Combining Philosophers

All the ideas for Diogenes Laertius, Douglas Edwards and John von Neumann

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21 ideas

2. Reason / C. Styles of Reason / 1. Dialectic
3035 Dialectic involves conversations with short questions and brief answers [Diog. Laertius]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
3340 Von Neumann defines each number as the set of all smaller numbers [Neumann, by Blackburn]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
15943 Limitation of Size is not self-evident, and seems too strong [Lavine on Neumann]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
3355 Von Neumann wanted mathematical functions to replace sets [Neumann, by Benardete,JA]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
13489 Von Neumann treated cardinals as a special sort of ordinal [Neumann, by Hart,WD]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
22716 Von Neumann defined ordinals as the set of all smaller ordinals [Neumann, by Poundstone]
12336 A von Neumann ordinal is a transitive set with transitive elements [Neumann, by Badiou]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / g. Von Neumann numbers
18179 For Von Neumann the successor of n is n U {n} (rather than {n}) [Neumann, by Maddy]
18180 Von Neumann numbers are preferred, because they continue into the transfinite [Maddy on Neumann]
15925 Each Von Neumann ordinal number is the set of its predecessors [Neumann, by Lavine]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
13672 All the axioms for mathematics presuppose set theory [Neumann]
8. Modes of Existence / B. Properties / 2. Need for Properties
18430 We accept properties because of type/tokens, reference, and quantification [Edwards]
8. Modes of Existence / B. Properties / 10. Properties as Predicates
18432 Quineans say that predication is primitive and inexplicable [Edwards]
8. Modes of Existence / E. Nominalism / 2. Resemblance Nominalism
18437 Resemblance nominalism requires a second entity to explain 'the rose is crimson' [Edwards]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
18434 That a whole is prior to its parts ('priority monism') is a view gaining in support [Edwards]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / a. Agrippa's trilemma
1816 Sceptics say demonstration depends on self-demonstrating things, or indemonstrable things [Diog. Laertius]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
1819 Scepticism has two dogmas: that nothing is definable, and every argument has an opposite argument [Diog. Laertius]
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
3064 When sceptics say that nothing is definable, or all arguments have an opposite, they are being dogmatic [Diog. Laertius]
14. Science / C. Induction / 4. Reason in Induction
3033 Induction moves from some truths to similar ones, by contraries or consequents [Diog. Laertius]
22. Metaethics / C. The Good / 3. Pleasure / b. Types of pleasure
1838 Cyrenaic pleasure is a motion, but Epicurean pleasure is a condition [Diog. Laertius]
23. Ethics / A. Egoism / 1. Ethical Egoism
1769 Cynics believe that when a man wishes for nothing he is like the gods [Diog. Laertius]