Combining Texts

All the ideas for 'Ethical Criticism and the Vice of Moderation', 'Investigations in the Foundations of Set Theory I' and 'Letters to Schlick'

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23 ideas

1. Philosophy / D. Nature of Philosophy / 8. Humour
22701 Jokes can sometimes be funny because they are offensive [Jacobson,D]
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]
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 / 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]
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 / 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]
19. Language / F. Communication / 6. Interpreting Language / a. Translation
18285 All translation loses some content (but language does not create reality) [Carnap]
21. Aesthetics / A. Aesthetic Experience / 2. Aesthetic Attitude
22703 We don't often respond to events in art as if they were real events [Jacobson,D]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
22702 Audiences can be too moral [Jacobson,D]
22696 'Autonomism' says the morality is irrelevant to the aesthetics [Jacobson,D]
22697 Moral defects of art can be among its aesthetic virtues [Jacobson,D]
22700 Immoral art encourages immoral emotions [Jacobson,D]
22699 Moderate moralism says moral qualities can sometimes also be aesthetic qualities [Jacobson,D]
22698 We can judge art ethically, or rate its ethical influence, or assess its quality via its ethics [Jacobson,D]