Combining Philosophers

All the ideas for Speussipus, Jan Westerhoff and John von Neumann

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26 ideas

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]
5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
13134 We negate predicates but do not negate names [Westerhoff]
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]
7. Existence / E. Categories / 1. Categories
13117 How far down before we are too specialised to have a category? [Westerhoff]
13116 Maybe objects in the same category have the same criteria of identity [Westerhoff]
13118 Categories are base-sets which are used to construct states of affairs [Westerhoff]
13125 Categories are held to explain why some substitutions give falsehood, and others meaninglessness [Westerhoff]
13126 Categories systematize our intuitions about generality, substitutability, and identity [Westerhoff]
13130 Categories as generalities don't give a criterion for a low-level cut-off point [Westerhoff]
13124 Categories can be ordered by both containment and generality [Westerhoff]
7. Existence / E. Categories / 2. Categorisation
13131 The aim is that everything should belong in some ontological category or other [Westerhoff]
7. Existence / E. Categories / 3. Proposed Categories
13123 All systems have properties and relations, and most have individuals, abstracta, sets and events [Westerhoff]
7. Existence / E. Categories / 5. Category Anti-Realism
13115 Ontological categories are like formal axioms, not unique and with necessary membership [Westerhoff]
13119 Categories merely systematise, and are not intrinsic to objects [Westerhoff]
13135 A thing's ontological category depends on what else exists, so it is contingent [Westerhoff]
9. Objects / B. Unity of Objects / 2. Substance / c. Types of substance
594 Speusippus suggested underlying principles for every substance, and ended with a huge list [Speussipus, by Aristotle]
9. Objects / D. Essence of Objects / 5. Essence as Kind
13129 Essential kinds may be too specific to provide ontological categories [Westerhoff]
28. God / C. Attitudes to God / 5. Atheism
2632 Speusippus said things were governed by some animal force rather than the gods [Speussipus, by Cicero]