Some philosophers think that we can't know any propositions to be possible *a priori*. One way to argue that we can't do this might go something like this: at best, you can only know something to be *conceptually* possible *a priori*; but conceptual possibility doesn't entail real (metaphysical) possibility, for which armchair investigation isn't enough. This is because, as Kripke demonstrated, some conceptual possibilities are metaphysically impossible.

(*Hesperus is not Phosphorus* is metaphysically impossible because 'Hesperus' and 'Phosphorus' refer rigidly to the same object something that requires empirical investigation to establish. But it seems in some sense conceivable. We might call this a mere conceptual possibility.)

I agree that not all conceptual possibilities are metaphysical possibilities. But I think that, given *a priori* access to conceptual possibility and conceptual impossibility, we can get some *a priori* access to metaphysical possibility. Because I think there is an *a priori* link between conceptual and metaphysical possibility.

Here's a principle that might be true and *a priori*:**For any proposition q, if q is conceptually possible but metaphysically impossible, then there is some conceptually possible proposition p such that p -> []~q is conceptually necessary.** (That's a material conditional and the box of metaphysical necessity.)

Why believe this principle? For one thing, for any such q, ~q is an *a posteriori* necessity, and *a posteriori* necessities follow *a priori* from empirical facts and concept possession. Since all empirical facts are conceptually possible, this is sufficient to prove the principle.

This principle gives us an *a priori* test for metaphysical possibility. (I'm assuming *a priori* conceptual modality.) Take some conceptually possible proposition q. If it is conceptually impossible that some conceptually possible proposition p is such that p conceptually entails necessarily not-q, then q is genuinely metaphysically possible.

For instance, it is conceptually possible for the Bears to have won the 2007 Super Bowl. Furthermore, there is no conceivable proposition p such that it is *a priori* that if p, then it is metaphysically impossible for the Bears to have won the 2007 Super Bowl. Therefore, it is metaphysically possible for the Bears to have won the 2007 Super Bowl.

If this is right, then one upshot is that it's worth getting clear on what conceptual possibility amounts to, and how it works.

I'd like to thank Eric for the opportunity to guest-blog for the past few weeks, and to thank everyone who's read and offered valuable comments. I hope and believe that this has helped get me back into the habit of philosophical blogging I'll be continuing back at my own blog, There is Some Truth in That. I hope to see some of you there.

[And from Eric: Thanks so much, Jonathan, for your thought-provoking posts!]

## Wednesday, February 28, 2007

### A Priori Metaphysical Possibility (by guest blogger Jonathan Ichikawa)

Posted by Eric Schwitzgebel at 8:35 AM

Labels: Jonathan Ichikawa

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## 12 comments:

Hi Jonathan,

the argument you cite for why we can't know any propositions to be metaphysically possible

a prioriis a strange one anyway. From the fact that conceptual possibility (CP) doesn'tentailmetaphysical possibility (MP) it only follows that the former doesn'tinfallibly guaranteethe latter. But in many, many cases the entailment seems just fine, even trivial. So, unless we don't require infallible reasons for our beliefs about possibility to count as knowledge, there's no real epistemological problem here. Yet, there's a specific philosopher's problem regarding the link between CPs and MPs. For, many of the most contentious philosophical claims about what is metaphysically possible and what isn't may fall in the category of potential counterexamples to CP -> MP. So, your proposal would still be very helpful at least for philosophers themselves.But I wonder how we are supposed to evaluate your conditional. Because, in order to do so, we have to evaluate whether some proposition (~q) is metaphysically necessary given that some other proposition (p) is conceptually possible. Let's say that "~q" is "Hesperus is Phosphorus". Why is it a conceptual truth that necessarily, Hesperus is Phosphorus, given that there's is some suitable conceptually possible p? And what kind of p would that be? (This may, after all, just be a request for clarification!)

Hi Joachim, thanks for the comment.

