Julien Murzi

Validity and Truth-Preservation

The revisionary approach to semantic paradox is commonly thought to have a somewhat uncomfortable corollary, viz. that, on pain of triviality, we cannot affirm that all valid arguments preserve truth (Beall 2007, 2009; Field 2008, (2009b). We show that the standard arguments for this conclusion all break down once (i) the structural rule of contraction is restricted and (ii) how the premises can be aggregated—so that they can be said to jointly entail a given conclusion—is appropriately understood. In addition, we briefly rehearse some reasons for restricting structural contraction.

Classical Harmony and Separability

According to logical inferentialists, the meanings of logical expressions are fully determined by the rules for their correct use. Two key proof-theoretic requirements on admissible logical rules, harmony and separability, directly stem from this thesis—requirements, however, that standard single-conclusion and assertion-based formalizations of classical logic provably fail to satisfy (Dummett in The logical basis of metaphysics, Harvard University Press, Harvard, MA, 1991 ; Prawitz in Theoria, 43:1–40, 1977 ; Tennant in The taming of the true, Oxford University Press, Oxford, 1997 ; Humberstone and Makinson in Mind 120(480):1035–1051, 2011 ). On the plausible assumption that our logical practice is both single-conclusion and assertion-based, it seemingly follows that classical logic, unlike intuitionistic logic, can’t be accounted for in inferentialist terms. In this paper, I challenge orthodoxy and introduce an assertion-based and single-conclusion formalization of classical propositional logic that is both harmonious and separable. In the framework I propose, classicality emerges as a structural feature of the logic.