Combining Texts

All the ideas for 'In Defense of Essentialism', 'Reality without Reference' and 'Investigations in the Foundations of Set Theory I'

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28 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
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]
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 / e. Individuation by kind
14193 'Substance theorists' take modal properties as primitive, without structure, just falling under a sortal [Paul,LA]
14195 If an object's sort determines its properties, we need to ask what determines its sort [Paul,LA]
14196 Substance essentialism says an object is multiple, as falling under various different sortals [Paul,LA]
9. Objects / C. Structure of Objects / 8. Parts of Objects / b. Sums of parts
14198 Absolutely unrestricted qualitative composition would allow things with incompatible properties [Paul,LA]
9. Objects / D. Essence of Objects / 2. Types of Essence
14190 Deep essentialist objects have intrinsic properties that fix their nature; the shallow version makes it contextual [Paul,LA]
9. Objects / D. Essence of Objects / 6. Essence as Unifier
14191 Deep essentialists say essences constrain how things could change; modal profiles fix natures [Paul,LA]
9. Objects / D. Essence of Objects / 15. Against Essentialism
14192 Essentialism must deal with charges of arbitrariness, and failure to reduce de re modality [Paul,LA]
14197 An object's modal properties don't determine its possibilities [Paul,LA]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
14189 'Modal realists' believe in many concrete worlds, 'actualists' in just this world, 'ersatzists' in abstract other worlds [Paul,LA]
19. Language / A. Nature of Meaning / 1. Meaning
6387 A minimum requirement for a theory of meaning is that it include an account of truth [Davidson]
19. Language / A. Nature of Meaning / 4. Meaning as Truth-Conditions
6391 A theory of truth tells us how communication by language is possible [Davidson]
19. Language / B. Reference / 1. Reference theories
6388 Is reference the key place where language and the world meet? [Davidson]
6390 With a holistic approach, we can give up reference in empirical theories of language [Davidson]
19. Language / B. Reference / 4. Descriptive Reference / b. Reference by description
6389 To explain the reference of a name, you must explain its sentence-role, so reference can't be defined nonlinguistically [Davidson]