Mathematics and the Mind
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by Edward Nelson
http://www.math.princeton.edu/~nelson/papers/tokyo.ps.gz
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Abstract:
"The non-algorithmic nature of mathematical insight " in The Emperor's New Mind [9, Chap. 10], can be phrased as follows: Godel's theorem shows that there is no algorithm producing all statements of Arithmetic that mathematicians can see to be true. Therefore consciousness acts non-algorithmically. I shall analyze this claim and then present some contrasting thoughts. What are statements of Arithmetic? Here there is no dispute. They are expressions formed from symbols 8 9: & ! = 0 S + \Delta ( ) x y z: :: according to certain rules. For example,
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