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
I think of variables as objects rather than as signs
6. Mathematics / A. Nature of Mathematics / 3. Numbers / o. Units
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
Dedekindian abstraction talks of 'positions', where Cantorian abstraction talks of similar objects
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
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
To obtain the number 2 by abstraction, we only want to abstract the distinctness of a pair of objects
We should define abstraction in general, with number abstraction taken as a special case
18. Thought / D. Concepts / 6. Abstract Concepts / h. Abstractionism critique
After abstraction all numbers seem identical, so only 0 and 1 will exist!