Combining Texts

All the ideas for 'Representation in Music', 'Primitive Thisness and Primitive Identity' and 'Investigations in the Foundations of Set Theory I'

expand these ideas     |    start again     |     specify just one area for these texts

29 ideas

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]
9. Objects / A. Existence of Objects / 5. Individuation / d. Individuation by haecceity
14508 A 'thisness' is a thing's property of being identical with itself (not the possession of self-identity) [Adams,RM]
14511 There are cases where mere qualities would not ensure an intrinsic identity [Adams,RM]
9. Objects / D. Essence of Objects / 9. Essence and Properties
12031 Essences are taken to be qualitative properties [Adams,RM]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
12034 If the universe was cyclical, totally indiscernible events might occur from time to time [Adams,RM]
14510 Two events might be indiscernible yet distinct, if there was a universe cyclical in time [Adams,RM]
16455 Black's two globes might be one globe in highly curved space [Adams,RM]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
14507 Are possible worlds just qualities, or do they include primitive identities as well? [Adams,RM]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / b. Worlds as fictions
11964 Possible worlds are world-stories, maximal descriptions of whole non-existent worlds [Adams,RM, by Molnar]
10. Modality / E. Possible worlds / 3. Transworld Objects / d. Haecceitism
16451 Adams says anti-haecceitism reduces all thisness to suchness [Adams,RM, by Stalnaker]
11901 Haecceitism may or may not involve some logical connection to essence [Adams,RM, by Mackie,P]
14512 Moderate Haecceitism says transworld identities are primitive, but connected to qualities [Adams,RM]
19. Language / B. Reference / 3. Direct Reference / a. Direct reference
12032 Direct reference is by proper names, or indexicals, or referential uses of descriptions [Adams,RM]
21. Aesthetics / B. Nature of Art / 4. Art as Expression
12167 Reference without predication is the characteristic of expression [Scruton]
21. Aesthetics / B. Nature of Art / 5. Art as Language
12166 If music refers to love, it contains no predication, so it is expression, not language [Scruton]
21. Aesthetics / B. Nature of Art / 8. The Arts / a. Music
12168 Music is not representational, since thoughts about a subject are never essential to it [Scruton]