Combining Philosophers

All the ideas for H.Putnam/P.Oppenheim, R Kaplan / E Kaplan and David van Reybrouck

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17 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]
14. Science / C. Induction / 3. Limits of Induction
The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan]
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction
Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / a. Sovereignty
Nowadays sovereignty (once the basis of a state) has become relative [Reybrouck]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / d. General will
Today it seems almost impossible to learn the will of the people [Reybrouck]
There are no united monolothic 'peoples', and no 'national gut feelings' [Reybrouck]
24. Political Theory / C. Ruling a State / 2. Leaders / d. Elites
Technocrats may be efficient, but they lose legitimacy as soon as they do unpopular things [Reybrouck]
Technocrats are expert managers, who replace politicians, and can be long-term and unpopular [Reybrouck]
24. Political Theory / D. Ideologies / 5. Democracy / a. Nature of democracy
Democracy is the best compromise between legitimacy and efficiency [Reybrouck]
24. Political Theory / D. Ideologies / 5. Democracy / b. Consultation
A referendum result arises largely from ignorance [Reybrouck]
24. Political Theory / D. Ideologies / 5. Democracy / c. Direct democracy
You don't really govern people if you don't involve them [Reybrouck]
24. Political Theory / D. Ideologies / 5. Democracy / d. Representative democracy
In the 18th century democratic lots lost out to elections, that gave us a non-hereditary aristocracy [Reybrouck]
Representative elections were developed in order to avoid democracy [Reybrouck]