Clayton ably summarizes Anand Jayprakash Vaidya’s piece in the August issue of The Reasoner. Vaidya’s piece is a defense of the claim that conceivability entails possibility:
(CET) C(x, p) → L(p)
(CET) says that if p is conceivable to x, then it is logically possible that p. Vaidya argues that it is impossible to counterexample (CET) in the standard way (i.e., by showing that it is possible to conceive of the simultaneous truth of its antecedent and falsity of its consequent); to do so would involve arguing that a situation S (in which p is conceivable to some x and it is not logically possible that p) is conceivable, hence logically possible, which is a self-defeating use of (CET).
Obviously, it’s possible to construct a reductio of (CET) out of this raw material though, as Clayton argues (or appears to, anyway) in his soon-to-be published piece. Here’s the reconstructed reductio:
1. CET → ¬L(S)
2. CET → [¬C(me, S) v L(S)]
3. CET (assume for reductio)
4. C(me, S) (plausible)
5. L(S) (2,3,4)
6. ¬L(S) (1,3)
To resist the argument, you need to resist (4) — i.e., you need to deny that S is conceivable to me. I.e., as Clayton says, you need to defend a substantive conception of “conceivable” on which … it is impossible to conceive of impossibilities. The question is whether (and to what degree) this substantive conception tracks our ordinary understanding of conceivability, since it is seems to be the ordinary understanding that is implicated in (CET).
For what it’s worth, the following sentences do sound fairly odd to me:
#I suppose it’s conceivable that he jumped off the bridge, but it’s not possible that he did.
#It’s possible, but impossible to conceive, of traveling to Alpha Centauri.
Note that the explanation for the oddness isn’t (or isn’t obviously) that these sentences are Moore-paradoxical, since they each involve the “it”-cleft, and neither directly implicates the speaker’s mental states (for example, it seems fine for a speaker to say that something is conceivable, even though he personally is unable to conceive it). A proponent of (CET) trying to resist the reductio has a ready explanation of the oddness: the sentences are contradictions. This strikes me as an exceptionally weak way to argue for the relevant notion of conceivability, but I’m interested in what others have to say.
ADDENDUM: It seems, to me anyway, that the obvious way to defend (CET) is to emphasize that the sentential complements of conceivability/conceiving-ascriptions are, like the sentential complements of most any attitude verb, intensional contexts. This is evidently the case, since the moves from (7) to (8) and (9) to (10) seem bad.
(7) It is conceivable to Chris that Samuel Clemens and Mark Twain were different people.
(8) It is conceivable to Chris that Mark Twain and Mark Twain were different people.
(9) It’s conceivable to Chris that water and H2O are different substances.
(10) It’s conceivable to Chris that water and water are different substances.
Intensional contexts have a special property: it’s generally possible to locally accommodate the presuppositions of expressions occurring in them. The lesson to take from (7) and (CET) is not that it is possible that Sam Clemens and Mark Twain are distinct individuals, so long as you’ve got a good account of local accommodation in intensional verb-ascriptions at hand. (Eric Swanson has emphasized just this point.) So (7) does not necessarily assert anything of the person we associate with the name ‘Samuel Clemens’, since the presupposition borne by the name need not project out into (7), and, likewise, (9) does not necessarily assert anything of the substance that we associate with the kind-term ‘water.’ (7) may assert (and on its most natural reading does assert) something about the individual Chris associates with the name ‘Samuel Clemens.’ What is conceivable to Chris is roughly speaking the following proposition: the individual that Chris associates with ‘Samuel Clemens’ and the individual Chris associates with ‘Mark Twain’ are different people. This proposition is, of course, also logically possible.
July 26, 2007 at 5:25 am
Nate,
I’m curious to know what you think about this argument. It’s pretty simple.
Audrey says
(1) I can conceive of a situation in which p & ~q.
Cooper says:
(2) Audrey can conceive of a situation in which p & ~q.
I ask, ‘But is that really possible?’, to which Coop replies:
(3) Of course not, p entails q.
Now, it seems to me that (3) doesn’t negate (2), which suggests that there’s something odd to the claim that ‘conceive’, as we ordinarily use it, should be understood in this way: you truly can conceive of S only if S is possible; if S is not possible, you can only truly claim to seem to conceive.
I have some hand-waving things to say about your argument, but I can’t tell whether you don’t buy the implicit methodology I’ve relied on to use (1)-(3) to attach CET or you don’t have the linguistic intuitions I have.
July 26, 2007 at 3:21 pm
I’m not sure about that case, but the data here is meager. To me, it seems that when Cooper says “Audrey can conceive of a situation in which p & ~q”, the “p & ~q” part of that utterance behaves differently than it does when not embedded in an attitude-ascription. Compare:
(4) Of Russell’s yacht, Moore believes it is longer than it is.
(5) But is it [longer than it is]?
(6) Well, of course not. Nothing is longer than itself.
Accommodating the ascribee’s beliefs about Russell’s yacht is what allows us to say (1) without attributing to Moore a belief in a contradiction. When accommodation isn’t possible (as in (2) and (3)), this strategy is no longer available.
So in your Audrey case I agree with your intuition that (3) isn’t negating (2), but I would explain it as follows: local accommodation by what’s believed to be a person’s doxastic state isn’t possible when we’re not talking about the person’s doxastic state. The interpretation of “p & ~q” often undergoes a (requisite) shift when it’s not in the scope of an attitude verb. My own view is that the proposition expressed by that sentence shifts in such cases, which is why (CET) wouldn’t be threatened by my (7) or (9).
