 On its face, the concept of pure thinking is obscure. Likewise for Cohen’s claim that pure thinking generates out of itself the principles that explain mathematical natural science’s objective validity. However, we can start to understand these ideas by recalling two of the commitments that underpin all of Cohen’s theoretical philosophy: first, his idealism, that is, his insistence that a priori laws of human knowledge determine what counts as an object for us; and second, his methodological rationalism, that is, his commitment to an unending search for reasons and his unwillingness to accept anything as given or brute.