 As Brouwer was more interested in developing pure mathematics than in developing logic, which for him was a form of applied mathematics, he never made an extensive study of the latter. In particular, he never made a systematic comparison of intuitionistic logic and classical logic as formalized, for example, in Principia Mathematica (Whitehead &amp; Russell 1910) or by the Hilbert school (Hilbert 1923; Hilbert &amp; Ackermann 1928). What motivated others to make such comparisons was the publication by Brouwer in international journals of weak counterexamples that showed how these also affected very general mathematical principles such as trichotomy for real numbers (see above,  section 3.2).