Empiricism and Logic

[Surlethe]

I've been thinking lately about empiricism and the structure of logic. Could one make an empirical argument for the existence of logic? That is, the definitions and rules of logic have been discovered empirically by trial and error, and are as set in stone as the laws of thermodynamics?

[Vyraeth]

If this is psuedo-logic babble, call me on it right away.

But, assuming there's a system when you need A and B to get C. And thus the logic of the system is A+B=C. Then couldn't you empirically verify the logic of the system by removing B, and thus not getting C. Or removing A, and again, not getting C?

[petesampras]

If this is psuedo-logic babble, call me on it right away.

But, assuming there's a system when you need A and B to get C. And thus the logic of the system is A+B=C. Then couldn't you empirically verify the logic of the system by removing B, and thus not getting C. Or removing A, and again, not getting C?

No. Logic is a general purpose set of rules. When people talk of a system having logic, what they mean is a specific set of rules made up of logical statements which govern how the system behaves. All you can prove via examples similar to the one above is that a set of logical rules you have stated to apply to a system are valid or not. Well, strictly speaking, you can't actually *prove* that, but let's not get into that here.

As for the OP, there is an interesting paper by Marvin Minsky (the A.I. guy) about a similar topic. He looks at all possible formal systems which can exist and finds basic maths to be the simplest system which conforms to certain essential properties. I can't remember any of the details, but I'll look it up. I imagine one could do a similar study with the various types of formal logic, maybe?

[Rye]

I've been thinking lately about empiricism and the structure of logic. Could one make an empirical argument for the existence of logic? That is, the definitions and rules of logic have been discovered empirically by trial and error, and are as set in stone as the laws of thermodynamics?

You need to have logic before you can construct an argument, and I'm not sure if you're allowed to do that and then make an argument confirming the existence of logic. That might be a bit circular.

[Kuroneko]

I've been thinking lately about empiricism and the structure of logic. Could one make an empirical argument for the existence of logic? That is, the definitions and rules of logic have been discovered empirically by trial and error, and are as set in stone as the laws of thermodynamics?

Yes and no, i.e., yes but not quite like you frame it. The claim that logic was discovered empirically would be a straightforward consequence of the core empiricist position, which is that there are no innate ideas or knowledge and that every such thing is derived from sense experience. The argument would not be about the existence of logic per se, but rather the mode of its acquisition.

[petesampras]

I've been thinking lately about empiricism and the structure of logic. Could one make an empirical argument for the existence of logic? That is, the definitions and rules of logic have been discovered empirically by trial and error, and are as set in stone as the laws of thermodynamics?

Yes and no, i.e., yes but not quite like you frame it. The claim that logic was discovered empirically would be a straightforward consequence of the core empiricist position, which is that there are no innate ideas or knowledge and that every such thing is derived from sense experience. The argument would not be about the existence of logic per se, but rather the mode of its acquisition.

I tend to disagree with this position. Logic is not a property of the natural world, it is a tool used to discribe the world. You can't, in truth, use logic to derive any new knowledge about the world that you didn't already know. The strength of logic, versus natural language, as a means of describing the world is that it doesn't accidently let you make statements which are vague, self-contradictory or which generate new knowledge about the world which isn't grounded. As such, it is a great tool, but it is ultimately just a tool not a property of the universe.

The empiricist position deals only with the natural world, it has no bearing on formal systems. A formal system can be whatever you want it to be. I could invent a new logic where A->B automaticaly means B->A. You first thought might be - 'that is clearly wrong', but this is not the case. Because any system of logic cannot create ground truths, in this system of logic I couldn't put forth a ground truth of A-> B without also believing B->A. This would make this system of logic inferior as a discriptive tool since I wouldn't be able to describe A->B relationships where it is not the case that B->A. However, neither forms would be 'right' or 'wrong', since they are ultimately just formal systems.

[Surlethe]

Yes and no, i.e., yes but not quite like you frame it. The claim that logic was discovered empirically would be a straightforward consequence of the core empiricist position, which is that there are no innate ideas or knowledge and that every such thing is derived from sense experience. The argument would not be about the existence of logic per se, but rather the mode of its acquisition.

