Combining Philosophers

All the ideas for Richard Cumberland, John von Neumann and Karen Armstrong

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22 ideas

2. Reason / A. Nature of Reason / 7. Status of Reason
6222 If a decision is in accord with right reason, everyone can agree with it [Cumberland]
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]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / d. Biological ethics
6217 Natural law is supplied to the human mind by reality and human nature [Cumberland]
22. Metaethics / B. Value / 1. Nature of Value / f. Ultimate value
6221 If there are different ultimate goods, there will be conflicting good actions, which is impossible [Cumberland]
23. Ethics / E. Utilitarianism / 1. Utilitarianism
6218 The happiness of individuals is linked to the happiness of everyone (which is individuals taken together) [Cumberland]
6220 The happiness of all contains the happiness of each, and promotes it [Cumberland]
25. Social Practice / D. Justice / 2. The Law / c. Natural law
6216 Natural law is immutable truth giving moral truths and duties independent of society [Cumberland]
28. God / A. Divine Nature / 4. Divine Contradictions
7602 In the Bible God changes his mind (repenting of creating humanity, in the Flood) [Armstrong,K]
28. God / C. Attitudes to God / 1. Monotheism
7605 Monotheism introduced intolerance into religious thinking [Armstrong,K]
29. Religion / A. Polytheistic Religion / 3. Hinduism
7599 Around 800 BCE teachers superseded gods in India [Armstrong,K]
29. Religion / B. Monotheistic Religion / 2. Judaism
7597 There is virtually no sign of monotheism in the Pentateuch [Armstrong,K]
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
7606 The idea that Jesus was God was only settled in the fourth century [Armstrong,K]
29. Religion / D. Religious Issues / 1. Religious Commitment / e. Fideism
7596 Faith is not just belief in propositions, but also putting trust in them [Armstrong,K]