Reply to a Comment on Tense Logic and the End of Time

A reader of this blog, Patrick, submitted a comment to my previous post, but because of some technical glitches I was experiencing with the Blogger software, I think I deleted the post his comment was attached to. Anyway, his comment is worth a response.

Interesting, Alan. You say, "Let us suppose that the time is now t-minus 10 and that at precisely t-minus 5 time stops for good. In that case, there never exists a time t. Hence, S neither obtains nor does not obtain at t. Hence, both "S will obtain at t" and "S will not obtain at t" are false." Initially I'd wanted to say that in such a case "S will not obtain at t" is true, but I'm not so sure about it now. I was thinking like this: "Look, S will not obtain at t precisely because t is never going to exist! S can't obtain at a time that doesn't exist, so if t is never going to exist, it's true to say that S will not obtain at that time." If that makes sense, then I think your argument may not go through. It looks like the argument depends on whether saying "S will not obtain at t" entails that time t exists. But there might be a meaningful way of saying that S will not obtain at t because t won't exist.

My reply is as follows:

Hi, Patrick. Actually, your response had occurred to me, but I don't think it works. The problem is that the response depends on the possibility of evaluating the truth of "will" propositions differently than one evaluates "will not" propositions. Thus, "S will obtain at t" is construed to imply the future existence of t , whereas "S will not obtain at t" is construed in a way that does not imply the future existence of t. The move is a natural for those who equate "will not" and not-"will". But since the legitimacy of that supposed equivalence is the very point at issue, to invoke it at this point would be question-begging. Moreover, consider the following:

Let t = tomorrow
Let p = Fred mows his lawn
Let q = Fred does not mow his lawn
Let WILL(p,t) be the proposition "Fred will mow his lawn tomorrow"

According to the proposed response to my argument, WILL(p,t) implies the future existence of t, but WILL(not-p,t) does not. But what about WILL(q,t)? Since this has the same form as WILL(p,t) we expect it to commit us to the future existence of t as well. If that is right, then both "Fred will mow his lawn tomorrow" and "Fred will not mow his lawn tomorrow" imply that there be a tomorrow. And if that's right, then the contrast between "will" and "will not" cannot consist in the fact that one implies the existence of a future time whereas the other does not.

To avoid this conclusion, one would have to say that WILL(p,t) is a fundamentally different type of proposition than WILL(q,t), in which case we cannot continue to construe WILL(,) as a univocal propositional operator. Instead, we'll need two future-tense operators. One that includes an existential comittment to future times, and another that does not. I don't find this move very plausible. Is it really necessary to multiply senses of "will" in this way? A better approach, I think, is to accept that WILL(p,t) and WILL(q,t) are of the same propositional type and to deny that WILL(not-p,t) and not-WILL(p,t) are of the same propositional type. But that, of course, plays right into my hands. I'm perfectly willing to grant that not-WILL(p,t) does not imply the future existence of t. Since the scope of the "not" applies to the whole WILL(p,t) proposition, it cancels whatever existential import the latter may have. But with WILL(not-p,t) the "not" occurs within the scope of the tense operator, and so it cannot cancel an existential commitment carried by the operator itself.