more from this thinker     |     more from this text

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 4 ideas with the same theme [inconsistencies resulting from set theory axioms]:

18062 Set-theory paradoxes are no worse than sense deception in physics [Gödel]
9003 Set theory was struggling with higher infinities, when new paradoxes made it baffling [Quine]
9932 The paradoxes no longer seem crucial in critiques of set theory [Burgess/Rosen]
8675 Paradoxes can be solved by talking more loosely of 'classes' instead of 'sets' [Friend]