Combining Texts

All the ideas for 'fragments/reports', 'Investigations in the Foundations of Set Theory I' and 'Nature Without Essence'

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27 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 / K. Features of Logics / 6. Compactness
17867 If a concept is not compact, it will not be presentable to finite minds [Almog]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / d. Natural numbers
17877 The number series is primitive, not the result of some set theoretic axioms [Almog]
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 / D. Essence of Objects / 4. Essence as Definition
17872 Definitionalists rely on snapshot-concepts, instead of on the real processes [Almog]
17871 Fregean meanings are analogous to conceptual essence, defining a kind [Almog]
17866 Essential definition aims at existence conditions and structural truths [Almog]
17868 Surface accounts aren't exhaustive as they always allow unintended twin cases [Almog]
9. Objects / D. Essence of Objects / 10. Essence as Species
17870 Alien 'tigers' can't be tigers if they are not related to our tigers [Almog]
9. Objects / D. Essence of Objects / 13. Nominal Essence
17869 Kripke and Putnam offer an intermediary between real and nominal essences [Almog]
9. Objects / D. Essence of Objects / 15. Against Essentialism
17876 Individual essences are just cobbled together classificatory predicates [Almog]
13. Knowledge Criteria / E. Relativism / 2. Knowledge as Convention
1556 By nature people are close to one another, but culture drives them apart [Hippias]
18. Thought / C. Content / 5. Twin Earth
17873 Water must be related to water, just as tigers must be related to tigers [Almog]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / e. Anti scientific essentialism
17864 Defining an essence comes no where near giving a thing's nature [Almog]
17863 Essences promise to reveal reality, but actually drive us away from it [Almog]