Combining Texts

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

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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]
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
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
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]
14. Science / C. Induction / 3. Limits of Induction
The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan]
18. Thought / C. Content / 2. Ideas
Cartesian 'ideas' confuse concepts and propositions [Scruton]
24. Political Theory / A. Basis of a State / 3. Natural Values / c. Natural rights
Allegiance is prior to the recognition of individual rights [Scruton]
25. Social Practice / C. Rights / 1. Basis of Rights
A right is a power which is enforced in the name of justice [Scruton]
25. Social Practice / E. Policies / 5. Education / b. Education principles
Learned men gain more in one day than others do in a lifetime [Posidonius]
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]