Wednesday, November 16, 2005

The Impossibly Conceivable Counteractual?

That last post got me thinking: isn't counteractuality an example of something that is ideally conceivable and yet metaphysically impossible?

On the standard understanding, p is metaphysically possible iff there is some possible world where p is true. But there is no possible world at which any world other than our own is really actual. (Just like there is no other country from which Wellington is not the capital of New Zealand. Once the index is fixed, the truth of an indexical statement is likewise fixed, no matter where you might "ask" it from. Our world is the only 'actual world' in the modal multiverse -- a static fact that's true everywhere you might ask of it, even on other possible worlds. See also my old post on modal indexicals.) So counteractuality is metaphysically impossible.

(It seems a straightforward consequence of this that there is no such thing as real possibility. The standard metaphysics of modality, as I understand it, thus commits us to narrow fatalism. This is a most unfortunate consequence. Perhaps I've just misunderstood the standard picture -- if so, I hope someone can reply and set me straight. Otherwise, I think, the standard picture is in serious need of revision. See the latter link for a somewhat radical alternative designed to avoid such problems. For now, though, I'm working with the standard picture.)

Nevertheless, it seems perfectly conceivable that some other possible world could have been actualized in place of ours. Indeed, I suggested in my last post that whenever we imagine, we imagine the fictional world as (counter-)actual. So we conceive of the impossible all the time. Unless there's something wrong with the analysis of possibility described above...

P.S. I've previously suggested a connection between conceivability and our explanatory practices, to the effect that, if Y is a conceivable alternative to some actual fact X, then we should want an explanation of why X is true rather than Y. Conceivability is the important notion, not metaphysical possibility. (Just as well, since the latter notion is so difficult to make sense of.) So, even if it's metaphysically necessary that our world is actual, it'd still be nice to have an explanation for why this world and not some other.

16 comments:

  1. Hi, Richard,

    You are right that this is so if it is true at every possible world that this is the actual world. But what reason do we have to think this? To do this we have to treat 'actual' as modifying 'world' in the same way that 'possible' does. But surely whether a world is actual is incidental to its being possible; only if we already assume that actuality of a world is something true at every possible world do we get the result. But it is quite reasonable to treat actuality as a foreign element in the account: actuality just isn't true of a world in the way that possibility is true of it.

    You know, it's rather curious: for it strikes me just now that your argument is an ontological argument (a Cartesian one, very similar to Spinoza's), and my response is the Kantian response that existence cannot be a real predicate. Crudely, Kant's ideas is something like this: If I have the concept of a hundred thalers without determining whether they exist I recognize that concept as indicating something possible; if existence is a real predicate, however, when I conceive of a hundred actual thalers, I would always be conceiving of something different from the merely possible thalers, because the two concepts would not be the same. But then the possible thalers would not be possible, and, moreover, we could never start by recognizing that X is possible and then come to recognize that X is not merely possible but actually exists, which is absurd. Therefore, determination that X exists is something distinct from conception of X itself.

    I would say something similar about possible worlds (indeed, I think it a stronger argument in the case of possible worlds, because it is much closer to our ordinary judgments about modality): actuality is not bound up in the whole manifold of possible worlds, so that something's being a possible world would imply that there are any truths about the actual world at any possible world. Rather, actuality of a world is something merely incidental and posterior to a thing's being a possible world. If we take '[p is true at the actual world] is true for all possible worlds' to imply that the actual world's being actual is true at all possible worlds, we get absurd results. On our usual senses of modality, it is gibberish; and on the one supposition on which it would make sense (that no world is possible unless it is actual) the proposition would have no meaning except 'p is true'. All modal talk would be otiose at best. If, on the other hand, we take '[p is true at the actual world] is true for all possible worlds' simply to pick out a given possible world in a way extrinsic to the manifold of possible worlds qua possible, then we can make sense of it. It will be '[p is true at this particular possible world] is true for all possible worlds' where 'this particular possible world' is picked out by its being actual.

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  2. actuality is not bound up in the whole manifold of possible worlds, so that something's being a possible world would imply that there are any truths about the actual world at any possible world.

    This would be clearer as: actuality is not bound up in the whole manifold of possible worlds, so that there are any truths about which world is actual at any possible world.

    In other words, my point is that possible worlds analysis only tells us about possibility, impossibility, and necessity; actuality is something else on top, that possible worlds analysis alone could never tell us anything about.

