Single Idea 9003

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

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 Reference

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.