We’re having a little logic conference this weekend in Calgary. If you’re in the area, please come! All talks in 1253 Social Sciences, University of Calgary. Relevant papers may be found by following the links below
Nuel Belnap (Pittsburgh)
Friday, March 27, 4 pm
Truth Values, Neither-True-Nor-False, and Supervaluations
My oral remarks are based on an essay to appear in Studia Logica. (The essay evidently has more sections that I can adequately treat in the time allotted.) The first section defends reliance on truth values against those who, on nominalistic grounds, would uniformly substitute a truth predicate. I rehearse with great brevity some practical, Carnapian advantages of working with truth values in logic. In the second section, after introducing the key idea of “auxiliary parameters,” I look at several cases in which logics involve, as part of their semantics, an extra auxiliary parameter to which truth is relativized, a parameter that caters to special kinds of sentences. In many cases, this facility is said to produce truth values for sentences that on the face of it seem neither true nor false. Often enough, in this situation appeal is made to the method of supervaluations, which operate by “quantifying out” auxiliary parameters, and thereby produce something like a truth value. Logics of this kind exhibit striking differences. I first consider the role that Tarski gives to supervaluation in first order logic, and then, after an interlude that asks whether neither-true-nor-false is itself a truth value. I consider sentences with non-denoting terms, vague sentences, ambiguous sentences, paradoxical sentences, and future-tensed sentences in indeterministic tense logic, I conclude my survey with a look at alethic modal logic considered as a cousin, and finish with a little “advice to supervaluationists,” advice that is largely negative. The case for supervaluations as a road to truth is strong only when the auxiliary parameter that is “quantified out” is in fact irrelevant to the sentences of interest–as in Tarski’s definition of ‘truth’ for classical logic. In all other cases, the best policy when reporting the results of supervaluation is to use only explicit phrases such as “settled true” or “determinately true,” never dropping the qualification.
Krister Segerberg (Uppsala/Calgary)
Saturday, March 28, 10 am
Three Deontic Paradoxes
I am trying to develop a dynamic deontic logic, the outlines of which I will sketch. To motivate this attempt, and also to assess its merits, I will consider three classic paradoxes: those due to Chisholm, Ross, and Forrester.
Aldo Antonelli (Davis)
Saturday, March 28, 2 pm
Free Quantification and Logical Invariance
In order to present the problem of providing a natural and well-behaved semantics for (positive) free logic, a number of approaches are considered, some old, some new — all of which are found wanting in some respect or other. We then shift our perspective in order to tackle the problem from the standpoint of the theory of generalized quantifiers, with accompanying emphasis on permutation invariance as a characteristic feature of logical notions. This will finally result in a natural and well-motivated semantic theory for positive free logic — which, however, also leads to questioning the logical nature of free quantification.