Logic

[RebelDog]

I thought some of the members here might like to read this recent article from a science magazine.


CHRIS ISHAM has a problem with truth. And he suspects his fellow physicists do too. It is not their honesty he doubts, but their approach to understanding the nature of the universe, the laws that govern it and reality itself. Together with a small band of allies, Isham is wrestling with questions that lie at the very core of physics. Indeed they run even deeper, to such basic concepts as logic, existence and truth. What do they mean? Are they immutable? What lies beyond them?

After years of effort, Isham and his colleagues at Imperial College London and elsewhere believe they can glimpse the answers to these profound questions. They didn't set out to rethink such weighty issues. When they started nearly a decade ago, the researchers hoped to arrive at a quantum theory of the universe, an ambitious enough task in itself. Yet in the process they might have bagged something bigger.

For if their results stand up, Isham and his colleagues appear to have found a new way of making sense of reality using concepts even more fundamental than mathematics and logic. Not only could their insights be good news for quantum theory, they could lead to a whole new way of constructing theories of reality.

Since its emergence around a century ago, quantum theory has become one of the cornerstones of modern science. It underpins everything from the behaviour of quarks and semiconductors to the power of medical scanners. And it has passed virtually every test thrown at it, its predictions agreeing with experiment to many decimal places.

With a track record like that, quantum theory might seem ideal for casting light on the ultimate questions about the universe, such as why it exists at all. Not so. In fact, it runs into very big trouble very quickly, because quantum theory has a problem with truth.

With hindsight, perhaps this shouldn't be so surprising. Right from the start, quantum theory has had a reputation for giving odd answers to even seemingly simple questions. In the everyday world, everything has nice, clear-cut properties: people are either dead or alive, electrons either spin up or down. Yet according to quantum theory, what we're seeing is just one manifestation of a whole panoply of possibilities, all mixed together.

How all those possibilities turn into just the one reality we see has caused endless debate among theorists. Their efforts have produced various interpretations of quantum theory, the most famous of which is the Copenhagen interpretation, named in recognition of its inventor, the Danish quantum pioneer Niels Bohr. According to this view, it is the act of observing that triggers the panoply of possibilities to collapse down to the single reality we experience.

Quite how this collapse process works isn't exactly clear. What is plain is that it raises profound questions about the whole notion of truth in quantum theory. For it implies that it is impossible to know the truth of any statement about, say, an electron until it has been observed. Unless that happens, it doesn't really make sense to talk of the electron - or anything else for that matter - as being real.

Things get much worse when quantum theory is applied to the entire universe. If the universe is as real as we believe, then it must have been cast into that state by an observer able to view it all. Yet since the universe includes everything, there can be no external observer.

Theorists have come up with all kinds of alternative interpretations to avoid the problem, which others have in turn torn apart. Small wonder, perhaps, that most workaday physicists are happy to leave them to it. Alas that's just not an option for quantum cosmologists, who have to find some way of turning the cosmic cornucopia into the one real universe we actually inhabit.

But who says they have to? Perhaps we're reading quantum theory all wrong, and there is no need to force the universe or anything else into rude reality. Rethinking quantum theory is an appealing thought, not least because it would pull the quantum world into line with common sense. Yet there is a problem with this vision. It is ruled out by an elegant result published in 1967 by mathematicians Simon Kochen and Ernst Specker.

Kochen and Specker's theorem puts some pretty severe constraints on anyone hoping to rid quantum theory of its weirdness. Put simply, the theorem shows that it is pointless expecting to get simple true and false answers from quantum theory. Every statement about a quantum system must either depend on a host of assumptions, or refuse to obey the standard rules of logic - and possibly both.

For quantum cosmologists, Kochen and Specker's theorem is particularly bad news. It rules out all hope of squaring quantum theory with the common-sense view that the universe is real and has simple, clear-cut properties. Or at least it does for those who believe the laws of logic are set in stone. What if they aren't? Could the problem lie not in quantum theory, but in our notion of truth? That is the question that Isham and his colleagues have dared to ask, with intriguing results.

Abandoning the standard laws of logic in order to make the universe real seems like a hefty price to pay. Yet some theorists have believed it is worth it, says Steven French, a philosopher and quantum physicist at the University of Leeds in the UK. That's one reason why mathematicians over the years have developed other systems of logic. "Along with standard true/false logic there are so-called non-classical logics out there which include true, false and indeterminate values," says French. "People looked at them as a way of dealing with problems in quantum theory, but it died out in the 1970s and 1980s because it wasn't really illuminating very much."

A big sticking-point lay in finding the alternatives to "AND", "OR" and "NOT", the logical operators of the standard or Boolean algebra that are routinely used by everyone from philosophers to computer programmers to make logical deductions. While this familiar form of logic works well enough in everyday situations, it fails to describe the behaviour of quantum systems.

Isham illustrates this using the example of ordering breakfast in a cafe. Imagine looking through the menu and finding that eggs, bacon and sausage are on offer. It states the choice as "eggs AND bacon, OR eggs AND sausage", but the chef could equally offer the same breakfast choice in a shorthand version: "eggs AND (bacon OR sausage)". That's because the operator AND possesses a mathematical property called distributivity, which links eggs with whatever is inside the brackets. Distributivity is vital for making common-sense deductions. Lose it - as you do in quantum theory - and you can expect some unusual results.

Take that cafe menu, for instance. If you ask for eggs AND bacon in the quantum world, you could get nothing at all says Isham. Ask for eggs, and bacon or sausage, and you'll get eggs plus some weird quantum mix of bacon and sausage. Clearly, relying on quantum logic to reason your way to a decent breakfast is likely to lead to disappointment.

There is a serious point lurking behind all this. Systems of logic lacking distributivity are very hard to reason with and quantum logic is one of them. Worse still, Kochen and Specker's theorem rules out any hope of tinkering with quantum logic to force it to give us simple true/false answers to statements about physical systems. Yet without those simple answers, it doesn't make sense to say a physical system has certain properties and is thus "real". Why does quantum logic have to be so frustrating?

Isham and Jeremy Butterfield at the University of Oxford decided to dig deeper into the problem. They dug so deep, in fact, that they found themselves under the foundations of standard mathematics and staring at something far more fundamental. That something is a concept called a topos, and it could be the basis of a whole new way of constructing theories of reality.

The idea of a concept even more general than mathematics and logic may seem mind-bending, yet mathematicians have happily contemplated such things for years. They have long known that the whole of standard mathematics and logic can be constructed from entities called sets. A set is just a collection of objects - anything from the infinite set of prime numbers to the set of all mammals or even the set of all universes. Crucially, sets obey the laws of standard logic and Boolean algebra.

Mathematicians have since discovered that sets themselves are merely the most familiar example of the even more general concept of a topos. The precise definition of a topos is highly technical, but all topoi share one key feature: each gives rise to its very own variety of logic. Suddenly an astonishing possibility opens up: we can break away from the familiar set-based variety of logic and describe the world via other topoi.

Isham and his colleagues saw topoi might offer a way to break the shackles of Kochen and Specker's theorem. The trick was to find topoi whose associated logic would reconcile quantum theory with the notion of a real universe. That meant searching for new definitions of the logical operators AND, OR and NOT. Others have tried this before, and it is far from trivial, says Isham. "In practice, the procedures have been rather hit and miss."

To pin them down precisely, he and his colleagues turned to the bigger mathematical palette offered by topos theory. Now they could see Boolean algebra for what it is: merely the most familiar of many possible types of algebra, each of which could act as the basis of entire new forms of logic.

Armed with these, Isham and his colleagues have identified the topoi for quantum theory. Not surprisingly, they are very different from anything we're familiar with, and of course come with their very own form of logic. That logic does at least have one familiar feature: it is distributive. At a stroke, this removes one of the most perplexing aspects of quantum theory. It allows us once more to make common-sense deductions about quantum systems. Finally, the universe can be real without having to fret about "outside" observers.
Another reality

But there is a price to pay, and it is precisely what the Kochen-Specker theorem warned of: the demise of simple truth and falsity. For all its drawbacks, Boolean algebra does at least allow every statement about our universe to be either true or false. Yet this turns out to be the exception among all the different types of algebras - including the one underpinning quantum theory. The logic associated with quantum topoi encompasses true, false and many shades of grey in between.

Does that mean we must accept a universe that is real, but about which any question will receive myriad answers, all of them true? According to Isham and his colleagues, the answer - appropriately enough - is both yes and no. If we are content to view reality through the window of classical physics, then we can enjoy straightforward true/false answers to our questions - as long as we avoid the realm of atoms. But if we insist on making statements about atoms, we must use the logic of quantum topoi and accept the existence of a whole host of realities, all as valid as each other.

And that might just be the start; after all, there are more topoi than just the standard and quantum ones. In a series of papers unveiled last month, Isham proposes an even more mind-bending idea: there may be myriad ways of viewing reality, each based on its own topos. Together with Andreas Doering of Imperial, he has shown that every physical system - from an electron to the whole universe - has a unique mathematical identity that dictates how it will appear when viewed through the prism of a particular topos.

Seen via the topos of set theory, an atom takes on its classical appearance with nice, well-defined properties. Viewed through the topos associated with quantum theory, it becomes altogether fuzzier and strange.

We needn't stop there. Why not opt for another topos? It could lead to a view of reality even more astonishing and successful than quantum theory. "What we're hoping is that topos theory becomes the basis for a whole new way of constructing theories", says Isham.

It is an exhilarating possibility, and one that could hardly be better timed. Theoretical physicists feel growing disquiet about the lack of progress on the truly fundamental questions. Attempts to understand the ultimate origin of the universe have spawned a host of ideas, but no consensus as to which is right. Meanwhile the search for a "theory of everything" that would unify all the forces and particles of nature has run into innumerable problems.

Not surprisingly, this has led to mounting suspicions that current theories of fundamental physics are missing something big. Could topos theory open the way? "There's no doubt that we need something radical", says Max Tegmark, a theorist at the Massachusetts Institute of Technology. "Whether this is it is another question. In the end the real test is: does it get us anywhere?"

Isham agrees, but stresses that he and his colleagues have only just begun to scratch the surface of topos theory. He hopes researchers will see his latest papers as a framework for going beyond quantum theory, perhaps to something even more profound.

So will topos theory trigger as big a change in our perceptions of reality as quantum theory did a century ago? That depends at least in part on how other theorists react to these first papers. Isham is under no illusions about that: "We are trying to change the way we construct theories of what reality is like," he says. "And that's always going to be problematic."

Robert Matthews is visiting reader in science at Aston University in Birmingham, UK
From issue 2599 of Neo Scientist magazine, 14 April 2007, page 30-33

[ComradeRed]

HOLY HELL! I'M ACTUALLY WORKING ON THIS!

Oh I feel all giddy all of the sudden.

