  Brouwer holds that mathematics is an essentially languageless activity, and that language can only give descriptions of mathematical activity after the fact. This leads him to deny axiomatic approaches any foundational role in mathematics. Also, he construes logic as the study of patterns in linguistic renditions of mathematical activity, and therefore logic is dependent on mathematics (as the study of patterns) and not vice versa. It is these considerations that motivate him to introduce the distinction between mathematics and metamathematics (for which he used the term “second order mathematics”), which he would explain to Hilbert in conversations in 1909 (Brouwer, 1928A2, p. 375n.2).