Boarders on Nostr: Platonism vs nominalism: an old fashioned debate in philosophy is that of universals ...

Platonism vs nominalism: an old fashioned debate in philosophy is that of universals - talking of triangle as a property commits oneself to the existence of the abstract concept of triangle or perhaps a “generic triangle”.

In this case, we can, to some extent, resolve the question mathematically in a precise way - there is a mathematical object called the moduli stack of triangles, the generic triangle is the generic point of this moduli stack. We can answer various precise questions about this generic triangle such as what automorphism group it has etc. It also specializes to various more particular triangles with a precise notion of specialize due to algebraic geometers. It seems to me this is a better formal apparatus for thinking about mathematical universals than any kind of vague waffle available, but the idea has not managed to escape the purview of mathematicians.