Are the "laws" of deductive logic empirically verifiable?

Question

"Is Logic Empirical?" strongly suggests a question that I would like very much to get a handle on.

That phrase is a title of an article by Hilary Putnam, and, according to synopses/reviews, the paper deals very narrowly with the possibility that laws of logic may need to be revised in view of new empirical knowledge about quantum mechanics. While that idea may be an intriguing idea, it seems very much beside the main point of my question, except for a tangential connection.

So maybe I should ask the question in this way: How on earth did humankind ever get the idea, at genesis, that deductive logic is useful for obtaining new knowledge? (Incidentally, by "logic" I mean deductive logic unless I indicate otherwise.) It seems inescapable that deductive logic must have developed in prehistoric times in conjoint parallel with the linguistic structures of logic. So in that sense, it may be said that the idea that deductive logic is indubitably valid has an empirical foundation.

Supposedly, something about human experience led humans to think they were on to something in developing a tradition of logic. But it also seems to me that belief in the indubitable validity of logic is very much a dogma; so it seems to me that, in the spirit of Descartes's questioning of philosophical foundations, one ought to examine by empirical, scientific studies if possible whether logic does indeed lead to indubitable new knowledge.

Also, although human history may be highly relevant empirically, human history in no way constitutes a double-blind, random, unbiased statistical test of hypotheses. (Such statistical tests seem to be considered the gold standard for empirical testing -- at least for medical research questions.) There is simply too much cultural preselection going on for things to be otherwise.

So how do we grapple with the essentially Cartesian question of empirical foundations for deductive logic?

By way of context, I am especially motivated in posing this question in view of the seemingly extremely towering theories of algebraic topology, seemingly towering all the way to the moon, to use hyperbole. That seems like a very incredible dependence on the idea that deductive logic leads to indubitable new knowledge. Very highly abstract, set-theoretic developments in theories of probability theory and stochastic processes also provide similar motivation for these questions.

Now, I realize that there seems to be a strain of mathematicians who simply regard such theories as merely a formalistic game in the axiomatic tradition of Euclidean geometry and that empirical relevance to the "real world" outside of mathematical theory is simply a non-issue in developing such theories.

There is another perspective that I should also mention here. One sometimes sees physical theories whose only empirical tests are relatively remote empirical verifications of empirical consequences. But of course, if logic is indubitable, there is a strong preference for directly verifying the theories themselves -- that is, to reach the chain of logic much earlier in the chain. It seems such verifications could lead to much stronger, more powerful, much more universally useful knowledge about the theories in question -- that is, provided logic is shown to be indubitably valid, say based on overwhelming empirical verification.

Finally, in regard to the Putnam discussion about the relevance of quantum mechanics: Beyond grandiose ideas of human capabilities, there seems to be no reason to presume that humans can ever develop a perfect theory of the physical universe; that idea of achieving theoretical perfection seems to be an empirically unconfirmable idea.

So it seems from the outset that issues about consistency with quantum mechanics are not at all compelling for a relevance to the question of empirical foundations of logic.

Perhaps I should make more explicit the implicit main question I have in mind. Namely, are there any published, comprehensive studies that thoroughly explore the empirical foundations for the idea that deductive logic is a reliable tool for obtaining new knowledge of the "natural" world outside the formalistic framework of logic? Of course, that a proposition follows from premises according to formalistic rules is often a matter of empirical verification by grinding through the rules. But my question focuses on whether logic adds any new knowledge of an empirical nature outside the formalism. Bertrand Russell said that the rules of logic are a priori knowledge. I think he was probably just recapping general rhetoric of the times about the idea. But that does not seem good enough. I find it hard to think that the rules of logic have no firm, scientifically empirical foundation in order for them, in a scientifically compelling fashion, to be considered useful outside of entertainment purposes. For example, I'm thinking that the Pythagorean theorem might form part of the fabric of such new knowledge of the natural world. The theorem does indeed seem very relevant and empirically verifiable in the natural world, up to small errors of measurement. And so it seems the theorem might be considered a partial proof by inductive logic that deductive logic has practical relevance to the natural world. But in the spirit of empiricism, it seems that much more proof of an empirical nature is needed.

