Axiom (cc)0 and Verifiability in Two Extracanonical Logics of Formal Inconsistency

Thomas Macaulay Ferguson

Abstract


In the field of logics of formal inconsistency (LFIs), the notion of “consistency” is frequently too broad to draw decisive conclusions with respect to the validity of many theses involving the consistency connective. In this paper, we consider the matter of the axiom (cc)0i.e., the schema ◦ ◦ϕ—by considering its interpretation in contexts in which “consistency” is understood as a type of verifiability. This paper suggests that such an interpretation is implicit in two extracanonical LFIs—Sören Halldén’s nonsense-logic C and Graham Priest’s cointuitionistic logic daC—drawing some interesting conclusions concerning the status of (cc)0. Initially, we discuss Halldén’s skepticism of this axiom and provide a plausible counterexample to its validity. We then discuss the interpretation of the operator in Priest’s daC and show the equivalence of (cc)0 to the intuitionistic principle of testability. These observations suggest that it may be fruitful for members of the LFI community to look outside the canon for evidence concerning the adoption of principles like (cc)0.


Keywords


Logics of formal inconsistency; Nonsense logic ; Priest–da Costa logic; Consistency operators; Verifiability

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DOI: https://doi.org/10.5007/1808-1711.2018v22n1p113

Copyright (c) 2018 Thomas Macaulay Ferguson

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Principia: an internationnal journal of epistemology
Published by NEL - Epistemology and Logic Research Group
Federal University of Santa Catarina - UFSC
Center of Philosophy and Human Sciences – CFH
Campus Reitor João David Ferreira Lima
Florianópolis, Santa Catarina - Brazil
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 ISSN: 1414-4217
EISSN: 1808-171

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