Here’s a sketch of an idea for the intro to a paper Andy Egan, John Hawthorne and I are doing on epistemic modals. It will almost certainly be changed, not least because writing it in what looks a lot like my style makes it look like my paper when in reality 90% of the ideas contained in it will be due to Egan and/or Hawthorne, but that’s no reason not to post it here.

Any novel thoughts about how to get out of the paradox at the end would be appreciated.

Might Makes Right?

The celebrity reporter looked discomforted, perhaps because there were so few celebrities in Cleveland.

“Myles”, asked the anchor, “where are all the celebrities? Where is Professor Grainger?”

“We don’t know,” replied Myles. “She might be in Prague. She was planning to travel there, and no one here knows whether she ended up there or whether she changed her plans at the last minute.”

This amused Professor Grainger, who always enjoyed seeing how badly wrong CNN reporters could be about her location. She wasn’t sure exactly where in the South Pacific she was, but she was certain it wasn’t Prague. On the other hand, it wasn’t clear what Myles had got wrong. He didn’t know where Professor Grainger was, and she had been planning to travel to Prague before changing her plans without informing anyone who could possibly be in Cleveland.

What about Myles’s second sentence, “She might be in Prague.”? Professor Grainger thought that sounded true as well. To a first approximation, she thought, that’s true if neither the speaker nor any of his mates know that she was not in Prague. And she knew that was true, because she had left quite a few clues that she in fact was in Prague, and she knew reporters always fell for those. But something about this reasoning rather confused Professor Grainger, for she was sure Myles had got something wrong. Trying to put her finger on just where the mistake was, she ran through the following little argument.

(1) When he said, “She might be in Prague” Myles said that I might be in Prague.
(2) When he said, “She might be in Prague” Myles spoke truly iff neither he nor any of his mates know that I’m not in Prague.
(3) Neither Myles nor any of his mates know that I’m not in Prague.
(4) If Myles spoke truly when he said that I might be in Prague, then I might be in Prague.
(5) I know I’m not in Prague.
(6) It’s not the case that I can know I’m not in Prague if I might be in Prague.

The problem, she thought, must be here somewhere for (1) to (6) are inconsistent. (Quick proof: (2) and (3) entail that Myles spoke truly when he said, “She might be in Prague”. From that and (1) it follows he spoke truly when he said Professor Grainger might be in Prague. From that and (4) it follows that Professor Grainger might be in Prague. And that combined with (5) is obviously inconsistent with (6).) Unless some fairly radical kind of scepticism is true, Professor Grainger can know by observing her South Pacific idyll that she’s not in Prague. And unless some fairly radical anti-sceptical doctrine is true, neither Myles nor any of his mates know that she’s not in Prague, since they all think it is quite likely that she is in fact in Prague. So the problem can’t be with (3) or (5). But the other four premises are all up for grabs.