Of course, my work isn't on exactly what Isham's doing. I have communicated with him once via email, and he was very encouraging with my work.

I'm working on formulating relational quantum mechanics in the language of topos logic.

And now I'm so ashamed that it's put in the philosophy forums of all places! :lol:

[RebelDog]

HOLY HELL! I'M ACTUALLY WORKING ON THIS!

Then can you help me with this bit:


Together with Andreas Doering of Imperial, he has shown that every physical system - from an electron to the whole universe - has a unique mathematical identity that dictates how it will appear when viewed through the prism of a particular topos.

How does this square with those who uphold that mathematics is a human construct? These mathematical identities surely relate to a subjective human reality placed upon them via mathematics and nothing more.

[ComradeRed]

Originally posted by The [email protected] 16, 2007 09:51 pm

HOLY HELL! I'M ACTUALLY WORKING ON THIS!

Then can you help me with this bit:


Together with Andreas Doering of Imperial, he has shown that every physical system - from an electron to the whole universe - has a unique mathematical identity that dictates how it will appear when viewed through the prism of a particular topos.

How does this square with those who uphold that mathematics is a human construct? These mathematical identities surely relate to a subjective human reality placed upon them via mathematics and nothing more.
Well, the basic idea is that topos is a language. It's a weird language with all most countless dialects (for math nerds: I am referring of course from the fact that the sheafs can be from any category, each physical theory is associated with different sheafs, e.g. one theory that is the logic of message passing in concurrent programming uses the sheafs from the category of monoids to the category of sets).

It's not really that these identities are "discovered" insomuch as they make predictions that work and are close enough to the experimental results.

So it's guess and check work with a virtually infinite number of dialects :lol:

My work is slightly different, dealing with making quantum mechanics observer dependent using topos.

The "mathematical identities" that they are talking about are "rules of inference" for categorical logic applied to the "functions" from the category of an algebraic object (e.g. the category of groups or monoids or whatever) mapped to the category of sets.

So it's really a misnomer with how it's being used, as I understand the math (categorical logic is the hardest math I've thus dealt with).

Lazy version these "mathematical identities" are really "rules for logical inference". These rules of inference allow you to ask certain questions (e.g. "Does X have a value in the range of...?") whilst retaining meaning.

I mean it's pretty meaningless to ask an electron "How are you today?" Or "If you were massless, would you have this property?" Or something else.

These rules of inference relatively constrain the questions that you may ask, and the responses that you can get.

I hope that made sense :unsure:

[Rosa Lichtenstein]

We have witnessed several attempts over the last 100 years to quesion classical logic (from the sciences), but none have been sucessful, mainly because they traded on confused 'definitions' of what counts as a scientific proposition.

All that has emerged so far, and I suspect this will happen here too, is that theorists will set up a new convention to depict certain phenomena. No problem with that; that is their job.

However, in order to do this, they will have to use logic (which they can hardly then undermine).

Of course, if they do not use logic, the conclusions will not follow.

Either way, classical logic should emerge unscathed.

[That is not to say it does not face other problems, but that is another story!]

[ComradeRed]

One last thing I neglected to mention, topos is a contextual formalism.

How I (try to) use it is that we have say an electron. It has certain properties, but these properties are only meaningful if defined in the presence of an observer.

Or at least some coordinate frame and test particles.

Think about the spin of the electron alone. If it helps, think about it like a clock that you can see front and back.

But if you look at it from the front it's arms move clockwise whereas from the rear it's moving anticlockwise. Which is the correct motion of the arms: clockwise or anticlockwise?

This is an extraordinarily elementary example, it gets more complicated with things like momentum or position.

I am unsure, and am highly skeptical, whether this could be applied to quantum field theory...which means it's useless for quantum gravity (in theory, I may turn out to be wrong here and it could crack the problem wide open).

But that is one of the major appeals of topos, especially with Isham's work: it's that it takes into account a contextual approach, which is rare in physics!

[gilhyle]

Originally posted by Rosa [email protected] 17, 2007 07:18 am


Of course, if they do not use logic, the conclusions will not follow.


I know only that I dont understand this stuff - I understand the idea of alternative logics, but this is something else. It seems to be some sort of variation on the the definition of a set......I dont understand it.

Anyway, I wonder if Rosa's comment is correct. If you define a set (oops !) of axioms and a set of rules and you apply those rules to the axioms, where does classical logic come in ?

Or have I answered my own question by using the word 'set' ?

[ComradeRed]

Originally posted by [email protected] 21, 2007 07:18 am
I know only that I dont understand this stuff - I understand the idea of alternative logics, but this is something else. It seems to be some sort of variation on the the definition of a set......I dont understand it.
No, a better way to think about this is as a sort of logic based on functions that take in a common type of argument, not necessarily a number, and spits out a number.

You can then use these functions as "objects", and have "functions" of these functions.

If you doodle a little diagram where the "objects" are dots, and the "functions" of these objects are arrows, there are a certain pattern that presents itself.

These patterns are the rules of inference.

The doodle of dots and arrows are a "topos". It's hard to explain, and even harder to understand, but once you understand it it's easy (though that's true for anything! :P).

[Rosa Lichtenstein]

Gil, I was speaking especially of an attack on classical logic from the sciences (or based on the alleged findings in the sciences).

If, on the other hand, you set up an alternative logic, then no problem.

But, that can hardly be used to attack classical logic, since they would be two separate systems.

A bit like attacking imperial measures by the use of the metric system.

If, however, you are using no logic at all, the conclusions would not follow, as I said.

[gilhyle]

Originally posted by ComradeRed+April 21, 2007 09:03 pm--> (ComradeRed @ April 21, 2007 09:03 pm)
[email protected] 21, 2007 07:18 am
I know only that I dont understand this stuff - I understand the idea of alternative logics, but this is something else. It seems to be some sort of variation on the the definition of a set......I dont understand it.
No, a better way to think about this is as a sort of logic based on functions that take in a common type of argument, not necessarily a number, and spits out a number.

You can then use these functions as "objects", and have "functions" of these functions.

If you doodle a little diagram where the "objects" are dots, and the "functions" of these objects are arrows, there are a certain pattern that presents itself.

These patterns are the rules of inference.

The doodle of dots and arrows are a "topos". It's hard to explain, and even harder to understand, but once you understand it it's easy (though that's true for anything! :P). [/b]
I thinkg I got that description ..rules of 'inference' derived from applying functions to functions.....vaguely....maybe now I can at least delude myself that I know what your talking about. :D

[syndicat]

I think that areas of human investigation outside logic could provide in principle grounds for challenging accepted logical theories. I don't think of logic as prior to science but as one of the sciences. Logicians are trying to account for how arguments can support conclusions. They use actual arguments -- good and bad -- as data in developing their theories. The theories must be consistent with the data, just as with any other science. I taught logic for a number of years. This is part of my area of professional expertise. I don't mention this to support an "argument from authority" but to explain my own reasons for having severe doubts about so-called "classical" logic. Logicians are aware of the problems with classical logic, but do not have a consensus on how to deal with the problems. That's why it would be inappropriate for me to justify my own solution on the basis of my "authority."

When I first started teaching the logic curriculum, i used to teach classical symbolic logic. This is a theory of deductive argument that was first developed back in the 19th century by a German philosopher/mathematician, Gotlob Frege, and then popularized by Bertrand Russell. That's why it is sometimes called the Frege/Russell logic. This is the standard treatment of deductive logic taught around the world.

Over time I moved away from teaching this to introductory students. There were two reasons for this.

First, the classical Frege/Russell logic, if interpreted as a theory to account for arguments expressed in ordinary human languages, is inadequate because it can be used to validate fallacious arguments. In other words, you can find obviously invalid arguments in English that exhibit one of the patterns that the Frege/Russell logic says is valid. Consider the following sentence:

(1) Jack praised Lydia and she kissed him.

Using the method of abbreviation practiced by logicians, we can abbreviate this
as:

P and K

By the rules of the Frege/Russell logic, it is valid to infer:

K and P

Translating this back into English, we have:

(2) Lydia kissed Jack and he praised her.

The problem here is that "and" in (1) suggests a causal relationship: that Lydia kissed Jack BECAUSE he praised her. But (2) suggests a different causal relationship. (2) suggests that Lydia's kissing Jack prompted him to praise her.

But if (1) is true, it is FALSE that Lydia's kissing Jack prompted him to praise her. So inferring (2) from (1) is fallacious. Yet it is provable in the classical Frege/Russell logic.

I could produce many other examples of fallacious inferences that can be validated using the classical Fregre/Russell logic.

Part of the problem here is that the Frege/Russell logic presupposes an atomistic worldview, that each fact is entirely independent of any other. The logical connectives like "and" and "if" as used in the Frege/Russell logic do not capture any sort of real relation between the facts denoted by the separate conjuncts (K and P in this case), such as a temporal or causal relationship.

I could give many other examples of invalid arguments in ordinary English that can be validated by the classical Frege/Russell logic.

My second reason for moving away from emphasis up classical logic in my teaching is that most reasoning in real life, and most of the way we use reasoning to find out about the world, isn't deductive.

In more recent years when I've taught an introductory class on logic, I tend to emphasize two other types of reasoning that we use, which logicians call inductive and abductive. Abductive inference is also called inference to the best explanation or the method of making a hypothesis and then testing it.

We use the abductive method all the time without even being conscious that is what we are doing. We're hard-wired to think this way. I'll give an ordinary example. Suppose i walk outside the door of my dwelling and look down the block. I see that the lights are on at Sami's market. So i infer "Sami's market is still open." The sentence "Sami's market is still open" is idea that I adopt because it explains what i experience: the fact that the lights are still on.

in this example, I could be wrong. It might be that Sami had to leave in a rush and didn't have time to turn off his lights, and the store is actually closed. To test my hypothesis, i can simply walk down the street and see if the store is actually open. This is not a deductive inference because the conclusion ("Sami's market is still open") doesn't NECESSARILY follow from the premise (the lights are still on at Sami's market). As I say, my inference could be mistaken. Nonetheless, the premise supports the conclusion.

Abductive inference or inference to the best explanation is in fact extremely important to human life. It is the main way we learn things about our world. it is in fact more basic than deductive inference. I'm not saying that deductive inference is not also needed. one way we test a hypothesis is we DEDUCE what must exist in order for our hypothesis to be true. We can then test the hypothesis by seeing if those things do exist. but deductive principles are themselves hypotheses.

Nowadays if i were to teach an introductory logic class, I'd place as much emphasis upon the method of making hypotheses (abduction) and inductive logic as I would on deductive logic. And when I teach deductive logic, I tend to prefer a theory of deductive inference known as "relevance logic." Relevance logic tries to take account of the real connections between the states of affairs denoted by the component sentences.

i don't think of logical principles as something we can somehow know apriori. is it reasonable to suppose human brains have some mystical ability to "intuit" facts outside the physical world stored up in Plato's heaven of abstract truths? I don't think so. I think of logical principles as very entrenched empirical hypotheses.

