### Single Idea 10040

#### [catalogued under 12. Knowledge Sources / E. Direct Knowledge / 2. Intuition]

Full Idea

By analyzing the paradoxes to which Cantor's set theory had led, ..Russell brought to light the amazing fact that our logical intuitions (concerning such notions as truth, concept, being, class) are self-contradictory.

Gist of Idea

Russell showed, through the paradoxes, that our basic logical intuitions are self-contradictory

Source

report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Kurt Gödel - Russell's Mathematical Logic p.452

Book Reference

'Philosophy of Mathematics: readings (2nd)', ed/tr. Benacerraf/Putnam [CUP 1983], p.452

A Reaction

The main intuition that failed was, I take it, that every concept has an extension, that is, there are always objects which will or could fall under the concept.