The consistency of arithmetic
Storrs McCall (McGill University)
CSL SEMINAR SERIESDATE: 2010-02-12
TIME: 16:00:00 - 17:00:00
LOCATION: RSISE Video Conference Room (A207)
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ABSTRACT:
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.
BIO:
Storrs McCall is Professor of Philosophy at McGill. He graduated from McGill and Oxford, and has taught at McGill for most of his life, except for 6 years at the University of Pittsburgh and 5 years at Makerere University, Uganda, where he was the initiator of philosophy teaching in the pre-Idi Amin years. He is the author of Aristotle's Modal Syllogisms and A Model of the Universe, and the editor of Polish logic, 1920-39.
