In an earlier thread James Anderson makes some observations that cast doubt on the standard entailment from inconceivability to impossibility. (I had objected that his theological mysterianism seems to break the inferential link connecting inconceivability and impossibility.) He writes,
But even though we have no direct epistemic access to any other inconceivability than our own, and despite the formidable historical pedigree of the idea, it still strikes me as implausible to maintain that inconceivability to us entails impossibility. [. . .] For the principle in question is logically equivalent to the principle that possibility entails conceivability. But is it plausible to think that absolutely whatsoever happens to be possible in this mysterious universe and beyond must be conceivable to the human mind, at least in principle? Can this really be right?
I want to emphasize that I'm not advocating some form of modal skepticism, i.e., the view that our intuitions as to what is possible or impossible are generally unreliable. On the contrary, I think they're reliable. I just deny that they're infallible.
This does indeed give me pause. Anderson is certainly right that if inconceivability entails impossibility, then, by contraposition, possibility entails conceivability. These entailments stand or fall together. But is it plausible to maintain that whatever is possible is conceivable? Why couldn't there be possible states of affairs that are inconceivable to us?
But there may be an ambiguity here. I grant that there are, or rather could be, possible states of affairs that we cannot bring before our minds. These would be states of affairs that we cannot entertain due to our cognitive limitations. But that is not to say that a state of affairs that I can bring before my mind and in which I find a logical contradiction is a possible state of affairs. Thus we should distinguish two senses of inconceivable, where S is a state of affairs and A is any well-functioning finite cognitive agent:
S is inconceivable1 to A =df A entertains S and finds a contradiction in S.
S is inconceivable2 to A =df A is unable to entertain (bring before his mind) S.
Now it seems clear that inconceivability2 does not entail impossibility. But I should think that inconceivability1 does entail impossibility. For if S is contradictory, then that very state of affairs as the precise accusative of my thought that it is, cannot obtain. Its possibility in reality is ruled out by the fact that it cannot be entertained without contradiction.
Now does possibility entail conceivability? No, in that the possible need not be thinkable by us: there could be possibilities that lie beyond our mental horizon. But possibility does entail conceivability if what we mean is that possible states of affairs that we can bring before our minds must be free of contradiction.
So, in apparent contradiction to what Anderson is claiming, I urge that we can be infallibly sure that a state of affairs in which we detect a logical contradiction cannot obtain in reality. There is more to reality, including the reality of the merely possible, than what we can think of; but what we can think of must be free of contradiction if it is to be possible.
Conceivability without contradiction is no infallible guide to possibility. But inconceivability1 is an infallible guide to impossibility. Where Anderson apparently sees symmetry, I uphold the traditional asymmetry.