Platonism in Mathematics
Master's Thesis, ENS Paris, March 1997
supervised by Joël Merker
Platonism is a classic topic in the epistemology of mathematics, as it deals with mathematical ontology.
The first part of this thesis is devoted to selected episodes in the history of mathematics – the discovery of group theory by Galois and the concept of continuity by Cauchy, both of which emerged more through intuition than through rigorous formalization – that particularly highlight the theses of Platonism. This part concludes with a statement of what is considered Platonism, comparing it with other definitions that looked too simplistic or even entirely foreign to Plato's philosophy.
The second part focuses on the major critiques of Platonism, namely those by Aristotle and Wittgenstein. Finally, the last part presents the author's opinion in favor of a "neo-Platonism" centered around the postulate that intuition guarantees ontology, supported by Gödel's views on the matter.