I have noticed that this is the refutation of the common misrepresentation of the empiricist argument for the acquisition of logic (e.g., in C.S. Lewis' Miracles), but the argument I'm trying to construct is, I think, subtly different. It's not one of acquisition, but rather of continued applicability, perhaps? That is, logic has not been seen to fail yet; it is not expected to ever fail.

You need to have logic before you can construct an argument, and I'm not sure if you're allowed to do that and then make an argument confirming the existence of logic. That might be a bit circular.

This is true. In argumentation, both sides must accept the validity of logic as a starting point, else there's no way of determining the truth of a given proposition from the truth of another proposition.

[petesampras]

It's not one of acquisition, but rather of continued applicability, perhaps? That is, logic has not been seen to fail yet; it is not expected to ever fail.

I think you misunderstand what logic is. How is it, you believe, that logic could ever be seen to fail? Describe an event which could occur in the world that would demonstrate a failure of logic.

[Rye]

How about this scenario? : There could be a strange rock found in a desert somewhere that everyone who measures it gets wildly different results. How would you resolve that?

[petesampras]

How about this scenario? : There could be a strange rock found in a desert somewhere that everyone who measures it gets wildly different results. How would you resolve that?

I fail to see how this invalidates logic in any way. I still think you guys don't fully understand what logic actually is. Express part or all of the situation in formal logic and show me where the problem is.

[Rye]

Uh, I don't know how? The idea was meant to be of an object in reality that gives out contradictory information somehow. If a contradiction exists in reality, won't logic say that it's false? And it's clearly not, so should we accept both even though they contradict too?

[Surlethe]

I think you misunderstand what logic is. How is it, you believe, that logic could ever be seen to fail? Describe an event which could occur in the world that would demonstrate a failure of logic.

Suppose there existed -- could be shown to exist -- propositions A and B such that it could be shown that A -> B, ~B, and A are simultaneously true. This would signify literally a failure in logic: for A and B, logic would fail to describe their relationship. I suppose that in order to avoid begging the question in this 'empirical' line of thinking, you have to show that the step from "hasn't failed in the past" to "unlikely to fail in the future" is deductively valid, even if you don't permit the rest of deductive logic?

As best I understand logic, it is a system (like mathematics) used to describe the world; like a mathematical system, it can then presumably fail to describe reality (for example, the mathematical system generated by the axioms of Newtonian mechanics don't completely describe nature).

[petesampras]

I think you misunderstand what logic is. How is it, you believe, that logic could ever be seen to fail? Describe an event which could occur in the world that would demonstrate a failure of logic.

Suppose there existed -- could be shown to exist -- propositions A and B such that it could be shown that A -> B, ~B, and A are simultaneously true.

I'll assume statements A->B, ~B and A are derived from observation of the real world and are being applied as premises (if they have been logicaly derived then you need to give full details about what your premises are and how you have derived these statements). Now, to make the statement A->B as a premise you are saying that you believe that whenever A is true that B is true. However, if you have witnessed ~B and A being true, then you know for a fact that you can't say A -> B. Of course, the key point is that you can never really say that A -> B in the real world, you can merely assume it is true until you see a counter example.

This would signify literally a failure in logic: for A and B, logic would fail to describe their relationship. I suppose that in order to avoid begging the question in this 'empirical' line of thinking, you have to show that the step from "hasn't failed in the past" to "unlikely to fail in the future" is deductively valid, even if you don't permit the rest of deductive logic?

As best I understand logic, it is a system (like mathematics) used to describe the world; like a mathematical system, it can then presumably fail to describe reality (for example, the mathematical system generated by the axioms of Newtonian mechanics don't completely describe nature).

I'm not sure what relevance this has to the issue at hand. Sure, there may exist knowledge which cannot be represented by logic, but this does not invalidate logic in anyway. Propositional logic cannot describe all sentances of predicate logic. This does not invalidate propositional logic, it merely places limits on what it can represent. Like any language, the various logics will have limits to what you can say in them.

My main point here is that the very idea of 'validating' logic represents a misunderstanding of what logic is. Logic is just a language. It requires no empirical proof, anymore than English, Chinese or C++ require empirical proof.

[petesampras]

Uh, I don't know how? The idea was meant to be of an object in reality that gives out contradictory information somehow. If a contradiction exists in reality, won't logic say that it's false? And it's clearly not, so should we accept both even though they contradict too?

