Mathmatics.

[BurnTheOliveTree]

I've just been reading Stephen Law's Philosophy Gym, I don't what you guys think about him, but anyway.

There's a chapter in it called "The curious realm of numbers". It's a fictional debate about whether maths is an objective sphere of knowledge or a human construct. It has absolutely bamboozled me. I can't even get a grip on the subject, it just seems to elude me utterly.


I need help! :( Is maths a stand alone 'thing' or an invention. Bring me some of that sweet clarity.

-Alex

P.S. Or, is the question a meaningless one based on misuse of language? (I'm getting there, Rosa.)

[Eleutherios]

It is not a "human construct". Mathematics is simply the rules of logic applied to quantities. Quantities exist, and they consist of things that follow the rules of logic. True, you can't reach out and touch math, but that doesn't mean it's a human construct. The same is true of spatial dimensions and gravity, and yet I don't hear anybody claiming those are human constructs.

[hoopla]

Empirical isn't it., Thats my guess at the moment.

[hoopla]

Originally posted by [email protected] 21, 2007 08:54 pm
It is not a "human construct". Mathematics is simply the rules of logic applied to quantities. Quantities exist, and they consist of things that follow the rules of logic. True, you can't reach out and touch math, but that doesn't mean it's a human construct. The same is true of spatial dimensions and gravity, and yet I don't hear anybody claiming those are human constructs.
Logicism is unfancied I hear.

[hoopla]

(I&#39;m getting there, Rosa.)I&#39;m sure she&#39;s very happy <3

;)

[Rosa Lichtenstein]

Burn, I only saw this late at night; I&#39;ll try and respond tomorrow&#33;

[BurnTheOliveTree]

Hoopla, I really have difficulty understanding you, I must admit. Remember I&#39;m a total layman of philosophy, I only have a vague understanding of what "Empiricism" even is.

Try and accomodate the less educated? :o

-Alex

[ComradeRed]

Logic applied to quantity may very well lead to math, I&#39;m too tired to debate that; but two questions come to mind: is Logic a priori? And is quantity a postereori? :huh:

Think about it...

And (for BurnTheOliveBranch) I&#39;m no philosopher (and I don&#39;t play one on TV), but the simple version to differentiate the a priori from the a postereori is such:
* Tautologies are a priori.
* Everything else is a postereori.
Or perhaps more accurately (from wikipedia):
"Rough and oversimplified explanations are as follows: a priori knowledge is independent of experience, while a posteriori knowledge is dependent on experience."

[The Feral Underclass]

Originally posted by [email protected] 22, 2007 09:08 am
I only have a vague understanding of what "Empiricism" even is.
Empiricism is a tool in which to understand knowledge/truth.

Empiricism posits that all knowledge/truth can be understood through one&#39;s sense experience of reality.

[Rosa Lichtenstein]

Burn, mathematics arose out of humanity&#39;s attempt to grapple with features of interest to us: the repetitive re-appearance of various items we could describe with the same general terms, like &#39;dog&#39;, or &#39;horse&#39; or "axe".

Number applies to these; so you have "3 dogs" or "5 horses", etc. Human beings invented rules for handling the new words they invented for recording the repetitive counting of such items (gathered together under the same general word).

So, mathematics originally arose as a set of practical rules for such activities (and not just for counting).

It was later mystified, and then applied to an ideal world (by Plato), so that its &#39;truths&#39; supposedly revealed to us a priori or ideal facts about unseen objects inaccessible to the senses. This is the most widely accepted view (and is thus part of the &#39;ruling ideas&#39; that always rule).

So, the a priori approach to mathematics mirrors the a priori approach to &#39;knowledege&#39; (that you have seen me criticise in other threads) -- both originating from the same source: the aim of ruling-class theorists to convince the rest of us that the material world is not fully real, but needs an ideal superstructure (or &#39;essence&#39;) to give it substantiality.

So, materialistically interpreted, mathematics is just a system of rules (and general terms) that human beings have developed over the centuries, and since rules cannot be either true or false, the terms &#39;a priori&#39; and &#39;a posteriori&#39; cannot apply to them. Mathematics does not deliver a superior form of knowledge, it merely records the intricate connections (that proofs have sanctioned) between the many rules (and terms of art) we have invented over the centuries.

This is a summary of Wittgenstein&#39;s approach to this topic, his most original contribution to &#39;Philosophy&#39;.

