In Wittgenstein, Tom Ricketts said something that reminded me that I need to write up a few more posts on Through the Looking-Glass. I’ll quote the important bit:
“‘You needn’t say “exactly,”‘ the Queen remarked. ‘I can believe it without that. Now I’ll give you something to believe. I’m just one hundred and one, five months and a day.’
‘I can’t believe that!’ said Alice.
‘Can’t you?’ the Queen said in a pitying tone. ‘Try again: draw a long breath, and shut your eyes.’
Alice laughed. ‘There’s no use trying,’ she said, ‘one can’t believe impossible things.’
‘I daresay you haven’t had much practice,’ said the Queen. ‘When I was your age, I always did it for half-an-hour a day. Why, sometimes I’ve believed as many as six impossible things before breakfast. There goes the shawl again!'”

If we grant that believability is sufficient for conceivability (which strikes me as prima facie plausible), then Carroll endorses the idea that conceivability does not entail possibility. However, we can still conceive of and believe in impossible worlds (although Carroll doesn’t go in for worlds talk). Don’t think we can? The White Queen replies: just try harder; maybe shut your eyes and breath deeply. It seems to me, (and this may get overly geeky), that Carroll would further reply to someone who says that such and such a scenario is inconceivable, in much the same way as Inigo Montoya: “You keep using that word. I do not think it means what you think it means.”