REALISM AND ANTI-REALISM IN THE PHILOSOPHY OF MATHEMATICS
Keywords:
Mathematics. Ontology. Relativism. Platonism. Fictionalism.Abstract
In this paper I review and analyze a series of proposals that represent the debate between the supporters of mathematical realism and its rivals. I list their various kinds of theses and their most characteristic arguments. I pay special attention to mathematical platonism, Popper's anomalous platonism and fictionalism. On the basis of the contributions of Carnap, Quine and Putnam, I try to show that the affirmation of the existence of mathematical entities is not necessarily a thesis proper to speculative metaphysics but the result of a choice within the framework of ontological relativism. I conclude that although there are no definitive arguments that show a convincing victory of platonism over fictionalism or vice versa, there are considerable reasons to recognize some mode of existence to abstract entities, in which case mathematical platonism enjoys a certain advantage.
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