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)
