Thursday, September 02, 2010

Varieties of Modality

We all know that metaphysical possibility isn't the same thing as physical possibility, or other 'restricted' notions.

It is sometimes suggested that the modifiers ‘metaphysically’, ‘physically’, ‘epistemically’, etc., in phrases like ‘metaphysically possible’ act as restrictors on the more general, univocal, property of possibility. (Compare: someone can be surprisingly wealthy, unjustly wealthy, or extremely wealthy — these are all just more specific ways of being wealthy.) On this model, there is a property — possibility — and modal language attributes it, often specifying the way in which the relevant situation is said to be possible. When we say that it is physically possible that a man should run the 100m-dash in 9.50 seconds, we say that this achievement is among a particular subset of the possible: the physically possible.

This isn't exactly how I think about possibility language, but it's not too far off.

One question raised by this approach concerns just what the unrestricted modality includes. It’s clear enough that the physically possible is a restriction on the metaphysically possible. One might continue to suggest that the metaphysically possible is a subset of the conceptual or logically possible—and perhaps further into various logically impossible ‘possibilities’. Or one might somewhere draw the line. George Bealer, in his contribute to the Gendler & Hawthorne Conceivability and Possibility anthology, draws the line at the metaphysically possible. He writes:
[S]ome people insist on distinguishing logical possibility and metaphysical possibility and so are led to the following: p is logically possible iff p is merely consistent with the laws of logic (i.e., not ruled out by logic alone). This usage, however, invites confusion. There are many logically consistent sentences that express obvious impossibilities (e.g., ‘Bachelors are necessarily women’, ‘Triangles are necessarily circles’, ‘Water contains no hydrogen’). If you buy into calling mere logical consistency a kind of possibility, why not keep going? For example: p is ‘sententially possible’ iff p is consistent with the laws of sentential logic. Then, since ‘Everything is both F and not F’ is not ruled out by sentential logic (quantifier logic is what rules it out), would it be possible in some sense (i.e., sententially possible) that everything is both F and not F?! Certainly not my ear! (78-79)

I don't think this comprises a very good argument, for at least two reasons.

First, the logical structure of the argument for drawing the line at metaphysical possibility is suspect. It follows a particular erroneous form of a slippery slope argument: if you permit X (which doesn’t seem too bad), then what’s to stop you from going on to permit Y (which seems terrible)? The difference in felt terribleness, if there is one, would provide just the needed traction between X and Y in order to avoid the slip. Remember that drawing the line at metaphysical possibility represents a substantive choice; one might try draw it even more narrowly — at physical possibility, say. Imagine a philosopher who refuses to countenance those ‘metaphysical possibilities’ which violate the laws of physics; he will insist that they’re in no sense possible. Against someone like Bealer, who believes in such physically impossible possibilities, he might offer just the same retort: “if you buy into calling mere metaphysical consistency a kind of possibility, then why not keep going?” If there is reason to countenance metaphysical possibilities—and I agree with Bealer that there is—then presumably, we will justify it by reference to the useful work to which thinking about metaphysical modality can be put. But for all Bealer has said, it may well be that further conceptual or logical possibilities can be put to similar work. (This seems to me very plausible.)

The second reason to be concerned with Bealer’s argument is that he makes an insufficient case for the undesirability of the bottom of his slippery slope. Bealer apparently finds the suggestion that there is a sense in which this contradiction is possible implausible. He doesn’t say why, but the invocation of how it strikes his ear suggests it may be based in a linguistic intuition; it just sounds terrible, perhaps, to say that there’s a sense in which it is possible that everything is both F and not F. But that there is some sense in which it possible does not, of course, imply that it’s a very interesting sense, or one that ordinary speakers are used to thinking about. Bealer ostends a notion of ‘sentential possibility’, abstracting away from any use to which thinking about it might be put. It shouldn’t come as any surprise, then, that, so presented, we shouldn’t have any interest in thinking about such ‘possibilities’. That doesn’t mean they’re not there, ready for us to take them up if and when the course of inquiry demands it. (Again, a philosopher who thought of physical possibility the way Bealer feels about metaphysical possibility might respond just the same way Bealer does, in response to what is conventionally recognized as the physically impossible metaphysically possible. "It's just not possible in any sense for humans to travel faster than light." Actually, I suspect that most people who haven't studied metaphysics are likely to respond this way.)


  1. I'm not sure how it affects the argument, but the notion of sentential possibility is actually a very useful one in a whole host of concepts. The proof of the completeness of predicate logic that I teach intermediate logic classes (i.e., Henkin's) makes very heavy use of this notion. And in general it's useful in logic because it is so easy to compute whether something is sententially possible. You just have to draw a truth table, and you know in advance how large that will be.

