Séminaire Philmath

Titre : Metaphysical Problems for Plenitudinous Platonism

Abstract :  How many types of mathematical object are there? In recent and contemporary philosophy of mathematics one finds three kinds of answer: zero, one and all possible ones. The third answer is the doctrine of Plenitudinous Platonism (also known as Full-Blooded Platonism).  It holds that mathematical objects are abstract and that there as many types of them as are consistently possible. Plenitudinous Platonists for example maintain that there are as many self-standing set universes as there are consistent set theories. Some of these satisfy the axioms of ZFC as well as the Continuum Hypothesis (CH), others the axioms of ZFC plus not-CH. In fact, according to Plenitudinous Platonists, the mathematical realm is as large as it could possibly be: every consistent mathematical theory corresponds to its own type(s) of mathematical object. My talk will raise some problems for the view. As the title indicates, I will focus on the metaphysical side of things.

 

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