Getting different readings from a rock does not mean a contradiction exists in reality. It means there is a rock which gives wildly different readings for some reason. There is no scenario you can come up with which will show a contradiction in reality. A contradiction cannot 'exist' in reality because a contradiction is a logical construct. When you get a contradiction from a set of premises in logic it is because you are confused about what you believe to be true - you have stated a premise which says one thing and another premise which says another. That just means you are dumb, it is no problem for the validity of logic nor does it mean that a 'contradiction' can somehow exist in the real world.

[Surlethe]

I'll assume statements A->B, ~B and A are derived from observation of the real world and are being applied as premises (if they have been logicaly derived then you need to give full details about what your premises are and how you have derived these statements). Now, to make the statement A->B as a premise you are saying that you believe that whenever A is true that B is true. However, if you have witnessed ~B and A being true, then you know for a fact that you can't say A -> B. Of course, the key point is that you can never really say that A -> B in the real world, you can merely assume it is true until you see a counter example.

This is true. Replace A->B with "A and B", which is, as I understand, empirically determinable. The point is that we can test logic, and have been doing so every time we've made an argument or prediction and then had it turn out to be true.

I'm not sure what relevance this has to the issue at hand. Sure, there may exist knowledge which cannot be represented by logic, but this does not invalidate logic in anyway. Propositional logic cannot describe all sentances of predicate logic. This does not invalidate propositional logic, it merely places limits on what it can represent. Like any language, the various logics will have limits to what you can say in them.

This is what I mean by showing that logic 'fails'; I thought I made that clear in the previous post.

My main point here is that the very idea of 'validating' logic represents a misunderstanding of what logic is. Logic is just a language. It requires no empirical proof, anymore than English, Chinese or C++ require empirical proof.

I understand this: logic as it's been developed is just as self-contained as mathematics. What I meant was that, like mathematics, it's been influenced in its development by empirical observations; the integers, for a mathematical example, have addition defined without respect to reality, but the addition is influenced by reality and models reality. So, we say that the mathematics of integer addition can't be wrong, in the sense that no empirical observations contradict it. Does this make sense?

[petesampras]

This is true. Replace A->B with "A and B", which is, as I understand, empirically determinable.

So you would be using (A and B) and ~B as the premises to your logical argument. Logic will just return a contradiction. I still don't see how this is a failing of logic. In your premises you are stating that you believe B and ~B to be true. It just means that you are confused, a proposition is either true or not true.

The point is that we can test logic, and have been doing so every time we've made an argument or prediction and then had it turn out to be true.

No, we cannot. Logic does not / cannot make predictions about reality. This is a misconception about what logic is. A logical argument consists of a set of premises connected via the rules of logic to a conclusion. It's meaning is that whenever the premises are true, the conclusion is also true. At first glance, this may seem able to generate predictions. Empirically verify the premises and you get a 'prediction' the conclusion. However, this is not the case. All the work you have done to verify you premises can be directly applied to verifying the conclusion. You need do no extra empirical work. There exists no logical argument where empirical data which verifies the premises does not also verify the conclusion. This is because what a logical argument really does is to rewrite you premises in another form. It is not generating new knowledge or making new predictions. It cannot. It has been designed that way[/quote]

This is what I mean by showing that logic 'fails'; I thought I made that clear in the previous post.

If the claim is just that there are somethings that logic cannot represent, then I have no argument with you. To me, however, the phrase "Could one make an empirical argument for the existence of logic?" implies that you believe logic could be empiricaly verified or falsified, which I strongly disagree with, for reasons already stated.

I understand this: logic as it's been developed is just as self-contained as mathematics. What I meant was that, like mathematics, it's been influenced in its development by empirical observations; the integers, for a mathematical example, have addition defined without respect to reality, but the addition is influenced by reality and models reality. So, we say that the mathematics of integer addition can't be wrong, in the sense that no empirical observations contradict it. Does this make sense?

I kind of agree with what you are saying here, I think. Logic has been developed with certain demands of expression from the type of things it needs to express. Therefore it is not surprising that it is good at expressing such things. Same is true for any natural language - English, Chinese, Spanish, etc.

[drachefly]

Surlethe, I never expected you to put forth the same argument as Montrosse...

