Combining Texts

All the ideas for 'Investigations in the Foundations of Set Theory I', 'Introduction to 'Causation'' and 'Why there isn't a ready-made world'

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
13486 Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD]
13020 The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy]
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 / D. Theories of Reality / 2. Realism
17644 Metaphysical realism is committed to there being one ultimate true theory [Putnam]
7. Existence / D. Theories of Reality / 4. Anti-realism
17648 It is an illusion to think there could be one good scientific theory of reality [Putnam]
9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
17643 Shape is essential relative to 'statue', but not essential relative to 'clay' [Putnam]
12. Knowledge Sources / B. Perception / 4. Sense Data / b. Nature of sense-data
17642 The old view that sense data are independent of mind is quite dotty [Putnam]
15. Nature of Minds / C. Capacities of Minds / 9. Perceiving Causation
8329 Either causal relations are given in experience, or they are unobserved and theoretical [Sosa/Tooley]
26. Natural Theory / C. Causation / 1. Causation
8324 The problem is to explain how causal laws and relations connect, and how they link to the world [Sosa/Tooley]
26. Natural Theory / C. Causation / 4. Naturalised causation
8328 Causation isn't energy transfer, because an electron is caused by previous temporal parts [Sosa/Tooley]
8327 If direction of causation is just direction of energy transfer, that seems to involve causation [Sosa/Tooley]
26. Natural Theory / C. Causation / 8. Particular Causation / c. Conditions of causation
8330 Are causes sufficient for the event, or necessary, or both? [Sosa/Tooley]
26. Natural Theory / C. Causation / 8. Particular Causation / d. Selecting the cause
17645 An alien might think oxygen was the main cause of a forest fire [Putnam]
26. Natural Theory / C. Causation / 9. General Causation / b. Nomological causation
8325 The dominant view is that causal laws are prior; a minority say causes can be explained singly [Sosa/Tooley]