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> the incompleteness theorems would be taken as evidence against Platonism I wonder if this is a map/territory thing. Incompleteness theorems apply to models (
by n4r9 2y ago
> the incompleteness theorems would be taken as evidence against Platonism
I wonder if this is a map/territory thing. Incompleteness theorems apply to models (axiomatisations) of mathematics, e.g. ZFC set theory. Platonism applies to the actual act of doing mathematics, i.e. persuading other mathematicians that certain statements about abstract entities are true or false.
- dr_dshiv 2y agoPlatonism is about the reality of math behind the notation and beyond the human mind — Like that spheres are real even though there is no perfect sphere in the material world. This is a common opinion among mathematicians and physicists even though it seems unscientific (as it poses reality beyond matter)
- n4r9 2y agoRight. According to Platonism, a mathematician publishing a result about spherical geometry is in fact exploring an objective reality beyond human minds. Contrast that with, say, intuitionism, according to which they are simply describing the mental activity which arises as a result of considering an object of shared understanding known as a "sphere".