Combining Texts

All the ideas for 'The Essence of Aesthetic', 'The Causal Theory of Names' and 'Investigations in the Foundations of Set Theory I'

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24 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
17607 Set theory investigates number, order and function, showing logical foundations for mathematics [Zermelo]
17608 We take set theory as given, and retain everything valuable, while avoiding contradictions [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
13486 Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD]
13020 The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy]
5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
9038 We must distinguish what the speaker denotes by a name, from what the name denotes [Evans]
5824 How can an expression be a name, if names can change their denotation? [Evans]
9042 A private intention won't give a name a denotation; the practice needs it to be made public [Evans]
5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
9041 The Causal Theory of Names is wrong, since the name 'Madagascar' actually changed denotation [Evans]
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 / B. Reference / 3. Direct Reference / b. Causal reference
5825 Speakers intend to refer to items that are the source of their information [Evans]
5823 The intended referent of a name needs to be the cause of the speaker's information about it [Evans]
19. Language / B. Reference / 4. Descriptive Reference / b. Reference by description
9039 If descriptions are sufficient for reference, then I must accept a false reference if the descriptions fit [Evans]
19. Language / F. Communication / 5. Pragmatics / b. Implicature
9043 We use expressions 'deferentially', to conform to the use of other people [Evans]
19. Language / F. Communication / 6. Interpreting Language / c. Principle of charity
9040 Charity should minimize inexplicable error, rather than maximising true beliefs [Evans]
21. Aesthetics / B. Nature of Art / 4. Art as Expression
20422 The experience of expression and communication are intermingled in art [Croce]