On your first point, that the argument against

a prioripossibility is bad, I think you're probably right. I wasn't careful to formulate it, since I was going to try to get around it anyway. But I do think there's some pressure beyond mere non-entailment. I think the challenge is,for all you know a priori, this could be a CP non-MP.On your second point, yeah, I know this post was pretty dense, and would have benefited from some examples. Here's what I think about

H is not P:H is not Pis conceptually possible, but metaphysically impossible. So my principle should apply -- there should be some conceptual possibility CP such thatif CP, then H is not Pisa priorifalse (conceptually impossible).Here is such a conceptual possibility:

'Hesperus' refers to Phosphorus. Or if you prefer:'Hesperus' and 'Phosphorus' co-refer.It is plausibly (obviously?)

a priorifalse thatIf 'H' and 'P' co-refer, then H is not P.Hi Jonathan, thanks back for your quick response.

The challenge you suggest sounds like: I cannot be a priori

certainif this is a CP non-MP or I cannot a prioriexcludethat this could be a CP non-MP. But the question remains: Why do I have to? Of course, certainty would always be better than "mere" knowledge - but that is true outside of modal epistemology, too.To the second point. I agree that it is a priori false (at least plausibly) that

If 'H' and 'P' co-refer, then H is not P. But why, then, can't we run a parallel argument with descriptions instead of names: It is a priori false thatIf "the shortest spy" and "the smartest guy" co-refer, then the shortest spy is not the smartest guy? It appears to me, therefore, that, in order to get your intended result, you need to claim that it is aconceptual necessitythat identities with names are metaphysically necessary while identities with descriptions are contingent. Maybe that's fine, all things considered, but at least it seems to be a bit more controversial (e.g. do we really need to possess the concept of metaphysical necessity in order to grasp the meaning of names?).Hi Joachim, thanks, this is an interesting point, if I understand it right.

You cite:

If "the shortest spy" and "the smartest guy" co-refer, then the shortest spy is not the smartest guy?I agree that this is

a priorifalse. This would show, given my principle, that the mere conceivability ofthe shortest spy is not the smallest guyis insufficient for that proposition's metaphysical possibility. But this isn't the kind of thing I wanted to rule out. Huh.It's not a counterexample, of course, as I'm only giving a sufficient condition, but I sure would like to have something better to say about this case.

I'm afraid I'm not following the last part of your comment. I'm actually in the following dialectical place: I think I'm happy to adopt the principle you say that I need, but I don't yet see how it will help me! Can you explain how it fits in?

Thanks.

Hi Jonathan,

let me briefly recapitulate your general idea in order to make really clear that I understand you correctly:

Your idea seems to be that if we do not find a conceptual possibility p that conceptually entails the metaphysically necessary falsity of q, then q is genuinely metaphysically possible.

Now, an example of a proposition q for which we

dofind such a conceptually possible p was supposed to be "H is ~P". For, the conceptual possibility that 'H' and 'P' co-refer conceptually entails that it is necessary that it is not the case that H is not-P, i.e. that H is P. Therefore, "H is ~P" ismerelyconceptually possible, in your words, but not genuinely metaphysically possible.So far, so good. But now my parallel reasoning with 'the shortest spy' and 'the smartest guy' was supposed to illustrate that

If 'H' and 'P' co-refer, then, necessarily, H is Pis only conceptuallynecessaryif we assume that it is a conceptual truth that 'H' and 'P' arerigid designators. For, if they werenotrigid designators, but definite descriptions instead (or semantically equivalent to descriptions), then the above conditionalwouldn'tbe conceptually necessary - just like the following parallel conditional isnotconceptually necessary:If 'the shortest spy' and 'the smartest guy' co-refer, then, necessarily, the shortest spy is the smartest guy. This led me to the conclusion that in order for your test to work you have to assume that "it is aconceptual necessitythat identities with names are metaphysically necessary while identities with descriptions are contingent." Does that make sense?Hi Joachim, thanks for the clarification. I get it now. Yes, I do think that

If 'H' and 'P' co-refer, then, necessarily, H is Pis conceptually necessary, in the sense I intend it. I think I may have introduced some terminological confusion. I haven't said what conceptually necessity is, and that might not be the best name for it.I really just mean something like 'ideally a priori true'.

