November 17, 2011

A Reductio Against the Static Theory of Time

Filed under: Metaphysics — camcintosh @ 2:25 am

Many philosophers believe there is a serious connection between actualism and presentism, perhaps even entailment. Many philosophers also believe that if the static theory if time is true, then presentism is false. Many philosophers also believe that if modal realism is true, then the only serious players are Plantinga’s view and Lewis’ view (actualism and concretism, respectively).

There are, of course, outliers; but the above three beliefs are fairly widely held among philosophers (for whatever that fact is worth; it’s also worth noting that these beliefs are eminently defensible, not to mention widely defended). Where A = actualism, C = concretism, P = presentism, and S = static theory of time, here is an interesting argument, predicated upon the above three assumptions:

(1)  A ↔ P…………………….P
(2)  A ∨ C……………………..P
(3)  S → ~P………………….P
(4)  (A → P) · (P → A)…1, ME
(5)  (A → P)…………………4, Simp
(6)  ~P → ~A………………5, Trans
(7)  S → ~A…………………3, 6, HS
(8)  ~A → C…………………2, MI
(9)  S → C…………………..7, 8, HS

As you can see, given those three beliefs (1-3), the static theory of time entails concretism. But an even more widely-held belief among philosophers is that concretism is absurd. Therefore, insofar these beliefs are true, the static theory of time entails an absurdity. Thus, this argument could be seen by many, if sound, to be a reductio (of sorts) against the static theory of time.

Note: a more modest version of this argument can be constructed given only A → P instead of the stronger A ↔ P. In that case, one could reach the same conclusion in two less steps.



  1. Accidentally put a ‘B’ in (1) instead of ‘P’. With that minor change, then it’s valid :-)

    Comment by Paul M. — November 17, 2011 @ 5:59 pm | Reply

  2. Whoops, nice catch!

    Comment by camcintosh — November 17, 2011 @ 7:05 pm | Reply

  3. I’ve seen work developing presentism in a way that is analogous to actualism, but I don’t understand how one entails the other. Can you explain, or cite something that discusses the issue?

    Comment by Andrew Brenner — November 18, 2011 @ 1:49 am | Reply

    • Nice hearing from you, Andrew. I hope ND is treating you well (I heard the phil or math conference was a real dig). I would like to get clearer on the details of that issue myself, which I am presently researching. I do not want to cite or explain in haste, so I’ll get back to you in a month or so.

      Comment by camcintosh — November 18, 2011 @ 2:31 am | Reply

      • Please do, if you remember. I can’t imagine how this sort of inference could be justified, but I’m all ears (I’m no fan of static theories of time). Fyi, I do see how some stances in the philosophy of time (namely, perdurantism) might lead one to adopt certain views of transworld identification. Check out Peter van Inwagen’s very interesting “Four-Dimensional Objects” (, if you haven’t already done so!

        Comment by Andrew Brenner — November 18, 2011 @ 3:54 am

  4. Andrew,

    Your suspicions were on target–the suggestion that there is an entailment relation (implication) between actualism and presentism is too strong.

    What I had in mind were claims made to the effect of “it is hard to see how one could be an actualist and not a prsentist (and vice versa)” which are common. But that leaves entailment an open question. So what is the relationship between actualism and presentism? This a good question, and one I’m researching. A tentative stab at an answer is this. Suppose we have the four (broad) different ways two propositions can be related, increasing in strength from left to right:

    Analagous –> Parody of Reasoning –> Implication –> Equivalence

    The relationship between actualism and presentism seems to be either analogous or parody of reasoning, or something in between (a natural reading of the claims I have in mind suggest parody of reasoning). Exploring how far parody of reasoning is from implication would be a useful endeavor. I naturally think of the two as very close, hence the claim in my post. Think of parodies of the ontological argument, for example, where, if successful, demonstrate something like the implication: “If ontological argument x is sound, then so is ontological argument y.”

