In this paper I consider three mathematicians who allowed some role for menial processes in the foundations of their logical or mathematical theories. Boole regarded his Boolean algebra as a theory of mental acts; Cantor permitted processes of abstraction to play a role in his set theory; Brouwer took perception in time as a cornerstone of his intuitionist mathematics. Three appendices consider related topics.

Brouwer’s intuitionistic program was an intriguing attempt to reform the foundations of mathematics that eventually did not prevail. The current paper offers a new perspective on the scientific community’s lack of reception to Brouwer’s intuitionism by considering it in light of Michael Friedman’s model of parallel transitions in philosophy and science, specifically focusing on Friedman’s story of Einstein’s theory of relativity. Such a juxtaposition raises onto the surface the differences between Brouwer’s and Einstein’s stories and suggests that contrary to Einstein’s (...) story, the philosophical roots of Brouwer’s intuitionism cannot be traced to any previously established philosophical traditions. The paper concludes by showing how the intuitionistic inclinations of Hermann Weyl and Abraham Fraenkel serve as telling cases of how individuals are involved in setting in motion, adopting, and resisting framework transitions during periods of disagreement within a discipline. (shrink)