Brouwer adhered to an intuitionist philosophy of mathematics, which is sometimes characterized by saying that its adherents refuse to use the law of excluded middle in mathematical reasoning, and wrote books on the subjects mentioned above in which he proceeded accordingly.
He was involved in an eventually demeaning controversy with David Hilbert.
He was member of the Significs group, containing others with a generally neo-Kantian philosophy. It formed part of the early history of semiotic study, around Victoria, Lady Welby.
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