Combining Texts

All the ideas for 'On the Natural Faculties', 'Investigations in the Foundations of Set Theory I' and 'The Concept of Mind'

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26 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
18005 Philosophy aims to become more disciplined about categories [Ryle]
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]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / e. Dispositions as potential
14297 A dispositional property is not a state, but a liability to be in some state, given a condition [Ryle]
8. Modes of Existence / C. Powers and Dispositions / 7. Against Powers
14300 No physical scientist now believes in an occult force-exerting agency [Ryle]
15. Nature of Minds / A. Nature of Mind / 3. Mental Causation
2622 Can one movement have a mental and physical cause? [Ryle]
15. Nature of Minds / C. Capacities of Minds / 1. Faculties
21799 We just use the word 'faculty' when we don't know the psychological cause [Galen]
16. Persons / C. Self-Awareness / 3. Limits of Introspection
1354 We cannot introspect states of anger or panic [Ryle]
1353 Reporting on myself has the same problems as reporting on you [Ryle]
16. Persons / F. Free Will / 5. Against Free Will
2624 I cannot prepare myself for the next thought I am going to think [Ryle]
17. Mind and Body / A. Mind-Body Dualism / 1. Dualism
2620 Dualism is a category mistake [Ryle]
17. Mind and Body / B. Behaviourism / 2. Potential Behaviour
2388 Behaviour depends on desires as well as beliefs [Chalmers on Ryle]
3354 You can't explain mind as dispositions, if they aren't real [Benardete,JA on Ryle]
17. Mind and Body / B. Behaviourism / 4. Behaviourism Critique
2387 How can behaviour be the cause of behaviour? [Chalmers on Ryle]