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arXiv · 2006.01057

How the Law of Excluded Middle Pertains to the Second Incompleteness Theorem and its Boundary-Case Exceptions

Dan E. Willard
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Abstract

Our earlier publications showed semantic tableau admits partial exceptions to the Second Incompleteness Theorem where a formalism recognizes its self consistency and views multiplication as a 3-way relation (rather than as a total function). We now show these boundary-case evasions will collapse if the Law of the Excluded Middle is treated by tableau as a schema of logical axioms (instead of as derived theorems).

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Dan E. Willard. 2020-06-01. How the Law of Excluded Middle Pertains to the Second Incompleteness Theorem and its Boundary-Case Exceptions. https://arxiv.org/abs/2006.01057

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