# Church turing thesis relevant proofs non computability

If you believe [functionalism] to be false … then … you hold that consciousness could be modelled in a computer program in the same way that, say, the weather can be modelled … If you accept functionalism, however, then you should believe that consciousness is a computational process.

Kleene, S. The equivalence of the analyses bears only on the question of the extent of what is humanly computable, not on the question of whether the functions generatable by machines could extend beyond the functions generatable by human computers even human computers who work forever and have access to unlimited quantities of paper and pencils.

For example: A man provided with paper, pencil, and rubber, and subject to strict discipline, is in effect a universal machine.

For example, the entry on Turing in the Blackwell Companion to the Philosophy of Mind contains the following claims: we can depend on there being a Turing machine that captures the functional relations of the brain, for so long as these relations between input and output are functionally well-behaved enough to be describable by … mathematical relationships … we know that some specific version of a Turing machine will be able to mimic them.

If the computer wishes to alter, say, squares then he or she performs successive operations. Wang, H. Several computational models allow for the computation of Church-Turing non-computable functions.

### Universal turing machine

It is, therefore, an open empirical question whether or not the weaker form of the maximality thesis is true. When applied to physics, the thesis has several possible meanings: The universe is equivalent to a Turing machine; thus, computing non-recursive functions is physically impossible. Barwise, H. Another example is the simulation thesis. Neither probabilistic nor quantum computation is covered by these axioms they admit this for probabilistic computation, and do not mention quantum computation at all , so it's quite clear to me these axioms are actually false in the real world, even though the Church-Turing thesis is probably true. The converse claim—amounting to the claim mentioned above, that there are no functions in S other than ones whose values can be obtained by an effective method—is easily established, since a Turing machine program is itself a specification of an effective method. Kleene Rejecting the conventional view, Kripke suggests that, on the contrary, the Church-Turing thesis is susceptible to mathematical proof. To summarize the situation with respect to the weaker form of the maximality thesis: At the present time, it remains unknown whether hypercomputation is permitted or excluded by the contingencies of the actual universe. Examples are: any number whose decimal representation consists of a finite number of digits e. This interpretation of the Church—Turing thesis differs from the interpretation commonly accepted in computability theory, discussed above. Turing He made the point a little more precisely in the technical document containing his design for the ACE: The class of problems capable of solution by the machine [the ACE] can be defined fairly specifically. Margolis, R. Hilbert, D. Doyle, J.

The Church-Turing thesis is about computation as this term was used inviz. Newell Yet the analyses Newell is discussing are of the concept of an effective method, not of the concept of a machine-generatable function. As previously mentioned, this convergence of analyses is generally considered very strong evidence for the Church-Turing thesis, because of the diversity of the analyses.

Some Key Remarks by Turing Turing prefaced his first description of a Turing machine with the words: We may compare a man in the process of computing a … number to a machine. Doyle, J. The method of storing real numbers on the tape is left unspecified in this purely logical model.

Olszewski, A.

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