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An Implication of Gödel's Incompleteness Theorem II: Not Referring to the Validity of Oneself's Assertion

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

An Implication of Gödel's Incompleteness Theorem II: Not Referring to the Validity of Oneself's Assertion

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Abstract

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.