Non-Boolean classical relevant logics II: Classicality through truth-constants

Synthese (3-4):1-33 (2021)
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This paper gives an account of Anderson and Belnap’s selection criteria for an adequate theory of entailment. The criteria are grouped into three categories: criteria pertaining to modality, those pertaining to relevance, and those related to expressive strength. The leitmotif of both this paper and its prequel is the relevant legitimacy of disjunctive syllogism. Relevant logics are commonly held to be paraconsistent logics. It is shown in this paper, however, that both E and R can be extended to explosive logics which satisfy all of Anderson and Belnap’s selection criteria, provided the truth-constant known as the Ackermann constant is available. One of the selection criteria related to expressive strength is having an “enthymematic” conditional for which a deduction theorem holds. I argue that this allows for a new interpretation of Anderson and Belnap’s take on logical consequence, namely as committing them to pluralism about logical consequence.



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Tore Fjetland Øgaard
University of Bergen (PhD)

Citations of this work

The Weak Variable Sharing Property.Tore Fjetland Øgaard - 2023 - Bulletin of the Section of Logic (1):85-99.
Confused Entailment.Tore Fjetland Øgaard - 2021 - Topoi 41 (1):207-219.

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References found in this work

Logical Pluralism.Jc Beall & Greg Restall - 2005 - Oxford, England: Oxford University Press. Edited by Greg Restall.
A New Introduction to Modal Logic.M. J. Cresswell & G. E. Hughes - 1996 - New York: Routledge. Edited by M. J. Cresswell.
Relevant Logics and Their Rivals.Richard Routley, Val Plumwood, Robert K. Meyer & Ross T. Brady - 1982 - Ridgeview. Edited by Richard Sylvan & Ross Brady.
Philosophy of Logics.Susan Haack - 1978 - London and New York: Cambridge University Press.

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