Saturday, February 25, 2006

Concepts of Possibility

So, I'm trying to make sense of the notion of 'possibility'. Again. I think it might be worth distinguishing the fundamental modal concept from various quasi-modal pretenders. By the latter, I have in mind the 'relative' and merely formal notion of what is 'allowed' within some limiting framework. We might, for example, define the 'logically possible' as that which entails no contradictions. (There it seems the fundamental notion - "contradiction" - is logical, not modal.) More generally, for any framework of limitations F, something is F-possible iff it is allowed by the rules of F. (I assume [perhaps falsely?] that this notion of what's "allowed" can be spelled out in non-modal terms.) But such relational accounts fail to do justice to our absolute concept. For any claim of "F-possibility", we can ask: "Yes, but is it really possible?"

The fundamental modal concept, then, concerns what really could have been the case. This seems conceptually distinct from logical notions of consistency and such. It's difficult to get a grip on, but I think we can roughly illustrate the concept by imagining time "rewinding", and then replaying with a different outcome. That alternative outcome is seen to be a "real possibility", or a way the world really could have turned out. The notion is clearer with regard to the future: we might think that the future is 'open' in various ways, that any one of various alternatives really could eventuate. Extending this intuitive notion back into the past, we will find various (now closed) branches that really were, at one point, metaphysically open possibilities.

The problem with this picture is that, at best, it only gets us as far as nomological possibility (worse, nomological possibility given initial starting conditions). But our intuitive notion of metaphysical possibility needs to be broader than that. It seems plausible that there really could have been different laws of nature, or different 'starting conditions', right back at [before?] the very beginning of time. (Perhaps there could have been no time at all!) But I'm not sure how to make sense of alternate possibilities atemporally.

We might imagine God choosing what physical laws (etc.) to make, or what possible world to actualize. Then the metaphysically ("really") possible worlds are those that God really might have chosen to make. Intuitively, a world W is metaphysically possible iff were we to 'rewind and replay' the decision enough times, then God would eventually actualize W.

Of course, that's a terribly rough notion. It wouldn't do as an analysis, since it appeals to modal (at least, counterfactual) notions itself. And it isn't clear whether the intuitive idea of "rewinding" God's atemporal decisions is genuinely coherent. (It isn't even clear whether the notion of an "atemporal decision" is coherent.) Also, I don't think God exists, which of course poses problems for any attempt to take this heuristic too literally! But I don't think God is playing any crucial role here (other than making the illustration a little easier to follow); we might just as well consider any other atemporal indeterminacy, or way in which it could somehow be "metaphysically open" which world gets to be made actual. (Atemporal indeterminacy really is a bizarre notion. Has anyone written about such things before? Sounds like the kind of thing theologians should be concerned about, at least. But of course I'd be more interested in analytic metaphysicians.)

So: while I'd previously given up on the concept of 'real possibility', I hope the above illustrations help to indicate that there is a rough concept in this vicinity. I'm not sure whether it can withstand further analysis though. (It does seem a very confused notion. Or, at least, I am very confused by it!) And it might be that the standard quasi-modal notions are all we really need for our philosophical purposes. (Perhaps my characterization of them is unfair, and they are fundamentally modal, but in a slightly difference sense to what I tried to point to above. I guess a lot hinges on the analysis of 'allowance' hinted at above.)

Fun but confusing topic. Comments welcome (as always).

P.S. Though the concept is distinct, absolute possibility will presumably end up coinciding with some limiting framework or other. For example, it may be that the world could really have turned out in any logically possible way. I take this to be a substantive claim, however, so the concepts of 'logically possible' and 'way the world really could have been' should be kept distinct.


  1. Interesting post! But i'm afraid our intuitions somewhat diverge.
    Do you have any argument for your thesis that consistency (or consistency with some theory) is conceptually distinct from possibility? Your open question-claim doesn't really convince me...
    Why, for example, couldn't we analyse "physically possible" as "is consistent with an ideal(maybe yet to be discovered) physical theory"?

  2. Kim, that analysis sounds fine to me. It just doesn't sound like a fundamentally modal analysis. It instead sounds (to me) like a reduction of the modal to the logical.


    I'm not sure. I know that I think of the two of them differently, as seen in the open question argument, but you might have different concepts from mine. As I understand it, "consistency" is a matter of obeying various formal rules (e.g. the law of non-contradiction), we might say it is a merely logical notion. Absolute possibility, as I use the term here, is a metaphysical notion, concerning "what might have been".

    But perhaps this distinction is a red herring. I think my real issue is with the distinction between 'relative' and 'absolute' modal concepts. I'm wanting to highlight the absolute notion of what is possible, simpliciter, as opposed to what is F-possible for some framework F.

    An analogy with ethics might help. We can say that an action is R-permissible when it is allowed according to some framework of rules R. (Then we can talk about what is legally permissible, or Biblically permissible, etc.) But none of those relative notions capture the fundamental normative concept, or what we really ought (or are permitted) to do. (See also the early paragraphs of this essay.)

  3. I thought the same as Kim. Why can't you say that, if "relative possibility of P" is consistency of P with respect to some assumed framework F, then "absolute possibility of P" is just that P is not self-contradictory? (nor entails any self-contradiction when joined with purely logical principles?

