I really enjoyed the Vagueness and Metaphysics workshop in Barcelona. I learned a lot from all the papers, and it got me interested in working on these topics in much more detail. Maybe I’ll even revive the idea of a writing a short book on vagueness, somehow melding “stuff”:http://brian.weatherson.org/manymany.PDF “from”:http://brian.weatherson.org/ttt.pdf “these”:http://brian.weatherson.org/vai.pdf “five”:http://brian.weatherson.org/Ch_8.pdf “papers”:http://brian.weatherson.org/VEatPoM.pdf. But first I wanted to touch on a point Robbie Williams made there.

In his “Truth and Paradox”:http://www.amazon.com/Truth-Paradox-Solving-Tim-Maudlin/dp/0199203911, Tim Maudlin argues that when we are dealing with ungrounded claims like the Liar, the norms of assertion do not include truth. Indeed, it is possible to assert the Liar (i.e., that the Liar is not true), even though it’s not true (and not assertable) that the Liar is not true. Robbie’s idea (I believe closely based on Tim’s) is that in ‘difficult’ areas, such as when we’re dealing with future contingents, vagueness, or the paradoxes, we should be looking for ‘local’ norms of assertion, not ‘global’ norms of assertion. A global norm is something like “Assert only what you know”, or “Assert only what is true”. A local norm might be something like “Assert a future contingent only if you know it”, or “Assert a vague sentence only if it is not determinately false”.

I’m not sure whether I agree with all these claims. I’d hoped to sit down with Tim’s book to read it more carefully, but sadly the Rutgers library doesn’t seem to stock it. (This is a little appalling – it’s an OUP book published by a Rutgers faculty member! Maybe I’ll head up to 42nd Street later this week and work in the public library for a day; they do have the book in stock.) But I do think they are interesting, and worth taking seriously. And that’s exactly what hasn’t happened in the existing norms of assertion literature. As far as I can tell, more or less no one in that literature cites Tim’s book at all, or for that matter worries about any of the paradoxes.

That’s bad, because I think there’s a fairly compelling argument that the knowledge norm can’t survive the paradoxes, even if a paradox-based argument against the truth norm succeeds. Consider (1).

(1) Brian does not know (1).

Assume I know (1). Then by the very plausible principle: Ksp → p, it follows that I don’t know (1). Contradiction. So I don’t know (1).

That argument looks perfectly sound. It certainly doesn’t look like I violated any norms of assertion in presenting it. But the last sentence is one that, as we just proved, I don’t know. So it’s perfectly OK to assert some things one does not know.

I’ve mentioned before that my outlook on a lot of philosophical questions has been changed by “Kevin Klement’s Compass papers”:http://people.umass.edu/klement/works.html on Russell’s paradox and Russell’s reactions to them. I think I might have to write up a short paper on the number of areas of contemporary philosophy where there has been insufficient attention paid to the paradoxes, with norms of assertion being one of the case studies.