Another example might be the uses of logic for Newtonian mechanics and Newtonian gravity and the consequences (of sorts) in celestial mechanics even though these applications may not have the relative "perfection" of Einsteinian relativity.

Answer 1

Michael Dummett says something similar to what Hilary Putnam is described by the OP as saying about quantum mechanics. Dummett is concerned with describing the differences between realists and anti-realists as a belief or not in the logical principle of bivalence with regard to various classes of statements.

For the class of statements about science he has this to say: (page 5-6)

The realists believe science progressively uncovers what the world is like in itself, explaining in the process why it appears to us as it does. They are opposed by instrumentalists, who regard theoretical entities as useful fictions enabling us to predict observable events; for them, the content of a theoretical statement is exhausted by its predictive power. This is one case in which the view opposed to realism is made more plausible by empirical results; for a realist interpretation of quantum mechanics appears to lead to intolerable antinomies.

Given falsifiability over verificationism it may make more sense to think of quantum mechanics as falsifying certain realist views rather than verifying anti-realist views. This would even work for which logic works best for a class of statements.

---

Dummett, M. The logical basis of metaphysics. (1991) Harvard University Press.

Answer 2

The question of whether the 'laws of thought' are empirical may depend on quite what we mean. Aristotle examined the way in which we think and formalised it in his laws for the dialectic, and I feel this could be called an empirical approach. The problem may be that 'empiricism' is often defined as being restricted to the evidence of our physical senses, and in this case their is no empirical evidence for thinking or for the use of inferential logic.

At least there is no evidence that empiricism outruns logic. Putnam may wonder about quantum mechanics but it we apply the laws properly physics gives us no reason to suppose they do not always apply. Heisenberg agreed with Putnam but both seem to ignore Aristotle's instructions for dialectic logic.

You say this - "Beyond grandiose ideas of human capabilities, there seems to be no reason to presume that humans can ever develop a perfect theory of the physical universe; that idea of achieving theoretical perfection seems to be an empirically unconfirmable idea."

This is incorrect. There is sound empirical evidence that we can achieve theoretical perfection. It would depend on what we mean by 'perfection', but I would call the neutral metaphysical theory on which rests the Perennial philosophy as being as close to perfect as we can expect from a theory, and that this theory is known to many people is empirically verifiable. The pessimism of academic philosophy is self-inflicted and unnecessary and should not be generalised to all philosophers.

Your question becomes a lot more interesting if we see the world as a product of mind, for then we must find it implausible that it ever disobeys the rules of ordinary logic and any examples would be counter-evidence.

Answer 3

Logic is not useful, for the most part in generating new knowledge, it is useful in deciding between alternative positions. As Wittgenstein has noted, all the results of logic are by definition tautologies. It cannot produce new ideas, only more and more complex combinations of existing ideas, which are not new information, in the strict sense, just greater applicable leverage on existing knowledge. We are not discovering or deciding anything, just putting things in order so that we can more clearly see what has already been decided. This is the feeling that makes Plato propose the theory of anamnesis.

What that implies is that you only need deduction when you already have too much information, and it is hard to use because it needs cleaning. So deduction is unlikely to have arisen as a way of gaining new knowledge, or even of maintaining a store of existing knowledge. It is more likely to arise for a different purpose, and to come to those uses afterward. I would propose that, as Dennett and others have suggested is true of the stream of consciousness, the labeling of qualia, and other aspects of our thought process, deduction arises from treating ourselves in a way that we originally treated others.

How did we decide that logic matters? Most probably starting with the concept of contradiction. This house cannot be both mine entirely and yours entirely. Does it have to be somebody's? Well, either it does or it doesn't... Let's either agree, or fight. If we can agree, there is lower odds of one or the other ending up dead. So there is survival benefit if feeling of agreeing is pleasant, but only to a degree that the agreement is not too slanted against me, and won't discomfit everyone else and make them gang up on us and make us change it. Logic is embedded in our pro-social sense of fairness and social stability.

The problem with finding empirical support for the laws of reason is that they are always empirically false to some tiny degree. As Quine has noted in discussing Natural Kinds, all useful definitions are necessarily vague, and if you leverage them far enough, that vagueness will result in contradictions if you use logic strictly. But we don't. The farther back in history you go, the faster your concepts come to the limit of vagueness. So it is highly unlikely that logic arose out of any experience of correctly using strict definitions. And without strict-enough definitions it does not accomplish anything.

