Ideas of William W. Tait, by Theme

[American, fl. 1996, ]

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1. Philosophy / F. Analytic Philosophy / 5. Against Analysis
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
The null set was doubted, because numbering seemed to require 'units'
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
We can have a series with identical members
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
Mathematics must be based on axioms, which are true because they are axioms, not vice versa
6. Mathematics / A. Nature of Mathematics / 3. Numbers / c. Priority of numbers
Cantor took the ordinal numbers to be primary
18. Thought / D. Concepts / 6. Abstract Concepts / b. Abstracta from selection
Abstraction is 'logical' if the sense and truth of the abstraction depend on the concrete
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
There is no reason why abstraction by equivalence classes should be called 'logical'
Abstraction may concern the individuation of the set itself, not its elements
18. Thought / D. Concepts / 6. Abstract Concepts / h. Abstractionism critique
Why should abstraction from two equipollent sets lead to the same set of 'pure units'?
Dedekind has a conception of abstraction which is not psychologistic
If abstraction produces power sets, their identity should imply identity of the originals