Combining Philosophers

All the ideas for Stephen Houlgate, Ernst Zermelo and Isaiah Berlin

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30 ideas

1. Philosophy / B. History of Ideas / 1. History of Ideas
7460 The great moments are the death of Aristotle, Machiavelli, and Romanticism [Berlin, by Watson]
1. Philosophy / B. History of Ideas / 5. Later European Thought
7662 Romanticism is the greatest change in the consciousness of the West [Berlin]
2. Reason / D. Definition / 8. Impredicative Definition
15924 Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
17608 We take set theory as given, and retain everything valuable, while avoiding contradictions [Zermelo]
17607 Set theory investigates number, order and function, showing logical foundations for mathematics [Zermelo]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
10870 ZFC: Existence, Extension, Specification, Pairing, Unions, Powers, Infinity, Choice [Zermelo, by Clegg]
13012 Zermelo published his axioms in 1908, to secure a controversial proof [Zermelo, by Maddy]
17609 Set theory can be reduced to a few definitions and seven independent axioms [Zermelo]
9565 Zermelo made 'set' and 'member' undefined axioms [Zermelo, by Chihara]
3339 For Zermelo's set theory the empty set is zero and the successor of each number is its unit set [Zermelo, by Blackburn]
17832 Zermelo showed that the ZF axioms in 1930 were non-categorical [Zermelo, by Hallett,M]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
13017 Zermelo introduced Pairing in 1930, and it seems fairly obvious [Zermelo, by Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
13028 Replacement was added when some advanced theorems seemed to need it [Zermelo, by Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / i. Axiom of Foundation VIII
13015 Zermelo used Foundation to block paradox, but then decided that only Separation was needed [Zermelo, by Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / m. Axiom of Separation
13020 The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy]
13486 Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD]
5. Theory of Logic / L. Paradox / 3. Antinomies
17626 The antinomy of endless advance and of completion is resolved in well-ordered transfinite numbers [Zermelo]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
13487 In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / e. Countable infinity
15897 Zermelo realised that Choice would facilitate the sort of 'counting' Cantor needed [Zermelo, by Lavine]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
18178 For Zermelo the successor of n is {n} (rather than n U {n}) [Zermelo, by Maddy]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
13027 Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Zermelo, by Maddy]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
9627 Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR]
18. Thought / A. Modes of Thought / 6. Judgement / a. Nature of Judgement
17613 We should judge principles by the science, not science by some fixed principles [Zermelo]
20. Action / C. Motives for Action / 3. Acting on Reason / b. Intellectualism
7665 Most Enlightenment thinkers believed that virtue consists ultimately in knowledge [Berlin]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / b. Defining ethics
21788 The moral will is self-determining, but the ethical will is met in society [Houlgate]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
7676 If we are essentially free wills, authenticity and sincerity are the highest virtues [Berlin]
23. Ethics / D. Deontological Ethics / 2. Duty
7664 The Greeks have no notion of obligation or duty [Berlin]
23. Ethics / F. Existentialism / 1. Existentialism
7677 Central to existentialism is the romantic idea that there is nothing to lean on [Berlin]
25. Social Practice / A. Freedoms / 5. Freedom of lifestyle
20544 Berlin distinguishes 'negative' and 'positive' liberty, and rejects the latter [Berlin, by Swift]
29. Religion / B. Monotheistic Religion / 2. Judaism
7663 Judaism and Christianity views are based on paternal, family and tribal relations [Berlin]