Two presumptions in Goedel's interpretation of his own, formal, reasoning that are classically objectionable

Details Two presumptions in Goedel's interpretation of his own, formal, reasoning that are classically objectionable Two presumptions in Goedel's interpretation of his own, formal, reasoning that are classically objectionable

2007-03-24

arxiv.org/abs/math/0703723v1

Mathematics

General Mathematics

26 pages; an HTML version is available at http://alixcomsi.com/Two_Presumptions.htm

Scientific paper

Standard expositions of Goedel's 1931 paper on undecidable arithmetical propositions are based on two presumptions in Goedel's 1931 interpretation of his own, formal, reasoning - one each in Theorem VI and in Theorem XI - which do not meet Goedel's, explicitly stated, requirement of classically constructive, and intuitionistically unobjectionable, reasoning. We see how these objections can be addressed, and note some consequences.

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