Philosophia Mathematica 6 (3):302-323 (1998)
|Abstract||This paper defends the traditional conception of Church's Thesis (CT), as unprovable but true, against a group of arguments by Gandy, Mendelson, Shapiro and Sieg. The arguments here considered urge that CT is provable or proved. This paper argues, first, that contra-Mendelson, CT does connect a mathematically precise concept (Turing computability) with an intuitive notion (effective calculability). Second, the various ‘proofs’ of (all or half of) CT fail to undermine the traditional conception of CT as unprovable. Either they do not conform to the sense of proof imbedded in the standard conception, or they prove something other than CT.|
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