Tuesday, August 11, 2009

Timeless vs. All-Time Facts

Jeremy is unsure what to make of the idea of 'timeless' facts, if this is not just to say that they are true at all times. One way to grasp the distinction is to start with a temporary object, like a speck of dust, and then imagine that it just happened to exist at all times. Then 'the speck exists (now)' is true at all times, but in a very different way from how 'the speck exists at t1' is true at all times. Only the latter fact is timeless.

This difference may also be revealed in the modal properties. A timeless proposition will typically still be true even if you added extra times. (An exception: call the final moment of the universe tN. It's a timeless fact that tN is the final moment. But if we added an additional moment, tN+1, then this would no longer be true at all.) On the other hand, something merely contingently 'true at all times' might not remain true if we added an additional time, say a moment that no longer contains any specks of dust. [Are there exceptions in this direction too? Try to think of a temporally immanent fact that is nonetheless necessary, so that it would also be true in any additional times that might be added. Perhaps "that there is space (now)"?]

I guess the principled way to state the distinction is to say that some things are true at all times because of what's immanent, present, or 'going on' at each time; whereas other (timeless) propositions are true at all times for a "cheaper" reason. A timeless truth doesn't need truthmakers at each time; it just has a single truthmaker (say, the speck's existing at time t1) which suffices for it to be true at all times, whatever else may be going on at them. Though technically true at all times, it isn't really about all times in any deep sense.

Anyone got a neater way to word all this?

12 comments:

  1. How about this: a proposition P is timelessly true at world W iff there exists a fact F such that for all times t, F makes P true in W at t.

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  2. A consequence of this formulation is that for any all-time but non-timelessly true proposition P, "P is true at all times" will be a timeless truth. This might not match your intuition, since it could still be possible to add extra time onto the world during which P would be false (thus, so would "P is true at all times").

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  3. That seems like an okay implication. Time-indexed claims (e.g. "P is true from t0 through tN") are themselves timeless, and I guess that shouldn't change just because we replace the precise specification of all times with a blanket universal quantifier.

    To make it more intuitive: use the term 'everlasting' for truths that are non-timelessly true at all times. If some truth P is everlasting, it seems plausible to say that the higher-order truth "P is everlasting" is itself a timeless rather than everlasting truth.

    (The contingency issue is but a very rough guide, as my 'tN+1' counterexample showed. So this could just be another case like that, where extrinsic features of a time -- such as whether there are subsequent times -- affect what is timelessly true of it.)

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  4. so now that we've got the distinction worked out, is there some philosophical work that it's supposed to do?

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  5. *shrug*, I didn't really have any further purpose in mind. (I suppose it might be useful for theologians arguing about the sense in which God is supposed to be 'eternal'?)

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  6. Is the proposal that are two kinds of truthmakers or two kinds of truthmaking relation? I can't tell from either your post or Jeremy's comment.

    I've been thinking a bit about this stuff for unrelated reasons. Maybe my slightly different perspective will be helpful here? Here's a proposal from a post I wrote about Field and truthmaking:

    "There are past, present, and future times, both actual and merely possible: these are abstract objects, MC sets of propositions. There are also past and present things, but [according the growing block theory I'm talking about in the post] no future things. The past and present things determine which of the past and present times are actualized, and, together with the laws of nature, constrain which of the future times are possible."

    On this way of carving things up, what's true according to a time just depends on which propositions the time contains, while what's timelessly true depends on what stuff there is.

    This way of drawing the distinction would be useful for explaining what's wrong with Bradley's argument: truth full stop is more basic than truth at a time. It would also come in handy if you wanted to make something like presentism or the growing block theory coherent. (I remain unsure as to whether one should really want that, but there you have it.)

    A timeless proposition will typically still be true even if you added extra times.

    You've pointed out a counterexample, and this looks dodgy to me anyway. Why not: the truth value of a tensed proposition indexed to t supervenes on what the world is like at t? If you're skeptical about ersatz times, you might prefer that suggestion to the first suggestion.