My answer to him was the same as to you: If you have a pair of statements A and B with the properties you described, then those statements are not actually propositions.

[Darth Wong]

Getting different readings from a rock does not mean a contradiction exists in reality. It means there is a rock which gives wildly different readings for some reason. There is no scenario you can come up with which will show a contradiction in reality.

Actually, there is one: an irrational universe. One could argue that the assumption of a rational universe is necessary in order to apply the rules of logic to reality. Alternatively, one could view the idea of a rational universe as a theory, which is supported by the consistency of the universe's behaviour.

[drachefly]

Even if the world were quite thoroughly irrational and without consistent form, there are at least some things in it that are not totally irrational and illogical: our minds. If our minds were thoroughly irrational and inconsistent, we would not be thinking.

So, we can still devise logic and use it. We would just have a harder time applying it to the world around us if we have a hard time devising properties which do not simultaneously apply and not apply in the same sense to the same thing.

[Darth Wong]

What makes you think we would have been able to devise logic in an illogical universe?

[drachefly]

If we can't think, then the idea 'we' loses all meaning. If we can, we can devise concepts and such. Among them would be the little mind-game we know of as logic.

So, our discussion would revolve around a world with some screwy things in it, but where not everything is screwy.

[Darth Wong]

If we can't think, then the idea 'we' loses all meaning.

Since when does the idea of logic represent the only possible means of thought?

If we can, we can devise concepts and such. Among them would be the little mind-game we know of as logic.

The fact that one can devise concepts in an irrational universe does not mean he will necessarily devise logic.

So, our discussion would revolve around a world with some screwy things in it, but where not everything is screwy.

A universe which is inconsistent need not be 100% inconsistent in order to be sufficiently inconsistent that logic has no meaning in reality. Logic allows us to deduce things, and you can't reliably deduce things when the universe does not behave in a consistent fashion.

Actually, the largest problem with this thought exercise is its underlying assumption that the universe's massive irrationality (so severe that rocks spontaneously change size significantly and constantly) would actually allow the bio-chemical processes that permit the generation and evolution of life.

[Kuroneko]

Foreword: there seems to be a kind of equivocation on the various senses we use the word "logic". Firstly, there is one sense of logic seen in phrases like "he's behaving illogically" that has a certain normative component in that we're evaluating the correctness of incorrectness of certain modes of thought. This has a direct empirical component--what patterns of thought accomplish a given goal depends directly on how the world is structured. Secondly, there are particular systems of logic, which are indeed self-contained and analogous to languages (as petersampras rightly contends), but we can still ask very relevant empirical questions about them, such as "how well do they describe [or can be used to describe] the world?" The property of being "self-contained" does not make logic particularly special, as one can also take, say, classical mechanics, neuter it from claiming any relevance to the universe, and use it as a kind of language to describe purely mathematical constructs, e.g., symplectic manifolds.

---

It's not one of acquisition, but rather of continued applicability, perhaps? That is, logic has not been seen to fail yet; it is not expected to ever fail.

Yes; empiricism would have to hold that logic is just a particularly general quasi-scientific theory--much more well-entrenched, perhaps, but in the end the same type of thing.

I tend to disagree with this position. Logic is not a property of the natural world, it is a tool used to discribe the world.

Perhaps, but it would be in the same sense that the laws of thermodynamics are not properties of the world, but tools used to describe the world. In the end, the distinction is a side issue of metaphysics; empiricism is compatible with just about any resolution to that question.

he empiricist position deals only with the natural world, it has no bearing on formal systems. A formal system can be whatever you want it to be.

Correct. But some formal systems can be used to describe the world in very general and powerful ways; others are much more limited in this regard. Logic would be a system of the former type. (Actually, it would be a bit improper to refer to it in the singular...)

My main point here is that the very idea of 'validating' logic represents a misunderstanding of what logic is. Logic is just a language. It requires no empirical proof, anymore than English, Chinese or C++ require empirical proof.

You're not seeing the real contention of empiricism. Yes, formal systems can be defined in nigh-arbitrary ways, and they do not require justification with respect to themselves. However, when we make the further claim that a given system is applicable to the universe, that is an empirical statement and can be verified or falsified empirically. To use your example of programming languages, neither C nor perl require "justification" in as much as they are languages, but it doesn't mean that one may be better suited for some tasks than the other, or that such claims of suitability cannot be empirically resolved.

