more from James Robert Brown

Single Idea 9617

[catalogued under 4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets]

Full Idea

The modern 'iterative' concept of a set starts with the empty set φ (or unsetted individuals), then uses set-forming operations (characterized by the axioms) to build up ever more complex sets.

Gist of Idea

The 'iterative' view says sets start with the empty set and build up


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

Book Reference

Brown,James Robert: 'Philosophy of Mathematics' [Routledge 2002], p.22

A Reaction

The only sets in our system will be those we can construct, rather than anything accepted intuitively. It is more about building an elaborate machine that works than about giving a good model of reality.