This distinction came up recently, and it isn’t clear to me what exactly is the difference between these two statements. At the very least, I am having a difficult time determining if there is a material distinction between them, or if the contents of one are equivalent to the contents of the other. Clearly we can say that there may be some logical difference between the two, but does that justify maintaining such a distinction? If every case of impossibility is materially equivalent to every case of inconceivability, then what more is verifiably added to our knowledge of the object of our consideration by saying that it is impossible? It seems like we are creating distinctions without a difference, and adding nothing of substance to our discourse with it.
I don’t really have an answer to this question, and I really suspect it is going to come down to demonstrating a material distinction between the two classifications, although perhaps there is something that can be said of the distinction even if the two do thoroughly coincide. But for the moment, all I can tell of the difference between the two is that impossibility carries with it the claim of representing a universal frame of reference, whereas inconceivability, unless otherwise qualified, is limited to the frame of reference of the speakers intellectual capacity, an easier claim to demonstrate. In fact, it is this very reason that causes me to be suspicious of impossibility, in that I don’t know how I would verify such a claim since I do not have any way of verifying that I have access to a universal perspective. I really would like to discuss this with my professor, but am not sure I the opportunity will come up.
On the other hand, isn’t it true that p and ~p are in fact contradictory, and so impossible for both to be true? I suppose so, but it also seems rather trivial, in that this claim of universality seems equivalent to saying something like this:
In the game of baseball, a hit ball that travels outside of the foul line before passing third base is considered a foul ball, and this is true of every possible world.
This is true, but it tells us nothing other than that this is a rule of baseball. Of course if you insist that these rules be kept, then it will universally be true that a ball that crosses the foul line before reaching the third base is foul, because it is an imposed condition of the question. The real question is if this is the only way to play baseball? Of couse it isn’t, and so likewise, I have to wonder if when we say something is logically impossible that all we are really doing is answering a question about the rules of our logic, of logic as we use and understand it and within the constraints of human capacity. Could there be another way of doing logic? That is the real question, the real issue of whether something is impossible, or merely inconceivable. I’m not sure how one would even go about answer it though, if the issue is one of the boundaries of human intellectual capabilities. It isn’t exactly an option to step outside of these limitations and evaluate them.
In essence, are we tracking the structure of the mind or some fundamental reality about the world? If it is just the mind, than a different mind would have a different logic. Claims of inconceivability are statements about how we perceive the world, whereas a statement of impossibility would seem to imply something beyond our subjectively imposed categories, and say something about the world itself, independent of our perceptions. Consider, if p and ~p truly are impossible in every possible world, this would include every possible intelligence generated by those worlds, and so be independent of the perspectives those intellects bring to their observations. It truly would seem to be making an objective claim about not just our reality, but of any reality, of all realities, a truly universal truth without even the possibility of referential boundaries. Can we really countenance such claims or hope to justify their incredible reach?