Combining Texts

All the ideas for 'Investigations in the Foundations of Set Theory I', 'Sociobiology' and 'Events'

expand these ideas     |    start again     |     specify just one area for these texts

22 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]
7. Existence / B. Change in Existence / 4. Events / a. Nature of events
15561 The events that suit semantics may not be the events that suit causation [Lewis]
15565 Events have inbuilt essences, as necessary conditions for their occurrence [Lewis]
15566 Events are classes, and so there is a mereology of their parts [Lewis]
15567 Some events involve no change; they must, because causal histories involve unchanges [Lewis]
7. Existence / B. Change in Existence / 4. Events / c. Reduction of events
15564 An event is a property of a unique space-time region [Lewis]
8. Modes of Existence / B. Properties / 10. Properties as Predicates
15563 Properties are very abundant (unlike universals), and are used for semantics and higher-order variables [Lewis]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / d. Biological ethics
22187 Genetic behaviours that have enhanced human success include aggression, rape and xenophobia [Wilson,EO, by Okasha]
26. Natural Theory / C. Causation / 1. Causation
15562 Causation is a general relation derived from instances of causal dependence [Lewis]