How definitive is the standard interpretation of Goedel's Incompleteness Theorem?

Abstract

Standard interpretations of Goedel's "undecidable" proposition, [(Ax)R(x)], argue that, although [~(Ax)R(x)] is PA-provable if [(Ax)R(x)] is PA-provable, we may not conclude from this that [~(Ax)R(x)] is PA-provable. We show that such interpretations are inconsistent with a standard Deduction Theorem of first order theories.

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References in corpus (2)

• Some consequences of a recursive number-theoretic relation that is not the standard interpretation of any of its formal representations
• Why we must heed Wittgenstein's "notorious paragraph"