Combining Texts

All the ideas for 'Essays on Intellectual Powers: Conception', 'Investigations in the Foundations of Set Theory I' and 'The Ultimate Constituents of Matter'

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27 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]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
7548 Classes, grouped by a convenient property, are logical constructions [Russell]
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 / 4. Anti-realism
7545 Visible things are physical and external, but only exist when viewed [Russell]
9. Objects / D. Essence of Objects / 4. Essence as Definition
23647 Objects have an essential constitution, producing its qualities, which we are too ignorant to define [Reid]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / b. Conceivable but impossible
11958 Impossibilites are easily conceived in mathematics and geometry [Reid, by Molnar]
12. Knowledge Sources / B. Perception / 4. Sense Data / b. Nature of sense-data
7549 If my body literally lost its mind, the object seen when I see a flash would still exist [Russell]
7553 Sense-data are purely physical [Russell]
16. Persons / D. Continuity of the Self / 2. Mental Continuity / b. Self as mental continuity
7546 A man is a succession of momentary men, bound by continuity and causation [Russell]
17. Mind and Body / E. Mind as Physical / 2. Reduction of Mind
7550 We could probably, in principle, infer minds from brains, and brains from minds [Russell]
19. Language / B. Reference / 1. Reference theories
23646 Reference is by name, or a term-plus-circumstance, or ostensively, or by description [Reid]
19. Language / B. Reference / 3. Direct Reference / c. Social reference
23645 A word's meaning is the thing conceived, as fixed by linguistic experts [Reid]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
7551 Matter is a logical construction [Russell]
7547 Matter requires a division into time-corpuscles as well as space-corpuscles [Russell]
27. Natural Reality / C. Space / 2. Space
7552 Six dimensions are needed for a particular, three within its own space, and three to locate that space [Russell]