more on this theme | more from this thinker
Full Idea
Number abstraction can be taken to be a special case of abstraction in general, which can then be defined without recourse to the concept of number.
Gist of Idea
We should define abstraction in general, with number abstraction taken as a special case
Source
Kit Fine (Cantorian Abstraction: Recon. and Defence [1998], §3)
Book Ref
-: 'Journal of Philosophy' [-], p.11
A Reaction
At last, a mathematical logician recognising that they don't have a monopoly on abstraction. It is perfectly obvious that abstractions of simple daily concepts must be chronologically and logically prior to number abstraction. Number of what?
| 9146 | After abstraction all numbers seem identical, so only 0 and 1 will exist! [Fine,K] |
| 9148 | I think of variables as objects rather than as signs [Fine,K] |
| 9149 | To obtain the number 2 by abstraction, we only want to abstract the distinctness of a pair of objects [Fine,K] |
| 9150 | We should define abstraction in general, with number abstraction taken as a special case [Fine,K] |
| 9152 | If green is abstracted from a thing, it is only seen as a type if it is common to many things [Fine,K] |