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  3. Richard: FWIW, I came to the same conclusion regarding "no such thing as real possibility" in Lewis's system. The actual world (like all the possible worlds) is fixed forever.

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  4. To say that it is possible that I am not sitting down right now (I am) has a ring of ridiculousness to it, but it is logically correct, as you all have been trained to understand. I happen to like modal logic. There's something extra-worldly to it (excuse the pun, but you know what I mean), like the cartoon Calvin and Hobbes. If we can imagine something, it must have a logical truth to it (often it does, after all). And I don't think that anyone among us would like to give up the "truth" of his imagination, regardless of its appeal to logic.

    On the other hand, to what extent does the "logic" relieve us of the necessity of discovering whether something is truly possible?
    How well are we really analyzing the other worlds (it's possible that all men are created equal), not to mention the backward travel tickets that return the analysis to the actual world? To a great extent it's the travel tickets that are the danger, not the sheer enjoyment of the logic itself.

    P.S. I just bumped into your site. You and I share interests, although we have a different approach to them. I look forward to some conversation.

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  5. NR: "To say that it is possible that I am not sitting down right now (I am) has a ring of ridiculousness to it"

    Only if you are talking about epistemic possibility, i.e. what is possible given what we know. Given that you know you are sitting down right now, the contrary simply isn't a live epistemic possibility. So it isn't "logically correct" at all: it seems ridiculous because it is. If you are certainly sitting, then it isn't possible that you aren't.

    Alternatively, if you mean to talk about metaphysical possibility (as I was in this post), then all the claim means is that, though you happen to be sitting right now, you could have been standing up instead. And that much is clearly possible, common sense, nothing "ridiculous" about it.

    So we simply need to be clear about what is being said.

    I'm afraid I don't understand what you're trying to say in the rest of your comment. (Glad you like the blog though -- it's always nice to have new visitors.)

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  6. One could argue (metaphysically) that if you are not sitting it was impossible that you would be sitting. AND even if you were sitting you wouldn't be "you".

    1) Using sittin as a metaphore.
    2) I am refering to a bit of determinism mixed with a consideration of what you would have to change in a nearest possible world in order for you to have ended up "sitting"

    Not sure I want to be too religious about arguing that (it restricts discussion a bit) but I would think it is a valid viewpoint.

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  7. Brandon, thanks for the very interesting comment. I've been trying to think of something intelligent to say in response, but keep coming up blank. I like your characterization of the issue: it does all seem to come down to whether we consider the world's status as 'actual' to be "bound up in the whole manifold of possible worlds". I've been assuming that it is -- I kind of imagine a stellar map with a big red dot marking 'the actual world' in modal space. That way, wherever in the map you go, the big red dot of 'actuality' is still over here. I'm not sure why this picture is "gibberish", perhaps you could explain that part further. But I do agree - as noted in the post - that the fatalistic implications of it are troubling, at least.

    One thing I am curious about: if 'actuality' is not contained within the multiverse/manifold of modal space, then where and what is it? And how do you guarantee it uniqueness -- or do you think that multiple possible worlds could [actually] be actualized? (And what on earth do we mean when we try to talk, like this, about the modal properties of modal space itself? Are there "possible multiverses", a step above "possible worlds"? But then we'd need another step up to talk about the modal properties of that, and so on, ad infinitum.)

    Okay, I guess that was more than one thing. As you've probably noticed, I find all this very puzzling...

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  8. If you concieve of somthing posible you could concieve of "100 white people" and then claim that 100 white people exist somwhere - or you could concieve of 100 white people with all their physical traits and relitive proximities - and claim they domt exist and will never exist.... reminds me of that post of Mike B's about arguments.

    So there is some arbirary point at which our precision moves from a real current example to a ral future example to a theoretically possible example to an impossible example (self contradictory) and posibly one more step.

    > If we take '[p is true at the actual world] is true for all possible worlds'

    Just getting up to speed here - but

    1) if you asked that question in another posible world the only meaningful perspective would be that that was the actual world (from your perspective)?

