history-page48 - Intuitionists rejected the Law of the...

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Intuitionists rejected the Law of the Excluded Middle, which says that statements are true or false. Thus, while they accepted A ⇒∼ ( A) as a logical identity, they didn’t accept ( A) A as a logical identity. Hilbert: “Taking the law of the excluded middle from mathematicians is the same as pro- hibiting the astronomer his telescope or the boxer the use of his Fsts.” Intuitionists rejected the Axiom of Choice. Intuitionists did not accept functions like f(x) = b 0 if x 0 1 if x > 0 . It is a theorem of Intuitionistic analysis that all functions are continuous. Weyl, a student of Hilbert’s who “converted” to Intuitionism: “In this book, I am not con- cerned to disguise the ‘solid rock’ on which the house of analysis is built with a wooden platform of formalism, in order to talk the reader into believing at the end that this plat- form is the true foundation. What will be proposed is rather the view that this house is largely built on sand.” Hilbert (1922): “What Weyl and Brouwer are doing is mainly following in the path of Kro-
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This note was uploaded on 12/29/2011 for the course MATH 378 taught by Professor Wen during the Fall '10 term at SUNY Stony Brook.

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