Combining Texts

All the ideas for 'Investigations in the Foundations of Set Theory I', 'Propositional Objects' and 'Letters'

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22 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]
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 / e. Belief holism
18969 How do you distinguish three beliefs from four beliefs or two beliefs? [Quine]
19. Language / D. Propositions / 2. Abstract Propositions / a. Propositions as sense
18967 A 'proposition' is said to be the timeless cognitive part of the meaning of a sentence [Quine]
19. Language / D. Propositions / 6. Propositions Critique
18968 The problem with propositions is their individuation. When do two sentences express one proposition? [Quine]
22. Metaethics / B. Value / 1. Nature of Value / b. Fact and value
4581 Virtues and vices are like secondary qualities in perception, found in observers, not objects [Hume]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
4580 All virtues benefit either the public, or the individual who possesses them [Hume]
26. Natural Theory / C. Causation / 3. Final causes
4579 The idea of a final cause is very uncertain and unphilosophical [Hume]
26. Natural Theory / C. Causation / 9. General Causation / d. Causal necessity
20705 That events could be uncaused is absurd; I only say intuition and demonstration don't show this [Hume]
27. Natural Reality / C. Space / 3. Points in Space
18970 The concept of a 'point' makes no sense without the idea of absolute position [Quine]