13 May 2016 2.:00 pm Aula Enzo Paci, Department of Philosophy, University of Milan
The purpose of this workshop is to provide a multidisciplinary perspective on the fascinating yet elusive notion of vagueness. Logical, philosophical and mathematical concepts and techniques will be brought to bear on the topic.
Attendance is free, all welcome!
- Vincenzo Marra (Department of Mathematics, University of Milan)
- Elisa Paganini (Department of Philosophy, University of Milan)
- Nicholas J J Smith (Department of Philosophy, University of Sydney)
Titles and abstracts
Vincenzo Marra: Questioning Boundaries
According to the received view, one key pre-theoretical feature of a vague predicate is that its extension lacks definite boundaries. Despite its intuitive appeal, as it stands this statement has hardly any content at all. Can the extension of a monadic vague predicate be a subset of the domain of discourse while still “lacking precise boundaries”? Even such a simple question has been answered both affirmatively and negatively in the literature — when raw intuitions are our best available weapons, the battle rages on. I bring more refined ideas from modern mathematics to bear on the issue; the deep and much-studied relationship between logic and geometry provides us with with a well-endowed arsenal. I then argue that the pre-theoretical assumption about boundaries can be clarified, and made useful.
Elisa Paganini: Vague Objects within Classical Logic and Standard Mereology, and without Indeterminate Identity
Weatherson (2003) argues that whoever accepts classical logic, standard mereology and the difference between vague objects and any others, should conclude that there are no vague objects. Barnes and Williams (2009) claim that a supporter of vague objects who accepts classical logic and standard mereology should recognize that the existence of vague objects implies indeterminate identity. I contend that whoever maintains classical logic, standard mereology and the difference between vague objects and any others, is not forced to conclude with Weatherson that there are no vague objects; nor is she compelled to revise her point of view according to Barnes and Williams’s proposal and to accept that the existence of vague objects implies indeterminate identity.
Nicholas JJ Smith: Solving the Sorites: You’re Doing it Wrong
A requirement on any theory of vagueness is that it solve the sorites paradox. It is generally agreed that there are two aspects to such a solution. One task is to locate the error in the sorites argument. The second task is to explain why the argument is nevertheless compelling — why the sorites reasoning constitutes a paradox rather than a simple mistake. I argue for a further constraint on approaches to the second task: they should conform to the standard modus operandi in formal semantics, in which the semantic theory one develops is taken to be implicit in the usage and/or intuitions of competent speakers. I then argue that, out of the current main contenders for a theory of vagueness, only theories that posit degrees of truth can meet this further constraint.