Getting different readings from a rock does not mean a contradiction exists in reality. It means there is a rock which gives wildly different readings for some reason. There is no scenario you can come up with which will show a contradiction in reality. A contradiction cannot 'exist' in reality because a contradiction is a logical construct.

Let's not substitute metaphysics for the real issue. It is a fairly facile observation that there are in fact many different systems, and that some of them are better suited to some tasks than others. For example, in standard propositional logic, truth values form a distributive lattice, so that p∧(q∨r) → (p∧q)∨(p∧r) is a validity. In quantum logic, this is no longer the case: for example, try the two-slit experiment with p="particle detected", q [r]="particle went through slit 1 [2]". Now, it doesn't take much further imagination that if we were to observe quantum phenomena as a matter of course in the real world and classical behavior as a limiting case (pervesely enough, a logically possible scenario), we would consider quantum logic as the real McCoy and classical logic as nothing more than an interesting curiosity, i.e., the reverse of the typical attitude. Logic in the first of the above senses is learned from experience, and the various systems of logic are just attempts to formalize those lessons; some formalizations are particularly well-adapted to certain contexts.

There may be some objections here. One might contend that I'm not framing the scenario correctly in the double-slit experiment, or that I'm thinking of a classical particle and that sort of thinking just doesn't apply at the quantum level. Of course one would be completely correct in this accusation, but it nevertheless misses the point. Classical logic requires rather heavy machinery to to make any sense of the two-slit experiment, and no doubt quantum logic would need contrivances of similar complexity to make sense of classical scenarios. But that's absolutely nothing special. One can flatten spacetime by introducing some cleverly designed fields. One can bring back absolute space by resurrecting aether. One can even go further to say that there is absolutely no scientific hypothesis that cannot be rescued from falsification by jumping through sufficiently many hoops in modifying other theories to accommodate it. The real question, as always, is whether those hoops are worth jumping through.

[drachefly]

Darth Wong, perhaps we are thinking of the exercise in different terms. I am saying,

"We are attempting to determine whether Logic is valid. We do not wish to bring in any sensory evidence; but that leaves us the knowledge of the state of our own minds (i.e. our subjective experiences). Logic is seen to be valid with it as a subject matter."

I don't know what you thought I was saying. No, don't answer until you've read the whole thing.

If we can't think, then the idea 'we' loses all meaning.

Since when does the idea of logic represent the only possible means of thought?

If you are referring to this, that's not what I meant:

Even if the world were quite thoroughly irrational and without consistent form, there are at least some things in it that are not totally irrational and illogical: our minds. If our minds were thoroughly irrational and inconsistent, we would not be thinking.

I did not here mean that our minds necessarily use logic to think; I meant that our minds can be described logically: at any one moment, you are not both thinking about cats and not thinking about cats (or whatever); if you define a symbol to mean one thing, it does not also mean something else (though it is perfectly possible to think you had defined a symbol well, but be wrong); and so on.

In other words, thought as we experience it is something which logic can describe. Even when the content of the thoughts are totally inconsistent and irrational thoughts, their ontology is consistent and rational.

If we can, we can devise concepts and such. Among them would be the little mind-game we know of as logic.

The fact that one can devise concepts in an irrational universe does not mean he will necessarily devise logic.

Logic went into the category of things which could be devised. I did not mean anything about what would be devised. This was ambiguously worded. My apologies.

So, our discussion would revolve around a world with some screwy things in it, but where not everything is screwy.

A universe which is inconsistent need not be 100% inconsistent in order to be sufficiently inconsistent that logic has no meaning in reality. Logic allows us to deduce things, and you can't reliably deduce things when the universe does not behave in a consistent fashion.

Actually, the largest problem with this thought exercise is its underlying assumption that the universe's massive irrationality (so severe that rocks spontaneously change size significantly and constantly) would actually allow the bio-chemical processes that permit the generation and evolution of life.[/quote]

The largest problem with this objection is its underlying assumption that rules which seem very odd to us are necessarily irrational. Consider a primitive's impression: the temperature changes significantly and spontaneously all the time. Light spontaneously pours from a small region of the sky which moves about. Water disappears when standing in the open. Other times it just falls from the sky. Dust motes dance around randomly in the air. And what's up with this 'fire' thing?

