maandag 1 april 2024

A new argument against mathematical Platonism

Ex nihilo nihil fit or from nothing nothing comes (Aristotle-Aquinas). Each truth having an ontological footprint must thus have a sufficient explanation. There are no brute facts in reality. Now, beyond a certain complexity threshold, mathematical truths aren’t provable (Gödel-Chaitin). But then it follows that mathematical truths have no ontological import. It's therefore not true that there exist mathematical abstract objects, so that we arrive at a new argument against mathematical Platonism.

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