Eduardo Rego is a Professor at the Department of Mathematics of the University of Porto. His research interests include philosophy of mathematics and Wittgenstein.
Professor - Department of Mathematics, Faculdade de Ciências UP
Research interests: Philosophy of mathematics, Wittgenstein, philosophy of mind and language.
Título do trabalho principal: A filosofia da matemática em Wittgenstein ? relações com o intuicionismo, nomeadamente com a metafísica do tempo e a analise intuicionista do continuum.(em ligação com o Projecto Convergences)
Outro trabalho em curso:
How not to defend unrestricted choice
We analyse examples of sorts of an argument, recurrent in the literature, that mount the defence of the unrestricted use in mathematics of the Axiom of Choice against the challenges set forth by the so called ?paradoxical decompositions? (i.e. results of the Banach-Tarski?s theorem type). We argue that underlying those arguments there is a strong, but not explicitly stated, platonistic bias and uncover some mathematical hocus pocus used to support those arguments. We conclude with some heuristics aiming to show that the Banach-Tarski?s paradox is a real one, in so far as it clashes with standard concepts associated with the use of the mathematics? real continuum in applications and modelling in the physical sciences.