### Single Idea 13546

#### [catalogued under 4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size]

Full Idea

We group under the heading 'limitation of size' those principles which classify properties as collectivizing or not according to how many objects there are with the property.

Gist of Idea

The 'limitation of size' principles say whether properties collectivise depends on the number of objects

Source

Michael Potter (Set Theory and Its Philosophy [2004], 13.5)

Book Reference

Potter,Michael: 'Set Theory and Its Philosophy' [OUP 2004], p.227

A Reaction

The idea was floated by Cantor, toyed with by Russell (1906), and advocated by von Neumann. The thought is simply that paradoxes start to appear when sets become enormous.