    I don't think either proposal is equivalent to the one you've made, but I'm not 100% sure I've got a handle on what your proposal is.

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  7. i didn't mean to imply any controversial metaphysics by speaking of truths at times. i think everything can be done just as well using time-indexed propositions (denoted P@t). The definition then becomes: a proposition P is timelessly true at world W iff there exists a fact F such that for all times t, F makes P@t true at W.

    the reason that the everlasting dust truth isn't timeless is that each of the time-indexed versions of the proposition has a different truthmaker--namely, a different time-slice of the dust particle.

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  8. Meh, my second proposal won't work; it doesn't distinguish between timeless truths about what happened at t and tensed truths that were true at t.

    Jeremy: I understand your proposal now, and like it. You might worry about what happens if not all truths have truthmakers, though. If there's no fact that makes it true that there are now no dinosaurs, then it's going to come out as timelessly true that there are now no dinosaurs on your proposal, and that seems wrong.

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  9. I don't understand the dinosaur thing. If "now" is indexical, then "there are no dinosaur now"@t seems to express a different proposition at each time, so it will have a different truthmaker at each time and not be timeless. If "now" is a name for a specific time, then it should be timeless that "there are no dinosaurs now" because it is semantically equivalent to "there are no times at t=8/12/09."

    in fact, i'm not sure you even need to invoke truth. consider this:

    a proposition P is timelessly true at world W iff there exists a proposition Q such that Q and for all times t, it is necessary that P@t iff Q.

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  10. Jeremy, the worry is that according to some views, not every truth has a truthmaker. In particular, true negative existentials don't have truthmakers. A truthmakers for p is usually thought of as a thing whose existence necessitates the truth of p. But nothing's existence necessitates the truth of statements like "there are no unicorns", because anything you like could co-exist with a unicorn. So the worry is that "there are no dinosaurs now" (which I intended to be read indexically and not rigidly, btw) can be true at a time without having any truthmaker at that time.

    Your rephrasing in terms of propositions looks unhelpful to me. Let P be the proposition that there is now dust (read indexically), and let Q=P. Suppose Q is true (now, or always if you like). Then it looks like on your proposal, P comes out as timelessly true.

    You could stipulate that Q has to be a timeless proposition, but that looks unhelpfully circular.

    Yet another proposal, probably inequivalent to all of the above:
    P a tensed proposition iff there are possible worlds where P is true at some times and false at other, and P is a timeless proposition otherwise. Timeless truths are just timeless propositions that are true.

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  11. Another thought for Jeremy: the assumption that truthmakers are things is controversial at best, and is going to interact in weird ways with (a) whether or not you're a counterpart theorist and (b) whether or not you're able to believe that every truth has a truthmaker. I guess the canonical article that takes truthmakers to be things (sort of) is Lewis's "Things Qua Truthmakers".

    If you figure out how to say anything of interest without using controversial metaphysics, please teach me!

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  12. haha, i just said that i didn't mean to imply any controversial metaphysics: i didn't say that i could avoid it ;) in particular, most of the work is being done by the P@t construction which I'm taking as a primitive.

    re: negative existentials. this is an issue if you take truthmakers to be concrete objects, i.e. states of affairs. but i put things in terms of facts, not states of affairs. (maybe i shouldn't have used the term "truthmaker" for this view.) perhaps this reformulation helps:

    A proposition P is timelessly true iff there exists a fact F such that for all times t, necessarily, if F exists then the fact that P@t exists.

    something has to be done to avoid vacuity, i.e., F can't be the fact that P is timelessly true! so something has to be said about that.

    re: indexical propositions. i don't think there are such things. in my view, there are just indexical sentences/thoughts that express run-of-the-mill propositions (although which proposition they express is a function of context, in the relevant ways).

    i think this is it for me on this topic: i can't get too worked up about this notion since i doubt it's good for anything. thanks for the Lewis reference.

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