David Deutch - The Fabric of Reality

CRYPTO-INDUCTIVIST: …

DAVID: I could go on like this ad infinitum. The point is, the more we consider the implications of your proposed anomaly, the more unanswered questions we find. This is not just a matter of your theory being incomplete. These questions are dilemmas. Whichever way they are answered, they create fresh problems by spoiling satisfactory explanations of other phenomena.

CRYPTO-INDUCTIVIST: …

DAVID: So your additional postulate is not just superfluous, it is positively bad. In general, perverse but unrefuted theories which one can propose off the cuff fall roughly into two categories. There are theories that postulate unobservable entities, such as particles that do not interact with any other matter. They can be rejected for solving nothing (‘Occam’s razor’, if you like). And there are theories, like yours, that predict unexplained observable anomalies. They can be rejected for solving nothing and spoiling existing solutions. It is not, I hasten to add, that they conflict with existing observations. It is that they remove the explanatory power from existing theories by asserting that the predictions of those theories have exceptions, but not explaining how. You can’t just say ‘spacetime geometry brings unsupported objects together, unless one of them is David, in which case it leaves them alone’. Either the explanation of gravity is spacetime curvature or it isn’t. Just compare your theory with the perfectly legitimate assertion that a feather would float down slowly because there would indeed be a sufficient upward force on it from the air. That assertion is a consequence of our existing explanatory theory of what air is, so it raises no new problem, as your theory does.

CRYPTO-INDUCTIVIST: I see that. Now, will you give me some help in adjusting my world-view?

DAVID: Well, have you read my book, The Fabric of Reality?

CRYPTO-INDUCTIVIST: I certainly plan to, but for the moment the help that I was asking for concerns a very specific difficulty.

DAVID: Go ahead.

CRYPTO-INDUCTIVIST: The difficulty is this. When I rehearse the discussion we have been having, I am entirely convinced that your prediction of what would happen if you or I jumped off this tower was not derived from any inductive hypothesis such as ‘the future resembles the past’. But when I step back and consider the overall logic of the situation, I fear I still cannot understand how that can be. Consider the raw materials for the argument. Initially, I assumed that past observations and deductive logic are our only raw material. Then I admitted that the current problem-situation is relevant too, because we need justify our theory only as being more reliable than existing rivals. And then I had to take into account that vast classes of theories can be ruled out by argument alone, because they are bad explanations, and that the principles of rationality can be included in our raw material. What I cannot understand is where in that raw material — past observations, the present problem-situation and timeless principles of logic and rationality, none of which justifies inferences from the past to the future — the justification of future predictions has come from. There seems to be a logical gap. Are we making a hidden assumption somewhere?

DAVID: No, there is no logical gap. What you call our ‘raw material’ does indeed include assertions about the future. The best existing theories, which cannot be abandoned lightly because they are the solutions of problems, contain predictions about the future. And these predictions cannot be severed from the theories’ other content, as you tried to do, because that would spoil the theories’ explanatory power. Any new theory we propose must therefore either be consistent with these existing theories, which has implications for what the new theory can say about the future, or contradict some existing theories but address the problems thereby raised, giving alternative explanations, which again constrains what they can say about the future.

CRYPTO-INDUCTIVIST: So we have no principle of reasoning which says that the future will resemble the past, but we do have actual theories which say that. So do we have actual theories which imply a limited form of inductive principle?

DAVID: No. Our theories simply assert something about the future. Vacuously, any theory about the future implies that the future will ‘resemble the past’ in some ways. But we only find out in what respects the theory says that the future will resemble the past after we have the theory. You might as well say that since our theories hold certain features of reality to be the same throughout space, they imply a ‘spatial principle of induction’ to the effect that ‘the near resembles the distant’. Let me point out that, in any practical sense of the word ‘resemble’, our present theories say that the future will not resemble the past. The cosmological ‘Big Crunch’, for instance (the recollapse of the universe to a single point), is an event that some cosmologists predict, but which is just about as unlike the present epoch, in every physical sense, as it could possibly be. The very laws from which we predict its occurrence will not apply to it.

CRYPTO-INDUCTIVIST: I am convinced on that point. Let me try one last argument. We have seen that future predictions can be justified by appeal to the principles of rationality. But what justifies those? They are not, after all, truths of pure logic. So there are two possibilities: either they are unjustified, in which case conclusions drawn from them are unjustified too; or they are justified by some as yet unknown means. In either case there is a missing justification. I no longer suspect that this is the problem of induction in disguise. Nevertheless, having exploded the problem of induction, have we not revealed another fundamental problem, also concerning missing justification, beneath?

DAVID: What justifies the principles of rationality? Argument, as usual. What, for instance, justifies our relying on the laws of deduction, despite the fact that any attempt to justify them logically must lead either to circularity or to an infinite regress? They are justified because no explanation is improved by replacing a law of deduction.

CRYPTO-INDUCTIVIST: That doesn’t seem a very secure foundation for pure logic.

DAVID: It is not perfectly secure. Nor should we expect it to be, for logical reasoning is no less a physical process than scientific reasoning is, and it is inherently fallible. The laws of logic are not self-evident. There are people, the mathematical ‘intuitionists’, who disagree with the conventional laws of deduction (the logical ‘rules of inference’). I discuss their strange world-view in Chapter 10of The Fabric of Reality. They cannot be proved wrong, but I shall argue that they are wrong, and I am sure you will agree that my argument justifies this conclusion.

CRYPTO-INDUCTIVIST: So you don’t think that there is a ‘problem of deduction’, then?

DAVID: No. I don’t think that there is a problem with any of the usual ways of justifying conclusions in science, philosophy or mathematics. However, it is an interesting fact that the physical universe admits processes that create knowledge about itself, and about other things too. We may reasonably try to explain this fact in the same way as we explain other physical facts, namely through explanatory theories. You will see in Chapter 6of The Fabric of Reality that I think that the Turing principle is the appropriate theory in this case. It says that it is possible to build a virtual-reality generator whose repertoire includes every physically possible environment. If the Turing principle is a law of physics, as I have argued that it is, then we should not be surprised to find that we can form accurate theories about reality, because that is just virtual reality in action. Just as the fact that steam engines are possible is a direct expression of the principles of thermodynamics, so the fact that the human brain is capable of creating knowledge is a direct expression of the Turing principle.