Cute quotation from Knuth - however Knuth was wrong. Brouwer would have no problem with the statement 'either it is raining outside or it is not raining outside' because he knew you could go and look. He did not insist on your actually looking. He had a problem with things like König's lemma - not quite the same. I have a problem with things like König's lemma too, but in the great scheme of things it is not very important.

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