adjectives used in abstracta or concreta contexts.

The only possible way out of this for your argument would be if we take a phrase like

"Two sevens are fourteen" - two times/mulitplied by seven equals fourteen.

However I am by no means certain that this is applicable to all languages- certainly not in Italian.

Rosa Lichtenstein

28th March 2011, 01:56

CM:

But.... numbers are also nouns in their own right without being adjectives.

But when we count them, it's only the word "number" that is a count noun, as in one (adjective) number (count noun), two numbers, three numbers, etc.

Unless, of course, you had something else in mind.

I'm not sure either about your interpretation either. So what? If I say "two cats" there's nothing strange here at all- we have the adjective two describing how many, i.e. quantity, of cats.

Cat(s) is a count noun anyway- even if I say "Look at that cat!"- cat remains a count noun despite the absence of number adjectives.

So, you do agree with my 'interpretation'? In fact, I knew you did even before we began this debate; your every day use of number language tells even you that you do.

And sure, count nouns are still count nouns even when we do not use them to count, or attach number words to them. Whatever gave you the idea I disagreed with this?

As for the rest of your bullshit...

Oh dear, have I been quoting you again?

"countable" and "uncountable" are grammatical terms- it seems now you can suddenly apply one of your many interpretations of definitions- unlike of course imaginary numbers and real numbers. The same person who can talk about "anti-philosophers" and "empty" words.

What are you blathering on about now? Are you high on something?

Looks like you are:

In linguistics, a count noun (also countable noun) is a common noun that can be modified by a numeral and that occurs in both singular and plural form, as well as co-occurring with quantificational determiners like every, each, several, etc. A mass noun has none of these properties. It can't be modified by a numeral, occur in singular/plural or co-occur with the relevant kind of determiner.
http://en.wikipedia.org/wiki/Count_noun

http://grammar.ccc.commnet.edu/grammar/noncount.htm

And you have the gall to accuse others of being mystics.

And what has all that hastily 'researched' information (which shows I was right, and you weren't) got to do with calling anyone a 'mystic'?

Whatever it is that you are on, it's messing with your head.

Your whole argument depends not on the actual content or factual material of your ideas but rather third-rate undergraduate sophistry and picking at words- with which you are not consistent.

Even if you are right, you still can't show I am wrong -- in fact, the more you post, the more even you can see I have been right all along.

Moreover, if my work is so poor, the fact that you can't show I am wrong suggests that you have yet to reach the dizzy heights of being 'third rate'.

[B]So, what's it like down there in the tenth rate area with all the other novices?

Now, all I can gather from your bizarre notions is that you seem to think that words are somehow autological per se,

And where have I argued that?

Yet more invention.

that count nouns/countable nouns, de facto refer to some quality of that which they describe-

Where have I said count nouns 'refer'?

well that seems to be a rather dilettante error.

Indeed it is, and it's your error, since I have never maintained this.

Yet more invention.

Money is a non-count/mass noun.... Have you never counted money?

You asked me this several posts ago. May I refer you back to my earlier answer (which you plainly did not read)?

You're confusing grammatical terminology and guilty of what you falsely accused me of doing regarding mathematical terms.

Except, that conclusion of yours is based on several inventions of your own befuddled brain, not on anything I have argued or said.

It still doesn't change the fact that number names are nouns, not count nouns as far as I can see, and also adjectives used in abstracta or concreta contexts.

1. You have already called them count nouns, above.:rolleyes:

2. You have yet to tell us what these odd words -- 'abstracta' and 'concreta' -- actually mean.

The only possible way out of this for your argument would be if we take a phrase like

"Two sevens are fourteen" - two times/multiplied by seven equals fourteen.

I have already told you what sentences like these are -- go back and re-read my posts, but with more care this time.

However I am by no means certain that this is applicable to all languages- certainly not in Italian.

So?

And we are still waiting for your monumentally important 'logical proof' that there is such a thing as the 'mind'.

ComradeMan

28th March 2011, 09:29

Rosa- you can't take facts and use them to suit your theory. That's what you do...

You've been intellectually dishonest throughout this discussion and when challenged to defend your points or explain them you've either come out with nothing or resorted to ad hominem attacks and circular reasoning.

Your ad nauseam- "I've already explained this"--- "You don't know what x is" is type arguments along with your quibbling about the use of words, when there is no quibble to be had just show you up for being a pseudo-intellectual with an inferiority complex about something.

