Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'The Art of the Infinite' and 'Introduction to 'Language Truth and Logic''

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14 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 / 4. Foundationalism / c. Empirical foundations
Basic propositions refer to a single experience, are incorrigible, and conclusively verifiable [Ayer]
14. Science / C. Induction / 3. Limits of Induction
The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / c. Knowing other minds
The argument from analogy fails, so the best account of other minds is behaviouristic [Ayer]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
A statement is meaningful if observation statements can be deduced from it [Ayer]
Directly verifiable statements must entail at least one new observation statement [Ayer]
The principle of verification is not an empirical hypothesis, but a definition [Ayer]
19. Language / D. Propositions / 1. Propositions
Sentences only express propositions if they are meaningful; otherwise they are 'statements' [Ayer]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / i. Prescriptivism
Moral approval and disapproval concerns classes of actions, rather than particular actions [Ayer]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]