Problems of Realism and Reality: A Brief Disquisition on Hilary Putnam and Scientific and Mathematical Realism

In watching the good interview below with Hilary Putnam, I got to think about his well known no miracle argument for scientific realism. Could it be possible that Putnam was right because he was wrong? That is, could scientific realism be correct because externalist semantics is wrong?

Putnam changed his position on a number of philosophical controversies in his career, which some (if not many) chided him for. I wouldn’t agree with that criticism. There’s nothing wrong with changing one’s position on scientific and philosophical questions, even ones which we might consider fundamental. This indicates a disposition toward open inquiry. What matters are the reasons offered for the change in disposition. Where there can be a problem is when there’s a basic shift in values. For example, in what used to be called “the moral sciences” we see this all the time. Academics, analysts, commentators, and the like can and do change their fundamental values for mostly political or material interests. That we don’t like, and for good reason. It demonstrates a change in, I’d say more forthrightly a betrayal of, intellectual values, for understanding the world no longer constitutes the value underpinning inquiry. Intellectual inquiry becomes a means of achieving fame, notoriety, power, status, money and the like. You don’t see this with Putnam. In fact, the change in his philosophical views can be said to reflect his commitment to intellectual virtue. This is something to admire, rather than criticise.

Putnam was given to realism, it is presented as the unifying theme of his work, and Putnam’s semantic externalism and his scientific realism are viewed as key parts of this unifying theme. His most well known argument for scientific realism was the “no miracle argument.” It would be a miracle if the concepts, laws, and entities of science, especially the physical sciences, did not have a real, physical, existence. Spacetime curvature is real, quarks are real, the equivalence principle is real, electromagnetic fields are real and so on. Time and again we make predications using scientific concepts and theories which are time and again confirmed by experiment. It would be a miracle, says Putnam, if they weren’t real, and because there are no miracles, therefore they are real. I’ve always found this argument a bit weak. It reminds me of Turing’s invocation of applications arising from science, like aeroplanes and computers, in his famous exchange with Wittgenstein. So far as I can see Turing’s argument is a no miracle argument.

These applications are basically one or another form of machine. Say Galileo were to have made a no miracle argument for scientific realism in his day. Now Galileo adhered to the mechanical philosophy so his conception of scientific realism would be mechanical, that is nature is a machine. This also entailed an epistemological thesis namely to know nature is to demonstrate how natural phenomena can be explained using a mechanical theory. Galileo would have been well within his rights to say it would be a miracle if his “idealised” controlled, and quantitative, experiments, inclined plane and all, did not provide insight into reality. Indeed, he might have added, look at all the applications, machines, we have constructed and will continue to construct as we advance understanding. It would be a miracle if all this should turn out to be a convenient fiction, and because there are no miracles (so much for Cardinal Bellarmine), it thereby follows scientific realism, that is the mechanical philosophy, must be correct. Wrong. We know the mechanical philosophy does not account for the fundamental nature of reality.

But let us take another tack. The concepts we use in science, such as mass, matter, energy, space and the like are not intuitive. We have innate concepts of each that are part of the furnishing of the mind, but those concepts we discard when we do science. The meaning of the concepts we use in science come from their use in the theory, which is an idea not unlike Wittgenstein’s use theory of meaning but you’ll find this in Carnap too. Now, because the concepts of our science are not the intuitive concepts that exist in the mind it thereby follows those concepts have a mind independent existence that is, they are real. So, therefore, scientific realism is correct. But notice this argument relies upon a semantic internalism. Meaning is not a question of reference, the meaning of our words and our concepts do not refer to things in the world, but rather meaning exists in the head, within the mind as it were. That science does not use those innate, or intuitive, mental concepts is precisely what makes the concepts of science real. There’s this view that somehow internalism is contrary to realism whereas externalism is consistent with realism if not an expression of its very essence. I don’t see things this way. Let us say that our intuitive mental concepts are innate. Given that there are no miracles, let’s say, it thereby follows their being innate is a consequence of a natural process. Those concepts are real, in the sense that they exist in the mind because of its physical structure and just because they don’t have an existence external to the mind does not make them any less real. In fact, it would be a miracle if our rich and complex conceptual apparatus should have arisen simply through processes of induction and association and there being no miracles and all we say externalism must be false.

