Topoi:1-13 (forthcoming)

Tore Fjetland Øgaard
University of Bergen
Priest argued in Fusion and Confusion (Priest in Topoi 34(1):55–61, 2015a) for a new concept of logical consequence over the relevant logic B, one where premises my be “confused” together. This paper develops Priest’s idea. Whereas Priest uses a substructural proof calculus, this paper provides a Hilbert proof calculus for it. Using this it is shown that Priest’s consequence relation is weaker than the standard Hilbert consequence relation for B, but strictly stronger than Anderson and Belnap’s original relevant notion of consequence. Unlike the latter, however, Priest’s consequence relation does not satisfy a variant of the variable sharing property. This paper shows that how it can be modified so as to do so. Priest’s consequence relation turns out to be surprisingly weak in some respects. The prospects of strengthening it is raised and discussed in a broader philosophical context.
Keywords Consequence relations  Entailment  Relevant logic  Substructural logic  Validity
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DOI 10.1007/s11245-021-09758-x
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Fusion and Confusion.Graham Priest - 2015 - Topoi 34 (1):55-61.
Begrundung Einer Strengen Implik.Wilhelm Ackermann - 1956 - Journal of Symbolic Logic 21:113.

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