structure for 'Formal Logic'    |     alphabetical list of themes    |     expand these ideas

4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Na´ve logical sets

[sets as defined by absolutely any concept]

6 ideas
Russell invented the na´ve set theory usually attributed to Cantor [Lavine on Russell]
Na´ve sets are inconsistent: there is no set for things that do not belong to themselves [Boolos]
Na´ve set theory has trouble with comprehension, the claim that every predicate has an extension [Hart,WD]
The paradoxes are only a problem for Frege; Cantor didn't assume every condition determines a set [Burgess/Rosen]
Na´ve set theory assumed that there is a set for every condition [Brown,JR]
Nowadays conditions are only defined on existing sets [Brown,JR]