Alfredo Watkins has a post up on the link (or lack thereof) between conceivability and (metaphysical/broadly logical) possibility. I've long suspected that the one does not entail the other, for the reasons supplied by this argument and others like it:
- If I suppose something, I conceive it.
- An argument can be binding on me only if I can follow all of its steps.
- If the supposition of A is a step in an argument, then I must suppose A if I am to follow that step.
- Every sound reductio argument is an argument having as a step the supposition of something impossible.
- Some sound reductio argument is binding on me.
- Some argument is binding on me that has as a step the supposition of something impossible. (4, 5)
- I can follow the supposition of something impossible as a step of an argument. (2, 6)
- I can suppose something impossible. (3, 7)
- I can conceive something impossible. (1, 8)
The trouble with this argument is that I just can't tell whether it's obviously sound or contains some hidden fallacy. Surely, if it were sound, the view it opposes could not have been accepted by so many eminent thinkers, which leads me to the latter opinion, but I can't for the life of me pinpoint my error.
If sound, the argument has the virtue of not relying on suspect entities like possible worlds, semantically charged notions concerning designation, or specifically theological problems like a conceivably necessary being.