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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.
 Fall '10
 wen
 Logic

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