Dates and tenses

It is dangerous to mix the timeless and the tensed modes of speech, and it would seem wise either to follow Quine and keep ourselves exclusively to Iamblichus’ intellectual time, or to construct a tense logic like Prior’s on the basis of McTaggart’s A series. But neither counsel can be followed through. I cannot, for the reasons I have given [ ¹ ], discount time from my own standpoint altogether, and refuse to give any indication whatsoever of how I stand in relation to the topics talked of. But neither can I express myself adequately with sequences of past-, present- and future-tense operators, even if allowed to iterate them indefinitely often. For they suffer from an indefiniteness of reference, which, although a natural economy of language, introduces a fatal vagueness into logic. I say ‘I am coming’, ‘He will come’, ‘We have had supper’, in contexts that make it adequately clear what range of dates is being referred to. And if on any occasion my hearer were uncertain whether I meant that he would come in the next half hour or the next six months, he could clarify the statement by asking me. In tense logic, however, as in ordinary logic, there is no provision for conversational elucidation. If I say ‘He will come’, I have to 283be taken as meaning that he will come sometime. Prior, the pioneer of tense logic, accepts this consequence, and uses it to reinforce the parallel with modal logic. There is a deep analogy between the modal ⅐ or L, indicating necessity, and the logical term ‘all’, and between the modal ◊ or M, indicating possibility, and the logical term ‘some’. In giving the future operator the modality of S4 and the past operator the modality of S4.3, we have assimilated P, more or less, to the ◊ or M of modal logic (see § 51, p. 267). But this interpretation requires us to construe P as ‘it was the case at some time’, where the italicized words at some time have the sense given by the existential quantifier in logic, (3t). It follows that if we deny a statement beginning with the past operator P, we are asserting that it was at no time the case; and if we then prefix the same negated operator to a negated proposition, we are asserting that it was at no time the case that not, i.e. that it was at all times the case that…. Prior has besides the past operator P, corresponding to the modal ◊ ^or M, another past operator H, corresponding to the modal ⅐ or L. But it accords ill with ordinary usage. In ordinary usage the tense is much more part of the reference than of the predicate; it shows us to what event we are referring rather than gives us a further description of the subject. If I say Caesar crossed the Rubicon, I mean that Caesar crossed the Rubicon at some time, which I could specify further but do not need to; I do not mean by ‘some time’ merely non nullo tempore but quodam tempore. Similarly, if I say ‘Peter was in lunch’, I am speaking elliptically, and mean ‘Peter was in lunch today’, not that Peter at some time or other was in lunch. It is not a quantified statement with an existential operator ranging over time, but a singular statement whose temporal reference has not been specified very fully. The proof is in negation. If I were to deny that Caesar crossed the Rubicon, or that Peter was in lunch, I am not committed to claiming that Caesar never crossed the Rubicon (how could he have been in a position to cross it into Italy then?) or that Peter has never had lunch in college, but only that Caesar did not cross the Rubicon when you said he did, or that Peter was not in lunch today. In our ordinary way of speaking, we first find out what particular date is being referred to, and then if we deny the statement, deny it as referring to that date: we do not take it as having an indefinite temporal reference, and deny it by claiming that no such event ever occurred. Of course, if it were true that Caesar never had crossed the Rubicon, or Peter never had had lunch in college, it would be false that Caesar crossed the Rubicon in 49 B.c . or that Peter was in lunch today. But, in the ordinary way of speaking, these are contraries, not contradictories, and if I deny that Caesar crossed the Rubicon or that Peter was in lunch, it does not refute me, but is merely irrelevant, to say that Caesar did cross the Rubicon in 51 B.c . or that Peter was in lunch last Michaelmas term.