Combining Philosophers

All the ideas for Plutarch, Eurytus and John von Neumann

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27 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]
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]
9. Objects / E. Objects over Time / 9. Ship of Theseus
1212 Replacing timbers on Theseus' ship was the classic illustration of the problem of growth and change [Plutarch]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / a. Idealism
5958 The sun is always bright; it doesn't become bright when it emerges [Plutarch]
15. Nature of Minds / A. Nature of Mind / 2. Psuche
5959 Some philosophers say the soul is light [Plutarch]
5960 When the soul is intelligent and harmonious, it is part of god and derives from god [Plutarch]
16. Persons / B. Nature of the Self / 7. Self and Body / c. Self as brain controller
5952 Rather than being the whole soul, maybe I am its chief part? [Plutarch]
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / a. Physicalism critique
5951 If atoms have no qualities, they cannot possibly produce a mind [Plutarch]
18. Thought / A. Modes of Thought / 3. Emotions / f. Emotion and reason
5963 Some say emotion is a sort of reason, and others say virtue concerns emotion [Plutarch]
20. Action / B. Preliminaries of Action / 1. Intention to Act / c. Reducing intentions
20796 Action needs an affinity for a presentation, and an impulse toward the affinity [Plutarch]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
1477 Being manly and brave is the result of convention, not of human nature [Plutarch]
22. Metaethics / C. The Good / 3. Pleasure / e. Role of pleasure
1478 Animals don't value pleasure, as they cease sexual intercourse after impregnation [Plutarch]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
5948 The good life involves social participation, loyalty, temperance and honesty [Plutarch]
25. Social Practice / F. Life Issues / 5. Sexual Morality
1479 Animals have not been led into homosexuality, because they value pleasure very little [Plutarch]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / g. Atomism
5950 If only atoms exist, how do qualities arise when the atoms come together? [Plutarch]
27. Natural Reality / G. Biology / 1. Biology
651 Eurytus showed that numbers underlie things by making pictures of creatures out of pebbles [Eurytus, by Aristotle]
28. God / B. Proving God / 3. Proofs of Evidence / e. Miracles
5974 People report seeing through rocks, or over the horizon, or impossibly small works [Plutarch]
28. God / C. Attitudes to God / 5. Atheism
5957 Absurd superstitions make people atheist, not disharmony in nature [Plutarch]
29. Religion / D. Religious Issues / 1. Religious Commitment / a. Religious Belief
5955 No one will ever find a city that lacks religious practices [Plutarch]