In a response to a great post by Kenny Pearce on Prosblogion, William McDoniel responded that what is happening with suggestions, such as Alvin Plantinga’s argument that if God possibly exists then God necessarily exists, is that logicians are using S5 Modal logic to collapse statements like “possibly necessarily X” with “necessarily X”. He continues:
Something can be logically possible but metaphysically impossible (I think). Something can be epistemically possible (is this a real phrase?) but logically impossible. Likewise for conceivability, and maybe even for a kind of possibility which is entirely independent of logical possibility. It’s this last kind which seems to me to be what you’re getting at with “I might be able to draw round squares”. The possible world that you’re talking about there is not a logically possible world, and for me it’s an inconceivable world, but it’s still a possible world drawn from a set of worlds with many different logics or metaphysics. Maybe it’s meta-logically possible.
I can imagine, and thus provisionally accept, something being logically possible and metaphysically impossible, such as time travel would be if the A theory of time were true (this paradox makes me suspect that A theory of time is not logically possible, though that’s terribly difficult to demonstrate). However, I object more strongly to the second suggestion that something can be epistemically possible without being logically possible. I imagine that the cases he has in mind involve cases analogous to classic cartesian skepticism, such as “perhaps 2+2=4 is false, but every time I think it an evil demon causes me to have the experience of thinking that it is true.” This seems to open the way to considerations which are not logically possible. I would respond, however, that a fundamental commitment to rationalism is enough to dissolve such problems. If one is a ‘rationalist’ in this particular epistemological sense then the Cartesian-like suggestions of “epistemic possibility” are of absolutely no epistemological concern. A rationalist might as well say that “epistemic possibility” is logically constrained. I will devote an upcoming post to developing in detail what I mean by this ‘rationalist epistemology’ but for now suffice it to say that this suggestion of logically impossible epistemic possibility is one I find disagreeable.
Now, perhaps this problem in the conversation arose because Pearce wrote the following:
… This implication of the standard semantics is, I submit, incorrect. I think the following conditional is true:
“If some humans were able to draw round squares, I might be able to draw round squares.”
I think that that sentence has the form of a proposition, but is bankrupt of any propositional content, and thus is not propositional at all. I might as well respond:
- If the Nothing Nothings itself, then nothing else needs to Nothing the Nothing
- The Nothing does Nothing itself
- Therefore, the Nothing doesn’t need anything else to Nothing itself
Thus, I am inclined to agree with McDoniel that the world in which humans are able to draw round squares is not a logically possible world. I cannot join him, however, when he further says that “it’s still a possible world drawn from a set of worlds with many different logics or metaphysics.”
In the end, I don’t know how to speak about ‘possibility’ absent logic. If something isn’t a logically possible world, I cannot imagine it being a meta-logically possible world. Anyone committed to a rationalist epistemology where logic is a constraint on epistemology will, it seems, have to agree that the suggestion of ‘logical-plurality’ (if that is a phrase) is unacceptable; it implies that logic is plastic. The suggestion that logic is plastic is not logically possible, ergo Meta-logically possible worlds cannot intelligibly be said (or thought) to exist.