Isn't this still assuming we can even determine what is true or false?

Newtonian physics is false, but it works well enough we teach it in college. But our best models of physics are currently in disagreement, so can we even say they are true? Given the replication crisis, especially in social sciences, how many of peer reviewed findings can be called true? Even experimental results can be false (consider studies that found FTL neutrinos, which were rejected as an error in the experiment, and which was eventually confirmed but it took quite a lot of work and in a softer field than physics with a claim less absurd than FTL, would have likely long been accepted as a true finding).

Even in math, basic statements aren't really true or false, but more a question of "given these axioms, can we prove or disprove it" noting that we have different systems with different axioms. If we are talking basic sets, most people are using naive set theory which is inherently contradictory, which means that notions like true or false probably can't be considered well defined.