Ideas of William W. Tait, by Theme
[American, fl. 1996, ]
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1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
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9978
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Analytic philosophy focuses too much on forms of expression, instead of what is actually said
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4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
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9986
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The null set was doubted, because numbering seemed to require 'units'
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4. Formal Logic / F. Set Theory ST / 7. Natural Sets
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9984
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We can have a series with identical members
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5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
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13416
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Mathematics must be based on axioms, which are true because they are axioms, not vice versa [Parsons,C]
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18. Thought / E. Abstraction / 2. Abstracta by Selection
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9982
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Cantor and Dedekind use abstraction to fix grammar and objects, not to carry out proofs
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9981
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Abstraction is 'logical' if the sense and truth of the abstraction depend on the concrete
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18. Thought / E. Abstraction / 7. Abstracta by Equivalence
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9985
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Abstraction may concern the individuation of the set itself, not its elements
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18. Thought / E. Abstraction / 8. Abstractionism Critique
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9972
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Why should abstraction from two equipollent sets lead to the same set of 'pure units'?
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9980
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If abstraction produces power sets, their identity should imply identity of the originals
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