Rosa Lichtenstein

28th March 2011, 10:16

CM:

Rosa- you can't take facts and use them to suit your theory.

1. I don't have a theory, nor do I want one.

2. You have yet to quote any facts that do not conform to what I have alleged about numbers

That's what you do...

In fact, what you do is post lies.

You've been intellectually dishonest throughout this discussion and when challenged to defend your points or explain them you've either come out with nothing or resorted to ad hominem attacks and circular reasoning.

That's a bit rich coming from someone who confuses "ad hominem" with "abuse", and who posts circular definitions.

Your ad nauseam- "I've already explained this"---

Your pretentious use of Latin phrases...

"You don't know what x is" is type arguments

And they will continue until you tell us what 'abstract objects', for example, are.

along with your quibbling about the use of words,

Where have I 'quibbled' over the use of words? All I have done is ask you for weeks to explain yourself -- which you either won't do, or can't do.

when there is no quibble to be had just show you up for being a pseudo-intellectual with an inferiority complex about something.

Indeed, I feel inferior to you in posting lies.

And we are still waiting for your epoch making 'logical proof' that there is such a thing as the 'mind'.

ComradeMan

28th March 2011, 11:52

CM:

1. I don't have a theory, nor do I want one.

2. You have yet to quote any facts that do not conform to what I have alleged about numbers .

According to you and your muddled reasoning. I notice you "allege" things now- why? Are numbers in court? Is there an accusation against them?

In fact, what you do is post lies..

Stop name-calling and grow up. Your hyperbole is befitting of a Moscow Show Trial. Everytime someone disagrees with you or posts material that may challenge your points it is not that they are posting lies- FFS! How old are you?

That's a bit rich coming from someone who confuses "ad hominem" with "abuse", and who posts circular definitions...

Err.... according to whom? Oh... I forgot.... YOU, more circular argumentation.

Abuse per se is not an ad hominem but when abuse is used to deride the opponent and win an argument it is a direct ad hominem or ad personam. All of your name-calling in order to poison the well of discussion, accusing people of being ignorant and novices etc etc falls into this category. I suggest you read to the bottom of the wikipedia entries/pages in future. :lol:

Your pretentious use of Latin phrases...

Err... sorry, but those are the terms and they are derived from Latin, nothing pretentious there. You're just showing more ignorance here I am afraid. Ignorantiam hoc ostendis itaque doleo.:lol:- some bad Latin for you there so you can feel rightiously full of indignation.

The fact that the way you respond in discussions is so full of classical, formal and informal errors of logic in debate doesn't help your case, definitional retreats and extensional pruning, quibbling over enthymemes, refuting examples,

But wait- this is a classic...

Even if you are right, you still can't show I am wrong -- in fact, the more you post, the more even you can see I have been right all along....

Argumentum ad ignorantiam

If ever there was a more pathetic comment- befitting of a fundamentalist Christian to be honest.

Rosa Lichtenstein

28th March 2011, 15:15

CM:

According to you and your muddled reasoning.

Well, you are welcome to try to show I have a theory. [Some hope! You have difficulty telling the difference between 'ad hominem' and abuse, and a syllogism from an identity statement!]

I notice you "allege" things now- why? Are numbers in court? Is there an accusation against them?

So, it's Ok for you to do this sort of thing now, eh:

your quibbling about the use of words

From your post, here (http://www.revleft.com/vb/showpost.php?p=2061178&postcount=159).

And you plainly have a limited grasp of the many uses of the English word "allege", which word we can now add to the ever-lengthening list of words you seem not to understand -- like "number", "counting", "empty", "decision", "reality", "humanity" and "education".

That under-used dictionary of yours must be buried under a pile of dust and cobwebs by now.

Stop name-calling...

I will when you show you stop posting lies, and you demonstrate you are no longer a novice.

and grow up

What, and do something you can't do?

Ok.:)

Your hyperbole is befitting of a Moscow Show Trial.

I've told you a million times, I never use hyperbole.

Everytime someone disagrees with you or posts material that may challenge your points it is not that they are posting lies- FFS! How old are you?

Once again, do you deny you posted the following lies about me?

