Session 4 6 May 6 2011

Nelson Gonçalves Gomes (Universidade de Brasília)

O Naturalismo de Neurath e a Questão da Consistência

A recente literatura especializada propõe uma nova forma de entendimento do formalismo de Hilbert, com ênfase sobre a ideia da apresentação autônoma do pensamento matemático, livre das tentativas de fundamentação que busquem bases na filosofia. Essa interessante tendência sugere que se repensem temas análogos desenvolvidos por Otto Neurath, cuja concepção de proposições protocolares é claramente enigmática. Por que Neurath insiste, reiteradas vezes, na necessidade de consistência de um conjunto de proposições que abrigue protocolos? Neurath é reticente ao falar sobre verdade, mas por que não o é no que diz respeito à exigência de consistência? A conferência versará sobre o tipo peculiar de antifilosofia com o auxílio da qual Neurath esquematizou a sua forma radical de naturalismo.

Session 3 11 March 2011

Michael Rathjen (University of Leeds)

Hilbert’s Second Problem Revisited

Abstract: Hilbert’s second problem addressed the consistency of mathematics. At one time the most distinguished mathematicians of the day were concerned with this problem. Nowadays discussions about consistency are rare. Why does this problem attract so little attention and why is it that there is a scarcity of new inconsistencies compared to the days of Russell and other luminaries?

Session 2 25 February 2011

Gabriel Uzquiano (University of Oxford)

Plural Quantification and Modality

Identity is a modally inflexible relation: if objects are identical, then they are necessarily identical. The necessity of identity is generally supported by the combination of Leibniz’s law of indiscernibility of identicals and the premise that every object is necessarily self-identical. How special is identity in this respect? Do any other relations have a comparable claim to modal inflexibility? In particular, we will look at the relation one object bears to some objects iff it is “one of” them. Is it the case that if one object is one of them, then it is necessarily one of them? What could be the justification for this claim?

Session 1 29 October 2010

Bernard Linsky (University of Alberta)

The Paradox in Russell’s Letter

In his famous letter to Frege, Russell presents a paradox that affects the theory of classes in Principles of Mathematics. In this paper I relate this problem to both the more famous contradiction in Frege’s system and the paradox for “naive set theory” which were the most important lessons from the letter for later philosophy of mathematics.