With the advent of science, we have created some results that can be combined to a very great degree with strict logic, but even those ultimately cannot do so indefinitely. We get results that we must at some degree discard. Our logic only applies to physics only works down to a given scale, taxonomy always has to admit intermediate forms, chemical reactions involve some degree of randomness in how the molecules come together and do not allow for strict predictions. Logic stops helping somewhere.

So it is more reasonable to come at this from an Intuitionist perspective, and presume that logic is a built-in emotional reaction like fear or passion, perhaps evolved to help us find common ground and encourage peaceful resolution of disputes. It is built into our grammar at a level that means we cannot escape it. But it is not true -- it is imposed on the world by our usage in spite of its failures.

By that theory, these conventions are as accurate as they manage to be because the better they worked, the greater advantage they afford. If we can agree about what other people will do, or about how stones behave, we are even more likely to be able to help one another survive. Some aspects of agreements between people are so common that we all share them to some degree, at an almost inescapable level. Seeing them invalidated makes us quaintly amused, deeply enthralled, unsettled, or even angry, depending upon how important the issue.

Answer 4

I'm confused by the question.

The solution to the tower of hanoi puzzle can be proven by mathematical induction, which itself is an example of deductive logic. Isn't it helpful to be able to prove things, to know that we have the right answer? The tower of hanoi is a highly abstract example, but the solution (how to solve it with the fewest moves possible) is not trivial, nor then the proof that we have the right solution.

Science also seems to use deductive reasoning, much more than induction, both in the classroom and out of it:

The truly great advances in our understanding of nature originated in a manner almost diametrically opposed to induction. The intuitive grasp of the essentials or a large complex of facts leads the scientist to the postulation of a hypothetical basic law, or several such basic laws. From the basic law (system of axioms) he derives his conclusion as completely as possible in a purely logically deductive manner. These conclusions, derived from the basic law (and often only after time-consuming developments and calculations), can then be compared to experience, and in this manner provide criteria for the justification of the assumed basic law.

I wasn't familiar with all of what was said in the question, especially the maths. so maybe I misunderstand.

Answer 5

are there any published, comprehensive studies that thoroughly explore the empirical foundations for the idea that deductive logic is a reliable tool for obtaining new knowledge of the "natural" world outside the formalistic framework of logic?

As I see it, deductive logic is fundamentally nothing but a capacity of the brain. As such, there is no reason that logic couldn't be scientifically investigated, as any natural phenomenon or property could be, at least in principle.

It tried to see where the current research was. As far as I know, it is still very limited in scope and still entangled in the preconception people now have that logic is essentially mathematical logic.

As a natural capacity, deductive logic does not deliver new knowledge in the sense that perception may be said to potentially deliver new knowledge. Rather, it is the fundamental mechanism that allows our brain to use the data it already has, and this essentially for the purpose of interpreting any new data coming in.

As such, logic is one of the few fundamental capabilities our brain has as cognitive system that help us survive and live our life as we do. There isn't much we can do that doesn't somehow involve logic. Thus, in particular, any acquisition of new knowledge involves deductive logic.

Yet, it seems that logic so understood isn't studied by anyone.

One reason that it is not may be that there is already plenty to do in terms of the scientific investigation of the human brain. Another reason seems to be that almost everybody with some professional interest in logic defer to mathematical logic to specify what logic is, which is sort of putting the cart before the horse.

For example, cognitive scientists seem to be looking for the empirical evidence that humans have or do not have an inborn capacity for formal logic rather than logic simpliciter. They sure aren't going to find that.

How on earth did humankind ever get the idea, at genesis, that deductive logic is useful for obtaining new knowledge?

Logic, as I defined it above, is something our brain does. As such, it helps us make sense of our environment and make our way through life and in the universe.

Without logic, we wouldn't understand each other to the extent that we do. We wouldn't have the kind of articulate language that we have. There would be no art, no technology, no science and no democracy. Our technological civilisation wouldn't exist. Thus, nearly the entirety of the knowledge we have today is indeed new knowledge that we got because logic is a capacity of our brain.

Thus, the scientific investigation of logic, as I defined it, will be crucial to the future of humanity. However, it seems we're not there yet.