Full Idea
A Platonist's interest focuses on axioms in which the decision of thought is played out, where an Aristotelian or Leibnizian interest focuses on definitions laying out the representation of possibilities (...and the essence of mathematics is logic).
Gist of Idea
Platonists like axioms and decisions, Aristotelians like definitions, possibilities and logic
Source
Alain Badiou (Briefings on Existence [1998], 7)
Book Reference
Badiou,Alain: 'Briefings on Existence', ed/tr. Madarsz,Norman [SUNY 2006], p.103
A Reaction
See Idea 12323 for the significance of the Platonist approach. So logicism is an Aristotelian project? Frege is not a true platonist? I like the notion of 'the representation of possibilities', so will vote for the Aristotelians, against Badiou.
Related Idea
Idea 12323 Existence is Being itself, but only as our thought decides it [Badiou]