Combining Philosophers

All the ideas for William W. Tait, Donald C. Williams and James Cargile

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13 ideas

1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
Analytic philosophy focuses too much on forms of expression, instead of what is actually said [Tait]
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' [Tait]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
We can have a series with identical members [Tait]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
Saying 'they can become a set' is a tautology, because reference to 'they' implies a collection [Cargile]
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 [Tait, by Parsons,C]
8. Modes of Existence / B. Properties / 13. Tropes / a. Nature of tropes
'Socrates is wise' means a concurrence sum contains a member of a similarity set [Williams,DC]
A 'trope' is an abstract particular, the occurrence of an essence [Williams,DC]
A world is completely constituted by its tropes and their connections [Williams,DC]
18. Thought / E. Abstraction / 2. Abstracta by Selection
Abstraction is 'logical' if the sense and truth of the abstraction depend on the concrete [Tait]
Cantor and Dedekind use abstraction to fix grammar and objects, not to carry out proofs [Tait]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
Abstraction may concern the individuation of the set itself, not its elements [Tait]
18. Thought / E. Abstraction / 8. Abstractionism Critique
Why should abstraction from two equipollent sets lead to the same set of 'pure units'? [Tait]
If abstraction produces power sets, their identity should imply identity of the originals [Tait]