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?