 Can one, in the case of purely mathematical constructions and transformations, temporarily neglect the presentation of the mathematical system that has been erected, and move in the accompanying linguistic building, guided by the principles of the syllogism, of contradiction, and of tertium exclusum, always confident that, by momentary evocation of the presentation of the mathematical constructions suggested by this reasoning, each part of the discourse could be justified? (Brouwer 1908C: 4 [van Atten &amp; Sundholm 2017: 40])