Vagueness, Truth and Restricted Quantification
Hartry Field. Rutgers- February 28, 2013
Both in dealing with vagueness and in dealing with the semantic paradoxes, there is strong reason to restrict classical logic.
But what is the non-classical logic to be like? In going non-classical, one must give up the usual treatment of both
- (i)the conditional ‘if A then B’
- (ii)universal restricted quantification ‘all A are B’.
Previous work of myself and others has largely been focused on (i), apparently in the belief that (ii) would then be automatically handled. It isn’t, and indeed none of the work that I know of on (i), either in the case of vagueness or in the case of the semantic paradoxes, is remotely adequate for (ii).
I’ll spend about half the talk going through some of the main motivations for a non-classical approach to vagueness and the semantic paradoxes, and some of the reasons for thinking that there are very close connections between these two phenomena. The other half will be on the problem posed by restricted quantification, both for vagueness and for the paradoxes. I had hoped to have a satisfactory solution by the time of the talk, but at the moment I don’t, and simply plan to say something about why it’s hard and perhaps on what some promising directions for solving it are.