Combining Philosophers

All the ideas for Anaximenes, Mark Sainsbury and John von Neumann

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22 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 / e. Empty names
10429 It is best to say that a name designates iff there is something for it to designate [Sainsbury]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
10425 Definite descriptions may not be referring expressions, since they can fail to refer [Sainsbury]
10438 Definite descriptions are usually rigid in subject, but not in predicate, position [Sainsbury]
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 / D. Theories of Reality / 10. Vagueness / b. Vagueness of reality
8983 If 'red' is vague, then membership of the set of red things is vague, so there is no set of red things [Sainsbury]
7. Existence / E. Categories / 2. Categorisation
8986 We should abandon classifying by pigeon-holes, and classify around paradigms [Sainsbury]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
8982 Vague concepts are concepts without boundaries [Sainsbury]
8984 If concepts are vague, people avoid boundaries, can't spot them, and don't want them [Sainsbury]
8985 Boundaryless concepts tend to come in pairs, such as child/adult, hot/cold [Sainsbury]
19. Language / B. Reference / 3. Direct Reference / b. Causal reference
10432 A new usage of a name could arise from a mistaken baptism of nothing [Sainsbury]
19. Language / B. Reference / 5. Speaker's Reference
10434 Even a quantifier like 'someone' can be used referentially [Sainsbury]
26. Natural Theory / A. Speculations on Nature / 3. Natural Function
10431 Things are thought to have a function, even when they can't perform them [Sainsbury]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / c. Ultimate substances
1497 For Anaximenes nature is air, which takes different forms by rarefaction and condensation [Anaximenes, by Simplicius]