[Rosa Lichtenstein]

Syndicat:


Logicians are trying to account for how arguments can support conclusions.

In fact, logicians study inference, not how arguments can 'support conclusions'.

And your alleged counterexample to classical logic only works because of the ambiguity in your use of 'and' (plus there are few suspect pronouns in there too).

Moreover, your faith in abductive inference is interesting in view of the fact that these are, if interesting, fallacious.

And your reference to 'relevance' logic suggests you are a visitor from LibCom, under a new name.

[syndicat]

Inferences are presented to others in the form of arguments. If I infer Q from P, I am assuming that the truth of P would support or warrant my inference of Q. Premises can support conclusions in different ways. With a deductive argument -- or inference, if you prefer -- the conclusion is advanced as following of necessity from the premises. That is, if a deductive inference is valid, there is no possibility of the conclusion being false if the premises are true.

Inductive and abductive arguments support or validate their conclusions in a different way. There is no claim that the conclusion follows of necessity from the premises. Rather, the truth of the premises makes the conclusion probable, assuming the argument withstands scrutiny of the various tests for a hypothesis, or for a good inductive argument.

I'd recommend taking a look at standard textbooks on this, such as Patrick Hurley, "A Concise Introduction to Logic", or Trudy Govier's "A Practical Study of Argument", or Kathleen Moore's "Inductive Arguments". I've used all of these in classes, and so do other logic teachers.

Ambiguity is of course pervasive in natural language. But given the natural way of understanding the premise and conclusion, my example is in fact an invalid argument, even tho it exhibits a pattern provable in classical logic. But I can give other examples. It's well known that the treatment of "if" in classical logic doesn't hold up.

In reality there are a number of argument -- or inference, if you prefer -- patterns that can be validated by the classical Frege/Russell logic that have fallacious instances in ordinary English -- this is true of contraposition, antecedent strengthening, modus tollens, and even modus ponens. Let's take antecedent strengthening. This is the pattern:

If P then Q
Hence, if P and R, then Q

Suppose that in fact my friend James, a political activist who greatly respects me, would never publish any personal attack on me, and in fact is never going to do so. I'm always pleased when he gets out another book. So the following premise is true:

(1) If James' next book is published, i will be pleased.

But now consider the following conclusion:

(2) If James' next book is published and contains a vicious personal attack on me,
I will be pleased.

(2) is false. Hence this is an invalid inference since the premise is true and the conclusion is false. But it's an instance of "antecedent-strengthening."

It is also notorious that the classical Frege/Russell logic gives the wrong interpretation of counter-factual conditionals. Consider this statement: "If I hadn't gone to Milwaukee, I wouldn't have met Reece."

Now I already knew Reece before I moved to Milwaukee, so this sentence is false. But because the antecedent (the "if" part) is false -- I did move to Milwaukee -- the sentence is treated as true in the classical Frege/Russell logic.

Modus ponens is regarded as one of the most obvious and basic of principles of classical logic. Modus ponens is an argument -- or inference, if you prefer -- that exhibits the pattern:

If P then Q
P
Hence Q.

But here's a counter-example to Modus Ponens:

(3) If a Republican wins the 1980 presidential election, then if it's not Reagon who wins, it will be Anderson. [Anderson and Reagan were the two main Republican candidates that year, so this is true.]

(4) A Republican will win. [Reagan won, so this is true.]

(5) Hence, if it's not Reagan who wins, it will be Anderson.

The conclusion is false. If Reagan hadn't won, it would have been Carter who would have won. Hence, this is an instance of Modus Ponens with two true premises and a false conclusion. Hence it is an invalid argument.

Rosa's comment about abductive inference is curious. Abductive method is the method of coming up with a hypothesis to explain something and then testing the hypothesis. This is the basis of the empirical sciences and is the main way we have of learning new things about the world. For a good introductory discussion of this type of inference, I highly recommend Kathleen Moore's treatment in her textbook "Inductive Arguments".

For a more sophisticated defense of the principle of inference to the best explanation (AKA abduction), take a look at John Post's discussion at:

http://www.vanderbilt.edu/~postjf/precistphil.htm

[syndicat]

A problem with the classical Frege/Russell logic is that is is built on an atomistic, radical empiricist worldview. We can see this if we consider how the conditional -- an "if...then..." sentence -- is treated. The sentence "If monkeys fly to the moon, Ralph Nader is president of the USA" is treated as true solely because the antecedent -- the "if" part -- is false. Similarly, "If campesinos are being driven off the land in Mexico, then Schwartzenegger likes Hummers" is true simply because the consequent -- the "then" part -- is true. The idea is that the truth or falsity of a conditional does not depend on any connection whatever -- causal or temporal or whatever -- between the states of affairs denoted by the "if" and "then" parts. That's the problem with the argument I gave using "and" in my previous post. The reason it's regarded as okayin classical Frege/Russell logic to infer

(2) Lydia kissed John and John praised her

from

(1) John praised Lydia and she kissed him

is because each fact -- John praising Lydia and Lydia kissing John -- is regarded as an independent atom, with no relation here being expressed between them.

But we don't live in an atomistic world of unrelated facts. We live in a world with all sorts of causal and other connections. Moreover, the atomistic world view of the radical empiricists is inconsistent with Marxism and with the tradition of radical social theory.

[FuckWar]

This article is extremely interesting, as this new idea has the potential to shed light on formal semantics and pragmatics, as well as the interface between the two in the field of linguistics and natural human language.

Interesting to imagine humans coming up with a different interpretation of reality to apply to grammar, i.e. a tool that humans use to cognitively interpret their reality.

[Rosa Lichtenstein]

Syndicat, since you have not said whether my inference was correct or not (that you were indeed a visitor from LibCom, with a changed name), I will have to make an inference to the best explanation that you are indeed Gatorojinegro.

In that case, I refer the honorable fibber to my last reply to him at LibCom.

[syndicat]

in other words, Rosa, you can't answer my arguments about the inadequacies of the classical Frege/Russell logic.

[ComradeRed]

Originally posted by [email protected] 25, 2007 07:53 am
Inferences are presented to others in the form of arguments. If I infer Q from P, I am assuming that the truth of P would support or warrant my inference of Q.
No...in order to deduce Q from P, you don't need to know whether P is true or false. You simply apply a rule of inference to "derive" Q from P. Truth is irrelevant in this regard.

If P is true, then Q would be true if and only if the deduction were a valid one. Q may possibly be true or possibly not if it is not a valid deduction (e.g. you can't deduce "beef comes from cows" from the proposition "On August 3d 2007 it rained in Sacremento California"...if the latter is wrong, does that make the former wrong? No, there is no valid deduction)

...but my bias as a physicist urges me to ask "Who gives a flying fuck about this chap's (or anyone's) philosophy?" And then I realize the age old truth: If a philosopher did anything of significance, it'd be called science. :lol:

[gilhyle]

LibCom ???

Abductive reasoning I know of from CS Pierce, I assume this is some type of pragmatist position or is it ??

Even accepting the fact that classical logic produces some strange results (and everyone accepts it does) ....the conclusion is not that it doesnt work only that it is not some sort of Leibnizian code to testing all valid argument.

But who thinks it is ?

[syndicat]

Comrade Red says: " No...in order to deduce Q from P, you don't need to know whether P is true or false. You simply apply a rule of inference to "derive" Q from P. Truth is irrelevant in this regard."

You're being pedantic. When I say, "If I infer Q from P, I am assuming that the truth of P would support or warrant my inference of Q", what I'm saying is that IF P were true, this would warrant the claim that Q is true, if the inference of Q from P is valid. Consider what I said: "if a deductive inference is valid, there is no possibility of the conclusion being false if the premises are true." This does not say that the premises have to be true for the argument to be valid. It says that IF the premises are true, then the conclusion must also be true. But of course, the premises might not be true. So, yes, the premises of a deductive argument don't have to be true for it to be valid.

if you think logic does nothing of any relevance, then why do you pay any attention to it? Moreover, the idea that anything that someone says can be disparaged because it isn't called "science" is elitist.

gilhyle, no, use of the term "abduction" doesn't imply agreement with pragmatism or any particular philosophical position. It is just a piece of jargon in logic. It refers to the method of proposing an explanatory hypothesis and then testing this.

The reason why the limitations of classical Frege/Russell logic are relevant is that there are many kinds of inferences that it would be useful to have some understanding of that classical Frege/Russell logic cannot deal with. And, secondly, it fails to deal with the whole area of inductive inferences and inferences to the best explanation (method of hypothesis and test). Learning about how to evaluate hypotheses, for example, can help in thinking more clearly about the world around us, and not be bamboozled by bogus theories.

[ComradeRed]

Originally posted by [email protected] 25, 2007 10:39 am
if you think logic does nothing of any relevance, then why do you pay any attention to it? <_< The orthomodular subspace of a hilbert space forms a heyting algebra, in case you forgot (you being an "expert" on logic should know this as "quantum logic").

Really, anything involving "projectors" or topos can be asserted as "logic". This is merely because of the mathematical structure of boolean algebra.

It has absolutely nothing to do with "applying" logic insomuch as the underlying math "looks like" mathematical logic.

Further, you&#39;re not talking about applying logic at all in your post...just maundering on about how "evil" classical logic, it&#39;s "shortcomings" and so forth.

This begs the question: Who Cares?

Since classical logic works "good enough" for every day purposes, and there hasn&#39;t been any reason as to why any other form of logic is "superior" than classical logic, your entire first post appears to be little more than intellectual masturbation.

You can continue to ramble on, continue calling me elitist for refusing to pay attention to complete bullocks, and - by all means - continue to speak with such a pretentious tone and bombastic vocabulary.

You still haven&#39;t coherently proven one damn thing yet (*gasp*, a mathematician is more useful than you&#33;).


Moreover, the idea that anything that someone says can be disparaged because it isn&#39;t called "science" is elitist.Oh my yes, I forgot about all those coal-mining philosophers&#33; Silly me :lol:

I think somehow we&#39;ll all manage to live if we ditch these rhetoric-boxes for the ruling class; unless of course we&#39;re going to ignore Marx&#39;s views on philosophers and the ruling class ideology <_<

I&#39;m afraid I&#39;ll have to settle for rejecting bullocks and receiving the title "elitist", nothing less could do&#33;

[syndicat]

"Pretentious" and "bombastic" are terms you should be careful about tossing around...people might notice they apply to your own arrogant language.

Actually most of human reasoning, and a vast sphere of reasoning throughout ordinary life and the "sciences", cannot be accounted for by classical logic, and your tidy little boolean algebras. but, hey, you, the big "scientist," cares not for this.

