It has been claimed that logic and mathematics is the study of which conclusions follow from which premises. But when we say that 2 + 2 = 4, are we really just assuming that? It seems like 2 + 2 = 4 was true well before anyone was around to assume it, that two apples equaled two apples before there was anyone to count them, and that we couldn't make it 5 just by assuming differently.

I think it's an assumption, depending on what you mean when you say something is an assumption. It seems to us like "2 + 2 = 4", but if we assumed differently then it would seem like "2 + 2 = 5". We seem to have justifications to point to to believe that "2 + 2 = 4", but if we assumed that "2 + 2 = 5" then we would also seem to have justifications for that point of view.

I personally have no problem with this and will continue to follow my current beliefs.