Sunday, December 07, 2008

Accessible Non-Actual Futures

The central argument of my recent post 'A Future Without Fatalism' might be clarified via possible worlds analysis. If it's true that I will φ, that's just a claim about how the actual world is, i.e. how things will - as a contingent matter of fact - turn out. It is not yet to introduce any substantive necessities whatsoever, for something is 'necessary' just in case it is true in all (relevant) possible worlds. For example, we may define some future truth as 'causally necessary' just in case it is true at all those possible worlds that share our history and causal laws. Note that if causal determinism is false, then there will be many causally possible futures. That is, there are many possible worlds with pasts and causal laws identical to ours, and yet different futures. So we can say that each of those worlds are (causally) 'accessible' from ours at this time.

We might define various other accessibility relations. Compatibilists will want something a bit weaker than causal accessibility: they may instead define a world as compatibilist-accessible to an agent if that's a way things would have turned out had the agent's desires been suitably different. (Or something along those lines.)

Note that an agent can (in sense r) bring it about that P iff there is a P-world that is r-accessible to the agent. The free will debate may thus be understood as concerning which accessibility relation 'r' is relevant to moral responsibility and the "ought implies can" principle. I won't get into that here: even the relatively strict requirement of "causal accessibility" will do for my purposes. I merely require some non-trivial accessibility relation (i.e. which doesn't rule out in advance the possibility that multiple possible worlds may be 'accessible' to us).

With the framework thus set up, it should now be obvious why future truth does not imply any kind of (non-trivial) necessity or fatalism. For the question of whether we 'can' do something is a question about what worlds are accessible to us. But the fact that some future-directed proposition P is actually true does not suffice to determine non-trivial accessibility relations. So the following are entirely compossible: (i) P is true in the actual future, and (ii) P is false in some non-actual future which is nonetheless accessible to me at this time. That conjunction is just another way of saying that I can (but won't) make it the case that not-P.

So, again: the argument from mere future truth to fatalism is mistaken for the fundamental reason that it confuses the modal implications of 'will' and 'must'. This is made especially clear through the above possible worlds analysis, whereby 'will' claims are analysed merely in terms of truth at the actual world, whereas 'must' claims also concern accessibility relations. You can't get from one to the other without adding further premises. So mere future truth is no threat to genuine contingency.


  1. Hey Richard, I wrote that loose post before reading the above. I think switching to this sort of possible worlds talk is interesting.

    I think some compatibilists (say of the religious sort) are open to denying causal determinism but accepting determinism in the sense that there is only one possible work but which is underdetermined by causal law. (Due to say foreknowledge by God)

    The interesting issue to raise given the way you are framing things is in how to conceive of block universes as in the typical interpretation of GR. (Let us assume for the moment that we allow QM of some sort so we aren't dealing with the strictly causally determinist form of GR but that there still is a block universe due to the relationship of space and time)

    Now one might say that in possible worlds there are many possible worlds compatible with whatever initial structures there were at the formation of the universe. Yet because there is a block universe the universe as a whole (including time) becomes actual at the same moment.

    This means that given a particular history this is just a subset of the block universe but that there are other possible block universes with that same history.

    The problem with foreknowledge is that it logically entails in this scheme that not only a past history but a partial future history be determined. Now what you would say is that all parts of space/time not logically required to be defined entail possible worlds for all those logically undetermined portions.

    So that I agree with you in. (And I did in the prior post as well)

    The problem is that while it's true that a possible world is accessible to you in the sense you specify clearly it is also not accessible. That is the possible worlds are accessible in terms of causality but are inaccessible in terms of being actualized. (Which I assume you agree with)

    For many people, as I'm sure you're aware, the big issue is the ability to actualize a possibility and not whether a possibility is causally open given a particular history.

  2. "Yet because there is a block universe the universe as a whole (including time) becomes actual at the same moment."

    I think that is strictly nonsensical. "Becoming actual[ized]" is not something that happens in time, or "at" a moment. Which world is actual is an atemporal fact. Assuming eternalism (as I meant to all along), then yes all moments exist equally -- the present has no special ontic status. But so what?

    You claim there is a sense of brute "accessibility" in which other worlds are not accessible (or able to be actualized) on this picture. I do not see why this is so. Suppose there are two block universes, w1 and w2, identical up to the present, that diverge depending on whether or not I φ tomorrow. Suppose I will φ, so w1 is actual, and timelessly so. That seems perfectly compatible with the claim that I (table-thumpingly really) could have done otherwise. I won't. But I could have, and if I had then w2 would have been timelessly actualized in place of w1. The timeless facts depend upon what happens in time, after all.

  3. Saying that you were assuming eternalism clarifies a lot. I was assuming you weren't making such an assumption.

    Now I tend to favor eternalism so it's hard to argue to much against you since I think we actually have the same views. It just seems to me that those on the other side just aren't in nearly as weak a position as you portray.

  4. To clarify for those not up on the jargon and discussion I think one way (of many) of portraying the Eternalist/Presentist debate is as a dispute over whether being actualized is something that happens in time.

    Given that the Eternalist/Presentist debate also impacts upon the free will debate the issues become tied. Indeed I've seen many arguments for presentism that end up taking Libertarian Free Will as the premise (hidden or otherwise) for the arguing.


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