Combining Texts

All the ideas for 'fragments/reports', 'First Things First' and 'The Art of the Infinite'

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12 ideas

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 / 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]
13. Knowledge Criteria / B. Internal Justification / 3. Evidentialism / b. Evidentialism
Evidentialism is not axiomatic; the evidence itself inclines us towards evidentialism [Conee]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / b. Anti-reliabilism
If pure guesses were reliable, reliabilists would have to endorse them [Conee]
More than actual reliability is needed, since I may mistakenly doubt what is reliable [Conee]
Reliabilism is poor on reflective judgements about hypothetical cases [Conee]
14. Science / C. Induction / 3. Limits of Induction
The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
Virtue comes more from habit than character [Critias]
28. God / C. Attitudes to God / 5. Atheism
Fear of the gods was invented to discourage secret sin [Critias]