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Single Idea 15894

[filed under theme 4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets ]

Full Idea

Russell was the inventor of the naïve set theory so often attributed to Cantor.

Gist of Idea

Russell invented the naïve set theory usually attributed to Cantor

Source

report of Bertrand Russell (The Principles of Mathematics [1903]) by Shaughan Lavine - Understanding the Infinite I

Book Ref

Lavine,Shaughan: 'Understanding the Infinite' [Harvard 1994], p.3

The 9 ideas with the same theme [sets as defined by absolutely any concept]:

15894 Russell invented the naïve set theory usually attributed to Cantor [Russell, by Lavine]
21695 The set scheme discredited by paradoxes is actually the most natural one [Quine]
10485 Naïve sets are inconsistent: there is no set for things that do not belong to themselves [Boolos]
13441 Naïve set theory has trouble with comprehension, the claim that every predicate has an extension [Hart,WD]
9933 The paradoxes are only a problem for Frege; Cantor didn't assume every condition determines a set [Burgess/Rosen]
9613 Naïve set theory assumed that there is a set for every condition [Brown,JR]
9615 Nowadays conditions are only defined on existing sets [Brown,JR]
23445 Naïve set theory says any formula defines a set, and coextensive sets are identical [Linnebo]
23623 Predicativism says only predicated sets exist [Hossack]