Incompleteness, mechanism, and optimism. (English) Zbl 0921.03005
The author examines three main areas of the literature on incompleteness: (1) arguments that Gödel’s theorems refute the mechanistic thesis, (2) the constructiveness of Gödel’s theorem, and (3) movement from a logical system to its Gödel sentence. Overall, he seems to argue that the mechanist is free to hold that a human is a Turing machine or to claim that arithmetical productions of a human are recursively ensumerable.
Reviewer: A.A.Mullin (Huntsville)
MSC:
| 03A05 | Philosophical and critical aspects of logic and foundations |
| 68T01 | General topics in artificial intelligence |
| 03F30 | First-order arithmetic and fragments |
| 03D10 | Turing machines and related notions |
Keywords:
Church’s thesis; incompleteness; Gödel’s theorems; mechanist; Turing machine; recursively ensumerableReferences:
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