Intuitionism has nothing to do with psychologizing math. The intuitionist is perfectly fine accepting that "the mind of the mathematician" is merely a metaphor

Intuitionism has nothing to do with psychologizing math. The intuitionist is perfectly fine accepting that "the mind of the mathematician" is merely a metaphor for some system capable of mathematical constructions, and that the "mathematician" in this argument can be replaced by a computer performing the same steps. In fact, a lot of computer science, particularly programming language theory, depends on this very notion.