Hilary Putnam was correct, because he was wrong.

I suspect what is at issue here is a confusion, if not a prejudice, about the concept physical. We don’t want to ascribe the mental world, indeed the mind tout court, with a real physical existence. I put it to you that our innate mental concepts are physical, just as chairs, rocks, and frogs are real,in that they arise from some unknown physical property of matter, or better still of some physical aspect to nature, obtaining in the brain. It is unknown because our best theories of the physical world do not capture the mental, at least not yet (some even say in principle it shan’t), and because physics does not tell us what “the physical” actually means. This confronts our intuitive, natural or mental or innate, concept of “physical” which entails a type of mind-body dualism. Now notice that under this construal we have an innate concept of the physical, but our science, in this case cognitive science, is suggesting that this innate concept is false and something that needs to be discarded when thinking of what Ryle called the concept of mind. In other words, the idea that mental concepts are real is not unlike the idea that quarks are real. That is, we have here a type of scientific realism. This is consistent with rationalism, or the doctrine of innate ideas and this is how rationalism connects with physicalism. Because mental concepts, and the mind, have a real physical existence, in ways that remain unknown to us, it thereby follows rationalism is correct. This is all neatly consistent, it seems to me.

Finally, I’d like to conclude on a point of mathematical realism. Putnam, of course, was also a philosopher of mathematics and logic. I remember a while back at Parkville attending a lecture by the noted Princeton mathematician Peter Sarnak. I can’t remember the title of the talk, something like “the unreasonable effectiveness of elliptic curves in number theory” or something like that. At some point Sarnak was talking about the Riemann Hypothesis and he said, as I recall it, maybe the problem with Riemann is that humans can’t dig randomness. Riemann is concerned with the question of whether there’s order in the distribution of prime numbers, and the zeros of the Riemann zeta function suggest that there is. My memory is hazy, but I think that’s how It went. However, humans can dig randomness. Just because we have an innate disposition for finding patterns and understanding the relationships that underpin them doesn’t mean we don’t understand randomness.

This is related to the problem of free will. We have three hypothesises here. The two most familiar namely free will is real and determinism, that is free will is an illusion. We have the third due to David Hume namely compatibilism which holds that determinism is compatible with free will. A problem with compatibilism is that to make it intelligible we need to know how determinism is compatible with free will, and it’s hard to do that without first understanding free will. Now we understand determinism and randomness. Perhaps free will relies upon a concept that goes beyond determinism and randomness, but we can’t formulate a hypothesis to deal with the problem of free will because determinism and randomness is all we have to work with. The concept lies outside of our H space, no not Hilbert space, that is our hypothesis space. So, If Sarnak is correct in what he says, and Riemann is something that cannot be cracked because of our mental makeup (as opposed to it being undecidable a la Godel), the problem wouldn’t be randomness the problem would be pretty much the same as free will. We just can’t formulate hypotheses or conjectures that go beyond determinism and randomness, and I suppose pseudo-random patterns are a type of compatibilism in this context. The distribution of prime numbers will always be a mystery for us because their distribution is neither ordered nor random. Perhaps that’s wrong, and Riemann does succumb to a proof.

Could it be possible, nonetheless, that there are some aspects of the number system which are like the problem of free will. Perhaps the number system exhibits features that are neither ordered nor random. Such features would never fall within the ambit of number theory, at least number theory as formulated by humans, and so we could not even formulate hypotheses with regard to them let alone establish proofs. This would mean that the number system has properties that are beyond the conceptual repertoire of human beings in which case the number system would have an existence beyond the mind. That being so the number system would thereby be real. Given that it appears there’s a fundamental unity to mathematics, this is one of the really interesting areas of research in modern mathematics, it would thereby follow that mathematics would also be real. We might have here a general category, unknown and unknowable, that applies well beyond the domain of free will alone. It is what we don’t know, or better still what we cannot know in principle, that is the most interesting and I would suggest the most fruitful vista of epistemology. Yet epistemology is, has been, and doubtless will continue to be dominated by that which we know. To know knowledge is to know what we cannot know in principle.

This entry was posted in Philosophy and Science and tagged , , , . Bookmark the permalink.