Everybody knows that Russell had a theory of definite descriptions. Not everybody realises that he had two: one for singular descriptions (the author of 'On Denoting'), another for plural descriptions (the co-authors of Principia Mathematica). After examining Russell's own ideas, I shall propose a new theory of descriptions which covers both singular and plural cases, and which covers cases where the predicate embedded in the description is collective (the logicians who wrote Principia Mathematica) as well as distributive (the logicians who smoke). The theory contrasts sharply with Richard Sharvy's influential account. I shall conclude by explaining how the theory accommodates so-called 'higher-level' plurality, in which the description does not simply denote one thing or many.
It is clear that psychology needs a much more broadly based approach to the syllogism than it has taken so far---essentially studies of peoples' classical logical theorem provers for this fragment. What mental grasp of syllogistic logic do `logically naive' subjects have? Stenning & Yule proposed that the `conclusion generation task' which has dominated psychological studies, is interpreted in at least two logically quite distinct ways, so psychologists have not even got to grips with what task their subjects are trying to perform. And this psychological insight suggests the logical possibility of more than one interpretation of the syllogism be taken seriously.
The present talk will summarise the (Stenning & Yule 1997) account of the close relation between defeasible and classical understandings of syllogistic tasks. `Ekthesis' (Aristotle's analogue of universal instantiation?) is a classically valid reasoning pattern which is closely related to defeasible understandings. The talk will then ask how these two logical interpretations can be teased apart experimentally, and illustrate it's answer with some preliminary results from a first experimental foray, coincidentally conducted on Amsterdam logic-students-to-be.
The symmetry problem is a problem that arises in many approaches to the derivation of Quantity-based pragmatic effects (scalar implicatures, exhaustivity) that are based on reasoning with alternatives (i.e. in classical Gricean pragmatics, in particular). When a sentence S has two stronger alternatives S1 and S2 which contradict each other (symmetric alternatives), neither the implicature [not S1] nor the implicature [not S2] can be derived. For example, S = "John ate some of the apples", S1 = "John ate all of the apples", S2 = "John ate some but not all of the apples". The symmetry problem consists in ruling out one of the symmetric alternatives so as to match the empirical pattern of quantity implicatures.
In this talk I will argue that sometimes symmetry is a welcome property, which helps explain the absence of standard exhaustivity implicatures, for instance, in negative and mixed answers to positive wh-questions, as in: "Who came to the party? Not Mary.", which neither implies that John, Bill, etc. did not come, nor that they came (see esp. Spector, 2005). This approach has non-trivial implications for the general architecture of a theory of quantity-based pragmatic effects. It establishes a preference for theories that do have the symmetry problem, but provide a general mechanism to break symmetry, as well as a special mechanism to bring symmetry back where needed, over theories that do not have the problem in the first place, such as various versions of predicate circumscription.
Another lambda-calculus (abstract in pdf)
In this talk, I present a snapshot of my PhD thesis Playing with Truth, which is a collection of papers that revolve around a single topic: that of self-referential truth. The talk will focus on the joint rationale of the three frameworks for truth that are developed in the thesis, which are:
1) Assertoric semantics.
2) The method of closure games.
3) The strict-tolerant calculus.
Assertoric semantics and the method of closure games are semantic valuation tools that are used to define theories of truth. The strict-tolerant calculus is a signed tableau calculus that can be used to obtain syntactic characterizations of various consequence relations that are induced by those theories. Assertoric semantics can be understood as a semantic counterpart of the strict-tolerant calculus and the method of closure games as a refinement of assertoric semantics. In a
sense then, all three frameworks have a `` tableau-like’’ character. In each of our frameworks, the (tableau-like) rules, including those of the truth predicate are interpreted as assertoric rules, whereas the (tableau-like) closure conditions are interpreted as assertoric norms, i.e., as norms that govern the practice of asserting and denying. In a nutshell, the three frameworks echo the assertoric conception of truth that I develop in my thesis. In the talk, we will articulate the relations between the three frameworks and the main results pertaining to them. However, the focus will be on applications of the frameworks. In particular, we will illustrate how:
i) Assertoric semantics can be used to argue for the claim that self-referential truth has
ii) Assertoric semantics and the strict-tolerant calculus jointly shed light on the strict-
tolerant conception of truth, which is a novel conception of truth that has recently
been proposed in joint work of Cobreros, Egré, Ripley and van Rooij.