I am puzzling over the inferential move from X is conceivable to X is (metaphysically) possible. It would be very nice if this move were valid. But I am having trouble seeing how it could be valid.
I exist, and I have a body. But it is conceivable that I exist without a body. 'Conceivable' in this context means thinkable without broadly logical contradiction. I distinguish between narrowly and broadly logical contradiction. 'Some cats are not cats' is NL-contradictory: it cannot be true in virtue of its very logical form. (It is necessarily false, and its being necessarily false is grounded solely in its logical form.) 'Some colors are sounds' is not NL-contradictory: the logical form of this sentence is such that some sentences of this form are true. And yet 'Some colors are sounds' is contradictory in a broad sense of the term since it is necessarily the case that no color is a sound, where the necessity in question does not have a merely formal-logical ground but a 'material' one.
Now my disembodied existence is conceivable: it is thinkable without BL-contradiction that I exist without a body. But that my body exist disembodied is not conceivable: it is not thinkable without BL-contradiction that my body exist disembodied. But the difficult question is this: does the conceivability of my disembodied existence entail the real (not merely epistemic) possibility of my disembodied existence? If yes, then a very interesting argument (from Saul Kripke's Naming and Necessity) appears sound:
1. If a = b, then necessarily a = b. (Necessity of Identity)
2. If possibly ~(a = b), then ~(a = b). (From 1 by Contraposition)
3. If possibly I am not identical to my body, then I am not identical to my body. (From 2 by Instantiation)
4. Possibly I am not identical to my body. (Premise)
Therefore
5. I am not identical to my body. (From 3, 4 by Modus Ponens)
This is a fascinating argument since it seems to establish a very significant metaphysical result on the basis of cogent reasoning from exceedingly plausible premises. The move from (2) to (3) presupposes that the first-person pronoun is a referring term, something denied by Elizabeth Anscombe under the (dubious) influence of Wittgenstein. I would say that Anscombe is mistaken about this, but I don't want to discuss it now. The substitution of the first-person singular pronoun 'I' for the arbitary constant 'a' strikes me as innocuous.
But what reason do we have to accept (4)? The soundness of the argument rides on this premise. We can argue for (4) as follows: Conceivability entails possibility. It is conceivable that I am not identical to my body (because I can conceive my disembodied existence). Therefore, possibly I am not identical to my body.
But why should we accept that conceivability entails possibility? The following argument sees to show that conceivability does not entail possibility:
6. It is conceivable that I am not identical to my body.
7. It is conceivable that I am identical to my body.
8. If conceivability entails possibility, then it is possible that I am not identical to my body and it is possible that I am identical to my body. (from 6, 7)
9. It is possible that I am not identical to my body iff I am not identical to my body.
10. It is possible that I am identical to my body iff I am identical to my body.
11. If conceivability entails possibility, then I am not identical to my body and I am identical to my body.
12. The consequent of (11) is a contradiction.
Therefore
13. Conceivability does not entail possibility.
Let me sum up the argument as follows. If we take seriously the Necessity of Identity, then either it is a necessary truth that I am identical to my body, or a necessary truth that I am not identical to my body. If the first is necessarily true, then the second is necessarily false, and vice versa. Thus neither are contingent. Now both my identity and my non-identity with my body are conceivable. Therefore, if conceivability entails possibility, then it is possible that I am not identical to my body and possible that I am. If it is possible that I am not identical to my body, then I am not identical to it, and if it is possible that I am identical to my body, then I am identical to it. But this is a contradiction. So if we accept the Necessity of Identity, then we must deny that conceivability entails possibility.
The crucial premise in the (6)-(13) argument is (7). Although my identity with my body strikes me as false –and I have some separate arguments for this conclusion — I am not sure how to turn aside (7).