09 April 2011

The Possible and the Thinkable

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:
  1. If I suppose something, I conceive it.
  2. An argument can be binding on me only if I can follow all of its steps.
  3. If the supposition of A is a step in an argument, then I must suppose A if I am to follow that step.
  4. Every sound reductio argument is an argument having as a step the supposition of something impossible.
  5. Some sound reductio argument is binding on me.
  6. Some argument is binding on me that has as a step the supposition of something impossible. (4, 5)
  7. I can follow the supposition of something impossible as a step of an argument. (2, 6)
  8. I can suppose something impossible. (3, 7)
  9. 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.


  1. I hate to break it to you but I think your argument is sound. What do you think could be wrong with it? Interesting thought: If your conclusion 9 is false then you cannot conceive something impossible, and hence you cannot conceive the proposition "I can conceive something impossible"? :-)

  2. Well, not all my arguments can be failures. Seriously, my fear is not so much that this or that step is wrong, but that Descartes, Hume, Kripke, & Co. just can't take a thesis so easily proved false to be all but self-evident. They're too clever for that.

    Good point about (9)! ;-)

  3. Don't worry, Leo. Descartes, Hume, and Kripke have been wrong about a lot of things.