In the following I am not considering substance dualism or idealism, but only materialist/physicalist theories.

The Church-Turing thesis states:

Every ‘function which would naturally be regarded as computable’ can be computed by the universal Turing machine.

The Church-Turing-Deutsch principle is a stronger version of the original Church-Turing thesis, that states:

Every finitely realizable physical system can be perfectly simulated by a universal model computing machine operating by finite means

A Turing machine functions using the basic laws of logic, and even very small Turing machines are universal (i.e. capable of simulating any other Turing Machine).

As I mentioned earlier, discounting the existence of non-physical entities, this means that anything finite in the universe can be simulated by and therefore reduced to, a very small set of rules. It seems to me that this just a restatement of reductionism.

My question is: If you agree with the Church-Turing-Deutsch principle, are you implicitly subscribing to reductionism (therefore disavowing non-reductionist materialist views such as emergentism)?

  • How does the principle differ from being a definition of "finitely realizable physical system". If it is a definition, how can one disagree. – Cheers and hth. - Alf May 23 '15 at 1:22

I am purposely going to avoid discussing the mind, and focus directly on the notion of emergentism per se, because I think that avoids biases and allows one to be clearer. The analogies to computation and the mind should be easily made.

There is no absolutely non-reductivist form of emergentism. Emergentism does not deny reducibility, it accepts the fact that the phenomenon emerging is, in fact, the product of a simpler, lower-order system. If you guessed perfectly, therefore, you could find the underlying form and then you would have reduced the phenomenon to the lower-order theory.

Emergentism only denies that you can always get there from here, except by sheer luck. The most common version suggests that the emergent phenomenon will become incomprehensibly complex part of the way through the reduction. You might find the correct reduction, but the complexity would keep you from being certain that you had. And it makes any productive result of attempting the reduction unlikely.

The point is not whether you can reduce or not, the point is whether there are strata where reduction is just not productive or sane to pursue, and you are better off adopting higher-level concepts and working on the unreduced problems.

For instance, it is better to pursue the thermodynamics of a car engine in terms of temperature pressure and other statistical values than to model the gasoline in its various states as individual atoms. The reduction is obviously possible, but it discards the most useful information and makes the system harder to understand, rather than easier.

  • Well then, does subscribing to emergentism imply that P ≠ NP ? – Alexander S King May 27 '15 at 3:47
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    No it implies the halting problem. You cannot determine the full range of behaviors of any turing machine by interrogating it with another turing machine. Polynomials have nothing to do with it. It is basically an 'affirming the consequent' fallacy argument from the halting problem backward in a sort of statistical way. That is why one can only talk about likelihoods when you go there. The 'complexity' form you could look at as requiring X != NX for some order of difficulty X well above P, as otherwise you could just guess well with great accuracy. – user9166 May 27 '15 at 3:48

According to Chalmers the answer is no, CTD does not entail reductionism; he believes both that the brain is computable and that consciousness is emergent.

in Strong and Weak Emergence he writes:

I think there is exactly one clear case of a strongly emergent phenomenon, and that is the phenomenon of consciousness.

and in A Computational Foundation for the Study of Cognition he writes:

We have every reason to believe that the low-level laws of physics are computable. If so, then low-level neurophysiological processes can be computationally simulated; it follows that the function of the whole brain is computable too, as the brain consists in a network of neurophysiological parts.

That said (or quoted), I personally believe CTD is false; for a start, Turing did not argue for anything like CTD; his thesis was about turing machines being able to "replace" human "computers" using pencil and paper and a finite procedure which does not require ingenuity; it had nothing to do with physics or the nature of the universe; while Church Turing thesis is widely accepted as True, Deutsch's principle is not; the article about the Church Turing thesis in SEP discusses the thesis and how it is "misinterpreted" by philosophers to justify computational theories of mind.

  • The SEP article does not suggest any reason to doubt Deutsch's claim that according to modern physics all physical systems are computable, it just says that this is a distinct claim from what Turing and Church were saying, so it's misleading to call it a "better defined" version of the Church-Turing thesis. But taking Deutsch's argument on its own, it does seem to support computational theories of mind. – Hypnosifl Mar 18 '20 at 19:56

The CTD does not imply reductionism. The CTD implies that any finite physical system can be simulated by a universal computer. However, it doesn't tell you how to program the computer to do that. The significance of the CTD is that if you come up with a theory to explain something, your ability to test it is not limited by your ability to figure out its consequences. The computer can figure out the consequences for you.

This leaves entirely open the possibility that there is some higher level explanation that selects some kinds of motion that could be simulated and not others. One example is discussed by Deutsch in Chapter 12 of "The Fabric of Reality": this chapter is about time travel. Deutsch discusses the problem that a closed timelike curve would apparently allow you to travel back in time with a mathematical proof and tell the creator about the proof. The proof would then have come into existence without any process of variation and selection. So a constraint on the motion allowed near CTCs would be necessary to keep the evolutionary principle intact. This would be a high level explanation, but would not contradict the CTD.

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