How not to use the Church-Turing thesis against Platonism. (English) Zbl 1266.00018
The author replies to an argument by Olzewski, who claimed that the Church-Turing thesis is incompatible with mathematical platonism. Oleszewski’s argument rest on the claim that by platonism there exists a function which some machine involving a random device computes, although the function is not effectively computable. The author refutes this argument conclusively. Firstly, Olszewski’s argument, if correct, might really be understood as undermining the Church-Turing thesis, and not platonism. More importantly, however, the function used in the argument is not effectively computable as it involves an unspecified way of finding the next number of random sequence. The author outlines the involved concepts of random functions and computatibility in detail.
Reviewer: Manuel Bremer (Düsseldorf)
MSC:
00A30 | Philosophy of mathematics |
03A05 | Philosophical and critical aspects of logic and foundations |
03D10 | Turing machines and related notions |
68Q05 | Models of computation (Turing machines, etc.) (MSC2010) |