Logical constants: a modalist approach (Q2867855)

This paper criticisizes the model-theoretic account of the nature of logical constants introduced by Tarski and further developed by \textit{G. Sher} [The bounds of logic. A generalized viewpoint. Cambridge, MA: MIT Press; New York, NY: Columbia University (Diss.) (1991; Zbl 1238.03001); Theoria, Segunda Epoca 18, No. 47, 189--198 (2003; Zbl 1054.03007)]. The authors argue, in effect, that that account pre-supposes too much logic and ontology to provide an appropriately neutral account of what logic is. In place of that model-theoretic account, the authors propose a `modalist approach'. This begins with a primitive notion of necessity and possibility, whereby one can say that \(B\) follows logically from \(A\) only if the conjunction of \(A\) and the negation of \(B\) is impossible. (Beyond that necessary condition, no further specification or explanation of `follows from' is given.) This is supposed to provide the key to a characterization of logical constants.NEWLINENEWLINE The paper, however, presents no account of the nature of logical constants at all, nor criteria by which to distinguish logical from non-logical constants. The most that is said is that logical constants are given in the object language by the introduction and elimination rules of Gentzen's sequent calculus, with the turnstile, \(\lvdash\), to represent modalized deduciblity, or `follows from', as above.NEWLINENEWLINE Much of the viewpoint of this paper is shaped by appeal to logical pluralism, the doctrine that many logics may have proper claim to be correct, depending on the domain of application.