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What is platonism?

What is platonism? Here are some definitions.

Noun
  1. Alternative letter-case form of Platonism
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Examples
They explicitly disavow the classical philosophies of formalism, logicism, Platonism, intuitionism, and social constructivism.
Platonism is the intellectual understanding of the ontological status of the good.
But to other philosophers and mathematicians Platonism seems extravagant, for reasons that are at least partly epistemological.
Some later commentators claim that by making this skeptical turn, Arcesilaus abandoned Platonism.
Finsler develops his approach to the paradoxes, his attitude towards formalised theories and his defence of Platonism in mathematics.
I find his insouciance about the difficulty of figuring out ethics disconcerting, though he's right that Nietzsche collapses into Platonism.

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