Combining Texts

All the ideas for 'Why coherence is not enough', 'Investigations in the Foundations of Set Theory I' and 'A Conversation: what is it? What is it for?'

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28 ideas

1. Philosophy / C. History of Philosophy / 1. History of Philosophy
21844 The history of philosophy is an agent of power: how can you think if you haven't read the great names? [Deleuze]
1. Philosophy / D. Nature of Philosophy / 1. Philosophy
21849 Thought should be thrown like a stone from a war-machine [Deleuze]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
21845 Philosophy aims to become the official language, supporting orthodoxy and the state [Deleuze]
1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
21839 When I meet objections I just move on; they never contribute anything [Deleuze]
1. Philosophy / H. Continental Philosophy / 1. Continental Philosophy
21841 We must create new words, and treat them as normal, and as if designating real things. [Deleuze]
2. Reason / C. Styles of Reason / 1. Dialectic
21842 Don't assess ideas for truth or justice; look for another idea, and establish a relationship with it [Deleuze]
21850 Dualisms can be undone from within, by tracing connections, and drawing them to a new path [Deleuze]
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]
5. Theory of Logic / L. Paradox / 2. Aporiai
21838 Before we seek solutions, it is important to invent problems [Deleuze]
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 / A. Nature of Existence / 3. Being / i. Deflating being
21847 Before Being there is politics [Deleuze]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / a. Agrippa's trilemma
8840 There are five possible responses to the problem of infinite regress in justification [Cleve]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / a. Foundationalism
8841 Modern foundationalists say basic beliefs are fallible, and coherence is relevant [Cleve]
15. Nature of Minds / A. Nature of Mind / 1. Mind / d. Location of mind
21840 A meeting of man and animal can be deterritorialization (like a wasp with an orchid) [Deleuze]
16. Persons / E. Rejecting the Self / 1. Self as Indeterminate
21843 People consist of many undetermined lines, some rigid, some supple, some 'lines of flight' [Deleuze]
25. Social Practice / A. Freedoms / 2. Freedom of belief
21848 Some lines (of flight) are becomings which escape the system [Deleuze]