Combining Philosophers

All the ideas for John Rawls, John von Neumann and James Van Cleve

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31 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
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
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
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
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
Von Neumann defined ordinals as the set of all smaller ordinals [Neumann, by Poundstone]
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
For Von Neumann the successor of n is n U {n} (rather than {n}) [Neumann, by Maddy]
Von Neumann numbers are preferred, because they continue into the transfinite [Maddy on Neumann]
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
All the axioms for mathematics presuppose set theory [Neumann]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / a. Agrippa's trilemma
There are five possible responses to the problem of infinite regress in justification [Cleve]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / a. Foundationalism
Modern foundationalists say basic beliefs are fallible, and coherence is relevant [Cleve]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
Human injustice is not a permanent feature of communities [Rawls]
22. Metaethics / C. The Good / 1. Goodness / c. Right and good
Rawls defends the priority of right over good [Rawls, by Finlayson]
23. Ethics / B. Contract Ethics / 1. Contractarianism
A fair arrangement is one that parties can agree to without knowing how it will benefit them personally [Rawls, by Williams,B]
23. Ethics / D. Deontological Ethics / 3. Universalisability
Check your rationality by thinking of your opinion pronounced by the supreme court [Rawls]
23. Ethics / E. Utilitarianism / 1. Utilitarianism
Utilitarianism inappropriately scales up the individual willingness to make sacrifices [Rawls, by Nagel]
23. Ethics / E. Utilitarianism / 4. Unfairness
The maximisation of happiness must be done fairly [Rawls, by Smart]
24. Political Theory / A. Basis of a State / 1. A People / c. A unified people
Rawls rejected cosmopolitanism because it doesn't respect the autonomy of 'peoples' [Rawls, by Shorten]
24. Political Theory / A. Basis of a State / 4. Original Position / a. Original position
Why does the rational agreement of the 'Original Position' in Rawls make it right? [Nagel on Rawls]
The original position models the idea that citizens start as free and equal [Rawls, by Swift]
24. Political Theory / A. Basis of a State / 4. Original Position / b. Veil of ignorance
Choose justice principles in ignorance of your own social situation [Rawls]
24. Political Theory / A. Basis of a State / 4. Original Position / c. Difference principle
All desirable social features should be equal, unless inequality favours the disadvantaged [Rawls]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
Power is only legitimate if it is reasonable for free equal citizens to endorse the constitution [Rawls]
24. Political Theory / D. Ideologies / 4. Social Utilitarianism
Utilitarians lump persons together; Rawls somewhat separates them; Nozick wholly separates them [Swift on Rawls]
24. Political Theory / D. Ideologies / 6. Liberalism / g. Liberalism critique
Rawls's account of justice relies on conventional fairness, avoiding all moral controversy [Gray on Rawls]
24. Political Theory / D. Ideologies / 7. Communitarianism / b. Against communitarianism
In a pluralist society we can't expect a community united around one conception of the good [Rawls]
25. Social Practice / A. Freedoms / 5. Freedom of lifestyle
Liberty Principle: everyone has an equal right to liberties, if compatible with others' liberties [Rawls]
25. Social Practice / D. Justice / 1. Basis of justice
The social contract has problems with future generations, national boundaries, disabilities and animals [Rawls, by Nussbaum]
Justice concerns not natural distributions, or our born location, but what we do about them [Rawls]
25. Social Practice / E. Policies / 1. War / b. Justice in war
If an aggression is unjust, the constraints on how it is fought are much stricter [Rawls]