Combining Texts

All the ideas for 'Investigations in the Foundations of Set Theory I', 'A World of Dispositions' and 'Tropes'

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21 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]
8. Modes of Existence / B. Properties / 13. Tropes / a. Nature of tropes
8526 We might treat both tropes and substances as fundamental, so we can't presume it is just tropes [Daly]
8. Modes of Existence / B. Properties / 13. Tropes / b. Critique of tropes
8527 More than one trope (even identical ones!) can occupy the same location [Daly]
8528 If tropes are linked by the existence of concurrence, a special relation is needed to link them all [Daly]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / e. Dispositions as potential
15797 All structures are dispositional, objects are dispositions sets, and events manifest dispositions [Fetzer]
9. Objects / C. Structure of Objects / 1. Structure of an Object
15800 All events and objects are dispositional, and hence all structural properties are dispositional [Fetzer]
26. Natural Theory / B. Natural Kinds / 2. Defining Kinds
15798 Kinds are arrangements of dispositions [Fetzer]
26. Natural Theory / D. Laws of Nature / 3. Laws and Generalities
15799 Lawlike sentences are general attributions of disposition to all members of some class [Fetzer]