Ideas from 'Frege versus Cantor and Dedekind' by William W. Tait [1996], by Theme Structure
[found in 'Philosophy of Mathematics: anthology' (ed/tr Jacquette,Dale) [Blackwell 2002,063121870x]].
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1. Philosophy / F. Analytic Philosophy / 5. Against Analysis
9978

Analytic philosophy focuses too much on forms of expression, instead of what is actually said

4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
9986

The null set was doubted, because numbering seemed to require 'units'

4. Formal Logic / F. Set Theory ST / 7. Natural Sets
9984

We can have a series with identical members

6. Mathematics / A. Nature of Mathematics / 3. Numbers / c. Priority of numbers
9983

Cantor took the ordinal numbers to be primary

18. Thought / D. Concepts / 6. Abstract Concepts / b. Abstracta from selection
9981

Abstraction is 'logical' if the sense and truth of the abstraction depend on the concrete

9982

Cantor and Dedekind use abstraction to fix grammar and objects, not to carry out proofs

18. Thought / D. Concepts / 6. Abstract Concepts / g. Abstracta by equivalence
9993

There is no reason why abstraction by equivalence classes should be called 'logical'

9985

Abstraction may concern the individuation of the set itself, not its elements

18. Thought / D. Concepts / 6. Abstract Concepts / h. Abstractionism critique
9972

Why should abstraction from two equipollent sets lead to the same set of 'pure units'?

9979

Dedekind has a conception of abstraction which is not psychologistic

9980

If abstraction produces power sets, their identity should imply identity of the originals