Naturally, this can be explicated in great detail, but that would be inappropriate here.

Check these out:

http://en.wikipedia.org/wiki/Ludwig_Wittgenstein

http://www.iep.utm.edu/w/wittgens.htm

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

http://www.phil.uni-passau.de/dlwg/ws03/08-1-95.txt

http://www.people.ex.ac.uk/PErnest/soccon.htm

[But the last 2/3rds of the latter.]

[BurnTheOliveTree]

So basically a bit of both, but practical rather than the superior, platonic view? That about right?

-Alex

[Rosa Lichtenstein]

A &#39;bit of both&#39; what?

[BurnTheOliveTree]

It&#39;s a human construct, but a legitimate one.

-Alex

[Rosa Lichtenstein]

Correct.

[BurnTheOliveTree]

Phew. I think I may have wept if I needed to be corrected again.

-Alex

[Ol' Dirty]

Mathematics is the study of quantities (keyword being study), so,as a sentient/sapient mind is required in the definition, it is a non-constant construct of the [sentient] mind. It&#39;s just like god and race in that is abstract and amaterial.

[Rosa Lichtenstein]

Muigwithania, I am sorry, but that is as clear as mud.

[Ol' Dirty]

Originally posted by Rosa [email protected] 23, 2007 04:23 am
Muigwithania, I am sorry, but that is as clear as mud.
Oh, sorry.

Um... Would you like for me to clarify this for you?

[RevMARKSman]

Originally posted by [email protected] 22, 2007 02:00 pm
It&#39;s a human construct, but a legitimate one.

-Alex
Well if you add
...
to
..

you will still get
.....
no matter what we call those quantities. So I guess the whole 1, 2, 3, etc. and decimal systems are our own, but the basic principles of algebra, geometry and calculus are there without us.

[RebelDog]

How could mathematics possibly be a human concept? Aliens must have pi (3.14) also.

[ComradeRed]

Originally posted by The [email protected] 23, 2007 01:07 pm
How could mathematics possibly be a human concept? Aliens must have pi (3.14) also.
Well, the argument here is this: is math something invented (like a language or something) or discovered (it&#39;s hiding under a rock somewhere or something)?

Well, you may say "Sure, suppose most of it is invented; but what about geometry&#33;"

Well, good question.

A dot is a human construct. That&#39;s life. It&#39;s an element of the R^n tuple for n-dimensional space. From a dot you can get two dots. From two dots, you get the definition of a line; which is an artificial construct dating back to Euclid in the Western tradition.

From a line and a dot, you get a plane; which is also a human construct. From a plane and a dot you get a space.

All of these were created by humans.

Now what you do with it is manipulations of the given definitions, e.g. creating shapes, finding the ratios of the parameter to the edge, whatever. That&#39;s all human manipulation. That&#39;s life.

[Raúl Duke]

When I first saw this thread I though it was about the "philosophy" in Math...but its more about whether its external from us or created by us. oh well (any way, if they were to discuss any philosophy in math I would surely get lost)


the aim of ruling-class theorists to convince the rest of us that the material world is not fully real, but needs an ideal superstructure (or &#39;essence&#39;) to give it substantiality.

Why does this remind me of solipsism and religion ("ideal essence" kinda reminds me of god in judeo-christian religions, which represents somewhat a human ideal, specially in christianity where all the believers which to behave like how jesus wanted&#33;) I suppose maybe thats why Rosa keeps calling DM mysticism....

(On a side note, philosophy is difficult, maybe I should just abandon it. Maybe its not worth my time&#33;)

[Ol' Dirty]

Originally posted by [email protected] 23, 2007 06:05 pm
When I first saw this thread I though it was about the "philosophy" in Math...but its more about whether its external from us or created by us. oh well (any way, if they were to discuss any philosophy in math I would surely get lost)


the aim of ruling-class theorists to convince the rest of us that the material world is not fully real, but needs an ideal superstructure (or &#39;essence&#39;) to give it substantiality.

Why does this remind me of solipsism and religion ("ideal essence" kinda reminds me of god in judeo-christian religions, which represents somewhat a human ideal, specially in christianity where all the believers which to behave like how jesus wanted&#33;) I suppose maybe thats why Rosa keeps calling DM mysticism....

(On a side note, philosophy is difficult, maybe I should just abandon it. Maybe its not worth my time&#33;)
Don&#39;t worry, dude. You&#39;re fine

Keep up the good work.

