Combining Texts

All the ideas for 'Investigations in the Foundations of Set Theory I', 'Tractatus de corpore Christi' and 'Straw Dogs'

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23 ideas

1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
9271 Human knowledge may not produce well-being; the examined life may not be worth living [Gray]
2. Reason / B. Laws of Thought / 6. Ockham's Razor
16676 Why use more things when fewer will do? [William of Ockham]
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]
13. Knowledge Criteria / C. External Justification / 9. Naturalised Epistemology
9275 Knowledge does not need minds or nervous systems; it is found in all living things [Gray]
16. Persons / F. Free Will / 5. Against Free Will
9276 The will hardly ever does anything; most of our life just happens to us [Gray]
25. Social Practice / A. Freedoms / 5. Freedom of lifestyle
9278 Nowadays we identify the free life with the good life [Gray]
26. Natural Theory / A. Speculations on Nature / 7. Later Matter Theories / b. Corpuscles
16675 Every extended material substance is composed of parts distant from one another [William of Ockham]
27. Natural Reality / G. Biology / 4. Ecology
9280 Over forty percent of the Earth's living tissue is human [Gray]
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
9272 Without Christianity we lose the idea that human history has a meaning [Gray]
9279 What was our original sin, and how could Christ's suffering redeem it? [Gray]