Combining Texts

All the ideas for 'Frege versus Cantor and Dedekind', 'The Scope and Language of Science' and 'Epistemic Justification'

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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]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Maths can be reduced to logic and set theory [Quine]
8. Modes of Existence / B. Properties / 1. Nature of Properties
The category of objects incorporates the old distinction of substances and their modes [Quine]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism
'Access' internalism says responsibility needs access; weaker 'mentalism' needs mental justification [Kvanvig]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / a. Foundationalism
Strong foundationalism needs strict inferences; weak version has induction, explanation, probability [Kvanvig]
17. Mind and Body / E. Mind as Physical / 6. Conceptual Dualism
A hallucination can, like an ague, be identified with its host; the ontology is physical, the idiom mental [Quine]
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]