[ComradeRed]

(On a side note, philosophy is difficult, maybe I should just abandon it. Maybe its not worth my time&#33;) Giving up philosophy is a good idea; there are better things to do with your time.

[Rosa Lichtenstein]

Dissenter:


How could mathematics possibly be a human concept? Aliens must have pi (3.14) also.

No one said it was only a human construct; if there are &#39;aliens&#39; and they do mathematics, they will have invented it too -- even if it is not like ours.

Unless, perhaps, you think it is a &#39;gift of the gods&#39;?

[Your argument is like: how can class society be a human invention? If there are aliens, they too will have classes (at some point in their history).]

[Rosa Lichtenstein]

Muigwithania:


Would you like for me to clarify this for you?

I&#39;d have thought you yourself would want to be clear, without worrying about me.

But, if it takes my prompting: yes, go ahead and expain this to us clearly.

[Rosa Lichtenstein]

Rev M:


Well if you add
...
to
..

you will still get
.....
no matter what we call those quantities. So I guess the whole 1, 2, 3, etc. and decimal systems are our own, but the basic principles of algebra, geometry and calculus are there without us.


But, if you add these: "....." to "........" (i.e., 5 + 8, you get 1 (if these &#39;quantities&#39; are hours on a clock; 5 o&#39;clock plus 8 hours is 1 o&#39;clock). There are many other examples.

So, the rules you assume to be eternal, depend on context, and, indeed, on what you are counting (and also upon what you consider &#39;addition&#39; to be). None of these are given to us by &#39;nature&#39;.

You say they are &#39;there&#39;, without us; but where are they? And how do we interact with them (if they are not material)?

[You need to read Frege on this, whose work, overnight, made &#39;theories&#39; like yours obsolete.]

[Rosa Lichtenstein]

Johnny Darko:


Why does this remind me of solipsism and religion ("ideal essence" kinda reminds me of god in judeo-christian religions, which represents somewhat a human ideal, specially in christianity where all the believers which to behave like how jesus wanted&#33;) I suppose maybe thats why Rosa keeps calling DM mysticism....

Exactly&#33;

These Idealist theories have one source: the need for the ruling class to persuade us that this material world is not fully real, or not enough in its own, or unreal -- so they can then impose their a priori state forms on us, and legitimate their power (since it is &#39;ordained of the gods&#39;, or is &#39;there&#39; and is thus &#39;natural&#39;, and we must just accept it, blah, blah).

The ruling ideas are always those of the ruling class.

No less so in mathematics (as it is generally sold to us).

[RebelDog]

Unless, perhaps, you think it is a &#39;gift of the gods&#39;?

Yes I think maths was given to us by Odin as a thank-you for not worshiping him anymore.


No one said it was only a human construct; if there are &#39;aliens&#39; and they do mathematics, they will have invented it too -- even if it is not like ours.

You acknowledge that if they are aliens and they &#39;do mathematics&#39; then they will have &#39;invented&#39; it too. Surely they would &#39;invent&#39; it for necessity, ie, to help plan production and calculate orbits etc, for space travel? Quantities, and systems to understand them, are vital to intelligent beings to survive and better exploit nature.

I can understand the ruling class thing, ie; those who stood back from crop production and took jobs counting and planning the harvest basically starting the seed of a ruling class. Mathematics helped them enforce their position but it also aided production.

What would mathematics look like in a future communist society?


[Your argument is like: how can class society be a human invention? If there are aliens, they too will have classes (at some point in their history).]

In the limited design space of our universe I would imagine any intelligent beings who survive long enough will have shades of our history in theirs, yes.

[Rosa Lichtenstein]

Dissenter:


Yes I think maths was given to us by Odin as a thank-you for not worshiping him anymore..

Sorry, it was the great God Mugumba, of the Amazon Splinge tribe, who really pased it on to us -- and he did so for ignoring the pseudo-mathematics of the Odinists.


You acknowledge that if they are aliens and they &#39;do mathematics&#39; then they will have &#39;invented&#39; it too. Surely they would &#39;invent&#39; it for necessity, ie, to help plan production and calculate orbits etc, for space travel? Quantities, and systems to understand them, are vital to intelligent beings to survive and better exploit nature.

Whatever it was invented for, and by whom, mathematics was invented and not discovered.

I am not sure what the word &#39;necessity&#39; is doing here, though.


