As Van Inwagen explains (pp.71-72):
It hardly follows that, because a certain thing cannot be proved to be impossible by a certain method, it is therefore possible in any sense of ‘possible’ whatever. Suppose that the infallible Standard Atlas marks many islands as uninhabitable, none as inhabitable, and makes no claim to completeness in this matter. We could, if we liked, say that the islands marked ‘uninhabitable’ in the Standard Atlas were “cartographically uninhabitable.” In doing this, we should be calling attention to the fact that our knowledge that these islands were uninhabitable had a certain source. But would there then be any sense in saying that an island was “cartographically inhabitable” just in the case that it was not cartographically uninhabitable? Very little, I should think. We could use words this way, but if we did we should have to recognize that “cartographical inhabitability” was not a species of inhabitability.
Or, as George Bealer writes in his 'Modal Epistemology and the Rationalist Renaissance' (in the excellent Gendler & Hawthorne anthology, Conceivability and Possibility, p.79):
If you buy into calling mere logical consistency a kind of possibility, why not keep going? For example, p is 'sententially possible' iff p is consistent with the laws of sentential logic. Then, since 'Everything is both F and not F' is not ruled out by sentential logic (quantifier logic is what rules it out), would it be possible in some sense (i.e., sententially possible) that everything is both F and not F!? Certainly not to my ear! At this juncture it seems to me that the best policy is to confine ourselves to the well-demarcated terms 'logically consistent' and 'metaphysically possible'.
(I prefer the term 'absolute possibility', since it better captures the non-relative nature of the concept. But that's a minor quibble.)