In a recent post you write:
I’m not convinced this is right. Conceivability has a close analogue with perception. If it seems to S that p, then S is prima facie justified in believing that (actually) p. So consider cases of perceptual seemings. Care must be taken to distinguish two forms of negative seemings:
Clearly, (1) is not properly a seeming at all; it is denying an episode of seeming altogether. If I assert (1), me and a rock are on epistemic par with respect to it seeming to us that p. (2) also faces an obvious problem: how could ~p, a lack or the absence or negation of something, appear to me at all? Photons do not bounce off of lacks. There are ways around this, but for now I just want to register the distinction between (1) and (2) and the prima facie difficulties with them that do not attend to positive seemings.
The Humean reasoning in defense of (3) rests on the assumption that conceivability entails possibility. To turn aside this reasoning one must reject this assumption. One could then maintain that the conceivability by us of the nonexistence of God is consistent with the necessity of God's existence.
I’m not convinced this is right. Conceivability has a close analogue with perception. If it seems to S that p, then S is prima facie justified in believing that (actually) p. So consider cases of perceptual seemings. Care must be taken to distinguish two forms of negative seemings:
1. It does not seem that p.
2. It seems that ~p.
2. It seems that ~p.
Clearly, (1) is not properly a seeming at all; it is denying an episode of seeming altogether. If I assert (1), me and a rock are on epistemic par with respect to it seeming to us that p. (2) also faces an obvious problem: how could ~p, a lack or the absence or negation of something, appear to me at all? Photons do not bounce off of lacks. There are ways around this, but for now I just want to register the distinction between (1) and (2) and the prima facie difficulties with them that do not attend to positive seemings.
BV: Excellent so far, but I have one quibble. Suppose I walk into a coffee house expecting to encounter Pierre. But Pierre is not there; he is 'conspicuous by his absence' as we say. There is a sense in which I perceive his absence, literally and visually, despite the fact that absences are not known to deflect photons. I see the coffee house and the people in it and I see that not one of them is identical to Pierre. So it is at least arguable that I literally see, not Pierre, but Pierre's absence.
Be this as it may. You are quite right to highlight the operator shift as between (1) and (2).
So now consider conceivability. The analogue: If it is conceivable to S that p, then S is prima facie justified in believing that possibly p. Now for our two negative conceivablility claims:
Again, (1’) is trivial; it is (2’) we’re interested in. Does (2’) provide prima facie evidence for possibly ~p? It depends. What we do when we try to conceive of something is imagine "in our mind’s eye" a scenario—i.e., a possible world—in which p is the case. So really (2’) translates:
So now consider conceivability. The analogue: If it is conceivable to S that p, then S is prima facie justified in believing that possibly p. Now for our two negative conceivablility claims:
1’. It is not conceivable that p.
2’. It is conceivable that ~p.
2’. It is conceivable that ~p.
Again, (1’) is trivial; it is (2’) we’re interested in. Does (2’) provide prima facie evidence for possibly ~p? It depends. What we do when we try to conceive of something is imagine "in our mind’s eye" a scenario—i.e., a possible world—in which p is the case. So really (2’) translates:
2’’. I can conceive of a possible world in which ~p.
BV: Permit me a second quibble. Although 'conceive' and 'imagine' are often used, even by philosophers, interchangeably, I suggest we not conflate them. I can conceive a chliagon, but I cannot imagine one, i.e., I cannot form a mental image of a thousand-sided figure. We can conceive the unimaginable. But I think we also can imagine the inconceivable. If you have a really good imagination, you can form the mental image of an Escher drawing even though what you are imagining is inconceivable, i.e., not thinkable without contradiction.
More importantly, we should avoid bringing possible worlds into the discussion. For one thing, how do you know that possibilities come in world-sized packages? Possible worlds are maximal objects. How do you know there are any? It also seems question-begging to read (2') as (2'') inasmuch as the latter smuggles in the notion of possibility.
Given that the whole question is whether conceivability either entails or supplies nondemonstrative evidence for possibility, one cannot help oneself to the notion of possibility in explication of (2'). For example, I am now seated, but it is conceivable that I am not now seated: I can think this state of affairs witout contradiction. The question, however, is how I move from conceivability to possibility. How do I know that it is possible that I not be seated now?
It is obvious, I hope, that one cannot just stipulate that 'possible' means 'conceivable.'
(2'') seems innocent enough, but whether it gives us prima facie evidence for possibly ~p will depend on what p is; in particular, whether p is contingent or necessary. Consider:
(3) seems totally innocent. I can conceive of worlds in which chipmunks exist and others in which they don’t.
3. There is a possible world in which there are no chipmunks.
4. There is a possible world in which there are no numbers.
4. There is a possible world in which there are no numbers.
(3) seems totally innocent. I can conceive of worlds in which chipmunks exist and others in which they don’t.
BV: It seems you are just begging the question. You are assuming that it is possible that there be no chipmunks. The question is how you know that. By conceiving that there are no chipmunks?
(4), on the other hand, is suspect. This is because numbers, unlike chipmunks, if they exist at all exist necessarily; that is, if numbers do not exist in one world they do not exist in any. Thus, what (4) really says is
With its conceivability counterpart being
which looks a lot like the above illicit negative seemings: negations or absences of an object of conceivability. But my not conceiving of something doesn't entail anything! But suppose we waive that problem, and instead interpret (4’) as a positive conceiving:
The problem now is that (4’’) is no longer a modest claim that warrants prima facie justification. In fact, (4*) has a degree of boldness that invites further inquiry: presumably there is some obvious reason—a contradiction, category mistake, indelible opacity—etc. apparent to me that has led me to think numbers are impossible. But if that’s so, then surely my critic will want to know what exactly I’m privy to that he isn’t.
Mutatis mutandis in the case of God qua necessary being. (4*) There is no possible world in which there are numbers.
BV: (4) and (4*) don't say the same thing; I grant you, however, that the first entails the second.
With its conceivability counterpart being
(4’) I cannot conceive of a possible world in which there are numbers.
which looks a lot like the above illicit negative seemings: negations or absences of an object of conceivability. But my not conceiving of something doesn't entail anything! But suppose we waive that problem, and instead interpret (4’) as a positive conceiving:
(4’’) It is conceivable to me that numbers are impossible
The problem now is that (4’’) is no longer a modest claim that warrants prima facie justification. In fact, (4*) has a degree of boldness that invites further inquiry: presumably there is some obvious reason—a contradiction, category mistake, indelible opacity—etc. apparent to me that has led me to think numbers are impossible. But if that’s so, then surely my critic will want to know what exactly I’m privy to that he isn’t.
Thoughts?
BV: You lost me during that last stretch of argumentation. I am not sure you appreciate the difficulty. It can be expressed as the following reductio ad absurdum:
a. Conceivability entails possibility. (assumption for reductio)
b. It is conceivable that God not exist. (factual premise)
c. It is conceivable that God exist. (factual premise)
d. God is a necessary being. (true by Anselmian definition)
Ergo
e. It is possible that God not exist and it is possible that God exist. (a, b, c)
Ergo
f. God is a contingent being. (e)
Ergo
g. God is a necessary being & God is a contingent being. (d, f, contradiction)
Ergo
~a. It is not the case that conceivability entails possibility.
Is short, as John the Commenter has already pointed out, it seems that the Anselmian theist ought to reject conceivability-implies-possibility.
Comments