Combining Philosophers

All the ideas for William W. Tait, David van Reybrouck and R Kaplan / E Kaplan

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25 ideas

1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
9978 Analytic philosophy focuses too much on forms of expression, instead of what is actually said [Tait]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
9986 The null set was doubted, because numbering seemed to require 'units' [Tait]
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]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
9984 We can have a series with identical members [Tait]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
13416 Mathematics must be based on axioms, which are true because they are axioms, not vice versa [Tait, by Parsons,C]
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]
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 / E. Abstraction / 2. Abstracta by Selection
9981 Abstraction is 'logical' if the sense and truth of the abstraction depend on the concrete [Tait]
9982 Cantor and Dedekind use abstraction to fix grammar and objects, not to carry out proofs [Tait]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
9985 Abstraction may concern the individuation of the set itself, not its elements [Tait]
18. Thought / E. Abstraction / 8. Abstractionism Critique
9972 Why should abstraction from two equipollent sets lead to the same set of 'pure units'? [Tait]
9980 If abstraction produces power sets, their identity should imply identity of the originals [Tait]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / a. Sovereignty
20086 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
20090 Today it seems almost impossible to learn the will of the people [Reybrouck]
20087 There are no united monolothic 'peoples', and no 'national gut feelings' [Reybrouck]
24. Political Theory / C. Ruling a State / 2. Leaders / d. Elites
20089 Technocrats may be efficient, but they lose legitimacy as soon as they do unpopular things [Reybrouck]
20088 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
20085 Democracy is the best compromise between legitimacy and efficiency [Reybrouck]
24. Political Theory / D. Ideologies / 5. Democracy / b. Consultation
20095 A referendum result arises largely from ignorance [Reybrouck]
24. Political Theory / D. Ideologies / 5. Democracy / c. Direct democracy
20094 You don't really govern people if you don't involve them [Reybrouck]
24. Political Theory / D. Ideologies / 5. Democracy / d. Representative democracy
20093 In the 18th century democratic lots lost out to elections, that gave us a non-hereditary aristocracy [Reybrouck]
20091 Representative elections were developed in order to avoid democracy [Reybrouck]