    One further thought (suggested to my by Alvin Plantinga). If actualism simpliciter does not entail presentism, they are related closely enough that, plausibly, actualism+ entails presentism, where the + is some proposition that bridges the gap. Looking into what that + is would be a worthwhile project.

    Comment by camcintosh — November 19, 2011 @ 6:29 pm | Reply

  5. Setting up actualism against concretism doesn’t seem to be entirely accurate. Actualism is a thesis about what exists, namely that everything that exists is actual (or something similar). The contrasting position is possibilism, the thesis that there are merely possible entities. Concretism is a thesis about what kind of entity possible worlds are, namely concrete. The contrasting position is abstractionism, where possible worlds are abstract entities.

    I think if you replaced every instance of ‘concretism’ with ‘possibilism,’ then the argument would not lose anything, and there would be a better symmetry between actualism/presentism and possibilism/eternalism.

    Comment by CGibbs — November 19, 2011 @ 6:38 pm | Reply

  6. Dr. Gibbs,

    Right–the real disjunct is between abstractionism and concretism (a la PvI and Plantinga). But both are clear that actualism is a corollary of what they call abstractionism, especially PvI. But you’re right–one can be an abstractionist and not be an actualist (e.g., Pollock). But that strikes me as a bit strange.

    Your last suggestion is a good one. I’ll definitely consider making that switch.

    Comment by camcintosh — November 19, 2011 @ 7:20 pm | Reply

  7. I can see a good line of thought from presentism to actualism.

    But how to go from actualism to presentism?

    Maybe the thought is this: “WAS and WILL are analogous to modal operators like AT-W. Now, just as the actualist agrees you can’t go from ‘AT W: x exists’ to ‘x exists’, so likewise you can’t go from ‘WAS: x exists’ to ‘x exists’. And the second is what presentism says.”

    But the thought that WAS and WILL are analogous to modal operators is only a thought an A-theorist or a concretist is going to find particularly plausible. A B-theorist actualist just sees them as sentential operators that shift the context of temporal evaluation, akin to the “OVER THERE” operator (from ‘OVER THERE: x exists’ one can infer ‘x exists’), rather than as modal operators.

    So I would replace 1 with:
    if P, then A
    if A and A-theory, then P

    If by “static theory of time” you mean B-theory (a tendentious name: one could just as well call presentism static since if presentism is true, there is no past or future :-) ), then this says:
    if P, then A
    if A and ~S, then P

    And with this modified set of premises the argument doesn’t go through.

    And if one sees WAS and WILL as akin to modal operators akin to AT-W, one wonders why data about the past is significantly inductively relevant to the present. After all, data qualified with an AT-W operator, where W is not the actual world, is not significantly inductively relevant to the actual world.

    Comment by Alexander R Pruss — November 20, 2011 @ 12:14 am | Reply

  8. Dr. Pruss,

    Thanks for the thoughtful reply!

    Indexical connections were one kind of connection I was thinking of. (Small clarification: Why would the actualist have a problem with going from ‘AT W: x exists’ to ‘x exists’? Wouldn’t the problem be the jump from ‘AT W: x exists’ to ‘AT α x exists’, or ‘x is actual’? After all, if it is true that ‘AT W: x exists,’ it is true that x exists as, say, as an abstract object.)

    Taking the modal operators to be sentential and to shift according to temporal evaluation seems like a good reply. I wonder, though, if this would force us to collapse or reduce all temporal indexicals to ‘spatial’ ones, and whether this can be plausibly done.

    But why think that “data qualified with an AT-W operator, where W is not the actual world, is not significantly inductively relevant to the actual world”? Suppose conceivability entails possibility (or, weaker, conceiving that p prima facie justifies S’s belief that p is possible). Our ability to conceive of propositions being true AT-W, especially if the proposition is either necessarily true or false, seems inductively relevant to what we take to be true in the actual world. Enough testimony formed on the basis of conceivability that “AT-W ‘I exist disembodied'” should strengthen the case for thinking “AT-α ‘I am not identical to my body'”.

    Comment by camcintosh — November 20, 2011 @ 2:50 am | Reply

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