Description

• Title:
  Inconsistent Models (and Infinite Models) for Arithmetics with Constructible Falsity
• Creator:
  Ferguson, Thomas Macaulay
• Description:
  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.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2018 Logic and Logical Philosophy
• Date:
  2018.08.08
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion
• Language:
  English
• Source:
  Logic and Logical Philosophy; Vol. 28 No. 3 (2019): September; 389-407;
  Logic and Logical Philosophy; Tom 28 Nr 3 (2019): wrzesień; 389-407;
  2300-9802;
  1425-3305
• Format:
  application/pdf
• Publisher:
  Uniwersytet Mikołaja Kopernika w Toruniu
• Relation: https://apcz.umk.pl/LLP/article/view/LLP.2018.011/15331
• Subject:
  strong negation;
  connexive logic;
  constructible falsity;
  first-order arithmetic;
  connexive arithmetic;
  Post consistency;
  paraconsistent logic;
  03F30;
  03H15
• Identifier: https://apcz.umk.pl/LLP/article/view/LLP.2018.011
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  text