Combining Texts

All the ideas for 'Varieties of Causation', 'Subjective and Objective' and 'Investigations in the Foundations of Set Theory I'

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23 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]
9. Objects / D. Essence of Objects / 12. Essential Parts
8443 Mereological essentialism says an entity must have exactly those parts [Sosa]
12. Knowledge Sources / B. Perception / 4. Sense Data / d. Sense-data problems
3296 Sense-data are a false objectification of what is essentially subjective [Nagel]
15. Nature of Minds / A. Nature of Mind / 1. Mind / a. Mind
3295 Inner v outer brings astonishment that we are a particular person [Nagel]
16. Persons / B. Nature of the Self / 4. Presupposition of Self
3293 If you assert that we have an ego, you can still ask if that future ego will be me [Nagel]
16. Persons / F. Free Will / 1. Nature of Free Will
3292 The most difficult problem of free will is saying what the problem is [Nagel]
23. Ethics / D. Deontological Ethics / 3. Universalisability
3294 As far as possible we should become instruments to realise what is best from an eternal point of view [Nagel]
26. Natural Theory / C. Causation / 9. General Causation / b. Nomological causation
8442 What law would explain causation in the case of causing a table to come into existence? [Sosa]
26. Natural Theory / C. Causation / 9. General Causation / d. Causal necessity
8445 The necessitated is not always a result or consequence of the necessitator [Sosa]
8444 Where is the necessary causation in the three people being tall making everybody tall? [Sosa]