Combining Texts

All the ideas for 'reports', 'The Art of the Infinite' and 'Short History of Modern Philosophy'

expand these ideas     |    start again     |     specify just one area for these texts

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11 ideas

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]

5. Theory of Logic / A. Overview of Logic / 2. History of Logic

5637	Nowadays logic is seen as the science of extensions, not intensions [Scruton]

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]

10. Modality / A. Necessity / 8. Transcendental Necessity

3016	Even the gods cannot strive against necessity [Pittacus, by Diog. Laertius]

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

15713

The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan]

18. Thought / C. Content / 2. Ideas

5636	Cartesian 'ideas' confuse concepts and propositions [Scruton]

24. Political Theory / A. Basis of a State / 3. Natural Values / c. Natural rights

5660	Allegiance is prior to the recognition of individual rights [Scruton]

25. Social Practice / C. Rights / 1. Basis of Rights

5653	A right is a power which is enforced in the name of justice [Scruton]