Compared to those highly real phenomena, rocks changing size spontaneously seems fairly tame. It isn't necessarily illogical or irrational at all, given a rather different rule-set than our own. Of course you're right that it seems hard to evolve life under such circumstances, but I can imagine fairly straightforward reasons for it that would not be too inimical to life (I can post it if you would like, but its' tangential and kind of long). So, you'd be selling logic short in that case.

Where logic encounters more serious trouble is when you have, say, rocks simultaneously being large and small, simultaneously in sight and not in sight, simultaneously existing and not... for all conceivable definitions of properties. That is necessarily illogical.

Even that, we would also be able to work around to a great extent, because our subjective experiences are consistent on the ontological level: a rock which was simultaneously large and small would produce only one (consistent) impression in our minds, and we would choose to use that impression as a property. Even if the impression were confusion (wow, that rock looks simultaneously large and small!), it would not actually be the idea of being large and not the idea of being large. It could be the idea of being large and the idea of not being large; that's fine. We can call that rock 'confusing'.

Now, we might not get very far doing so; but the usefulness of external models is a different question than the validity of logic.

[Kuroneko]

The issue is not that logic is completely impotent at describing the situation--clearly, one can invent hypotheses about the rock's size-changing abilities that preserve the standard rules of logic. What empiricism as a philosophical position is mainly concerned about is the why behind this fact; it claims that the reason is that when we have sensory experiences, we abstract away some commonalities between them, and some of those common patterns are what we call the rules of logic. In other words, logic would be in some way dependent on the working of the universe, in as much as the working of the universe force our sensory experiences. Mr. Sampras put forward the view that logic is a kind of self-contained language that needs to external justification--this is perfectly true for particular logic systems, but confining the topic to that level is not very interesting.

I did not here mean that our minds necessarily use logic to think; I meant that our minds can be described logically: at any one moment, you are not both thinking about cats and not thinking about cats (or whatever); if you define a symbol to mean one thing, it does not also mean something else (though it is perfectly possible to think you had defined a symbol well, but be wrong); and so on.

If you wish to simply re-affirm the law of non-contradiction, you are of course free to do so, as it can always be rescued after making sufficiently many distinctions, but this doesn't mean it has any more a priori import beyond the fact that this law is present in some systems of logic. A proposition like "I am in a house right now" has an unclear truth value when one is stepping through the door. Moreover, it's not even the case that all systems of logic strictly obey this particular law--for example, relevance logics and their dialetheist kin are paraconsistent.

As you are a physicist, I wonder whether you are ever bothered by the Everett many-world interpretation of quantum mechanics. One can say that such things are not 'really' part of our ontology, and that we merely play a kind of language-game when we engage in such talk, but there always seemed to me something deeply unsatisfying in such "we pretend they're there but they're not" moves. In many reasonable cases, the contortions one goes through to preserve classical logic are very similar. For example, the classically true statement "if I am the prime minister of Canada, then the moon is made of cheese" seems to be blind to any relevance (or rather, lack of it) between the government of Canada and the composition moon. Even if I were actually the Canadian prime minister in disguise, most people would affirm that the moon would still not be made of cheese, but note that any such examinations of counterfactuals or relevance (or modal statements) require some sort of "possible-world" talk in classical logic. Relevance logics, which deny the law of non-contradiction, would deal with such cases more directly.

Theories that require many layers of ad hoc hypotheses and distinctions are less preferable to those that do not. That's why I simply can't buy into an empathic affirmation of the rules of logic. In the abstract sense, they're as valid as the rules of any other formal system, but once we treat it as a language, we're assigning interpretations, in which case we can then ask if they are applicable to certain situations. Put more bluntly, the important issue is simply whether it works, not whether we can rearrange formal symbols in some prescribed ways. Earlier, Mr. Sampras compared logic to a tool of describing the universe. I agree fully, but he didn't seem to take his own analogy seriously enough, for then it naturally follows that select models of this tool may be better than others for particular tasks. Determining such things is a manifestly empirical question, just as determining whether phlogiston or caloric or classical thermodynamics are superior is an empirical question.