Well, you made up these accusations (among others): that I thought numbers were abstract objects, that I was using linguistics, that I had confused numbers with numerals (we are still waiting for you to cite a single quotation from my posts that even so much as hints at this), that I had used definitions when I haven't, that I had defined "information" when I haven't even tried to do so, that I had an ontology when you had been told several times I reject all ontologies as non-sensical (and then it turned out you were trying to foist one on us), that I had referred to 'language universals' when I hadn't, that I had made certain allegations about "the logical non-existence of the mind" when I hadn't, and then that "most" of my argument rests on "inverted commas", when it doesn't (and you failed to say how you had arrived at that fabrication), and so on. [Links provided on request.]

In which case, we must now add the phrase "making up anything" to the words "number" and "language" with which you seem to be struggling.

And you have continued to make then since; here is the latest batch from your last but one post:

If you use arguments that come from that side of the playing field then so be it

But which arguments of mine "come from that side of the playing field" -- that is, from the logical positivist side?

You have failed to say -- so this is yet another baseless allegation/fib of yours.

You are the person who seems to feel the mind does not exist, that would be pretty much a denial of the mind, wouldn't it?

For the tenth time, where have I denied the existence of 'the mind'? And where have I been involved in a "denial of the mind"?

Yet more fibs.

Yet strangely in another thread here at RevLeft you were talking about inner minds etc....

Where did I do this? I note, yet again, you neglected to provide the link.

One more fib to add to the growing list.

The above is just a small sample of some of your more recent lies.

How old are you?

Oh, I don't think I know you well enough to tell you, you naughty boy.http://serve.mysmiley.net/love/love0067.gif

Err.... according to whom? Oh... I forgot.... YOU, more circular argumentation.

That's a bit rich coming from you, with your circular 'definitions'.

Abuse per se is not an ad hominem but when abuse is used to deride the opponent and win an argument it is a direct ad hominem or ad personam. All of your name-calling in order to poison the well of discussion, accusing people of being ignorant and novices etc falls into this category. I suggest you read to the bottom of the wikipedia entries/pages in future.

Looks like you are determined to prove my accusation that you are a novice is indeed correct -- you still do not seem to know what "ad hominem" means.

And the list just keeps on growing...

Err... sorry, but those are the terms and they are derived from Latin, nothing pretentious there.

Add one more to that list, you plainly do not know what "pretentious" means, either.

You're just showing more ignorance here I am afraid.

Indeed, I'm totally ignorant of what your next screw up will be.:confused:

But, I'm sure you'll clear that up presently.

Ignorantiam hoc ostendis itaque doleo.- some bad Latin for you there so you can feel [righteously] full of indignation.

Pretention taken to the next level. Nice one!:thumbup1:

The fact that the way you respond in discussions is so full of classical, formal and informal errors of logic in debate doesn't help your case, definitional retreats and extensional pruning, quibbling over enthymemes, refuting examples,

Yet more baseless allegations unsupported by even so much as a single quotation from my posts.:lol:

Argumentum ad ignorantiam

Pretentious, eh?

If ever there was a more pathetic comment-

Indeed there is, and we can always rely on you to supply endless examples. Cheers!

befitting of a fundamentalist Christian to be honest.

A confirmed liar like you, honest? Pull the other one...

ComradeMan

28th March 2011, 16:51

You've actually said nothing other than more logically fallacious argumentation, tu quoque and your usual string of fallacies and ad hominem attacks.

Basically your whole line of argument is "You are wrong because I don't agree with you!"-

A confirmed liar like you, honest? Pull the other one...

Why do you have to be so obnoxious and insulting? A confirmed liar, by the way,--- LOL!!! Can a liar be confirmed? And what if the liar told the truth....? Running into a bit of a paradox here... :laugh: Or should I say you walked right into it.

Now, why is it okay for you constantly to question every last damn word or definition and insist only on your own narrow views- that support your argument and yet when challenged to practise what you preach you suddenly retreat?

Then you play the victim all the damn time. One only has to key in Rosa Lichtenstein and/or Antithesis Cloner to find that you leave a trail of flamewars and bad feeling all over the Internet. Different people, different places but one always gets the feeling of deja vu reading through threads in which you are involved. Why is that? :laugh:

Now, stop insulting people all the time and being an obnoxious child or otherwise no one will ever listen to you- and what good will that do your anti-dialects? LOL!!!

