Combining Texts

All the ideas for 'Truth', 'Investigations in the Foundations of Set Theory I' and 'Approaches to Intentionality'

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25 ideas

1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
10838 To explain a concept, we need its purpose, not just its rules of usage [Dummett]
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]
3. Truth / A. Truth Problems / 1. Truth
10837 It is part of the concept of truth that we aim at making true statements [Dummett]
3. Truth / A. Truth Problems / 2. Defining Truth
10840 We must be able to specify truths in a precise language, like winning moves in a game [Dummett]
3. Truth / F. Semantic Truth / 2. Semantic Truth
19171 Tarski's truth is like rules for winning games, without saying what 'winning' means [Dummett, by Davidson]
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]
11. Knowledge Aims / A. Knowledge / 4. Belief / a. Beliefs
2986 Belief is the most important propositional attitude [Lyons]
15. Nature of Minds / B. Features of Minds / 4. Intentionality / b. Intentionality theories
2978 Consciousness no longer seems essential to intentionality [Lyons]
17. Mind and Body / E. Mind as Physical / 4. Connectionism
2984 Perceptions could give us information without symbolic representation [Lyons]
18. Thought / A. Modes of Thought / 2. Propositional Attitudes
2979 Propositional attitudes require representation [Lyons]
18. Thought / A. Modes of Thought / 4. Folk Psychology
2987 Folk psychology works badly for alien cultures [Lyons]
18. Thought / C. Content / 1. Content
2977 All thinking has content [Lyons]
18. Thought / E. Abstraction / 1. Abstract Thought
10839 You can't infer a dog's abstract concepts from its behaviour [Dummett]