Hi Jonathan, what you now call 'ideally a priori true' seems to be very much the same as what Chalmers stipulates 'a priori' to mean in his work on two-dimensionalism. However, I'm worried about two things here: First, the idealization involved makes it unclear if finite, non-ideal minds like ours are really able to evaluate many instances of your conditional. Second, in order to establish in an a priori way that e.g. names are rigid designators one probably needs some thought experiments and modal premises. So, this could, on the one hand, make your idea circular, since the supposed route to knowledge of metaphysical possibility already presupposes a lot of modal knowledge. On the other hand, it would, then, probably not be "conceptual" knowledge in the traditional sense, because modal knowledge is more likely to be "synthetic a priori".

All these are not knock-down objections, of course, but I wanted to illustrate that your proposal gets much more controversial and theoretically demanding if you use such a thick notion of "conceptual possibility/necessity".

Hi Jonathan,

while reflecting on these issues a bit further I think I've now found a more serious and probably decisive problem for your proposal:

The reason is quite simple: Your test does not work as an

a prioriway of coming to know if a certain proposition is metaphysically or merely conceptually possible. Take, again, the proposition "Hesperus is not Phosphorus" as an example. According to your proposal, we can come to knowa priorithat it is not metaphysically possible. But what if,in fact, Hesperusis not identical withPhosphorus, which we cannot, by assumption, rule out a priori? Then, on the contrary, "Hesperus is Phosphorus" would be the proposition that is merely conceptually possible, while "H is not-P" would be metaphysically possible (and necessary) instead. But we can't decide the issue just bya priorireasoning!Another way to put the problem: Your test would make

If 'H' and 'P' do NOT co-refer, then, necessarily, H is not Palso come out as conceptually necessary. So, if your proposal is right, then not only "H is not P", but also "H is P" come out as merely conceptually possible, i.e. as metaphysically impossible. But since one is the negation of the other, they cannot bebothimpossible. Thus, your proposal fails: We cannot know in a purelya prioriway if "H is not P" is metaphysically possible or not.The only thing we can come to know by 'ideal

a priorireasoning' is that either "H is not P" is metaphysically impossible or else metaphysically necessary - but which disjunct is true depends onempiricalpremises (e.g. on ourempiricalknowledge that Hesperus is in fact Phosphorus).Joachim, you're attributing to me a stronger view than the one that I hold. I agree that we can't in general know

a prioriwhether or not a conceptually possible proposition is metaphysically possible, for the reasons you give.So this is definitely a mischaracterization of my view:

According to your proposal, we can come to know a priori that it [H is not P] is not metaphysically possible.I agree, this would be an untenable proposal. My proposal explains why we cannot know

a priorithat it is possible; it points to a relevant difference between this proposition and the kinds of propositions whose modal status we can knowa priori.My claim is just this: in some cases, like the Bears case, the method I outline can give

a prioriknowledge of metaphysical possibility.This is consistent with the true point that for some conceptually possible propositions, like

H is not P, we can't knowa prioriwhether they are metaphysically possible.Ah, I see! So your a priori test was only meant to identify these propositions (e.g. about Hesperus and whom it is identical to) where we cannot know a priori if they are metaphysically possible or not - and to identify those (e.g. about the Bears winning) where we can and very often do know a priori that they are metaphysically possible. Yes, this really wasn't fully clear to me so far! But if this is your actual proposal, then we also cannot come to know a priori if some proposition is

merelyconceptually possible. For, the most we can establish with your test is that we cannot know a priori of certain propositions (e.g. "H is P") if they are metaphysically possible or notin additionto being conceptually possible. But you are surely right to insist that this is already something!Hi Jonathan,

by the way, all my critical attempts notwithstanding, I really enjoyed your posts on

The Splintered Mindand I definitely hope to read more of this aprioristic stuff on your own blog!http://metaphysicalfiles.blogspot.com/

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http://the-funny-place.blogspot.com/

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