Conceivability as an Inductive Guide to Possibility
We know that positive conceivability is a good inductive guide to possibility. And we know negative conceivability is a good inductive guide to possibility.
What kind of induction is this? What we do know is that sometimes what seems conceivable on first sight later turns out to be incoherent (and thus inconceivable in the technical sense introduced by Dave Chalmers and deployed by Brian). We also know that this doesn't happen very often, and that it happens mainly when we consider rather complicated stories or hypotheses. So we have good inductive reason to assume that there is no hidden contradiction in, say, the hypothesis that there could be an apple in a basket. But this only supports the claim that prima facie conceivability is a good inductive guide to ideal conceivability.
If ideal conceivability entails possibility then we can infer that prima facie conceivability is also a good inductive guide to possibility. But if not, the gap between ideal conceivability and possibility still needs to be closed. Could this gap, too, be closed by induction? Do we know by induction that usually, when something is ideally conceivable it is also possible? Only if we have independent access to modal reality. Then whenever something is ideally or prima facie conceivable we could check whether it is really possible. If the test is mostly positive, conceivability could be called a good inductive guide to possibility. But I don't think we have any such test. Or at least I haven't, and I wouldn't accept anyone's claim of having one. -- What would you say if the oracle told you that even though it is ideally conceivable that there be an apple in a basket, inspection of all possible worlds reveals that unfortunately none of them contains an apple in a basket? I would say the oracle is fraud. (On the other hand, I could be convinced that in the actual world, no apple ever is in any basket. Contrary to what I said recently, my belief that there could be an apple in a basket therefore can't be based on my belief that there actually is an apple in a basket.)
So I think the only reason to believe in Brian's claim is to accept that at least for a wide range of statements ideal conceivability entails possibility.