What would mathematics look like in a future communist society?

Not very different, except it won&#39;t be mystified (a la Penrose, for example).


In the limited design space of our universe I would imagine any intelligent beings who survive long enough will have shades of our history in theirs, yes.

Well, exactly; so mathematics is part of our history, just as it would be a part of theirs -- but, not part of an ideal world that lies behind the material universe.

[RebelDog]

Sorry, it was the great God Mugumba, of the Amazon Splinge tribe, who really pased it on to us -- and he did so for ignoring the pseudo-mathematics of the Odinists.


I reject your god, let the all powerful Odin smite him. I expect he will work out mathematically how much smite to use.



I am not sure what the word &#39;necessity&#39; is doing here, though.

It is surely critical for intelligent lifeforms to derive greater and greater yields of food from nature to have ways of counting, forecasting, etc.
There must be ways of describing a material universe that all observers could theoretically agree if they have the technology and knowledge, for example mathematics.


Well, exactly; so mathematics is part of our history, just as it would be a part of theirs -- but, not part of an ideal world that lies behind the material universe.

Do you mean that mathematics cannot describe the material universe?

[Rosa Lichtenstein]

D:

I
reject your god, let the all powerful Odin smite him. I expect he will work out mathematically how much smite to use.

Too late, Mugumba has already organised a strike and massed secondary picketting of Odin&#39;s heavenly residence.

The might (and mathematical superiority) of the inter-galactic working-class gods, will put paid to him.


It is surely critical for intelligent lifeforms to derive greater and greater yields of food from nature to have ways of counting, forecasting, etc.

It is certainly necessary for this, but I was asking about your use of the word &#39;necessity&#39;.

If you were merely using it in its everyday sense (as I am in the above sentence), then no problem.

But this word is often used in relation to mathematics in a Platonic sense.


There must be ways of describing a material universe that all observers could theoretically agree if they have the technology and knowledge, for example mathematics.

Human observers certainly; we cannot speak about aliens until we know more about them.


Do you mean that mathematics cannot describe the material universe?

Mathematics is not desrciptive, but normative. It is a system of rules we use to balance the books (among other things).

[By &#39;balance the books, I do not wish to restrict mathematcis to book-keeping; this is a term of art we use in philosophy to depict out attempt to make sense of nature numerically and quantitatively.]

[RebelDog]

Too late, Mugumba has already organised a strike and massed secondary picketting of Odin&#39;s heavenly residence.

Then Odin, I fear is finished.



If you were merely using it in its everyday sense (as I am in the above sentence), then no problem.

The everyday sense, yes.


But this word is often used in relation to mathematics in a Platonic sense.

I&#39;m not familiar with its use in this context.


Human observers certainly; we cannot speak about aliens until we know more about them.

I think we can make certain &#39;assumptions&#39; (Odin forgive me for using that word) that intelligent life in this universe will have (constrained by the same physical laws as us, as they must be) developed mathematics as a necessity to progress. Mathematics would help all intelligent life in this universe develop better, more efficient ways of food production, transportation, architecture, population management etc, etc. The circle must be an important feature of this universe that is easily observable by all intelligent life, nomatter where. Surely the value of pi then manifests itself and we can agree on its value with other beings, in other areas of the universe.


Mathematics is not desrciptive, but normative. It is a system of rules we use to balance the books (among other things).

I could send you a mathematical paper to build a machine, wouldn&#39;t those mathematics &#39;describe&#39; the machine in mathematical language.

[Rosa Lichtenstein]

On Platonism, check this out:

http://en.wikipedia.org/wiki/Philosophy_of...atics#Platonism (http://en.wikipedia.org/wiki/Philosophy_of_mathematics#Platonism).


I think we can make certain &#39;assumptions&#39; (Odin forgive me for using that word) that intelligent life in this universe will have (constrained by the same physical laws as us, as they must be) developed mathematics as a necessity to progress. Mathematics would help all intelligent life in this universe develop better, more efficient ways of food production, transportation, architecture, population management etc, etc. The circle must be an important feature of this universe that is easily observable by all intelligent life, nomatter where. Surely the value of pi then manifests itself and we can agree on its value with other beings, in other areas of the universe.

Maybe so, but we cannot say how they appropriated these ideas, or how they made certain decisions.

[Our mathematics is full of these sorts of things (see below), something you do not hear about in standard histories of the subject. And these decisions determine the nature of the mathematical concepts we have developed.]