All of your bullshit "you plainly don't know what xyz means"- ad nauseam as a poisoning the well tactic.

Now, far be it from me to bring educational background into the argument but seeing as you feel free to do so, allow me- I have studied rhetoric and linguistics, both of which were a major part of my degrees and also have a good background in Latin, less so Greek- whatever- I can see through your bullshit rhetorical trickery and word games straight away. All of this blinding with science to push forward your anti-dialectic political agenda to the detriments of any kind of discourse or civilised debate.

Rosa Lichtenstein

28th March 2011, 19:20

CM:

You've actually said nothing other than more logically fallacious argumentation,

Which you have yet to show are 'fallacious'. And a novice like you has no room to lecture us about logic; after all, you tried to con us with the claim that "A=A" is a syllogism.

tu quoque

You do it. If so, why can't I?

and your usual string of fallacies and ad hominem attacks.

Well, we already know you have confused "ad hominem" with "abuse".

Basically your whole line of argument is "You are wrong because I don't agree with you!"

Yet another baseless allegation for which you supply no evidence.

Why do you have to be so obnoxious and insulting?

Why do you post lies all the time?

A confirmed liar, by the way,--- LOL!!! Can a liar be confirmed? And what if the liar told the truth....? Running into a bit of a paradox here...

Yet another word to add to the ever-lengthening list of words over which you struggle: "number", "counting", "empty", "decision", "reality", "humanity", "ad hominem", "education", "pretentious" and now "confirmed".

Or should I say you walked right into it.

Say what you like -- few here will be able to follow you anyway.

Ah, here comes another set of lies, further confirming your status as a serial fabulist:

Now, why is it okay for you constantly to question every last damn word or definition and insist only on your own narrow views- that support your argument and yet when challenged to practise what you preach you suddenly retreat?

Where have I "question[ed] every last damn word or definition"?

Perhaps you mean those circular definitions you tried to palm us off with a few days ago? You have posted no other 'definitions', as far as I can recall.

and insist only on your own narrow views

Where have I 'insisted' on anything? In fact, you are the only one here who has done that.

that support your argument and yet when challenged to practise what you preach you suddenly retreat?

Where have I 'retreated'?

So, that's another three lies to add to the list I posted earlier.

Then you play the victim all the damn time.

Not so; I took five minutes off yesterday.:)

You don't seem to be able to get anything right do you?:(

But, don't give in! I'm sure you'll get something right one day...:)

Not sure when..., but at least I have faith in you.

One only has to key in Rosa Lichtenstein and/or Antithesis Cloner to find that you leave a trail of flamewars and bad feeling all over the Internet.

I have just 'keyed in' "Antithesis Cloner", and not one mention of little old me came up!

So, it seems you are still lost in that fantasy world of your own making.

No worries, while there you are no danger to anyone -- other than yourself, of course.

Different people, different places but one always gets the feeling of deja vu reading through threads in which you are involved.

Stop reading them then.

Why is that?

Well, I know you regard me as the fountainhead of all knowledge -- in view of the fact that you keep asking me stuff -- but some things you will just have to work out for yourself.:)

[Who knows? It might help speed up the day when you actually get something right. You know I'm rooting for you!]

Now, stop insulting people all the time

Wrong again! I had 3 minutes off last Saturday.

So, the wait goes on until the day when you get something right...

and being an obnoxious child

Cheek! I'm nothing like you.

or otherwise no one will ever listen to you- and what good will that do your anti-dialects? LOL!!!

Wrong again, scores of comrades 'listen' to me.

And the wait goes on...:(

All of your bullshit "you plainly don't know what xyz means"- ad nauseam as a poisoning the well tactic.

In fact, there's not even a well for me to [i]try to poison, and there won't be until you tell us what you mean by 'abstract object', 'numerosity' and 'numerical cognisance'.

Unless, of course, you are using "well" in a new and-as-yet-unexplained sense. If so, what is it?

Now, far be it from me to bring educational background into the argument but seeing as you feel free to do so, allow me- I have studied rhetoric and linguistics, both of which were a major part of my degrees and also have a good background in Latin, less so Greek- whatever- I can see through your bullshit rhetorical trickery and word games straight away. All of this blinding with science to push forward your anti-dialectic political agenda to the detriments of any kind of discourse or civilised debate.

Is that where a novice like you learnt the 'civilised' word "bullshit"?