Inconsistent Models (and Infinite Models) for Arithmetics with Constructible Falsity

Thomas Macaulay Ferguson

DOI: http://dx.doi.org/10.12775/LLP.2018.011

Abstract


An earlier paper on formulating arithmetic in a connexive logic ended with a conjecture concerning C♯ , the closure of the Peano axioms in Wansing’s connexive logic C. Namely, the paper conjectured that C♯ is Post consistent relative to Heyting arithmetic, i.e., is nontrivial if Heyting arithmetic is nontrivial. The present paper borrows techniques from relevant logic to demonstrate that C♯ is Post consistent simpliciter, rendering the earlier conjecture redundant. Given the close relationship between C and Nelson’s paraconsistent N4, this also supplements Nelson’s own proof of the Post consistency of N4♯ . Insofar as the present technique allows infinite models, this resolves Nelson’s concern that N4♯ is of interest only to those accepting that there are finitely many natural numbers.

Keywords


strong negation; connexive logic; constructible falsity; first-order arithmetic; connexive arithmetic; Post consistency; paraconsistent logic

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References


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