3 ms·

Neither Brouwer nor Hilbert claimed the other was wrong, only which axioms they preferred to use.

• gnulinux 3y ago
  This is not true at all, Brouwer truly thought the original Aristotelian concept of the "law of excluded middle" was epistemologically unfounded. I would recommend his original paper introducing intuitionistic mathematics but it's very dense. You can refer to: https://plato.stanford.edu/entries/brouwer/ https://plato.stanford.edu/entries/brouwer/ Later, he argued he found mathematical proofs of counterexamples of LEM. From above source: > “Intuitionist Reflections on Formalism” of 1928 identifies and discusses four key differences between formalism and intuitionism, all having to do either with the role of PEM or with the relation between mathematics and language. Brouwer emphasises, as he had done in his dissertation, that formalism presupposes contentual mathematics at the metalevel. He also here presents his first strong counterexample, a refutation of PEM in the form ∀x∈R(Px∨¬Px), by showing that it is false that every real number is either rational or irrational. See the supplement on Strong Counterexamples.