Logical constants and the glory of truth-conditional semantics.
William G. Lycan · Notre Dame Journal of Formal Logic · 1989
This paper endorses and defends M. J. CresswelΓs view that the distinction drawn in linguistic semantics between strictly "logical" implication and merely lexical implication is bogus, and then explores the bad consequences that concession has for the Davidsonian semantic program.A pattern of semantic explanation made famous by Davidson's "The logical form of action sentences" is shown to be far less interesting than has been thought.This paper commemorates Davidson's "The logical form of action sentences" [4].In so doing it also celebrates the logical forms of action sentences.Those logical forms are still with us, since action sentences themselves are; but for linguistic semantics generally the magnificent promise of Davidson's classic article has never been fulfilled.My purpose here is to explore one reason that this is so. /According to (loosely) Davidsonian semantic theory, 1 the core meaning of a sentence -its propositional or locutionary content as recorded in indirect discourse by a 'that'-clause -is that sentence's truth-condition.The sentence's truth-condition is determined by the meanings of the sentence's smallest meaningful parts together with their grammatical mode of composition, and it is best represented by a formula of some explicitly truth-defined logical system acting as a canonical idiom.Such a formula wears its own truth-condition on its sleeve, in that its truth-condition is computable on the basis of the usual Tarskian set of valuations for the atomic elements of that system plus a set of recursive rules that project the semantic values of a formula's elements through truth-functional and other syntactic compounding into a truth-condition for the formula as a whole.So we have our original natural language sentence, endowed with its