And because logic in fact is a science, logicians have been trying to work out a logical theory to supercede classical logic. It&#39;s just that there is not yet any consensus.

[ComradeRed]

Originally posted by [email protected] 25, 2007 01:37 pm
"Pretentious" and "bombastic" are terms you should be careful about tossing around...people might notice they apply to your own arrogant language.You&#39;re the expert :rolleyes:


Actually most of human reasoning, and a vast sphere of reasoning throughout ordinary life and the "sciences", cannot be accounted for by classical logic, and your tidy little boolean algebras. Seeing as you haven&#39;t really presented a coherent argument as far as why this is true, rather than just spewing technical jargon and saying "ZOMG KLAZZIKAL LOGIC FAILS&#33;&#33;&#33;&#33;1+1=3&#33;"

Perhaps you could take a page from the mathematician&#39;s book and organize your work in a coherent and reasonable manner.

Oh, and also - another very important part from the mathematician&#39;s book - prove something.

If "logic" is a science, then it&#39;s not enough to say "KLAZZICAL LOGIC FAILZ&#33; ZOMG&#33;" You have to replace it with a superior theory, that&#39;s how science basically works...but don&#39;t let that stop you <_<


but, hey, you, the big "scientist," cares not for this. It&#39;s "care not" for this, and you&#39;re right I&#39;ve got more exciting things to do like formulate relational quantum mechanics in topos or present quantum field theory with a finite dimensional hilbert space.

Because that can actually be tested and do something.

Or I could be doing something useful like help plan a protest, as opposed to watch you intellectually masturbate.


And because logic in fact is a science, logicians have been trying to work out a logical theory to supercede classical logic. It&#39;s just that there is not yet any consensus. Logic is a science? Oh really?

You can discover, what, rules of inference under a rock? :lol:

[syndicat]

me: "Actually most of human reasoning, and a vast sphere of reasoning throughout ordinary life and the "sciences", cannot be accounted for by classical logic, and your tidy little boolean algebras. "

Comrade Red:


Seeing as you haven&#39;t really presented a coherent argument as far as why this is true

Actually i did. but you prefer to puff yourself up and spew.

The empirical data for logic are the arguments that people generate, actual human inferential practices. Something you should pay attention to sometime.

[ComradeRed]

Originally posted by [email protected] 25, 2007 02:34 pm
me: "Actually most of human reasoning, and a vast sphere of reasoning throughout ordinary life and the "sciences", cannot be accounted for by classical logic, and your tidy little boolean algebras. "

Comrade Red:


Seeing as you haven&#39;t really presented a coherent argument as far as why this is true

Actually i did. but you prefer to puff yourself up and spew.
Oh, well, if you say so, then it must obviously be true :rolleyes:

Remember that part I said about the proof? Yeah, that is kinda relatively important.

Then again, you&#39;re the self-appointed expert <_<


The empirical data for logic are the arguments that people generate, actual human inferential practices. So let me get this straight, your reasoning is that logic does not exist without people.

People "generate" arguments, and thereby somehow "discover" logic...or "generate" it?

I guess it boils down to this: is logic invented or discovered?

You&#39;re not giving a clear answer; from the concept that logic is somehow tied to arguments "generated" by people, it would imply that logic would be "generated" (either directly or indirectly) by people.

But that would mean that logic is not a science as it&#39;s invented NOT discovered.

[syndicat]

Then again, you&#39;re the self-appointed expert

Nope. I said at the outset i would make no appeals to authority.

Are hypotheses invented or discovered? You tell me. People come up with hypotheses. That suggests they are created. But, oh, that would mean it isn&#39;t part of a science, say you.

Inference -- an activity of humans -- plays a role in warranting beliefs, and providing arguments to others is a social practice which provides them with reasons to accept the conclusions. Since humans aren&#39;t telepathic, these arguments are provided in words, and are made up of sentences. Sentences and beliefs -- things that can be true or false -- are the subject matter of logic. if there were no humans, these things wouldn&#39;t exist. Some of the states of affairs that we describe or denote in our sentences or beliefs might exist even if we weren&#39;t around. Relations between these beliefs or sentences may also hold in virtue of relations among the states of affairs in the world. And a given logical principle may be explained by such relations.

Consider the law of non-contradition, as it applies to basic subject/predicate sentences, such as "This cat weighs eight pounds", "This cat weighs ten pounds." It is a physical fact that weighing eight pounds and weighing ten pounds are contraries -- one excludes the other. If I say "This cat doesn&#39;t weigh ten pounds", this will be true if there is some weight other than ten pounds it has, such as eight pounds. In other words, I take a negation of a simple subject/predicate sentence F(a) to imply that there is some true sentence G(a) where G denotes a property that excludes F, and this is why ~F(a) is true.

We could suppose as a hypothesis that this empirical physical fact of exclusion by contraries is why the law of non-contradiction holds. Thus understood, the law of non-contradiction could be regarded as an empirical hypothesis. Thus there could in principle arise reasons from one of the empirical sciences for saying it doesn&#39;t hold in certain situations, as happened to the axiom of parallels in geometry. This would affect how inferences concerning those situations are to be evaluated. Adjustments to the theory would be needed.

Humans create sentences and thus arguments, which are made up of sentences. But it is the world that makes the sentences true or false. And logic is supposed to be a theory about inferences that won&#39;t lead us from true premises to false conclusions.

[ComradeRed]

Originally posted by [email protected] 25, 2007 04:14 pm
Are hypotheses invented or discovered? You tell me. People come up with hypotheses. That suggests they are created. But, oh, that would mean it isn&#39;t part of a science, say you.
Yeah, "says me" and the basic concept of science.


Humans create sentences and thus arguments, which are made up of sentences. But it is the world that makes the sentences true or false. And logic is supposed to be a theory about inferences that won&#39;t lead us from true premises to false conclusions. Let me get this straight: your thesis boils down to logic is a posteriori?

The justification is that humans make a conjecture with some rules of inference, then test this conjecture, and then modify the rules of inference as needed, right?

This sounds like applied math to me, as far as model construction and verification of the accuracy of the model.

Regardless, you are too hasty to jump to the conclusion that logic is thus "discovered" as it is checked against reality.

By such a definition of science, math is then science&#33; Alas, it is nothing more than a human invention.

Further, you don&#39;t seem to deny that logic is invented by humans...which then makes the whole "Logic is a science" argument self-defeating.

There isn&#39;t convincing enough grounds to argue that logic is a posteriori, perhaps you could elaborate your thoughts on it?

[syndicat]

Yes, I am saying that logic is aposteriori. I am totally opposed to traditional philosophy in this sense.

Consider the way the classical Frege/Russell logic was developed and adopted. The process bears a certain resemblance to the development of physics. Before Frege, there were a variety of areas of inference that had been studied and some minor "theories" of when inferences would work, as with Aristotle&#39;s syllogistic (logic of "all" and "some"), medieval studies of inferences with "and", "or", "if", "not" and then Boole&#39;s logical algebra. Frege basically came up with a theory that was far more comprehensive, accounting for the vast majority of existing logical theory but extending it. In this sense, compare it to the achievement of Newtonian mechanics, in developing a physical theory that was more comprehensive and unifying than what had been done before in "natural philosophy".

What logicians actually do is to look at groups of inferences and try to find a theory -- such as a pattern that can be encoded in a set of formal rules -- to account for these inferences. These inferences of ordinary life are then the empirical data.

Since Frege logical theory has had both its syntactic and semantic sides. The syntactic side looks at the actual linguistic patterns, the plausible rules of inference, the structures of the language. The semantic side looks at what needs to be assumed to actually exist apart from language to account for the validity of the inferences. It was because of this division that you could get things like proofs of adequacy of formal theories, or inadequacy -- as with Goedel&#39;s famous incompleteness proof for arithmetic.

More recently there have been attempts by logicians to develop a new theory that can account for the inferences that are clearly valid that the Frege/Russell logic can&#39;t capture, and can explain the failures of the classical Frege/Russell logic.

I&#39;m referring to things like situational or relevance logics. Here in the Bay Area Xerox has actually been financing research in this area. The reason is because these new logical theories have practical applications the capitalists are interested in. An area of application is in the building of inference engines. An inference engine will take as input an ordinary language sentence, such as a question posed in English, and then make inferences from that sentence...for example, to answer a question. The classical Frege/Russell logic is woefully inadequate for building a viable inference engine because of the fallacious inferences it allows, as I pointed out before.

This also has relevance for a post-capitalist society because one of the things we&#39;d like to do is reduce to the minimum labor we have to do. And if we can automate answering questions that people have and access to information -- and we want to make access to information much greater -- then this would save us labor.

[ComradeRed]

Originally posted by [email protected] 25, 2007 06:46 pm
Yes, I am saying that logic is aposteriori. I am totally opposed to traditional philosophy in this sense.
Yes, that&#39;s what I suspected you meant.

It&#39;s a posteriori but not discoverable (as much as you dislike it, logic is not discoverable; it is not there hiding under a rock for us to find).

The very proposition that logic is a posteriori has specks of idealism (I daresay PLATONISM) in it...which would contradict materialism. How then could it be a science?

On the other hand, saying that it is invented and a posteriori (supposing such a thing could exist), it would be a tool rather than a science...very much like the status of math.

(Math too is not a science, as much as it pains mathematicians. It&#39;s a legitimate human construct.)

There has been very little as far as your thoughts on this matter, as you&#39;ve well said precious little on it specifically.

[syndicat]

No, Platonism is the exact opposite of what I am adovcating. It is the Platonists who hold that logic and math are apriori. They hold that the truths here are discovered by way of some mysterious "intuition" that enables the brain to somehow get hold of abstract eternal propositions in Plato&#39;s heaven. I totally reject that view.

The view I&#39;m advocating here is completely materialist. The entities that would be included in the semantics of any logical theory would be physical particulars and features.

Logic is a tool but its utility requires an explanation. For example, what is it for sentences and beliefs to be true? It is in fact quite possible to explain this in a materialist way, as for example with biosemantics.

[ComradeRed]

Originally posted by [email protected] 25, 2007 07:20 pm
No, Platonism is the exact opposite of what I am adovcating. It is the Platonists who hold that logic and math are apriori. They hold that the truths here are discovered by way of some mysterious "intuition" that enables the brain to somehow get hold of abstract eternal propositions in Plato&#39;s heaven. I totally reject that view.
OK, so we have gone all the way around and let me assess the situation as it stands now:

1. Logic is a posteriori
2. Logic is invented and not discovered

Those are the two main points that have really been answered that I&#39;ve asked.

And you propose that Logic be put on the level of science.

Given the two propositions above, isn&#39;t it problematic that logic is not found in nature?

If it is found in nature, proposition 2 is wrong and you need to elaborate what you mean.

If it is not found in nature, then Logic isn&#39;t a science and proposition 1 needs to be revisited.

