Combining Texts

All the ideas for 'Investigations in the Foundations of Set Theory I', 'Lysis' and 'A Defense of Abortion'

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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]
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]
22. Metaethics / C. The Good / 1. Goodness / a. Form of the Good
295 The good is beautiful [Plato]
23. Ethics / C. Virtue Theory / 4. External Goods / d. Friendship
294 People say that friendship exists only between good men [Plato]
25. Social Practice / F. Life Issues / 3. Abortion
4058 Is someone's right to life diminished if they were conceived by a rape? [Thomson]
4060 The right to life does not bestow the right to use someone else's body to support that life [Thomson]
4062 No one is morally required to make huge sacrifices to keep someone else alive for nine months [Thomson]
4061 The right to life is not a right not to be killed, but not to be killed unjustly [Thomson]
4057 A newly fertilized ovum is no more a person than an acorn is an oak tree [Thomson]
4695 Maybe abortion can be justified despite the foetus having full human rights [Thomson, by Foot]
4059 It can't be murder for a mother to perform an abortion on herself to save her own life [Thomson]
4696 The foetus is safe in the womb, so abortion initiates its death, with the mother as the agent. [Foot on Thomson]