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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.
| 13829 | If logical truths essentially depend on logical constants, we had better define the latter [Hacking on Quine] |
| 13010 | In order to select the logic justified by experience, we would need to use a lot of logic [Boghossian on Quine] |
| 9001 | Frege moved Kant's question about a priori synthetic to 'how is logical certainty possible?' [Quine] |
| 9002 | Elementary logic requires truth-functions, quantifiers (and variables), identity, and also sets of variables [Quine] |
| 9003 | Set theory was struggling with higher infinities, when new paradoxes made it baffling [Quine] |
| 9004 | If set theory is not actually a branch of logic, then Frege's derivation of arithmetic would not be from logic [Quine] |
| 13681 | Logical consequence is marked by being preserved under all nonlogical substitutions [Quine, by Sider] |
| 9005 | Examination of convention in the a priori begins to blur the distinction with empirical knowledge [Quine] |
| 9006 | Commitment to universals is as arbitrary or pragmatic as the adoption of a new system of bookkeeping [Quine] |