I was thinking about this in the shower the other day. Circles don't "exist" because they are a pure abstraction; as an element of mathematics they are simply a

I was thinking about this in the shower the other day. Circles don't "exist" because they are a pure abstraction; as an element of mathematics they are simply a bag of conclusions that are inevitable if you are willing to accept other axioms. The language with which we talk about these axioms and conclusions might be fallible, and certainly the conclusions themselves may be fallible (though not likely so for elemental enough mathematics), but the kernel of truth in logic at the middle is, I think, unassailable.