Combining Philosophers

All the ideas for Hermarchus, Michael Smith and John von Neumann

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31 ideas

1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
23728 Analysis aims to express the full set of platitudes surrounding a given concept [Smith,M]
2. Reason / D. Definition / 1. Definitions
23744 Defining a set of things by paradigms doesn't pin them down enough [Smith,M]
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
12336 A von Neumann ordinal is a transitive set with transitive elements [Neumann, by Badiou]
22716 Von Neumann defined ordinals as the set of all smaller ordinals [Neumann, by Poundstone]
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]
18. Thought / A. Modes of Thought / 5. Rationality / a. Rationality
23743 Capturing all the common sense facts about rationality is almost impossible [Smith,M]
20. Action / C. Motives for Action / 1. Acting on Desires
23723 In the Humean account, desires are not true/false, or subject to any rational criticism [Smith,M]
23735 Subjects may be fallible about the desires which explain their actions [Smith,M]
23736 A person can have a desire without feeling it [Smith,M]
23739 Goals need desires, and so only desires can motivate us [Smith,M]
23738 Humeans (unlike their opponents) say that desires and judgements can separate [Smith,M]
23742 If first- and second-order desires conflict, harmony does not require the second-order to win [Smith,M]
23746 Objective reasons to act might be the systematic desires of a fully rational person [Smith,M]
23724 A pure desire could be criticised if it were based on a false belief [Smith,M]
20. Action / C. Motives for Action / 3. Acting on Reason / a. Practical reason
23733 Motivating reasons are psychological, while normative reasons are external [Smith,M]
23740 Humeans take maximising desire satisfaction as the normative reasons for actions [Smith,M]
23745 We cannot expect even fully rational people to converge on having the same desires for action [Smith,M]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / h. Against ethics
23731 'Externalists' say moral judgements are not reasons, and maybe not even motives [Smith,M]
23732 A person could make a moral judgement without being in any way motivated by it [Smith,M]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / b. Rational ethics
23729 Moral internalism says a judgement of rightness is thereby motivating [Smith,M]
23730 'Rationalism' says the rightness of an action is a reason to perform it [Smith,M]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / h. Expressivism
23727 Expressivists count attitudes as 'moral' if they concern features of things, rather than their mere existence [Smith,M]
22. Metaethics / B. Value / 1. Nature of Value / a. Nature of value
23741 Is valuing something a matter of believing or a matter of desiring? [Smith,M]
25. Social Practice / F. Life Issues / 6. Animal Rights
6005 Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley]