Combining Texts

All the ideas for 'Investigations in the Foundations of Set Theory I', 'The Theory of Communicative Action' and 'Our Knowledge of Mathematical Objects'

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26 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
20962 Habermas seems to make philosophy more democratic [Habermas, by Bowie]
1. Philosophy / E. Nature of Metaphysics / 4. Metaphysics as Science
15670 The aim of 'post-metaphysical' philosophy is to interpret the sciences [Habermas, by Finlayson]
1. Philosophy / H. Continental Philosophy / 5. Critical Theory
15665 We can do social philosophy by studying coordinated action through language use [Habermas, by Finlayson]
2. Reason / A. Nature of Reason / 4. Aims of Reason
20573 Rather than instrumental reason, Habermas emphasises its communicative role [Habermas, by Oksala]
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]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
9224 Proceduralism offers a version of logicism with no axioms, or objects, or ontological commitment [Fine,K]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
9222 The objects and truths of mathematics are imperative procedures for their construction [Fine,K]
9223 My Proceduralism has one simple rule, and four complex rules [Fine,K]
12. Knowledge Sources / A. A Priori Knowledge / 11. Denying the A Priori
20961 What is considered a priori changes as language changes [Habermas, by Bowie]
19. Language / A. Nature of Meaning / 1. Meaning
15667 To understand a statement is to know what would make it acceptable [Habermas]
19. Language / A. Nature of Meaning / 3. Meaning as Speaker's Intention
15668 Meaning is not fixed by a relation to the external world, but a relation to other speakers [Habermas, by Finlayson]
24. Political Theory / D. Ideologies / 6. Liberalism / a. Liberalism basics
15669 People endorse equality, universality and inclusiveness, just by their communicative practices [Habermas, by Finlayson]
25. Social Practice / B. Equalities / 2. Political equality
23416 Political involvement is needed, to challenge existing practices [Habermas, by Kymlicka]