The more I think about math the more it seems like an arbitrary system that only works in so far as it corresponds to physics. There is no abstract, higher mathematical truths, things like Euler's identity aren't deep aesthetic things of beauty. They're obvious consequences of a self prescribed system whose rules are,basically, a kind of grammar. There's no real mathematical truth, only real physical truth.
Imagine if I say "The bottle is blue." That sentence is true insofar as it corresponds to a reality in which the referred bottle is blue. It's true (or correct) in itself insofar as it follows English grammatical conventions, but a sentence that isn't true in itself can't correspond to a reality at all. Saying "Those bottle are blue." Is a grammatical mistake and thus corresponds to no reality at all, even if there is a blue bottle.
Similarity "2+2=4" is true insofar as there are two things of two in reality to be referred to and clearly seen that they're all together 4. "2+2=5" is incorrect in its own mathematical-grammatical rules and thus has no corresponding reality just like "Those bottle is blue."
To merely say “2+2=4” when there are no groups of objects to refer to is “grammatically” / mathematically correct. But it isn’t true in any sense. It’s like saying “The bottle is blue” with no bottle in sight. The sentence is grammatically correct and meaningful, but has no truth-value.
Grammatical, and thus Mathematical, truth have no higher or purer value or privilege. They're all just truth of convention. Their “correctness” depends on the correct use of grammar or math. Their truth-conditions are determined solely by the realities they correspond to.
>t.slightly drunk math and philosophy major soon to change to statistics and philosophy because at least statisticians don't have the ego to pretend they’re doing some higher level buddha shit