Ideas from 'Cantorian Abstraction: Recon. and Defence' by Kit Fine [1998], by Theme Structure
[found in 'Journal of Philosophy' (ed/tr ) [ ,]].
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5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
9148

I think of variables as objects rather than as signs

6. Mathematics / A. Nature of Mathematics / 3. Numbers / o. Units
9147

Number cannot be defined as addition of ones, since that needs the number; it is a single act of abstraction

6. Mathematics / B. Foundations for Mathematics / 6. Mathematical Structuralism / b. Varieties of structuralism
9153

Dedekindian abstraction talks of 'positions', where Cantorian abstraction talks of similar objects

15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
9152

If green is abstracted from a thing, it is only seen as a type if it is common to many things

18. Thought / D. Concepts / 6. Abstract Concepts / b. Abstracta from selection
9149

To obtain the number 2 by abstraction, we only want to abstract the distinctness of a pair of objects

9150

We should define abstraction in general, with number abstraction taken as a special case

18. Thought / D. Concepts / 6. Abstract Concepts / h. Abstractionism critique
9146

After abstraction all numbers seem identical, so only 0 and 1 will exist!