So there&#39;s a seeming inconsistency here that you could elaborate either the first or the second (or both) propositions on.

[syndicat]

As I said before, I think your statement 2 is unclear. Are hypotheses in the sciences "invented"? Well, yes in the sense that a human being comes up with the idea. Then we test to see if this hypothesis denotes or describes a factual situation or not. We distinguish between the real states of affairs in the world and our hypotheses, don&#39;t we?

We do find in nature a distinction between particulars and features. This is reflected in the universal subject/predicate structure of all human natural languages. I think this could be regarded as a "logical feature" in nature. But I agree there is no "if-ness", "or-ness" or "not-ness" in nature. On the other hand, our language, and inferences we make, does reflect real relations in nature such as causal or temporal relations. There are temporal logics that try to capture some of this.

So, i&#39;m not sure what the import is of saying that logic is "invented". I think human language has an actual logic. This logic is not arbitrary. There are inferences that transfer warrant in believing a conclusion is true from the premises if the premises are warranted. Logicians try to figure out a theory that captures this logic. This is an exercise in discovery as with the development of any theory.

[ComradeRed]

Originally posted by [email protected] 25, 2007 07:55 pm
As I said before, I think your statement 2 is unclear. Are hypotheses in the sciences "invented"? Well, yes in the sense that a human being comes up with the idea. Then we test to see if this hypothesis denotes or describes a factual situation or not.
Here&#39;s where you lose me, my proposition 2 says logic is invented...not hypotheses.

All logic is really reducible to is connectives and propositions. Semantics dealing with the meaning of the propositions, and so forth.

A hypothesis on the other hand is simply reducible to a mathematical formula, of one form or another.


We distinguish between the real states of affairs in the world and our hypotheses, don&#39;t we? MMmm...not really.

Supposing you mean of course that our hypotheses are only "approximations" to "reality" (whatever that term is supposed to mean).

Given two hypotheses that make no distinguishable difference in prediction, which one is a better "approximation to reality"?

Such a question is so metaphysical in nature it makes me nauseous.


We do find in nature a distinction between particulars and features. This is reflected in the universal subject/predicate structure of all human natural languages. I think this could be regarded as a "logical feature" in nature. But I agree there is no "if-ness", "or-ness" or "not-ness" in nature. But this basically assents to my original thesis that logic is not a science.

So we&#39;re in agreement I guess.


So, i&#39;m not sure what the import is of saying that logic is "invented". I think human language has an actual logic. This logic is not arbitrary. There are inferences that transfer warrant in believing a conclusion is true from the premises if the premises are warranted. Logicians try to figure out a theory that captures this logic. This is an exercise in discovery as with the development of any theory. But from the sounds of it, the context of "Human language has an actual logic" the use of "logic" appears to be synonymous with "pattern".

Whereas the "logic" I am referring to is not pattern recognition or anything of the sort, it&#39;s dealing with the truth of propositions...as you&#39;ve mentioned prior.

Thus I think there is a problem here with your use of "discovery" with regards to logic, as it refers to the process of recognizing patterns.

On the other hand, logic refers to the validity of inferences and so forth. Math is what deals with patterns, Logic is part of math that deals with propositions.

[syndicat]

Here&#39;s where you lose me, my proposition 2 says logic is invented...not hypotheses.

Distinction without a difference. Logic is made up of hypotheses. The law of non-contradiction is a hypothesis. Logic tries to explain why certain inferences are valid and others are not.


All logic is really reducible to is connectives and propositions. Semantics dealing with the meaning of the propositions, and so forth.

I don&#39;t think there are such things as "propositions" unless this is just your way of referring to sentence tokens. Since you talk about the "meaning" of propositions, I guess you must mean sentences. In the USA "propositions" is used to refer to the Platonist idea of abstract "meanings" of sentences.

Logic, on my view, includes inductive logic and evaluation of hypotheses ("abduction"), not just deduction. These other branches of logic involve more than what you seem to allow here.


A hypothesis on the other hand is simply reducible to a mathematical formula, of one form or another.

No. You&#39;re showing a certain physics chauvinism here. Not all sciences formulate their hypotheses in mathematical formulas. Moreover, the method of inferring a hypothesis to explain something we experience is a part of everyday human inferential practice, not just the "sciences". Moreover, there is a lot of pseudo-scientific crap that is formulated in mathematical formulas as with bourgeois economics.

me: "We distinguish between the real states of affairs in the world and our hypotheses, don&#39;t we?"


MMmm...not really.

Supposing you mean of course that our hypotheses are only "approximations" to "reality" (whatever that term is supposed to mean).

A hypothesis is a sentence. As with any sentence, there is a distinction between the sentence and the real situation that makes it true.


Given two hypotheses that make no distinguishable difference in prediction, which one is a better "approximation to reality"?

Historically there have in fact been criteria used to answer this question, such as the principle of simplicity (Ockham&#39;s Razor). The reason this is a reasonable principle is that if a hypothesis is more complex than necessary we expose ourselves to more risk of error if we prefer it over the simpler theory.


But from the sounds of it, the context of "Human language has an actual logic" the use of "logic" appears to be synonymous with "pattern".

Whereas the "logic" I am referring to is not pattern recognition or anything of the sort, it&#39;s dealing with the truth of propositions...as you&#39;ve mentioned prior.

Logic is not just "pattern recognition". In the case of the example I gave previously of an invaliid argument that exhibits the pattern of "antecedent strengthening", my proposed explanation for why the argument doesn&#39;t work involves the particular semantics of a situational or relevance logic. But this gets into what you refer to in your second sentence...the conditions on truth. Another way of looking at this is in terms of "background information", or the context in which the argument takes place.


On the other hand, logic refers to the validity of inferences and so forth. Math is what deals with patterns, Logic is part of math that deals with propositions.

It&#39;s true that logic deals with the bigger picture of the semantics, the conditions that we place on the truth of the sentences. in math this is in the background or taken for granted.

[Rosa Lichtenstein]

Gator:


in other words, Rosa, you can&#39;t answer my arguments about the inadequacies of the classical Frege/Russell logic.

I refer the honourable fibber to my last reply.

[gilhyle]

Seems to me you are involved in speculating that drawing a conclusion involves making an inference in more cases than those that comply with what you call classical logic. I have no doubt that you can model rules that classes of conclusions will comply with. I have no doubt also that many conclsuions will not be derivable by applying your rules.

Whether you want to call this logic or not is open to debate. Im quite happy to call it logic. But it idoesnt invalidate or supercede what you call &#39;classical logic&#39; and makes it no less valid to teach &#39;classical logic&#39;. The anti-classical logic comments still seem quite unjustified.

Whether it proves of any significance depends on the significance of the class of conclusions over which the rule (or rules) will range. What does it explain ?

Personally, once I go beyond classical logic, I prefer a logic that doesnt rely on rules that predict conclusions - dialectics. But come back and tell us your results when your finished. ;)

[syndicat]

It&#39;s not a question of "speculating". So-called "classical logic" -- the Frege/Russell system of symbolic logic -- is a theory of deductive inferences.

First of all, there are many good inferences that are not deductive. For example, cans of hair spray say that it can cause eye injury. This conclusion was reached by tests on rabbits. The scientists then concluded that, since the structure of human eyes is similar to that of rabbits, it will cause injury to human eyes. This is a form of inductive arugment known as an argument by analogy.

Secondly, there are problems with "classical" logic even in its own area of deductive inference. If an argument leads from true premises to a false conclusion, it is a deductively invalid argument. Yet there are many deductively invalid arguments that can be validated using classical symbolic logic. I&#39;ve already given examples.

Logic isn&#39;t just about "rules". It&#39;s also about understanding why, and in what circumstances, the rules hold. But logic is always about the relationship of premises to conclusions. That&#39;s because logic is about arguments, and arguments contain one or more premises and a conclusion, which is being inferred from the premise(s). If "dialectic" (whatever that might be) isn&#39;t about conclusions being inferred from premises, it isn&#39;t logic.

[ComradeRed]

Here&#39;s the problem Syndicat:

1. Science studies nature.
2. You assert Logic is a science. (Here&#39;s the quote:
Originally posted by syndicat+April 24, 2007 08:33 pm--> (syndicat &#064; April 24, 2007 08:33 pm)I don&#39;t think of logic as prior to science but as one of the sciences.[/b]--emphasis added)
3. You agree that Logic isn&#39;t in nature. (Here&#39;s the quote:
[email protected] 25, 2007 07:55 pm
But I agree there is no "if-ness", "or-ness" or "not-ness" in nature.--emphasis added)

There is an obvious inconsistency here...unless you are going to redefine science.

That was my original problem with your assertion.

You haven&#39;t provided a clear consolidation of this problem.

[gilhyle]

Originally posted by [email protected] 26, 2007 06:42 pm
It&#39;s not a question of "speculating". ..... there are many good inferences that are not deductive. .....If "dialectic" (whatever that might be) isn&#39;t about conclusions being inferred from premises, it isn&#39;t logic.
I can go with a narrow definition of logic, where it studies entailment, I can go with a broad definition of logic where it maps arguments, even without including predictive rules or schemas; but I very much doubt that you can come up with predictive rules for significant classes of inferences other than entailment.

The concept of argument from analogy does not have predictive force. I very much doubt you can make your project work - but this has all been articulated before - many times. We get told again and again that this can be done and then ......strangely it never quite works.

It either works post factum only (in which case its mere rationalisation) or it works only for arbitrarily selected or insignificant classes of inferences. But you go off and prove it and then come back - PROVE yourself correct.

[syndicat]

Comrade Red, I didn&#39;t agree that logic isn&#39;t in nature. Arguments exist. Some arguments are fallacious, some succeed in supporting their conclusions. There are different ways we can understand how they support their conclusions. The proposed explanations for this are hypotheses, which make up a logical theory. Our explanations inevitably do posit entities that we require to exist to have explanations for argumentative success. We need to have, in particular, a theory about when sentence tokens are true and when false, and what counts as a truth-bearer. Among the sentences are simple subject/predicate sentences. We can propose to account for this by positing a distinction in nature between particular things, physical systems, social groups, etc. that can be subjects of discussion, the referents of the subject terms, and properties denoted by the predicate terms.

These can be differentiated thru patterns in real situations (facts) that correspond to the different terms. I&#39;ve mentioned biosemantics as one theory that provides this kind of theory. When a thing has a particular feature -- this cat here has yellow eyes -- we have a real state of affairs which renders the sentence "This cat has yellow eyes" true. So we can develop in this way a theory of truth for simple subject/predicate sentences. From this i could go on to talk about how we can understand the truth-conditions for disjunctions, negations, conjunctions, and conditionals. The best available theory of conditionals, in my opinion, requires real physical possibilities as part of the semantics.

