more from George Cantor

Single Idea 13454

[catalogued under 18. Thought / E. Abstraction / 2. Abstracta by Selection]

Full Idea

Cantor thought that we abstract a number as something common to all and only those sets any one of which has as many members as any other. ...However one wants to see the logic of the inference. The irony is that set theory lays out this logic.

Gist of Idea

Cantor says (vaguely) that we abstract numbers from equal sized sets


comment on George Cantor (works [1880]) by William D. Hart - The Evolution of Logic 1

Book Reference

Hart,W.D.: 'The Evolution of Logic' [CUP 2010], p.19

A Reaction

The logic Hart has in mind is the notion of an equivalence relation between sets. This idea sums up the older and more modern concepts of abstraction, the first as psychological, the second as logical (or trying very hard to be!). Cf Idea 9145.

Related Idea

Idea 9145 We form the image of a cardinal number by a double abstraction, from the elements and from their order [Cantor]