Can Turing machines capture everything we can compute?

Details Can Turing machines capture everything we can compute? Can Turing machines capture everything we can compute?

2003-04-24

arxiv.org/abs/math/0304379v2

Mathematics

General Mathematics

v2; introduced standardised ACI compliant notation for citations; 13 pages; an HTML version is available at http://alixcomsi

Scientific paper

If we define classical foundational concepts constructively, and introduce
non-algorithmic effective methods into classical mathematics, then we can
bridge the chasm between truth and provability, and define computational
methods that are not Turing-computable.

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