more from James Robert Brown

### Single Idea 9613

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

Full Idea

In the early versions of set theory ('naïve' set theory), the axiom of comprehension assumed that for any condition there is a set of objects satisfying that condition (so P(x)↔x∈{x:P(x)}), but this led directly to Russell's Paradox.

Clarification

See Idea 6407 for Russell's Paradox

Gist of Idea

Naïve set theory assumed that there is a set for every condition

Source

James Robert Brown (Philosophy of Mathematics [1999], Ch. 2)

Book Reference

Brown,James Robert: 'Philosophy of Mathematics' [Routledge 2002], p.19

A Reaction

How rarely any philosophers state this problem clearly (as Brown does here). This is incredibly important for our understanding of how we classify the world. I'm tempted to just ignore Russell, and treat sets in a natural and sensible way.

Related Idea

Idea 6407
The class of classes which lack self-membership leads to a contradiction **[Russell, by Grayling]**