Combining Texts

All the ideas for 'works', 'Philosophy of Language' and 'Investigations in the Foundations of Set Theory I'

expand these ideas     |    start again     |     specify just one area for these texts

25 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]
5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
7306 If the only property of a name was its reference, we couldn't explain bearerless names [Miller,A]
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]
13. Knowledge Criteria / D. Scepticism / 2. Types of Scepticism
7322 Constitutive scepticism is about facts, and epistemological scepticism about our ability to know them [Miller,A]
17. Mind and Body / B. Behaviourism / 2. Potential Behaviour
7325 Dispositions say what we will do, not what we ought to do, so can't explain normativity [Miller,A]
19. Language / A. Nature of Meaning / 1. Meaning
7324 Explain meaning by propositional attitudes, or vice versa, or together? [Miller,A]
19. Language / C. Assigning Meanings / 6. Truth-Conditions Semantics
7323 If truth is deflationary, sentence truth-conditions just need good declarative syntax [Miller,A]
19. Language / E. Analyticity / 2. Analytic Truths
7315 'Jones is a married bachelor' does not have the logical form of a contradiction [Miller,A]
19. Language / F. Communication / 6. Interpreting Language / c. Principle of charity
7328 The principle of charity is holistic, saying we must hold most of someone's system of beliefs to be true [Miller,A]
7329 Maybe we should interpret speakers as intelligible, rather than speaking truth [Miller,A]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / h. Expressivism
7333 The Frege-Geach problem is that I can discuss the wrongness of murder without disapproval [Miller,A]
29. Religion / B. Monotheistic Religion / 4. Christianity / d. Heresy
16713 Philosophers are the forefathers of heretics [Tertullian]
29. Religion / D. Religious Issues / 1. Religious Commitment / e. Fideism
6610 I believe because it is absurd [Tertullian]