Absurdity

Taken from the preface of “Brouwer’s Cambridge lectures on intuitionism”:

A feature that might irritate a modern reader, but which typically belongs to Brouwer, is the consistent refusal to use symbolic notation. It seems tempting to ascribe this to Brouwer’s aversion for formalization with its Hilbertian undertones. I think, however, that it was simply a characteristic of Brouwer’s style.

Now taken from his actual lectures:

THEOREM: Absurdity of absurdity of absurdity is equivalent to absurdity

PROOF: Firstly, since implication of the assertion \(y\) by the assertion \(x\) implies implication of absurdity of \(x\) by absurdity of \(y\), the implication of absurdity of absurdity by truth (which is an established fact) implies the implication of absurdity of truth, that is to say of absurdity, by absurdity of absurdity of absurdity. Secondly, since truth of an assertion implies absurdity of its absurdity, in particular truth of absurdity implies absurdity of absurdity of absurdity.

Taken from “Brouwer’s Cambridge lectures on intuitionism”.