 Psychologism is the view that mathematical sentences and theories are about mental objects. Probably the most common version of this view holds that numbers are something like ideas in our heads, and ordinary mathematical sentences like ‘3 is prime’ provide descriptions of these ideas. This view was popular in the late 19th Century; it was endorsed by, e.g., the early Husserl (1891), as well as the intuitionists, Brouwer (1912, 1948) and Heyting (1956). But Frege (1884, 1893–1903) provided a host of arguments against the view and essentially buried it. To give just one argument here, it seems that psychologism is just as incapable as physicalism is of dealing with the huge infinities in mathematics. As was just seen, standard set theories entail that there actually exist huge infinities of mathematical objects. But it’s just not believable that there are that many ideas in our heads. Indeed, it seems clear that there are only finitely many ideas in our heads. Therefore, it is not plausible to maintain that the claims of set theory are made true by mental objects.