For example, if they never invented decimals, or the number zero, of it they had decided that concave polygons were not real polygons, or had used clock arithmetic, or had eschewed negative numbers (as human beings once used to), and a whole host of things we have decided because of contingencies in our own history -- their mathematics would be different from ours.

Recall, that nowhere in reality is there such a thing as a mathematical point, line, plane or curve (nor are there circles, matrices, vetors, scalars, cardinal numbers...). Even the planets, which move in elliptical orbits, do not move along real ellipses, since mathematical ellipses do not exist. Moreover, they cannot exist -- why? well, that&#39;s another story&#33;

These are all our inventions, made to help us make sense of nature in order to control it.


I could send you a mathematical paper to build a machine, wouldn&#39;t those mathematics &#39;describe&#39; the machine in mathematical language.

It would tell me the rules I&#39;d need to use in order to build it.

[Ol' Dirty]

Originally posted by Rosa [email protected] 24, 2007 07:53 am
Muigwithania:


Would you like for me to clarify this for you?

I&#39;d have thought you yourself would want to be clear, without worrying about me.

But, if it takes my prompting: yes, go ahead and expain this to us clearly.
Sorry. Are you mad? I... oh whatever.

Time is persons construct. Quantities are material, but math isn&#39;t.

That&#39;s basicaly what I said.

[RebelDog]

The platonism looks very interesting I&#39;ll give it a good hard look over.


For example, if they never invented decimals, or the number zero, of it they had decided that concave polygons were not real polygons, or had used clock arithmetic, or had eschewed negative numbers (as human beings once used to), and a whole host of things we have decided because of contingencies in our own history -- their mathematics would be different from ours.

But so what if these senarios did happen, it would only be a disaster, when, from that foundation, all further research, took place. We know from our own experience that many people develop ideas and concepts, right or wrong, at the same time. The wrong ones eventually should fall. You allude to that yourself when you say "as human beings once used to."


Recall, that nowhere in reality is there such a thing as a mathematical point, line, plane or curve (nor are there circles, matrices, vetors, scalars, cardinal numbers...). Even the planets, which move in elliptical orbits, do not move along real ellipses, since mathematical ellipses do not exist. Moreover, they cannot exist -- why? well, that&#39;s another story&#33;

I suppose we can observe imperfect circles in nature and &#39;theorise&#39; about perfect ones and agree with aliens on the value of pi to a certain decimal place. (What I just said reminds me how important the use of language is in phylosophy, I don&#39;t want to step on a semantic landmine, but inevitably I will)

[Rosa Lichtenstein]

D:


I suppose we can observe imperfect circles in nature and &#39;theorise&#39; about perfect ones and agree with aliens on the value of pi to a certain decimal place. (What I just said reminds me how important the use of language is in phylosophy, I don&#39;t want to step on a semantic landmine, but inevitably I will)

But, there is no such thing as a perfect circle, even in the imagination.

And pi is the result of the application of certain algebraic rules to a limiting process (i.e., successive approximations -- but to what? if these things do not exist&#33;) that we take to be consistent with other definitons we have of circles.

There is nothing in nature (or anywhere else) that says we have to do things this way.

We have simply chosen these things or own purposes.

[RebelDog]

When you say that a perfect circle cannot exist are you alluding to a indeterminant in nature which stops such perfection (ie quantum fluctuation), simply the natural forces acting on any circle or the apparent never ending re-evaluations of pi to ever more decimal places?


And pi is the result of the application of certain algebraic rules to a limiting process (i.e., successive approximations -- but to what? if these things do not exist&#33;) that we take to be consistent with other definitons we have of circles.


What is pi to a trillion more decimal places than is currently known moving toward then? What does it then better quantify than the previous number?
Did Karl Popper have a polemic of mathematics?

[ComradeRed]

Originally posted by Muigwithania+February 24, 2007 01:15 pm--> (Muigwithania @ February 24, 2007 01:15 pm)
Rosa [email protected] 24, 2007 07:53 am
Muigwithania:


Would you like for me to clarify this for you?

I&#39;d have thought you yourself would want to be clear, without worrying about me.

But, if it takes my prompting: yes, go ahead and expain this to us clearly.
Sorry. Are you mad? I... oh whatever.

Time is persons construct. Quantities are material, but math isn&#39;t.

