Combining Texts

All the ideas for 'fragments/reports', 'Interview with Baggini and Stangroom' and 'Investigations in the Foundations of Set Theory I'

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26 ideas

1. Philosophy / D. Nature of Philosophy / 8. Humour
6847 Humour can give a phenomenological account of existence, and point to change [Critchley]
6848 Humour is practically enacted philosophy [Critchley]
1. Philosophy / G. Scientific Philosophy / 3. Scientism
6844 Scientism is the view that everything can be explained causally through scientific method [Critchley]
1. Philosophy / H. Continental Philosophy / 1. Continental Philosophy
6835 German idealism aimed to find a unifying principle for Kant's various dualisms [Critchley]
6837 Since Hegel, continental philosophy has been linked with social and historical enquiry. [Critchley]
6836 Continental philosophy fights the threatened nihilism in the critique of reason [Critchley]
6838 Continental philosophy is based on critique, praxis and emancipation [Critchley]
6845 Continental philosophy has a bad tendency to offer 'one big thing' to explain everything [Critchley]
1. Philosophy / H. Continental Philosophy / 2. Phenomenology
6846 Phenomenology is a technique of redescription which clarifies our social world [Critchley]
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]
23. Ethics / F. Existentialism / 2. Nihilism
6843 Perceiving meaninglessness is an achievement, which can transform daily life [Critchley]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
1748 Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / G. Biology / 3. Evolution
5989 Archelaus said life began in a primeval slime [Archelaus, by Schofield]