It seems like there is a universal sense in which statements like 1+1=2" or "7 is a prime number" are true, no?

I disagree, it is not universal. 1+1=2 is just a specific system of notation with consistency. There was a time when no human conceptualized this idea of 1+1=2, they did not have numerals or know about addition. Before you get to 1+1=2 you need a bunch of prior concepts that are themselves contingent on culture and history.

If by "universal" we mean median adult human which are apt and willing to engage in basic mathematical thoughts, yes. That’s certainly already a very greatly reduced set of entities compared to everything in existence, though.

Mathematics does its best, but it's still a language, and fallible. It's trying to explain things, and the concepts like "prime number" and "one" can be shaken by later improvements to understanding.

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