About the characterization of a fine line that separates generalizations and boundary-case exceptions for the Second Incompleteness Theorem under semantic tableau deduction

Our previous research showed that the semantic tableau deductive methodology of Fitting and Smullyan permits boundary-case exceptions to the second incompleteness theorem, if multiplication is viewed as a 3-way relation (rather than as a total function). It is known that tableau methodologies prove...

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Published in:Journal of logic and computation 2021-01, Vol.31 (1), p.375-392
Main Author: Willard, Dan E
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description Our previous research showed that the semantic tableau deductive methodology of Fitting and Smullyan permits boundary-case exceptions to the second incompleteness theorem, if multiplication is viewed as a 3-way relation (rather than as a total function). It is known that tableau methodologies prove a schema of theorems verifying all instances of the law of the excluded middle. But if one promotes this schema of theorems into formalized logical axioms, then the meaning of the pronoun of ‘I’, used by our self-referencing engine, changes quite sharply. Our partial evasions of the second incompleteness theorem shall then come to a complete halt.
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title About the characterization of a fine line that separates generalizations and boundary-case exceptions for the Second Incompleteness Theorem under semantic tableau deduction
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