That&#39;s basicaly what I said. [/b]
It&#39;s a different base system is Rosa&#39;s point.

Like saying 1+1=?

You say 2? Well my computer says 10. Which is right? Both answers are correct; you&#39;re answer is in base 10 (or any base greater than 2) and the computer&#39;s is in base 2 (you see 1*2^1 + 0*2^0 = 2 in base 10).

That&#39;s the basic point Rosa was making; a clock was the easiest way to do this since only nerds like me bother to learn binary.

[Rosa Lichtenstein]

D:


When you say that a perfect circle cannot exist are you alluding to a indeterminant in nature which stops such perfection (ie quantum fluctuation), simply the natural forces acting on any circle or the apparent never ending re-evaluations of pi to ever more decimal places?

No, it&#39;s because mathematical &#39;objects&#39; are not made of anything, they have no substance; lines have no thickness, but cannot be broken, and they are &#39;infinite&#39; in &#39;length&#39; (except we use lines to measure lines); points have no size at all; circles are made of curves that have no dimensions at all (except we say they have a dimension of &#39;one&#39;, by default), but whose curcumference is always a fixed distance from the central point, which cannot exist for the same reasons. None exist in time; they do not age, wear away or deteriorate.

So, it has nothing to do with quantum variation.


What is pi to a trillion more decimal places than is currently known moving toward then?

We only &#39;know&#39; this because of a computer calculation, which cannot be checked.

It is not moving toward anything, since it is not moving --, and there is no &#39;anything&#39; toward which it is &#39;moving&#39;.

Pi is merely the product of the indefinite working out of a rule that generates a series of numerals.


Did Karl Popper have a polemic of mathematics?

He certainly had his own views, which, fortunately, no one (except a few of his disciples) now bothers with.

[RebelDog]

None exist in time; they do not age, wear away or deteriorate.

Doesn&#39;t the photon fit that criterion.


We only &#39;know&#39; this because of a computer calculation, which cannot be checked.

You do not trust computers?


It is not moving toward anything, since it is not moving --, and there is no &#39;anything&#39; toward which it is &#39;moving&#39;.

That is just semantics. You know what I mean, don&#39;t act like a computer Rosa. It is better quantifying something, what is it?

[Rosa Lichtenstein]

D:


Doesn&#39;t the photon fit that criterion.

Photons exist in space and time; mathematical objects do not.

Photons, though, are theoretical objects, hence they are heavily constrained by the mathematics used to understand them.

Only in that sense is there a similarity.


You do not trust computers?

It&#39;s not a case of trusting, it is that mathematics is based on proof not empirical experiments (which is what a computer engages in).

If we have no proof in mathematics, then we cannot claim to &#39;know&#39;.


That is just semantics. You know what I mean, don&#39;t act like a computer Rosa. It is better quantifying something, what is it?

I wasn&#39;t being obtuse, it is that ever since Greek times we have used metaphors to depict mathematics, and these metaphors are then take literally (and bingo, you have Platonism).

So, in pure mathematics we speak of &#39;convergence&#39; and &#39;approaching&#39; a limit, and then we imagine that there is something empirical that we are getting closer to, when all we are doing is following a rule. We thus confuse mathematics with empirical science (or even with exploration).

Given my approach to philosophy, I try to be very careful over the use of words.

So, there was a reason for my comment.

[RebelDog]

Photons, though, are theoretical objects, hence they are heavily constrained by the mathematics used to understand them.

Do you think nuclear physicists view of a photon is skewed by the only real language they have of understanding its reality?


I wasn&#39;t being obtuse, it is that ever since Greek times we have used metaphors to depict mathematics, and these metaphors are then take literally (and bingo, you have Platonism).

I&#39;m sorry. You have to understand that I use them in their contemporary context.


So, in pure mathematics we speak of &#39;convergence&#39; and &#39;approaching&#39; a limit, and then we imagine that there is something empirical that we are getting closer to, when all we are doing is following a rule. We thus confuse mathematics with empirical science (or even with exploration).

I can grasp that. Observation is not the same as science, as Marx was fully aware.


Given my approach to philosophy, I try to be very careful over the use of words.

I think we all have to be careful in this respect but are we not in danger of reducing phylosophy to the definitions of words.

[Rosa Lichtenstein]

D:


Do you think nuclear physicists view of a photon is skewed by the only real language they have of understanding its reality?