Because logic develops theories about how truth can be conveyed from premises to conclusions, or at least the probability of truth, it also needs hypotheses about the conditions of truth of the sentences. The assumptions about what there needs to be apart from the sentences for the sentences to be true are fairly simple, but the theory about this can be defended in a purely empirical manner.

There&#39;s a very good discussion of this in John Post&#39;s little book, "Metaphysics: A Contemporary Introduction", which, despite its title, has a lot of discussion about the theory of language, and does a good job of explaining biosemantics.

Gilhyle, i don&#39;t know what you mean by "predictive rules" nor do i know what this has to do with logic. if by "entailment" you mean deductive validity, in fact there is such a thing as inductive logic and inference to the best explanation. I have no idea what you mean when you say an argument from analogy has "no predictive force." It seems to me that I gave an example where predictions can in fact be made from the argument. The argument&#39;s conclusion is that a certain hair spray is likely to cause injury to eyes if sprayed in them. That seems to be a prediction.

I also don&#39;t know what your demand for a "proof" is. Inductive arguments and arguments to the best explanation cannot be "proven" to be deductively valid for the simple reason they aren&#39;t deductive arguments. so what?

[ComradeRed]

Originally posted by [email protected] 26, 2007 04:00 pm
Comrade Red, I didn&#39;t agree that logic isn&#39;t in nature. Arguments exist.
Several questions arise from this:

Do arguments exist in nature?

Or do they exist because humans make arguments?

Can logic exist without arguments?

[syndicat]

ComradeRed:

Do arguments exist in nature?

Yes. Arguments are made up of sentence tokens, and thoughts or beliefs in people&#39;s heads. These things exist in nature.


Or do they exist because humans make arguments?

If humans make arguments, then arguments exist. And the only place for them to exist is in nature. Humans are a part of nature.


Can logic exist without arguments?

Logic is made up of theories about arguments, so the subject matter won&#39;t exist without the arguments.

However, the theory is also about the conditions of truth of the sentences making up arguments, and the conditions that make premises supportive of conclusions. In the example I gave of an argument from analogy, there is a relation of similarity between the structures of rabbits&#39; eyes and the human eye. That relationship is independent of the arguments.

Logic isn&#39;t arbitrary because the conditions of truth, and the relations in nature that support inferences, are independent of the sentences making up the arguments. If humans didn&#39;t exist, we wouldn&#39;t be able to generate sentences that describe or denote real states of affairs, but those states of affairs might be such that it would be valid to infer certain things from them, if humans did exist. But the actual inference would be made up of thoughts or sentences, if it exists.

There are real conditions in the world in virtue of which the equations of quantum mechanics hold, and those conditions could hold even if those equations (which are human creations) didn&#39;t exist.

Logic also can assume that there are conditions in the world in virtue of which its theories about arguments make sense. I mentioned the example of how we could suppose that the law of non-contradiction holds because of an empirical fact, that properties are ordered into contraries that exclude each other. If an empirical science provided reasons for thinking this isn&#39;t true in a certain domain, this would require a revision to the logic. This assumption has to be empirical since, in my opinion, we have no way of knowing anything apriori about the world.

[ComradeRed]

Originally posted by [email protected] 26, 2007 04:40 pm
ComradeRed:

Do arguments exist in nature?

Yes. Arguments are made up of sentence tokens, and thoughts or beliefs in people&#39;s heads. These things exist in nature.
So can you find an argument under a rock? Can you find it just sitting there idly by a particle? That is what I meant by "Do arguments exist in nature?".

But it seems your reasoning goes:
1. Humans exist in nature.
2. Arguments exists in humans.
3. Logic consists of arguments.
C0: Arguments exists in nature.
C1: Logic exists in nature.
C2: Because Science studies nature, and Logic exists in nature, then Logic is a science.

This is rather specious reasoning if that is your argument.

First off, C0 is idealistic. "Ideas have to exist somewhere&#33;" That bothers me as a materialist...and frankly I reject it as Platonic.

Premise 3 is rather odd, perhaps it could be revised as Logic is an algebra over the set (class/collection/whatever set-theoretic jargon you want to use) of arguments? There is more to logic than simply a check-list of arguments.

Further, it follows from the premises that without humans arguments would not exist and thus neither would logic&#33; Or in other words, logic does not exist in nature.

That would disqualify Logic from being a science.

[syndicat]

Yes, you can find an argument under a rock....if someone put a piece of paper under the rock with an argument written on it.

Arguments are made up of sentence tokens. Sentence tokens are physical inscriptions or sounds. Arguments can also be made up of thoughts which are brain events that play a certain functional role (mediating between sensory inputs and physical actions).

These things are physical entities.


3. Logic consists of arguments.

No. I said arguments are what logic is about, arguments are the subject matter. A clearer way to restate the argument:

1. Arguments are made up of sentence tokens and thought tokens.
2. Sentence tokens and thought tokens are physical entities, existing in nature.
3. Arguments are the subject matter of logic.
4. Hence, the subject matter of logic are entities that exist in nature.

If arguments are made up of physical entities, why is it "idealist" to suppose they exist in nature? Where else would they exist?


without humans arguments would not exist and thus neither would logic&#33; Or in other words, logic does not exist in nature.

That would disqualify Logic from being a science.

Now your physics chauvinism is showing. By this line reasoning, linguistics, sociology and anthropology are also not sciences since they are about humans and their subject matter wouldn&#39;t exist if humans didn&#39;t.

[ComradeRed]

Originally posted by [email protected] 26, 2007 05:49 pm

without humans arguments would not exist and thus neither would logic&#33; Or in other words, logic does not exist in nature.

That would disqualify Logic from being a science.

Now your physics chauvinism is showing. By this line reasoning, linguistics, sociology and anthropology are also not sciences since they are about humans and their subject matter wouldn&#39;t exist if humans didn&#39;t.I&#39;d hate to break it to you, but anthropology, sociology, psychology, and so forth aren&#39;t sciences.

Science studies nature. That means that biology (and all its subfields like ecology, etc.), geoscience, physics, and chemistry are all sciences...economics, political "science", et al. are not sciences.

They can be formulated mathematically, but their subject matter does not exist in nature.

Their subject matter is aspects of human society as opposed to aspects of nature and only nature.

Does that mean that these subjects don&#39;t work through paradigm shifts? No, it simply means they are not scientific fields.

Sorry but crediting my "physics chauvinism" (what a lousy insult :lol:) to simple definitions from the philosophy of science is rather misleading. I&#39;m referring to the Kuhnian explanation that scientific paradigms arise from explaining physical phenomena.

If you really want you can get a similar explanation from Popper.

[syndicat]

Where do human beings exist if not in nature? if biology is about things that exist in nature, so is psychology, sociology and linguistics, since human beings, human social formations, and human actions all exist in nature. The human capacity to generate sentences is a biological trait, so it&#39;s actually inconsistent to say that biology is a science but linguistics isn&#39;t. Humans are animal organisms of a certain sort. Human society actually exists. Their social structures give powers to people within them, such as the powers exercized by the capitalists within capitalism, or of people in positions in institutions.

There&#39;s no place for human society to exist other than in nature. If institutions like the state exist, if actions of the state have consequences, if corporations exist, and if their actions have consequences, then they exist. And if they exist, they are a part of nature. To say these institutions, social groupings, social events and so on do not exist in nature is to say they don&#39;t exist. If they don&#39;t exist they can have no effects and there can be no true statements about them.

[ComradeRed]

I realize that you suddenly don&#39;t have much of an argument now that science has been defined...other than attempt sophistry, of course.

You may continue to say "Science studies nature. Human society and arguments are in nature. Thus it is part of science" all you want, but you are really purposefully missing the whole point and you know it.

But there&#39;s only a few things that I really hate, and one of them is academic sophists. So there is little room here for me to do other than leave this conversation with one.

Good luck with your platonism.

[syndicat]

I don&#39;t know what your point is, actually. If you want to say human society, institutions and social structures are "not part of nature", go right ahead. Seems obviously false to me.

And i&#39;m obviously not a platonist. I already explained that.

[Lynx]

Originally posted by [email protected] 26, 2007 10:12 pm
I&#39;d hate to break it to you, but anthropology, sociology, psychology, and so forth aren&#39;t sciences.
And paleontology?
Is not science?
Is not a science?
Is not a field of science?
Is not scientific?

Which box fits all?

[Lynx]

When in doubt, wiki it:
http://en.wikipedia.org/wiki/Science

[ComradeRed]

Originally posted by Lynx+April 26, 2007 07:45 pm--> (Lynx &#064; April 26, 2007 07:45 pm)
[email protected] 26, 2007 10:12 pm
I&#39;d hate to break it to you, but anthropology, sociology, psychology, and so forth aren&#39;t sciences.
And paleontology?
Is not science?
Is not a science?
Is not a field of science?
Is not scientific?

Which box fits all?[/b]
Paleontology? You mean the biological study of "prehistoric" life?

Hell the average textbook (say Newman, Garfield, et al (2001). Echoes from the past: world history to the 16th century. Toronto: McGraw-Hill Ryerson Ltd.) on Paleontology defines it as: ...the study of prehistoric life forms on Earth through the examination of plant and animal fossils.

Biology of really old life forms...gee I wonder what that could be <_<


When in doubt, wiki it:
http://en.wikipedia.org/wiki/Science Sorry, but wikipedia&#39;s not a technical reference&#33;

Nor is dictionary.com :lol:

[Lynx]

Originally posted by [email protected] 27, 2007 12:08 am
Paleontology? You mean the biological study of "prehistoric" life?

Hell the average textbook (say Newman, Garfield, et al (2001). Echoes from the past: world history to the 16th century. Toronto: McGraw-Hill Ryerson Ltd.) on Paleontology defines it as: ...the study of prehistoric life forms on Earth through the examination of plant and animal fossils.

Biology of really old life forms...gee I wonder what that could be <_<


When in doubt, wiki it:
http://en.wikipedia.org/wiki/Science Sorry, but wikipedia&#39;s not a technical reference&#33;

Nor is dictionary.com :lol:
I mentioned paleontology because of anthropology. (I suppose paleo-anthropology is a mix of the two?)

Wikipedia classifies logic as a formal science. The debate whether formal science should be considered a part of science is based on empirical vs a priori approaches. No mention of human-only disqualification. That which studies nature is called natural science; that which concerns humans, social science.

I&#39;m trying to find an appropriate box you can both agree upon.

Then, hopefully, the discussion can continue?

[ComradeRed]

Originally posted by [email protected] 26, 2007 09:14 pm
That which studies nature is called natural science; that which concerns humans, social science.

Yes, and...?

Frankly logic is philosophy, as is causality, or anything of a similar manner.

With the social sciences, you "observe" human society. With nature, you observe nature. With logic, you analyze arguments. Do you see the break in the pattern here?

