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Antinomies of Mathematical Reason: The Inconsistency of PM Arithmetic and Related Systems

Dr. S. Fennell
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Abstract

We give a proof of the inconsistency of PM arithmetic, classical set theory and related systems, incidentally exposing an error in Goedel's own proof of Goedel's Theorems. The inconsistency proof, that formulae of the form R and ~R occur as theorems in the PM-isomorphic system P, proceeds from a reflexive substitution instance of the first axiom of the propositional calculus (axiom II.1 of P). Goedel's formalism is used throughout.

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Dr. S. Fennell. 2006-09-08. Antinomies of Mathematical Reason: The Inconsistency of PM Arithmetic and Related Systems. https://arxiv.org/abs/math/0007096

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