Classical Logic without Bivalance

Alexander V. Gheorghiu

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arXiv · 2506.22326

Classical Logic without Bivalance

Alexander V. Gheorghiu

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Abstract

Sandqvis's semantics for classical logic without bivalence resolves the question of an anti-realist account of classical reasoning after Dummett. This paper applies the framework to the essential questions of metamathematics. The system intuitively handles $\omega$-incompleteness, makes induction meaning-constitutive, and yields an elementary consistency proof for Peano Arithmetic using only ordinary induction on the natural numbers, with no appeal to transfinite ordinals or recognition-transcendent truth.

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BibTeX RIS

Alexander V. Gheorghiu. 2025-06-27. Classical Logic without Bivalance. https://arxiv.org/abs/2506.22326

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