Even with social sciences it&#39;s pretty shaky as no social scientist really observes society except the sociologist...and sociology is such a divided field it makes one wonder if there is any scientific advancement whatsoever.

To assert there is no break in the pattern is to assert Platonism is correct. It makes, as syndicat has openly boasted, ideas physical things which are discovered. Apparently he cannot see the inherent idealism in such a statement, which leads me to question his credentials.


I&#39;m trying to find an appropriate box you can both agree upon. I doubt that very much since he&#39;s a philosopher and I&#39;m a scientist. Naturally, both of us think we know what science is (since philosophers are apt to call everything a "science", and scientists are the opposite).

Apparently defining science as the philosophers of science have is out of the question :lol:


Then, hopefully, the discussion can continue? No, I&#39;ve all ready left the conversation, I couldn&#39;t tolerate speaking any further to such a platonic fellow decoupled from science so. It&#39;s like speaking to a String theorist when I speak with this fellow; except String theorists don&#39;t use sophistry.

[syndicat]

I never said I was a "philosopher". I said it was something I used to teach. At present I work in the manufacturing sector. You essentialize "scientist" as if this is a special breed apart. A completely elitist notion. The methods of the scientists derive from native human cognitive capacities, in particular the method of inference to the best explanation, of seeing if hypotheses survive the test of practice. This means inferring what the consequences of some hypothesis H would be...A, B, C...and seeing if in fact this is what we observe.

How do people get jobs as "scientists"? "Scientists" are employed in universities, corporate R&D operations, government institutes, and the like. Their jobs are based on credentials, like who recommends them, having a degree such as a PhD, and so on.

Now, who can gain access to the university system to attain these sorts of credentials? Not very many members of the working class these days. Tuition has skyrocketed over the last few decades in the USA. The concentration of expertise into the hands of a relative few is a product of the logic of capitalist development. In the era of coporate...or "late" as some say...capitalism, it means the emergence of a third main class, the coordinator class, based not on owneship, but relative monopolization over empowering conditions such as management positions, kinds of expertise that are useful to management to control labor...lawyers breaking unions, engineers designing equipment and software and jobs to control workers, etc. The disolution of the dominance of this class over the working class is one of the central tasks of proletarian self-liberation. Of course, meritocracy is the characteristic ideology of the coordinator class, and wrapping themselves in their superior expertise is their basis for claiming they should be the ones to make the decisions.


Frankly logic is philosophy, as is causality, or anything of a similar manner.

And let&#39;s see if ComradeRed can define coherently what the distinction is. And the denial of causality is a philosophical, not a scientific position. It&#39;s an expression of the philosphical ideology known as extreme empiricism.

The data for logic are arguments. We do observe arguments. We can observe them in print, in scientific papers, in newspaper editorials, in everyday convesation.


It makes, as syndicat has openly boasted, ideas physical things which are discovered. Apparently he cannot see the inherent idealism in such a statement, which leads me to question his credentials.

Now you&#39;ve decided to put words in my mouth, and attribute to me things I never said. I talked about hypotheses and arguments, which are made up of sentence tokens, which are physical entities, or thoughts, which are brain events. I&#39;ll leave it up to you to say what "ideas" are since I didn&#39;t talk about "ideas".

And platonism is something I reject, as I&#39;ve pointed out. But ComradeRed prefers the method of innuendo and misdescription of someone&#39;s viewpoint rather than honest discussion. Platonism is the view that there are eternally existing abstract entities outside physical nature, which are the structures that are the alleged subject matter of logic and math, and which we allegedly have some apriori access to. Now, as I&#39;ve made plain on numerous occasions in this thread, I reject this entire viewpoint. I don&#39;t think there are any such entities or any apriori access mode to reality.

In another thread he says Marxism is a "paradigm" not a "science". So maybe he&#39;d like to explain to us what that difference is, and what the difference is between "philosophy", "science" and "paradigm." Since he makes such a big hoohah over the difference, surely he can explain what it is.

[Lynx]

Frankly logic is philosophy, as is causality, or anything of a similar manner.
I can accept hypotheses being categorized as philosophy.

With the social sciences, you "observe" human society. With nature, you observe nature. With logic, you analyze arguments. Do you see the break in the pattern here?
I don&#39;t. Are you asking if logic is falsifiable?

Even with social sciences it&#39;s pretty shaky as no social scientist really observes society except the sociologist...and sociology is such a divided field it makes one wonder if there is any scientific advancement whatsoever.
Perhaps some examples would help clear the air:
Anthropology would be categorized as a social science; paleontology would not.
According to your earlier posts, anthropology is not science; paleontology is

Apparently defining science as the philosophers of science have is out of the question :lol:
Defining science from various perspectives for the purpose of semantics is quite reasonable. It&#39;s not like an engineer would come along and cut off your funding&#33;

No, I&#39;ve all ready left the conversation,
Ah, but have you left the building? ;)

I couldn&#39;t tolerate speaking any further to such a platonic fellow decoupled from science so. It&#39;s like speaking to a String theorist when I speak with this fellow; except String theorists don&#39;t use sophistry.
If String theorists don&#39;t use sophistry, do they use the scientific method?

[ComradeRed]

Originally posted by [email protected] 27, 2007 05:36 am

With the social sciences, you "observe" human society. With nature, you observe nature. With logic, you analyze arguments. Do you see the break in the pattern here?
I don&#39;t. Are you asking if logic is falsifiable?
I&#39;m saying there is no observation, hypothesis formulation, testing, and so forth.

There is no empiricism with logic. The arguments that logic is empirical stems from one of two stances: 1. Platonism, or 2. a gross misunderstanding of the "Quantum Logic" interpretation of Quantum Mechanics (despite its name it actually has nothing to do with logic, no more so than Newton&#39;s equation does ;)).

(As I&#39;ve said half-jokingly elsewhere, economists e.g. are failed scientists because they can&#39;t properly use empiricism. Similar statements could be said about a few other social "scientists".)



Even with social sciences it&#39;s pretty shaky as no social scientist really observes society except the sociologist...and sociology is such a divided field it makes one wonder if there is any scientific advancement whatsoever.
Perhaps some examples would help clear the air:
Anthropology would be categorized as a social science; paleontology would not.
According to your earlier posts, anthropology is not science; paleontology is Anthropology deals with cultural and physical (although chiefly the former) aspects of ancient humans.

Paleontology deals with the biological study of life prior to the existence of humans.



No, I&#39;ve all ready left the conversation,
Ah, but have you left the building? ;) After this post, I&#39;ll "leave the building" (hell, I&#39;m sprinting just to get away from this Platonist&#33;).



I couldn&#39;t tolerate speaking any further to such a platonic fellow decoupled from science so. It&#39;s like speaking to a String theorist when I speak with this fellow; except String theorists don&#39;t use sophistry.
If String theorists don&#39;t use sophistry, do they use the scientific method? No, they don&#39;t (as shocking as that may be to some). They use the "mathematical method" of proofs rather than coming up with anything testable.

Further, you can see the Platonism of String Theory in their String Cosmology...viz. their use of the "multiverse".

As you might expect, I fully reject String Theory.

[gilhyle]

Originally posted by [email protected] 27, 2007 12:00 am
i don&#39;t know what you mean by "predictive rules" .......

I also don&#39;t know what your demand for a "proof" is.
Isnt there a basic difference between all other forms of &#39;logical&#39; agument and arguments which rely on entailment. You can symbolise the deductive inference and re-apply it to any case that follows the form and truth will follow. You cant do that with arguments from analogy or inductive arguments - you have to know that its about hairspray to know the argument works. There are no universal rules - hence the theory is ownly a morphology and when it comes to morphology I prefer dialectics : for political reasons.

[syndicat]

I&#39;m saying there is no observation, hypothesis formulation, testing, and so forth. There is no empiricism with logic.

What is observed, as I pointed out, are actual arguments. These occur in books and papers of all sorts, in daily conversation, in the ways that "scientists" try to support their conclusions (science is filled with arguments and debates), and so on. Since arguments are physical entities -- inscriptions and sounds -- they can be observed.

My claim that logic can be understood as aposteriori had nothing whatsoever to do with quantum mechanics.

Logicians formulate "principles" or "rules" (these are roughly equivalent) to account for the validity of the arguments they observe. Any proposed rule could be falsified if there are instances of the rule that are clearly invalid. I gave examples of invalid arguments that are instances of the rules of the classical Frege/Russell logic. This falsifies the claim that that logical theory is an adequate theory of deductive inferences formulated in natural human languages. Testing occurs through trying to come up with or find arguments that falsify proposed rules or are not captured by the theory.

When we develop the semantics for a logical theory, we may posit fairly simple aspects of realiity such as the distinction between particular things (anything that can be the subject of discussion) and features (things that we might predicate or attribute to subjects of discussion). This is reflected in the universal trait of human natural languages, the subject/predicate structure. What is the explanation of this natural fact?

This semantics can be defended through an empirical theory about the origin and nature of language. Humans are biological entities, and our language facility is an inherited biological trait of humans. Why do we have it? This calls for an answer in terms of evolutionary theory.

Platonism presupposes a very different approach to understanding logic. The platonist believes that sentences correspond to eternally existing abstract entities called "propositions." The logical connectives, on this view, correspond to real structural features of these abstract entities. The logical principles are understood as eternal, necessary truths that exist in this eternal abstract realm. On this view the way we gain access to insights about this realm is thru intellectual intuition, an apriori mode of knowledge. I reject platonism for a variety of reasons. I don&#39;t think there is any apriori mode of access...how could human brains somehow get hooked up to an eternally existing abstract realm outside nature? And I don&#39;t see any need to posit eternal abstract entities. They aren&#39;t needed. They are not what we encounter when we encounter arguments. We encounter arguments as made up of inscriptions on paper or sounds.

[syndicat]

Isnt there a basic difference between all other forms of &#39;logical&#39; agument and arguments which rely on entailment. You can symbolise the deductive inference and re-apply it to any case that follows the form and truth will follow.

Truth will "follow" only if the premises are true. And how do you learn that?

Inductive logic can be formulated in terms of rules or principles. There are also techniques for evaluating hypotheses and comparing competing hypotheses. You can find these in any textbook on the subject, such as "Inductive Arguments" by Kathleen Moore.

For example, an argument by analogy will go something like this:

1. A has features W, X, Y, Z
2. B has features W, X and Y
3. Therefore, B probably also has feature Z.

But that&#39;s not all there is to it. With inductive logic, there are also a number of guiding rules. In an argument by analogy the number and relevance of the features shared between A and B is important to the plausibility of the argument.

And what is "dialectic"? You&#39;ve not explained that.

[gilhyle]

No and nor will I cos it would take us from our point. I mention it only to illustrate that I am not opposed to having typologies of inferences or judgements.

