Re:Structuralism as a Philosophy of Mathematics
by klysm on Sunday April 07, 2024 @11:28AM
(#39961403)
I think sometimes obvious concepts like symmetries are hard to distill into the appropriate mathematical language. I’m willing to bet the isomorphism there is obvious to most folks, but the expression of its mathematical essence is not.
Re:Structuralism as a Philosophy of Mathematics
by woopsn on Sunday April 07, 2024 @12:56PM
(#39962030)
This is really an important point for mathematical philosophy. It is a single enterprise going back to ancient Babylon, China, India, Greece, Egypt, and before. The elementary meta-theory needs to be syntonic to mathematical activity and knowledge predating (or otherwise practiced without) formalism, structuralism, categoricity, platonism, etc.
One fish says to another fish: "The water's nice today." and swims off, the other fish says "What's water?". Your entire mathematical world view is so permeated with the language of structuralism that you can't see it any more.