Combining Texts

All the ideas for 'Essays on Intellectual Powers: Conception', 'Investigations in the Foundations of Set Theory I' and 'Anti-essentialism'

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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
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]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
12766 Logical space is abstracted from the actual world [Stalnaker]
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 / C. Structure of Objects / 7. Substratum
12764 For the bare particular view, properties must be features, not just groups of objects [Stalnaker]
9. Objects / D. Essence of Objects / 4. Essence as Definition
23647 Objects have an essential constitution, producing its qualities, which we are too ignorant to define [Reid]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / a. Essence as necessary properties
12761 An essential property is one had in all the possible worlds where a thing exists [Stalnaker]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / b. Essence not necessities
12763 Necessarily self-identical, or being what it is, or its world-indexed properties, aren't essential [Stalnaker]
9. Objects / D. Essence of Objects / 15. Against Essentialism
12762 Bare particular anti-essentialism makes no sense within modal logic semantics [Stalnaker]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / b. Conceivable but impossible
11958 Impossibilites are easily conceived in mathematics and geometry [Reid, by Molnar]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
12765 Why imagine that Babe Ruth might be a billiard ball; nothing useful could be said about the ball [Stalnaker]
19. Language / B. Reference / 1. Reference theories
23646 Reference is by name, or a term-plus-circumstance, or ostensively, or by description [Reid]
19. Language / B. Reference / 3. Direct Reference / c. Social reference
23645 A word's meaning is the thing conceived, as fixed by linguistic experts [Reid]