A Not So Fine Modal Version of General Relativism
8 de Janeiro de 2010, 16:00
Faculdade de Letras de Lisboa
Sala Mattos Romão, Departamento de Filosofia
Abstract: Russell's Paradox is standardly interpreted as showing that there cannot be a set of all sets. But at the same time that it establishes something, this result raises some peculiar questions. One could ask, for example, how to understand a collection that is not a set or why is it that there cannot be a set of all sets. In the following we will say some things about the first question, but will be particularly concerned with an answer that has been provided for the second. We thus begin by presenting the naive and the iterative conceptions of set, describe the construction of the set-theoretical hierarchy and discuss the notion of proper class. The discussion then moves on to whether it is possible to make sense of the claim that the set-theoretical hierarchy is to be understood as being indefinitely extensible. In particular, we discuss a modal version of generality relativism that has been put forward by Kit Fine and try to understand if it allows us to come up with a non self-defeating formulation of the generality relativist thesis. We will argue that Fine's modal version is not of much help in this task.
Apoios: Fundação para a Ciência e a Tecnologia, Faculdade de Letras da Universidade de Lisboa