Journal of Philosophical Logic

, Volume 41, Issue 5, pp 901–922

Real Analysis in Paraconsistent Logic

Article

DOI: 10.1007/s10992-011-9210-6

Cite this article as:
McKubre-Jordens, M. & Weber, Z. J Philos Logic (2012) 41: 901. doi:10.1007/s10992-011-9210-6

Abstract

This paper begins an analysis of the real line using an inconsistency-tolerant (paraconsistent) logic. We show that basic field and compactness properties hold, by way of novel proofs that make no use of consistency-reliant inferences; some techniques from constructive analysis are used instead. While no inconsistencies are found in the algebraic operations on the real number field, prospects for other non-trivializing contradictions are left open.

Keywords

Paraconsistent logic Non-classical mathematics Compactness theorems 

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CanterburyChristchurchNew Zealand
  2. 2.School of Historical and Philosophical StudiesUniversity of MelbourneMelbourneAustralia

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