    The only answer I can imagine is that you would be relativizing your notion of "possibility", after all, to a set of logical principles which determine what is and what is not contradictory, and there may be alternative logics to choose. But if one believes in alternative possible logics, then I imagine the most natural thing would be to stop looking for a notion of metaphysical "absolute" possibility (which would bring with it an associated absolute notion of necessity) and instead take a pragmatic (Quinean?) view of both logic and modality.

  4. I'm throwing in with Alejandro and Kim. I don't think it makes any more sense to refer to "possibility" without any relative frame of reference than it does to refer to ethical permissability without any context. (e.g. "Is it permissible to lie?" It depends! Relative to what situation?) I don't see why this would be unsatisfactory or surprising either -- we know that we can't even refer to motion in a non-relative sense, which runs even more afoul of our everyday intuitions. Sometimes your intuitions are just wrong.

  5. Matt, that's certainly what I used to think, but what do you make of the intuitive concept ("what really might have been") that I've pointed to in the main post? Do you lack this concept? Or do you think it hides a deeper incoherency? Or do you simply think that nothing in reality satisfies it?

    I think only the second option can form an adequate rebuttal here. The third option is plainly foolish: at the very least, what is actual is (trivially!) something that is really possible in my sense. Perhaps you think nothing else is really possible, other than what is actual, but then you're not rejecting my concept but instead making substantive claims about its application. The first type of response also seems inadequate, since the problem there presumably lies with the people who lack the concept, and not with the concept itself.

    So what we need to do is argue that the notion of absolute possibility is somehow incoherent. But what sort of argument would that be? The common-sense notion sure seems coherent enough, at least on first glance, though its certainly difficult to analyse!

  6. Alejandro, I think my postscript addresses your questions. I don't know whether it's true that the world really could have turned out in any logically possible way; at least it doesn't strike me as a trivial truth, the way your analysis would make it.

  7. > we will find various (now closed) branches that really were, at one point, metaphysically open possibilities.

    it is clear from physics that almost everything is possible it is just that most things are unlikely - so I expect a fuzzy boundary between possible and not possible. There may not even be such a thing as "not possible" (in this sense).

    Otherwise of course if we exclue the way the universe realy is and look at the philosophical representation then I guess one would say, as other posters have said, that it is a matter of contradicting known principles (the problem is WHAT ARE these known principles?).

    In relation to "what might have been" I would assume (correctly or incorectly) that the person meant "in relation to the normal laws of physics" and "in relation to some assumptions about individuals behaviour" that would result in some sort of a coherent useful answer. The problem is I might have different assumptions to you

    For example you might ask "what might have been yesterday -
    to me "richard killed matt" is a "might have been" but it may not be - you have more information than me but also probably more assumptions.

  8. Richard, I'm with the second option myself. I'm pretty sure the reason it's hard to analyze is because there's no there there (much the same way I feel about qualia). I don't have a knockout argument, but the way that any attempt at making sense of such a notion of non-relative modality seems to fail is good enough for me. I really don't even see why we need it.

  9. I think there is something in your notion of absolute possbility which is very deep and very important to the way we relate to the world. Attempts to reduce it seem to miss the essential flavor. I look forward to your further thoughts on this.
    Best -
    Steve Esser

  10. Hello,

    I had a quarrel with a friend lately about the issue of possibility.

    My friend told me that he read about the soccer team of Togo. He said: "It is impossible that this team will win the World Cup 2006".

    I was somehow astonished and replied: "Well, I think it is highly improbable, but not impossible, for how can you exclude this-and-this scenario on the basis of your current knowledge. After all, there are situations that do not contradict any logical or natural laws."

    Clearly what I had in mind was some kind of epistemic possibility. My friend, however, maintained that this is not what is meant by "Togo cannot become worldchampion".

    I find Richard's remarks quite plausible and helpful.

    It is of course logically possible that Togo wins.

    And it also seems physically possible.

    But, according to Richard (as I understand him) my friend could still have asked, "You are right, for all we know it is possible that Togo wins, but is it really possible?"

    According to Richard's conception it would be possible only, if it passes the "rewinding test".

    I think this is a very useful heuristic. It becomes highly plausible with regards to mathematical truths. For example, it is possible on the basis of our current knowledge that Riemann's Hypothesis turns out true. It is also possible in this sense that it turns out false. However, mathematical truths are necessary true, or false respectively, if they are true (or false). Suppose Riemann's hypothesis turns out true. We wouldn't say that it was "really" possible that it could have been false, since it fails to pass the Rewinding Test.

    But in the Togo case, what reasons do we have to suppose that Togos winning the WC fails to pass the rewinding test?

    I think there are non except one assumes a strong determinism or necessary laws of nature. Suppose Togo does not win the WC. Is there a metaphysical or subjunctive possibility that Togo could have won. If laws of nature are contingent than it seems yes. If laws of nature are necessary it seems not. If determinism is true, The world could have turned out just as it has turned out. This would mean, as Richard said that only the actual world is a possible world. So if Togo wins, it is possible that it wins and impossible otherwise.

    In terms of possibility regarding future events it seems that we mean epistemic possibility. If not we would have to answer on the question "Is it possible that this-and-this will happen": "I don't know, because in order to know it I must know all the facts there are to know and determinism has to be true" or "I tell you after the event has actually taken place so that I can conduct the rewinding test". But this sounds somehow queer to me.


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