    Oddly, I think it's less than clear that "Everything is F and not F" is impossible. I think it's arguable at least that the empty world is possible, and in that `world', everything is indeed F and not F.

  2. Thanks, Brian -- that's helpful.

    Your first point seems relevant to the argument in this way: I tried to explain away Bealer's intuition that there's no sense in which it's possible that everything is F and not-F by citing the fact that, in the relevant context, the notion of sentential possibility was an obscure and uninteresting one. You've helpfully introduced reasons why it might be very useful to think about what's sententially possible. If my suggestion is right, then this should loosen us up to considering this to be a 'kind of possibility'.

    Your second point seems correct, and it looks like an additional argument against Bealer. However, this one looks relatively easy for him to patch. I suspect he'd take the point, and simply change the example to "Something is F and not F".

  3. That's funny, I've got a draft of a paper with this exact title (here:

    I don't particularly like Bealer's argument either, but I would actually like to draw the line at metaphysical possibility as well: logical (and also conceptual) possibility are merely pseudo-possibilities. My reason for thinking this comes from a (modified) Finean understanding of metaphysical modality though: it's a special case of essence. Accordingly, metaphysical possibility is possibility in virtue of the natures of all things.

    But I think that conceptual and logical possibility can perhaps be understood as restrictions of metaphysical possibility in the same sense as physical possibility. Here I would be sympathetic to something that Bealer says, i.e., mere (logical or conceptual) consistency is not enough. It seems to me that if we take the essentialist account of modality seriously, we could insist for a positive account of conceptual and logical possibility.

    I actually use the example of travelling faster than light in my draft as well. Now, the possibility of travelling faster than light is not ruled out by the natures of concepts, but nor do the natures of concepts *make* it possible to travel faster than light. This could be expressed in terms of truthmaking: the natures of concepts are not viable truthmakers for the possibility of superluminal travel, which would surely be a physical process. Presumably, it is not even physically possible to travel faster than light, so it appears that if it is possible at all, it must be metaphysically possible, that is, there is a metaphysically possible world in which the laws of physics allow for faster than light travel. And this is the only positive definition that we can give for the possibility of superluminal travel. It may be conceptually and logically consistent, but these do not express genuine possibilities since the subject-matter of the possibility does not concern either the natures of concepts or logical concepts.

    Well, this is a pretty controversial idea, but that's what I've been entertaining anyway...

  4. [...] Ichikawa talks about Varieties of Modality at his blog There is Some Truth in That. I had to link to this because I’ve got a draft of a paper with the exact same title. [...]

  5. Thanks for the link, Tuomas -- I'll check it out.
    I don't think I understand your suggestion. When you say that logical and conceptual possibility are restrictions of metaphysical possibility, do you mean they're strictly stronger? That's the reverse of the usual way of looking at things. Maybe you mean to be suggesting that superluminal travel is metaphysically possible, but not conceptually possible or logically possible? I don't see why it should be conceptually impossible just because its possibility isn't grounded in concepts.
    But maybe I'll just have to read your paper.

  6. Yeah, the idea that I'm entertaining here is certainly not the usual way of looking at things, and I'm not even sure if it's worth developing because it messes up the standard terminology, but I decided to have a go anyway.

    In a sense I'm thinking of logical and conceptual possibility as stronger than metaphysical possibility, but actually I don't want to define them quite like that at all, because I don't want to say that conceptual and logical possibility entail metaphysical possibility. But I don't want to say the reverse either, rather, I want to reserve each type of possibility for those modal truths which are true strictly in virtue of the natures of the relevant concepts. So that's why I get the strange sounding result that superluminal travel is metaphysically possible, but not conceptually possible or logically possible. That's really just a twisted usage of the terminology, but I think it's more suitable for some purposes.

    So really I think we got just one modal space, metaphysical modality, and we can and do define chunks of it by restriction. But I want to talk about those chunks as if they were independent modal spaces (because that's what we often do anyway, as your example of the layman talking about superluminal travel shows), hence no entailment from conceptual possibility to metaphysical possibility, nor its reverse.

    I think this works nicely with alternative logics as well: you can talk about logical necessity in terms of classical, intuitionistic or paraconsistent logic without worrying about whether they entail metaphysical possibility. But there are actually a couple of different ways to think about logical possibility here. Scott Shalkowski (2004) has a good paper related to this: ‘Logic and Absolute Necessity’, The Journal of Philosophy 101 (2): 55–82.