Your answer still seems to elide over the difference between a formal system for the study of entailment and a formal system for the study of induction.

The former gets you to a point where you can say that if the rules of the system are followed, the conclusion will follow without referrring to the content of any proposition and you can substitute actual propositions for the symbols.

This is not the case with the schemas of inductive argument to which you refer. You CANNOT know whether the conclusion follows except by assessing the particular propositions. An inductive argument that works for one proposition fails for another.

The methodology is entirely different. What inductive logic schemas do is try to devise models and then see how large a class of accepted inferences the schema conforms to.

This is a very fundamental difference between propositional logic and the inductive schema to which you refer.

[syndicat]

Inductive methods includes mathematical probability techniques like multivariate regression used in the social sciences. This is a formal mathematical method. THere are formal developments of probability.

If you&#39;re going to try to apply symbolic deductive logic, you also have to take the context into account, in how you choose the abbreviate the argument.

And as i pointed out, there are classes of deductive arguments that cannot be accounted for by the classical Frege/Russell symbolic logic. This logic&#39;s treatment of conditionals is known to be defective, for example. There are alternative logics that also have formal symbolic developments, like temporal logic, modal logic, relevance logic.

Not all inferences are warranted solely in virtue of a pattern or form.

[gilhyle]

In propositional logic you dont take context into account. YOU take context into account to assess whether propositional logic accords with ordinary language inferences, but that behaviour on your part is outside the discipline of propositional logic.

Your criticisms of this type of logic are that it doesnt account fully for ordinary language usage. But that would only be a problem if it was the purpose of such logic to observe and classify ordinary language inferences. That is not what propositional logic is; it is a formal system. Logicians have always known that the ordinary language terms (if...then, or, and, not, iff) only aproximate to the inferential patterns of the logical relations they are used to label. It - correctly - does not bother them until they try to use propositional logic to determine real world issues - which they shouldnt.

My point is this: you are correct that propositional logic is of limited practical application. You are correct that propositional logic does not exhaust the potential for the study of ordinary language inferences. You are incorrect if you think these observations are a critique of propositional logic.

And what I object to is the idea that the further study of ordinary language inferences can be conducted by studying classes of inferences which are defined by formal characteristics. This is a prejudice. The classes of inferences that are studied need to be defined by reference to their social role. For example - inferences in musical compositin are correctly studied (and studied quite well) in musical theory, inferences in economic decision making are correctly studied (although not very well) in economic theory. Inferences made by groups are correctly studied in social psychology (not too badly).

Of course there are common features whcih will cross these social contexts. Those common features often have a lot to do with probability judgements. That insight is, however, trivial since a) the actual inferences made are seriously underdetermined by the statistical laws they refer to (not least because humans are miserable assessors of probability) and b) because (unlike a logic of entailment) there is no capacity to predict correct inferences for socially significant classes of inferences from their formal features.

Effectively you recognise this point when you say "Not all inferences are warranted solely in virtue of a pattern or form." Exactly &#33; Now work out the consequence of that fact for your area of study. It is a consequence of that that you should not define your subject matter by reference to form as for example Kathleen Moore does. You define your field of study by reference 1) to who you are and 2) the nature of the social practice to be studied.

[syndicat]

It is a consequence of that that you should not define your subject matter by reference to form as for example Kathleen Moore does. You define your field of study by reference 1) to who you are and 2) the nature of the social practice to be studied.

Have you read Kathleen Moore&#39;s book? She doesn&#39;t define inductive inferences soley be reference to form. Who you are usually isn&#39;t relevant to whether an argument is cogent or not. Moreover the considerations she adduces for evaluating inductive inferences are not subject matter dependent in the sense of applying only within some subject.

There are is quite a bit that can be said about the criteria of adequacy of hypotheses that is independent of the particular subject matter. From the fact that a logic isn&#39;t developed as a formal mathematical theory, it doesn&#39;t follow it is not independent of the particular subject matter. For example, Ockham&#39;s Razor is a principle for evaluating hypotheses, but it isn&#39;t formulated as part of a formal theory.

There is in fact a large class of deductively valid inferences that cannot be accounted for by the classical Frege/Russell logic, and a large class of invalid arguments that are instances of the inference patterns of the classical logic. That&#39;s why the theory is inadequate. The theory is not developed for its own sake as a formal game. It is supposed to be a theory OF valid deductive inferences. The inadequacy of the theory for large classes of inferences is precisely why other logics have been developed, such as tense logic and modal logic and attempts to develop a new theory of conditionals. These theories are all developed as formal theories.

[gilhyle]

The heart of your point is that there are a broad range of valid arguments not accounted for by propositional logic. It is your gloss that this is a fundamental problem with propositional logic. It is that point - which I think seems obvious to you - which I think is problematic.

As to your suggestion that my point against kathleen Moore does not work because she does not assess arguments merely formally; Dont think that argument works - you seem to confuse the definition of the subject matter with the methodology for evaluating the arguments. I did not say that she assesses arguments by reference to formal features only - rather I said the opposite (and agreed with you in that). What I did say was that she defines her subject matter by reference to common formal characteristics - this is necessarily so if you define your subject matter as the class of inductive arguments : induction is a formal concept.

I doubt the capacity of such study to produce siginficant results. For example, Ockham&#39;s razor is actually of little use in evaluating hypotheses. On the contrary, it can be used retrospectively to rationalise why a certain conclusion was drawn, but it cannot be used in advance with any reliability to reach conclusions. Shoudl it be breached that has no consequences for the validity of the inference.

But dont get me wrong. If people can develop formal systems as powerful as propositional logic, good luck to them - it&#39;ll be impressive.

But we live in a society which is dominated by an ideology which likes to develop post hoc rationalising models of human behaviour in order to obscure the social forces and class conflicts which actually work to create those behaviours. If we as communists fail to distinguish clearly between formal analysis and substantive social analysis, we will not be able to reject the spurious rationalising modeling which mascarades as science. Some of the methodologies you are attracted to, I suspect, fall into these ideological categories.

[syndicat]

If we as communists fail to distinguish clearly between formal analysis and substantive social analysis, we will not be able to reject the spurious rationalising modeling which mascarades as science. Some of the methodologies you are attracted to, I suspect, fall into these ideological categories.

What "methodologies" are you talking about? The method of inference to the best explanation? That is the main way that humans have for acquiring knowledge about our world. It is you who defend the importance of classical formal logic. I was arguing precisely that its importance had been greatly over-emphized in traditional philosophy. In fact its value is subordinate to the method of hypothesis and practical test. Your distinction between "formal analysis" and "substantive social analysis" is thus entirely specious.

[gilhyle]

There is just no relationship between the claim that certain schools of philosophy have overemphasised the importance of formal logic and the claim that you can develop logics of induction etc.

This is illustrated by my claim that there is an alternative approach based on defined social practices rather than forms of inductive argument. Right or wrong, the claim illustrates that the limitations of propositional logic do not legitimate the alternative you advocate.

[syndicat]

This is illustrated by my claim that there is an alternative approach based on defined social practices rather than forms of inductive argument. Right or wrong, the claim illustrates that the limitations of propositional logic do not legitimate the alternative you advocate.

I did not rest my claim that inference to the best explanation is the most important method we have for learning about the world on the limitations of classical Frege/Russell logic. On the contrary, I was pointing out that classical Frege/Russell logic is limited as an account of its own domain of deductive inference. That&#39;s a different question from the existence of other inferential practices that warrant conclusions, apart from deductive chains of reasoning.

What do you mean by "an alternative approach based on defined social practices"? how does this give us an understanding of inferential practices that warrant acceptance of conclusions?

My claim that there are inductive logics that work is based on the actual existence of such logics, not any evaluation of "different schools of philosophy".

[gilhyle]

Originally posted by [email protected] 30, 2007 11:14 pm


What do you mean by "an alternative approach based on defined social practices"? how does this give us an understanding of inferential practices that warrant acceptance of conclusions?

My claim that there are inductive logics that work is based on the actual existence of such logics, not any evaluation of "different schools of philosophy".
No, mine is, yours isnt - I gave the example of the Theory of Music earlier. Composition of music is a social practice and there is theory as to how this social practice happens. Some of that theory is formal (theory of composition) some of it is sociological ....etc.

The difference I would suggest between the kinds of theories of social practice that interest me and what interests you is that the inductive logics to which you refer significantly under-determine the practices to which they refer; the theories to which I refer under-determine the inference event to a much lesser degree .

The theories of inductive logic are at such a level of abstraction that they provide little insight to the actual inferences to which they refer. To understand those actual inferences you need understand the social practices they are part of.

If I was a Wittgensteinian (which Im not) I might say that you cannot study &#39;induction&#39; without understanding the rules of the games from within which inferences appear.

[syndicat]

It seems to me that you confuse a theory with the methodologies used in developing and evaluating a theory. A theory is a set of hypotheses that explain phenomena that occur in some terrain. A plausible theory of some set of phenomena can&#39;t be developed if you aren&#39;t familiar with that terrain. but a theory must hold up to what we might call the test of truth. if H is a hypthesis, we can infer consequences from it, X, Y, Z...things that would hold in the world if H is true. We can then try to see if X, Y, Z do hold. we can also evaluate a theory by how comprehensive it is, that is, how far it goes in accounting for the facts.

to take an example, we posit class structure as an inference to the best explanation. it is reasonable to suppose that society is divided into classes based on what we observe in terms of things like differences in group behavior. Marx&#39;s labor/capital polarity is one theory of the class structure of capitalism. but i think this theory is defective in that it fails to account for the emergence of a new main class in corporate (some would say "late") capitalism, the class of managers and top professionals. This class is hired labor, has maybe small capital holdings but that isn&#39;t what defines their life prospects or the basis of their power over the working class. The conflicts between this class and wage-earners suggests a class division.

There is a characteristic ideology, meritocracy, which this class tends to use to justify its power, why they should make the decisions. the emergence of this class suggests that a different class theory is needed, to supercede Marx&#39;s overly simple bipolar scheme.

[gilhyle]

Originally posted by [email protected] 01, 2007 06:25 pm
It seems to me that you confuse a theory with the methodologies used in developing and evaluating a theory. A theory is a set of hypotheses that explain phenomena that occur in some terrain. A plausible theory of some set of phenomena can&#39;t be developed if you aren&#39;t familiar with that terrain. but a theory must hold up to what we might call the test of truth. if H is a hypthesis, we can infer consequences from it, X, Y, Z...things that would hold in the world if H is true. We can then try to see if X, Y, Z do hold. we can also evaluate a theory by how comprehensive it is, that is, how far it goes in accounting for the facts.



Yes the issue is about what a discipline of inductive logic can achieve given that its method is primarily inductive. But I am not confusing the two - I am relating them.

(I&#39;ll defend Marx&#39;s conception of class another day &#33;&#33;&#33;)