We have as yet, a very poor understanding of the nature of scientific language; I hope to publish an Essay on this next year (since it is integral to my analyisis of metaphysics). If you&#39;ll forgive me, I won&#39;t say anything more on this now.


I think we all have to be careful in this respect but are we not in danger of reducing phylosophy to the definitions of words.

Quite, but I was referring to careful use of words, which is independent of definition (in most cases).

[Janus]

Math: Discovered or invented? (http://www.revleft.com/index.php?showtopic=47001&hl=)

[Raúl Duke]

Hey, someone mentioned how math would look in a communist society and someone responded with something like: "less mystified than it is now." (and than in the same sentence mentioned Penrose)

How much so is math mystified? If we got rid of this mystification, what implications would it have?

[Rosa Lichtenstein]

JD, this mystification does not affect the application of mathematics to the real world, just how it is regarded theoretically, and how it affects the interpretation of the more mathematical parts of Physics.

Cleared of mysticism, certain &#39;proofs&#39; in advanced number theory, set theory and the foundations of mathematics will either be jetisoned or be totally re-interpreted. For example, it is integral to Godel&#39;s infamous incompleteness &#39;proof&#39;, that infinite sets be interpreted Platonistically, that is, as completed entities. How an incomplete series can be regarded as complete is, of course, a mystery, but one Godel was happy to side-step because he believed mathematics was a science of discovery, not of invention, and since mathematicians are discovering things which already exist, there must already exist, for instance, a complete set of natural numbers.

[Liberal Kid]

Demystification of mathematics that sounds just a wee bit like fantasy.

But onto the discussion.

Mathematics descriptive or invented.

I&#39;d just say math was invented to describe behavior and leave it at that.

The question would be brought simply when newton (lets use the word found as a neutral word not referring to either discovered or invented for now) found calculus to describe gravity, was he inventing calculus or simply describing calculus.

Well partially Newton was wrong because he made the conjecture that gravity is instant which it isn&#39;t. Gravity moves at the speed of light, but thats general relativity and an entire other discussion. Now disregarding that Newton was partially wrong, Calculus describes gravity through derivatives and the like. A derivative is a mathematical concept so no it does not exist in nature exactly, but it can describe what occurs in nature.

But that question doesn&#39;t bother me so much because math is a vital part of our current society.
What bothers me more is zero.

Now the following proof was shown to us one day in class and we were supposed to find the error.

a=1 b=1

a=b
a^2=ab
a^2-b^2=ab-b^2
(a+b)(a-b)=b(a-b)
divide both sides by (a-b)*
a+b=b
2=1

Now the error is at the star, a=1 b=1 so 1-1=0. So therefore your dividing both sides by zero which makes the whole equation null, according to my teacher.

But at the same time the rest of me thinks, wait though you just got 2=1 from simple algebra. Generally simplification is not done until the end of the problem and I suppose that you are dividing by zero but something about this problem always screams flaw in math.

Anyway just curious for some feedback on that last equation.

[krakatoan]

I analized those equations, your teacher is right, you cannot divide by zero. Here is how I would explain it in an analogy:
50(0)=20(0)
they are equal because they are both zero, but you cannot divide to take out the zeroes, if you did you will have 50=20, which is not right.
If you divide by zero like in the equations you can make any two numbers or variables equal, but the thing is you can&#39;t divide by zero. Any number divided by zero is undefined.

[Rosa Lichtenstein]

Which, on its own, shows that mathematics has been invented, not discovered.

What would it mean to &#39;discover&#39; that dividing by zero is &#39;not defined&#39;?

By whom? &#39;God&#39;?

[JimFar]

Rosa wrote:


Cleared of mysticism, certain &#39;proofs&#39; in advanced number theory, set theory and the foundations of mathematics will either be jetisoned or be totally re-interpreted. For example, it is integral to Godel&#39;s infamous incompleteness &#39;proof&#39;, that infinite sets be interpreted Platonistically, that is a completed entities.

So Rosa, do you then subscribe to a constructivist (http://en.wikipedia.org/wiki/Constructivism_%28mathematics%29) philosophy of mathematics?

[Rosa Lichtenstein]

No -- and once more -- I subscribe to no philosophy of mathematics -- we do not need one (any more than we need other philosophies of X, Y or Z).

I do however subscribe to exposing the mysticism behind other &#39;philosophies&#39; of mathematics (along neo-Wittgensteinian lines).