Communications in Mathematical Analysis

An implication of Gödel's incompleteness theorem II: Not referring to the validity of oneself's assertion

Hitoshi Kitada

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In [10] we reviewed Gödel's incompleteness theorem and gave a new proof along with an application which leads to a contradiction when applying the Gödel's discussion to the set theory ZFC itself. We stated a possible solution to avoid contradiction by removing the self-reference by appealing to the axiomatic formulation of a theory with referring to its validity in no explicit ways. We will in this paper give a more specific possible solution that one can avoid the Gödel type self-contradiction by preventing oneself from telling anything definite about the validity of oneself's assertion.

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Commun. Math. Anal., Volume 10, Number 2 (2011), 24-52.

First available in Project Euclid: 28 November 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03F40: Gödel numberings and issues of incompleteness
Secondary: 03F15: Recursive ordinals and ordinal notations 03B25: Decidability of theories and sets of sentences [See also 11U05, 12L05, 20F10] 03E99: None of the above, but in this section

Incompleteness Inconsistency Gödel Self-reference Validity


Kitada , Hitoshi. An implication of Gödel's incompleteness theorem II: Not referring to the validity of oneself's assertion. Commun. Math. Anal. 10 (2011), no. 2, 24--52.

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