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Single Idea 18062

[filed under theme 5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / a. Set theory paradoxes ]

Full Idea

The set-theoretical paradoxes are hardly any more troublesome for mathematics than deceptions of the senses are for physics.

Gist of Idea

Set-theory paradoxes are no worse than sense deception in physics

Source

Kurt Gödel (What is Cantor's Continuum Problem? [1964], p.271), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 03.4

Book Ref

Kitcher,Philip: 'The Nature of Mathematical Knowledge' [OUP 1984], p.63

The 6 ideas from 'What is Cantor's Continuum Problem?'

9942 Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam]
10868 The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg]
13517 If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD]
18062 Set-theory paradoxes are no worse than sense deception in physics [Gödel]
8679 We perceive the objects of set theory, just as we perceive with our senses [Gödel]
10271 Basic mathematics is related to abstract elements of our empirical ideas [Gödel]