The Joint Session was fun, although it was a shame that lots of the accommodation was so far from the conference venue - strolling in across the common was nice in the morning sunshine but at 2am it was less appealing to walk back.
Like last year, I thought the open sessions were in need of some degree of refereeing. Still, I very much enjoyed giving my paper in one of them, on ontological commitment and vague existence. The purpose of this paper (which is a much improved version of this post) is to present the following argument and then wonder what should be done about it:
1 (Quinean premise): One is committed to Fs iff there are Fs among the range of the quantifiers appearing in one's best theory.
2 (Assumption): We think it's a vague matter whether there are any Fs (and that's all we have to say on the question of whether Fs exist or not).
3 (From 2): We are not committed to there being any Fs.
4 (Contraposing on the right-to-left direction of 1, then MPP using 3): There are no Fs among the range of the quantifiers appearing in our best theory.
5 (Premise): Our quantifiers are precisely those which appear in our best theory.
6 (From 4 and 5): There are no Fs among the range of our quantifiers.
7 (From 6): We can truly assert 'There are no Fs'.
8 (From 7, disquoting): It is not a vague matter whether there are any Fs: it is settled that there are no Fs.
9 (From 2 and 8): We are mistaken.
10 (Discharging 2, using 9): If we think it's a vague matter whether there are any Fs (and that's all we have to say on the question of whether Fs exist or not), then we are mistaken.
Some members of the audience suggested that rejecting contraposition was the best thing to do, a response I've not come across before. (Although as Daniel pointed out to me later, we really only need modus tollens. But maybe the people who'd want to reject contraposition would want to reject MTT too, for similar reasons?)