Abstract
There has been a bit of discussion, of late, as to whether Church’s thesis is subject to proof. The purpose of this article is to help clarify the issue by discussing just what it is to be a proof of something, and the relationship of the intuitive notion of proof to its more formal explications. A central item on the agenda is the epistemological role of proofs.
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Notes
- 1.
Some later writers invoke a different notion of computability, which relates to mechanical computing devices. Prima facie, this latter notion is an idealization from a physical notion. So, for present purposes, the issues are similar.
- 2.
The letter, which was dated November 29, 1935, is quoted in Davis [12, p. 9].
- 3.
Clearly, this is not a sufficient condition. A one or two line argument whose sole premise and conclusion is a previously established proposition does not constitute a proof of that proposition.
- 4.
Boolos [28] is a delightful challenge to some of the more counter-intuitive consequences of ZFC, suggesting that we need not believe everything the theory tells us. If anything even remotely close to the conclusions of that paper is correct, then, surely, the axioms of ZFC fall short of the ideal of self-evident certainty.
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Shapiro, S. (2015). Proving Things About the Informal. In: Sommaruga, G., Strahm, T. (eds) Turing’s Revolution. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-22156-4_11
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