The church-turing thesis breaking the myth

Some computational models are more efficient, in terms of computation time and memory, for different tasks. For example, it is suspected that quantum computers can perform many common tasks with lower time complexity , compared to modern computers, in the sense that for large enough versions of these problems, a quantum computer would solve the problem faster than an ordinary computer. In contrast, there exist questions, such as the halting problem , which an ordinary computer cannot answer, and according to the Church-Turing thesis, no other computational device can answer such a question.

On the other hand, there is a limit to the significance of purely historical questions  of what Church and Turing said or thought. Church could simply turn out to be wrong  in his rather simplistic assumption about machines. He clearly could not have thought about the nature of the physical world as it is investigated today — black holes, superstrings, the lot. Church and Turing could hardly be blamed if their perception of the physical world in 1937 was rendered obsolete by new discovery. Science moves on, and sometimes the greatest figures are left behind. But Copeland apparently wants to adhere to two things: (1) Church's thesis and (2) the possibility of 'hypercomputing': physical systems that have machine-like properties but are not computable. The only way to reconcile these two things is to hold that Church's thesis was never meant to apply to machines, only to people. This assertion of Copeland is now often cited by other people, and has become part of philosophical lore. But it is not consistent with the record.

Thesis M is not the only problematic thesis that is linked to the Church-Turing thesis. An error which, unfortunately, is common in modern writing on computability and the brain is to hold that Turing's results somehow entail that the brain, and indeed any biological or physical system whatever, can be simulated by a Turing machine. For example, the entry on Turing in the recent A 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" (Guttenplan 1994: 595). Searle writes in a similar fashion:

The church-turing thesis breaking the myth

the church-turing thesis breaking the myth


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