more from William D. Hart

Single Idea 13506

[catalogued under 5. Theory of Logic / G. Quantification / 3. Objectual Quantification]

Full Idea

All the main set theories deny that there is a set of which everything is a member. No interpretation has a domain with everything in it. So the universal quantifier never gets to mean everything all at once; 'all' does not mean all.

Gist of Idea

The universal quantifier can't really mean 'all', because there is no universal set


William D. Hart (The Evolution of Logic [2010], 4)

Book Reference

Hart,W.D.: 'The Evolution of Logic' [CUP 2010], p.111

A Reaction

Could you have an 'uncompleted' universal set, in the spirit of uncompleted infinities? In ordinary English we can talk about 'absolutely everything' - we just can't define a set of everything. Must we 'define' our domain?