Combining Texts

All the ideas for 'Science and Method', 'Epistemic Norms' and 'The Art of the Infinite'

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19 ideas

3. Truth / A. Truth Problems / 1. Truth
Rules of reasoning precede the concept of truth, and they are what characterize it [Pollock]
3. Truth / H. Deflationary Truth / 2. Deflationary Truth
We need the concept of truth for defeasible reasoning [Pollock]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
Using Choice, you can cut up a small ball and make an enormous one from the pieces [Kaplan/Kaplan]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
One geometry cannot be more true than another [Poincaré]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
1 and 0, then add for naturals, subtract for negatives, divide for rationals, take roots for irrationals [Kaplan/Kaplan]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
The rationals are everywhere - the irrationals are everywhere else [Kaplan/Kaplan]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
'Commutative' laws say order makes no difference; 'associative' laws say groupings make no difference [Kaplan/Kaplan]
'Distributive' laws say if you add then multiply, or multiply then add, you get the same result [Kaplan/Kaplan]
10. Modality / A. Necessity / 2. Nature of Necessity
Statements about necessities need not be necessarily true [Pollock]
11. Knowledge Aims / A. Knowledge / 4. Belief / f. Animal beliefs
Defeasible reasoning requires us to be able to think about our thoughts [Pollock]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / b. Need for justification
What we want to know is - when is it all right to believe something? [Pollock]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / c. Knowledge closure
Logical entailments are not always reasons for beliefs, because they may be irrelevant [Pollock]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism
Epistemic norms are internalised procedural rules for reasoning [Pollock]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / c. Empirical foundations
Reasons are always for beliefs, but a perceptual state is a reason without itself being a belief [Pollock]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / c. Coherentism critique
If we have to appeal explicitly to epistemic norms, that will produce an infinite regress [Pollock]
13. Knowledge Criteria / C. External Justification / 1. External Justification
Norm Externalism says norms must be internal, but their selection is partly external [Pollock]
Externalists tend to take a third-person point of view of epistemology [Pollock]
13. Knowledge Criteria / C. External Justification / 10. Anti External Justification
Belief externalism is false, because external considerations cannot be internalized for actual use [Pollock]
14. Science / C. Induction / 3. Limits of Induction
The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan]