 In response, one might claim that even if there aren’t infinitely many ideas in our heads, it seems likely that we have ideas of infinities in our heads. This is no doubt true—there are such ideas in our heads—but this does not save psychologism from the above objection. For our mathematical theories entail that there actually exist infinitely many different mathematical objects. E.g., standard theories of arithmetic entail that there is such a thing as 1, and that there is such a thing as 2 (and that it’s distinct from 1), and that there is such a thing as 3 (and that it’s distinct from both 1 and 2), and so on. So our mathematical theories are true descriptions of ideas in our heads only if there actually exist infinitely many different ideas in our heads. Thus, since there aren’t that many ideas in our heads, we cannot maintain that our mathematical theories are true descriptions of such things.