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EthanHeilman 4 days ago

Most mathematicians, but not all, take a philosophical position of platonic idealism [0] in which numbers and other mathematical entities have an independent reality and are not invented but discovered.

> All abstract concepts brought about solely by humans.

That is a defendable philosophical position to hold but many thinkers disagree with it or at least admit there is more nuance [1]. People have been debating the question of the independent reality of mathematical concepts for thousands of years.

If abstract concepts are brought about solely by humans, does that mean the first human to invent a proof of some property actually decides the reality of that property? If Godel hadn't proved incompleteness, could another mathematician created a completeness proof instead? On the hand, if that isn't the case and the truth or falsity of a math statement exists prior a human thinking it, doesn't it have some reality beyond human thought? What about mathematical statements which are true which can't be proven?

[0]: Platonism in the Philosophy of Mathematics https://plato.stanford.edu/entries/platonism-mathematics/

[1]: Mathematics: Discovery or Invention? https://royalinstitutephilosophy.org/article/mathematics-dis...