Constituents of Times

Some people define a time as a maximally consistent set of propositions.  It seems to me that this is false because a set has its members essentially, but what is true at a time is only contingently true at that time.  (So that Bill walks to the store is the true at t, but it could have been false at t.)

But a bunch of smart people think of times as sets of propositions.  Consider:

Thomas Crisp:

"x is a time =df. For some class C of propositions such that C is maximal and consistent, x=[Ay(y is a member of C -> y is true]." ("Presentism and the Grounding Objection", Nous 41:1, 2007, p. 99)

(The "A" should stand for the universal quantifier.  In the article, Crisp cites Chisholm, Edward Zalta, Arthur Prior, Kit Fine, and Matthew Davidson as holding similar views.  Crisp's view strikes me as bizarre, since the only time that exists is the present time since that's the only one that's true.  But I bet I'm missing something really obvious.)

Ned Markosian

"There is the abstract present time, which is a maximal, consistent proposition.  There are many things that are similar to the abstract present time in being maximal, consistent propositions that either will be true, are true, or have been true.  Each one is a time.  The abstract present time is the only one of all of these abstract times that happens to be true now." ("A Defense of Presentism", Oxford Studies in Metaphysics 1, 2003, p. 76)

Robin Le Poidevin

"An instant, that is, is equated with all the propositions which would ordinarily be described as being (contingently) true at that instant.  The content of the propositions concerns the states of affairs taking place at that instant..." (Change, Cause, and Contradiction, 1991, p. 37)

(Here, Le Poidevin is referring to Prior's views, though he thinks that all presentists are committed to this definition.)

Craig Bourne

"I propose we construct times using maximally consistent sets of u-propositions, which intuitively we can see as those u-propositions that are true at that time." (A Future for Presentism, 2006, p. 53-54)

(By "u-proposition", Bourne is referring to a proposition without a past or future tense operator on it.)

The point that what is true at a time is contingent was pointed out by W.L. Craig in his critique of Le Poidevin's critique of presentism (A Tensed Theory of Time, p. 213), and Craig cites van Inwagen as noting this in his article "Indexicality and Actuality", 1980, footnote 3).

I think that Craig and Van Inwagen are right.  But doesn't this then make Crisp, Markosian, and Bourne's view of times implausible?

Comments

[Ian Spencer]

I wonder if this shows that presentists should be counterpart theorists about times. So they may say, for instance, that while it is actually the case that time T = set S, they may not have been (since this single entity's time-counterparts and set-counterparts may be distinct in some possible worlds). Then the question would be whether this kind of counterpart theory is really plausible. Otherwise, I think you're right.

[Andrew Moon]

Hmm, in general, I don't like counterpart theory (and I'm not sure I fully understand it), but this could be a way out.

Another way out is to say that times are mereological sums of propositions. It doesn't seem that such a sum would have each of its parts (i.e. each proposition) essentially, and that a certain mereological sum of propositions could have been comprised of different parts (or propositions). But then you might have to gerrymander which propositions a certain time has essentially and accidentally. The proposition that it is Oct. 16, 2007 would be an essential part of time t, the present time, but the proposition that Andrew types would be an accidental part. How does this sound?

[Patrick]

Hey Andrew,

Nice post. Here's another worry for the times-as-sets view. It seems to make sense to say "Future times will be present, and past times were present." But it isn't obvious that it does make sense on the 'sets' view. What could it mean to say that a set will be present? It seems much better to say of a set of propositions that it will be true than that it will be present. But insofar as it *does* make sense to say that a future *time* will be present, it seems there's reason for resisting (or modifying) the times-as-sets view.

[Andrew Moon]

Quick note: I realize now that my above criticism only applies to Crisp and Bourne, who think that times are sets (or classes) of propositions. Markosian thinks that a time is just one big, maximally consistent proposition. So one might think that we avoid the problem. But we still get, on this view, the problem that what is true at a time is necessarily true at that time. p is maximally consistent iff for any q, either p entails q or ~q. So p is probably a big conjunctive proposition, and Markosian presumably thinks that what is true at a time is what is entailed by the proposition that is that time. But conjunctive propositions have their conjuncts essentially. So it is necessarily the case that a time entails what it entails. So what is true at a time is necessarily true at that time. (To put it another way, if p is true at t, it's not possible that that time obtain and p is false.) So we should reject that times are maximally consistent propositions.

So there is the view that times are one proposition or a set of propositions. You get the same problem either way.

[Andrew Moon]

Patrick,
Thanks for the comment. I think that these presentists are okay with just saying that a time is present iff each member of the time (the set) is true. Does this seem troubling to you? Maybe it's odd in the first place to even say that a time is the sort of thing that can be true (or have true members).

Here would be an interesting argument. Times aren't the sorts of things that can be true or have members. Therefore, times aren't propositions or sets. Is this a bad argument?

We could get out of this problem by taking a more distinctively Plantingian route and saying that a time is a maximally consistent state of affairs. Even though times aren't the sort of things that are true or false, they do seem to be the sort of thing that can be actual or obtain. But I think that my argument in the last comment still works against this view.

[Patrick]

Hey Andrew,

I don't think that's a bad argument at all. It's what I had in mind. At the fundamental level, times are the sorts of things than can be present, e.g. "The time he was talking about is now present." But sets of propositions can't be present, so at the fundamental level, times aren't sets of propositions.

I like the suggestion about times consisting of states of affairs (where the distinction btwn. SOA's and facts is that facts are SOA's that obtain in the present). And yeah, the worry you first brought up seems to work against this view, too.

[Andrew Moon]

Patrick,
Okay, if it is a good worry, then it's going to work for worlds. A lot of people want to say that worlds are maximally consistent propositions. A possible world (where 'possible world' is a technical shorthand for what the folk mean by 'a way the world could've been') is not the sort of thing that could be true (or the sort of thing that could have true members). So a possible world is not a proposition (or set of propositions).

Notice that, as with times, this oddity goes away if we talk of possible worlds as states of affairs. Worlds are the sorts of things that can obtain or be actual. States of affairs are the sorts of things that can obtain or be actual. (In NofN, Plantinga plays with the idea that states of affairs just are propositions, but doesn't go into it. If we're right, he was wise for not equating them.)

Kenny Boyce told me in conversation that the view I am suggesting (where a time is a mereological sum of propositions) is odd since I seem to be committed to a view where abstract objects can stand in contingent relations with each other. And it's just weird to talk about propositions being parts of composite objects.

Yeah, I think that the view that times are identical to SOAs runs into the same problem. So what's a better view of times? Do you have a suggestion? I'll have to go take another look at WLC's view again.

[Kephalos Clazomenoon]

Gosh,
This is all too silly, as may be readily shown using 'a hot coffee' argument. In the following "An instant, that is, is equated with all the propositions which would ordinarily be described as being (contingently) true at that instant. The content of the propositions concerns the states of affairs taking place at that instant..." , replace 'an instant' with 'a hot coffee' to derive "A hot coffee, that is, is equated with all the propositions which would ordinarily be described as being (contingently) true of that hot coffee. The content of the propositions concerns the states of affairs occuring in that cup..."

The purpose of the exercise (a) to pun the notion of an instant being somehow "equated" a set of statements; and (b) to cause some discomfort as to whether an "instant" is a particular or a universal. If a particular, it occurs but once... Bah! The whole train of argument stinks. What's happening is a misguided attempt to repackage an ontic as a set of statements. You'll have better luck turning a silk purse into a pig's ear.