    2) Of course you do need another level to explain a possible world in which there is some specific relationship to other possible worlds because that requires a larger infinity. In the same way that I can have all the sand in the world in a bucket but not all the combinations of locations of sand)

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  9. Richard, for my part, I don't see how your assumption that the actual is bound up in the whole manifold of possible worlds could be wrong. If we bring this back to earth, what is the object of modal logic if not an examination of argumentation that affects the actual world? Is any logician or philosopher really interested in other worlds, even if he creates them and leaves us wondering where they might be and what they do to the reality of the actual world?

    Back to "I am sitting as I type this" (again I am). I hope I do a better job this time, because I seem to have said very little the first time, especially given that I agree with you. Basic texts of logic (and that's all I meant, by the way, about your training) tell us that this is a contingent, not a necessary, truth and could be translated as "x is true but it is possible that x is not true." If I say on the other hand that "I am a human being" or "I am alive as I type this," I am stating a necessary truth. I do think that there is something to the "logical" difference between the two types of statements, even if it is "ridiculous" epistemically to say that it is possible that I am not sitting down. We can recognize, I believe, that if I were to ask you, "What room in my house am I sitting in?" and "Am I a human being?", you would be able to answer the latter, but not the former, even though the answer in both cases would be a truth in the actual world. They are different types of truth, if we accept the notions of contingent and necessary. As I stated in my previous post, I like the mental exercise provided by the distinction; but I was making fun of it when I introduced Calvin and Hobbes. A truth is a truth to me (and I think to you, if I've read you correctly, but sometimes these technical discussions leave me scratching my head). But frequently we as people would like to imagine truths and bring them back to this world as realities. That was my point about Calvin and Hobbes. (Have you read the comic strip? Obviously I shouldn't make assumptions about someone who lives in New Zealand.)

    Then I asked, to what extent does the logic relieve us of (to reword) the burden of proving that the possibility is possible -- in the actual world. This is where, I think, the discussion of outer space doesn't help, because, again, modal logic can only have its eye in the end on the actual. If we say, "All men are created equal" or "God created the world in seven days" or "We are all evolved from a single-celled replicating organism that grew out of a crystalline substance like clay" or "Put your own here," we will raise skeptical eyebrows somewhere. In each case, we lack complete evidence. But as soon as we put "It is possible that..." before each, we enter the realm of modal logic and can begin to create worlds. It is as hard to refute the possibility of each of those statements as it is to prove the actuality. So do we have different worlds here? Do the people who commonly argue for any of those possibilities care about any world but the actual? I think not. But modal logic allows them to "travel" to their world, and then, perhaps with just the right space-ship of logic (another topic of discussion), to travel back with their possibility on board as an actuality.

    It is that final motivation that most interests me, not the logic itself.

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  10. Hi, Richard,

    I think we need to be clear on what the possible worlds manifold actually is. As I see it, it's effectively just a posit used in the analysis of certain modalities, namely, possibility, impossibility, and necessity. In that sense, I don't think that there's any problem with 'where' the actuality is; when we are thinking in terms of the possible worlds manifold itself, we are simply abstracting from the actual world, so it doesn't come up. Actuality is just not one of the fundamental concepts of possible worlds analysis. Sometimes we use the fact that a given possible world is actual as an index to distinguish out one possible world from the others, but this is extrinsic to anything about a possible world that makes it a possible world, or anything about the manifold that makes it the set of possible worlds.

    'Gibberish' is perhaps too strong a word. What I should have said is something more like this. I don't think the problem is what possible worlds analysis tells us about the actual world; rather, it's whether we are going to build anything about the actual world into the possible worlds analysis itself. In other words, we aren't talking about a conclusion but about the usefulness of building the metaphysical impossibility of a non-actual possible world into our possible worlds analysis from the very beginning. It's only if we've already effectively assumed that actuality and possibility are convertible for worlds that we get the conclusion. And in this sense, I don't see that there's any particular value for that sort of approach -- as I said, it seems that if we start doing that, we're better off just going for a much simpler and less involved modal idiom, one that eliminates possibility altogether as a misleading way of talking about actuality. It's not gibberish, strictly speaking, since there is one metaphysical system that is (at least prima facie) intelligible and effectively does just this: Spinoza's.

    On multiple actual worlds, I'm inclined to think that that's impossible, because I don't see how we can coherently regard distinct possible worlds as compossible -- precisely what makes them distinct is that they contradict each other at some point. If there were some way to have distinct but compossible possible worlds -- to divide reality into sections, as it were, so that one possible world is actual under this aspect and another possible world is actual under that aspect -- then it would be different, but since we are talking not about distinct universes but about collections of possibilities, I don't see how that would be possible. Further, since every possible world is one distinct set of possibilities, we could never know another possible world as actual, so arguably the point is moot.

