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mathematical anti-Platonism
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mathematical anti-Platonism

philosophy
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Mathematical anti-Platonism is a philosophical stance that rejects the existence of abstract objects, which are considered to be nonspatiotemporal, nonphysical, and nonmental entities. This view contrasts with mathematical Platonism, which posits that mathematical theorems are true descriptions of these abstract objects.12

Anti-Platonist positions include:
* Realistic anti-Platonism: This view accepts that mathematical theorems are true descriptions of some part of the world but denies that the objects described are abstract. It includes psychologism (mathematics is about mental objects) and physicalism (mathematics is about physical objects).1
* Nominalism: This is an antirealist view that rejects both the existence of numbers, sets, and similar entities, and the idea that mathematical theorems accurately describe anything.1

A significant challenge for Platonism is the epistemological argument, which questions how humans, existing within space-time, can acquire knowledge of abstract objects that exist outside of it.3

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6 Britannica Sources
  1. philosophy of mathematics - The Fregean argument for Platonism
  2. philosophy of mathematics - The epistemological argument against Platonism
  3. Platonism - Greek Platonism from Aristotle through Middle Platonism: its nature and history
  4. philosophy of mathematics - Realistic anti-Platonism
  5. philosophy of mathematics - Ongoing impasse
  6. philosophy of mathematics - Formal definition

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