ellauri096.html on line 186: But the skeptic should not lose his nerve. Proof does not always yield knowledge. Consider a student who correctly guesses that a step in his proof is valid. The student does not know the conclusion but did prove the theorem. His instructor might have trouble getting the student to understand why his answer constitutes a valid proof. The intransigence may stem from the prover’s intelligence rather than his stupidity. L. E. J. Brouwer is best known in mathematics for his brilliant fixed point theorem. But Brouwer regarded his proof as dubious. He had philosophical doubts about the Axiom of Choice and Law of Excluded Middle. Brouwer persuaded a minority of mathematicians and philosophers, known as intuitionists, to emulate his inability to be educated by non-constructive proofs.
ellauri309.html on line 589: Fundamentalism Steve Brouwer, Paul Gifford ja Susan Rose spekuloivat, että
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