Combining Texts

All the ideas for 'fragments/reports', 'The Art of the Infinite' and 'Existence,Ontological Commitment and Fictions'

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10 ideas

2. Reason / C. Styles of Reason / 1. Dialectic

20768

Like spiderswebs, dialectical arguments are clever but useless [Ariston, by Diog. Laertius]

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX

15717

Using Choice, you can cut up a small ball and make an enormous one from the pieces [Kaplan/Kaplan]

4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory

8972	What in the real world could ground the distinction between the sets {A,{A,B}} and {B,{A,B}}? [Inwagen]

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number

15712

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

15711

The rationals are everywhere - the irrationals are everywhere else [Kaplan/Kaplan]

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic

15714

'Commutative' laws say order makes no difference; 'associative' laws say groupings make no difference [Kaplan/Kaplan]

15715

'Distributive' laws say if you add then multiply, or multiply then add, you get the same result [Kaplan/Kaplan]

14. Science / C. Induction / 3. Limits of Induction

15713

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 / f. The Mean

3049	The chief good is indifference to what lies midway between virtue and vice [Ariston, by Diog. Laertius]

23. Ethics / D. Deontological Ethics / 1. Deontology

3549	Ariston says rules are useless for the virtuous and the non-virtuous [Ariston, by Annas]