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
Source
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]