Review: "A Calculus of 'Before," by David R. Luce

Abstract

Luce's motivation for his calculus is to provide "a purely relational account of temporal phenomena without events and without momentary particulars." Exactly what a "relational account" amounts to is not specified but apparently it is rooted in Leibniz's classical version that instants apart from things are nothing. In this, the recently resurrected tense logicians would certainly agree, except that their basic formula operators, e.g. P and F, correspond to such phrases as 'it was the case that' and 'it will be the case that,' whereas Luce's basic connective, # , corresponds to 'before' (or better perhaps 'and then'). The usual treatment of temporal reference through the introduction of a time parameter in which things are not said simply to possess a property but rather to possess it at a time t is metaphysically misleading unless the phrase 'at a time t' is given a purely derivative status in the overall conceptual scheme. It is ontologically innocuous to refer to moments of time in the semantical metalanguage for tense logic or for Luce's calculus of 'before' so long as such reference is understood in some such derived sense. An alternative semantics could equally well be provided, e.g. in higher-order tense logic, in which such reference need not occur. In his semantics, Luce allows himself to refer—as we shall in this review—to moments of time (cf. his semantical clause 5.12) although he attempts to rephrase such reference (cf. clause 5.13) by means of tensed sentences of a natural language. His rephrasing is inappropriate in that he speaks of such tensed sentences only as being (tenselessly?) true (false) and not of having been true (false), being (in the present tense) true (false) and going to be true (false). More of this anon.