Combining Philosophers

All the ideas for William W. Tait, Augustin-Louis Cauchy and Hamid Vahid

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20 ideas

1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
9978 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
9986 The null set was doubted, because numbering seemed to require 'units' [Tait]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
9984 We can have a series with identical members [Tait]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
13416 Mathematics must be based on axioms, which are true because they are axioms, not vice versa [Tait, by Parsons,C]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals
18085 Values that approach zero, becoming less than any quantity, are 'infinitesimals' [Cauchy]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits
18084 When successive variable values approach a fixed value, that is its 'limit' [Cauchy]
11. Knowledge Aims / A. Knowledge / 1. Knowledge
19712 Maybe there is plain 'animal' knowledge, and clearly justified 'reflective' knowledge [Vahid]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / a. Justification issues
19703 Epistemic is normally marked out from moral or pragmatic justifications by its truth-goal [Vahid]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism
19705 'Mentalist' internalism seems to miss the main point, if it might not involve an agent's access [Vahid]
19706 Strong access internalism needs actual awareness; weak versions need possibility of access [Vahid]
19707 Maybe we need access to our justification, and also to know why it justifies [Vahid]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / b. Pro-externalism
19709 Internalism in epistemology over-emphasises deliberation about beliefs [Vahid]
13. Knowledge Criteria / C. External Justification / 1. External Justification
19704 Externalism may imply that identical mental states might go with different justifications [Vahid]
13. Knowledge Criteria / C. External Justification / 4. Tracking the Facts
19710 With a counterfactual account of the causal theory, we get knowledge as tracking or sensitive to truth [Vahid]
13. Knowledge Criteria / C. External Justification / 10. Anti External Justification
19711 Externalism makes the acquisition of knowledge too easy? [Vahid]
18. Thought / E. Abstraction / 2. Abstracta by Selection
9981 Abstraction is 'logical' if the sense and truth of the abstraction depend on the concrete [Tait]
9982 Cantor and Dedekind use abstraction to fix grammar and objects, not to carry out proofs [Tait]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
9985 Abstraction may concern the individuation of the set itself, not its elements [Tait]
18. Thought / E. Abstraction / 8. Abstractionism Critique
9972 Why should abstraction from two equipollent sets lead to the same set of 'pure units'? [Tait]
9980 If abstraction produces power sets, their identity should imply identity of the originals [Tait]