Classical Logic without Bivalance
Logic
2026-03-09 v2
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 -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.
Keywords
Cite
@article{arxiv.2506.22326,
title = {Classical Logic without Bivalance},
author = {Alexander V. Gheorghiu},
journal= {arXiv preprint arXiv:2506.22326},
year = {2026}
}