Admittedly that assumes a lot of controversial stuff, but hopefully the basic idea is reasonably intuitive.
July 26, 2007 at 3:57 pm
i am suspicious of the pseudo-logical statements.
“Vaidya argues that it is impossible to counterexample (CET) in the standard way (i.e., by showing that it is possible to conceive of the simultaneous truth of its antecedent and falsity of its consequent)”
(CET) C(x, p) → L(p)
i am suspicious that is the standard way. for one, it would be false. that counterexample would not work unless (CET) is taken as necessarily true. but i don’t think people are claiming that it is necessary that conceivability entails possibility, just that actually conceivability entails possibility. in which case, a counterexample would be giving an actual situation where p is not conceivable to x and p is not possible. (also, i thought M is possibility and L is necessity, in that notation.)
umm, if i knew more about modal logic, i’d also be able to say more why there might be some problems with modal predicate logic. i think that was pretty much clayton’s point. and i realized this after writing it. so i feel silly.
anyway, another question is the quantification of x. i think for the proof to work, there just needs to be one x. but after the corrections i really don’t see any intuitive pull for (CET’):
(CET’) nec(Vp(ExC(x, p) → poss(p)))
also, p is a variable, but for Vaidya’s proof to work, there needs to be a proposition in that position. in possible world terms, p should pick out some individuals or other, but the proposition is a description of what holds of certain individuals.
i am not sure what all this amounts to, and i need to eat lunch. but two more follow-ups on the last point:
1. fine and plantinga make this distinction of a proposition true in and true of a world. that is, there are some proposition that holds of a world but isn’t an individual in the world, S might be one of them.
2. also, modal languages tend to have trouble talking about the “moving parts” of the system, i.e. what the language uses to talk about other things. see shawn’s post on this: http://indexical.blogspot.com/2007/05/moving-parts-of-modal-logic.html
July 26, 2007 at 5:14 pm
Nate,
Fair enough. Whatever interest I have in conceivability, it is an interest in the epistemological issues. If you can’t conceive of what’s possible, then appeals to what you can conceive of will work more like claims about what you can perceive. If you can conceive of what’s not genuinely possible, then appeals to what you can conceive of will work more like claims about what you thought you saw. I can’t see how going one direction rather than the other could matter all that much.
The linguistic data I offered was, admittedly meager, but I didn’t want to say that the argument I’ve offered is the last word. It’s simply that there’s no obvious reason why we ought to treat the conceivable any different from the believable. You might tell a complicated story about how my (2) and (3) seem or are consistent on the hypothesis that CET is true and it would be cool to see what it looks like. However, it will take work to place CET back on sure ground. From what I can see, I can see no good reason to affirm it.
July 27, 2007 at 11:03 am
Sam: is the bit about CET being merely contingent right? I am doubtful, for two reasons. One, the slogan is “conceivability entails possibility,” and entailment is about strict implication. Two, if this is true, then I don’t understand Vaidya’s article in the slightest, since S’s possibility won’t be a counterexample to CET. About the quantification in CET, I was assuming that any unbound variables were actually universally quantified (and that the domain of quantification was unrestricted); this seems like the right way of reading the principle:
CETU: ∀p∀x[C(x, p) → L(p)]
Clayton: I didn’t mean to suggest that your data was somehow exceptionally meager. All the data seems equally meager to me. I understand why you want to put epistemological issues to the fore, but the linguistic issues are extremely important too — people too often don’t notice that when they talk about the relationship between mental states and other things, they’re actually talking about the logical relationship between mental state-ascriptions and other things. Anyway, what’s interesting is that if I’m right about the opacity of conceivability-ascriptions, they’ll work, at the linguistic level, less like perceivability claims and more like belief-ascriptions; the opacity of perceivability claims is minimal, if it exists at all, while the opacity of conceivability-ascriptions is pretty thoroughgoing, since it seems obvious that Newton could conceive of water being a different thing than H2O, and that of Russell’s yacht, Moore could conceive that it is longer than it is (though it is impossible that it is longer than it is). I don’t think my story is all that complicated — it’s the same as the correct story about other intensional verbs, and I don’t think it’s a merely ad hoc defense of CET, since there seems to be some evidence for thinking that the relationship between (2) and (3) is a lot like the relationship between (4) and (6).
July 27, 2007 at 11:17 am
re: CETU: ∀p∀x[C(x, p) → L(p)]
isn’t that too strong? if that were the principle, then i don’t see how philosophers move from conceivability to possibility. they’d have to show that everyone is able to conceive of a proposition, and that is no a priori matter.
July 27, 2007 at 11:41 am
Hmm. I think that would be the case for CETU’, not CETU.
CETU’:∀p[∀x(C(x, p)) → L(p)]
CETU: ∀p∀x[C(x, p) → L(p)]
Intuitively, with CETU (but not CETU’), you can move to (A) by universal instantiation:
(A) C(me, unicorns are horses) → L(unicorns are stallions)
July 27, 2007 at 12:13 pm
you are definitely right about that. my mistake.
if ∀x is outside of the scope though, then i don’t understand vaidya’s proof, particularly the move from:
1. C(x, S)
2. C(x, S) -> poss(S)
3. poss(S)
if (2) were understood via CETU as ∀x[C(x, S) → L(S)], and this is not equivalent to ∀xC(x, S) → L(S), then the inference does not follow unless the x in (1) is not read as a variable. or am i wrong and (1) can be understood as ∀xC(x, S) and the inference would go through?