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Full Idea
Unlike elementary logic, the truths of set theory are not obvious. Set theory was straining at the leash of intuition ever since Cantor discovered higher infinites; and with the added impetus of the paradoxes of set theory the leash snapped.
Gist of Idea
Set theory was struggling with higher infinities, when new paradoxes made it baffling
Source
Willard Quine (Carnap and Logical Truth [1954], II)
Book Ref
Quine,Willard: 'Ways of Paradox and other essays' [Harvard 1976], p.111
A Reaction
This problem seems to have forced Quine into platonism about sets, because he felt they were essential for mathematics and science, but couldn't be constructed with precision. So they must be real, but we don't quite understand them.
| 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] |