    Genius,

    You asked, "if you asked that question in another posible world the only meaningful perspective would be that that was the actual world (from your perspective)?"

    I take it that the answer would be yes; of course, in a non-actual possible world in which you ask the question, the question and your answer are only possible, and the answer is (as it happens) wrong. But if I'm right, whether the answer is right or wrong is not something that can be discerned simply by considering possible worlds as such.

    On the question of possible worlds and the higher levels, if I understand the question properly, I think that the standard view is that possible worlds are constituted in part by their relations to other possible worlds. Part of what makes this possible world this possible world is that it is similar to or different from that possible world in such-and-such way.

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  11. "the question and your answer are only possible, and the answer is (as it happens) wrong. "

    Can you say the answer is wrong if the question is imposible to ask?

    1)If possible world A was true then X would happen 2)if possible world B was true Y would happen

    Given that - if possibly world A was not true would a person inside possible world A see X or Y?

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  12. Possible worlds are integrated collections of distinct possibilities; so for every particular possibility there is a possible world in which it occurs. That is, a possible world is one particular way the world could be. It's not impossible for someone in a possible world to ask if their possible world is the actual world, because that's a real possibility: someone could ask such a question, so there's a possibility for it, and a possible world which would include it.

    Assuming that you can't have a world with both X and Y, anyone within possible-but-non-actual world A would see X, not Y, because anyone within A would be part of the whole tapestry of possibilities that includes X and not Y. But strictly speaking anyone within A would also be merely a possible observer whose observation (in that possible world) would be an observation of X. Everything in a non-actual possible world is merely possible.

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  13. Brandon, regarding multiple actual worlds, such as the famous interpretation of quantum mechanics. I'm not sure it necessarily leads to where you suggest it leads. After all I think that all that happens is that the meaning of "here" becomes most important rather than "actual." The problem might occur when people have philosophical commitments which don't lend themselves to duplication. But I'm not sure that is an argument against multiple actual worlds so much as an argument against it for people with certain commitments. Given that probably nearly all proponents of MWI of QM are naturalists, I'm not sure they'd have problems. Some theists might, but that's an other matter.

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  14. Clark,

    Your answer presumes that multiple actual worlds in quantum mechanics would be distinct possible worlds in a possible worlds analysis. But I see no reason to hold such a view rather than (say) the view that they are different regions of one possible world. There's no reason to think that the many worlds of QM are necessarily many worlds in a possible worlds sense; or, at least, I would have to see the argument for its being so.

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  15. It seems though that if you take that reading of the MWI of QM that there is then but only one possible world and one actual world, given the commitments that theory contains. I don't see how it is fruitful to call them different regions of one possible world, given that they appear essentially disconnected. i.e. it seems one is led to a discussion of the fruitfulness of our metaphors at this point.

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  16. Well, the reasons for treating them as all part of one possible world is that they are taken as all actual but not conflicting with each other: so at least one way of working out what a possible world is (compossibility) would put the many worlds interpretation on the one-world side. (Causal and physical disconnection is not, I think, relevant to distinguishing worlds in possible worlds analysis, only whether you can logically have both. Further, while MWI worlds don't interact with each other, they do interfere with each other, which suggests in itself that they are part of one possible world.) Given that we build any possible worlds analysis by starting with what is actual, there's good reason to think that all the compossible actual worlds will be lumped together as a one possible world. And, further, I think MWI needs to be treated as a statement about one possible world, on its own terms: MWI proponents are putting forward their view as a possibility for how things actually are, which means they are putting it forward as a candidate for this possible world.

    I'm not sure that there's really any problem with the metaphor of regions; it's precisely because the MWI worlds are disconnected, I take it, that MWI proponents don't find a contradiction in saying that two worlds expressing contrary possibilities are both actualized -- the possibility that is actualized in each case is distinct (possibility of MWI world 1 vs. possibility of MWI world 2), so despiting occupying the same space (on what seems to be the most common account), they occupy different regions of logical space and can be compossible parts of a possible world. I don't think there's any problem with this use of 'region' unless we are apt to jump the gun on analogies and start confusing logical regions with some sort of physical region.

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