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

Logic and Logical Philosophy 28 (3):389-407 (2019)
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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.

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Author's Profile

Thomas Ferguson
City University of New York

Citations of this work

Connexive logic.Heinrich Wansing - 2008 - Stanford Encyclopedia of Philosophy.

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References found in this work

Constructible falsity.David Nelson - 1949 - Journal of Symbolic Logic 14 (1):16-26.
Constructible falsity and inexact predicates.Ahmad Almukdad & David Nelson - 1984 - Journal of Symbolic Logic 49 (1):231-233.
Minimally inconsistent LP.Graham Priest - 1991 - Studia Logica 50 (2):321 - 331.
A semantical study of constructible falsity.Richmond H. Thomason - 1969 - Mathematical Logic Quarterly 15 (16-18):247-257.

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