Goedel's Incompleteness Theorems hold vacuously

Details Goedel's Incompleteness Theorems hold vacuously Goedel's Incompleteness Theorems hold vacuously

2002-07-09

arxiv.org/abs/math/0207080v2

Mathematics

General Mathematics

v2. Introduced ACI compliant notation for citations. 9 pages. An HTML version is available at http://alixcomsi.com/index01.htm

Scientific paper

In an earlier paper, "Omega-inconsistency in Goedel's formal system: a constructive proof of the Entscheidungsproblem" (math/0206302), I argued that a constructive interpretation of Goedel's reasoning establishes any formal system of Arithmetic as omega-inconsistent. It follows from this that Goedel's Theorem VI holds vacuously. In this paper I show that Goedel's Theorem XI essentially states that, if we assume there is a P-formula [Con(P)] whose standard interpretation is equivalent to the assertion "P is consistent", then [Con(P)] is not P-provable. I argue that there is no such formula.

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