Combining Philosophers

All the ideas for Friedrich Schlegel, Benedetto Croce and Ernst Zermelo

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29 ideas

1. Philosophy / C. History of Philosophy / 4. Later European Philosophy / c. Eighteenth century philosophy
Irony is consciousness of abundant chaos [Schlegel,F]
1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
Plato has no system. Philosophy is the progression of a mind and development of thoughts [Schlegel,F]
2. Reason / D. Definition / 8. Impredicative Definition
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
We take set theory as given, and retain everything valuable, while avoiding contradictions [Zermelo]
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
ZFC: Existence, Extension, Specification, Pairing, Unions, Powers, Infinity, Choice [Zermelo, by Clegg]
Zermelo made 'set' and 'member' undefined axioms [Zermelo, by Chihara]
Zermelo published his axioms in 1908, to secure a controversial proof [Zermelo, by Maddy]
Set theory can be reduced to a few definitions and seven independent axioms [Zermelo]
For Zermelo's set theory the empty set is zero and the successor of each number is its unit set [Zermelo, by Blackburn]
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
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
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
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
Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD]
The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy]
5. Theory of Logic / L. Paradox / 3. Antinomies
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
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
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
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
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
Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / b. Transcendental idealism
Poetry is transcendental when it connects the ideal to the real [Schlegel,F]
18. Thought / A. Modes of Thought / 6. Judgement / a. Nature of Judgement
We should judge principles by the science, not science by some fixed principles [Zermelo]
21. Aesthetics / B. Nature of Art / 4. Art as Expression
The experience of expression and communication are intermingled in art [Croce]
21. Aesthetics / B. Nature of Art / 8. The Arts / b. Literature
For poets free choice is supreme [Schlegel,F]
21. Aesthetics / C. Artistic Issues / 1. Artistic Intentions
Historical interpretation aims to recapture the author's view of the work [Croce]
22. Metaethics / A. Value / 2. Values / e. Love
True love is ironic, in the contrast between finite limitations and the infinity of love [Schlegel,F]
23. Ethics / F. Existentialism / 3. Angst
Irony is the response to conflicts of involvement and attachment [Schlegel,F, by Pinkard]