The consistency of arithmetic
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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The paper presents a proof of the consistency of Peano Arithmetic (PA) that does not lie in deducing its consistency as a theorem in an axiomatic system. PA’s consistency cannot be proved in PA, and to deduce its consistency in some stronger system PA+ is self-defeating, since the stronger system may itself be inconsistent. Instead, a semantic proof is constructed which demonstrates consistency not relative to the consistency of some other system but in an absolute sense
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