Combining Texts

All the ideas for 'Essays on Intellectual Powers: Conception', 'Modern Moral Philosophy' and 'The Art of the Infinite'

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13 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]
9. Objects / D. Essence of Objects / 4. Essence as Definition
Objects have an essential constitution, producing its qualities, which we are too ignorant to define [Reid]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / b. Conceivable but impossible
Impossibilites are easily conceived in mathematics and geometry [Reid, by Molnar]
14. Science / C. Induction / 3. Limits of Induction
The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan]
19. Language / B. Reference / 1. Reference theories
Reference is by name, or a term-plus-circumstance, or ostensively, or by description [Reid]
19. Language / B. Reference / 3. Direct Reference / c. Social reference
A word's meaning is the thing conceived, as fixed by linguistic experts [Reid]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
It would be better to point to failings of character, than to moral wrongness of actions [Anscombe]
23. Ethics / D. Deontological Ethics / 1. Deontology
'Ought' and 'right' are survivals from earlier ethics, and should be jettisoned [Anscombe]
Between Aristotle and us, a Judaeo-Christian legal conception of ethics was developed [Anscombe]