Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'Investigations in the Foundations of Set Theory I' and 'A Theory of Justice'

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29 ideas

2. Reason / D. Definition / 8. Impredicative Definition
Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
We take set theory as given, and retain everything valuable, while avoiding contradictions [Zermelo]
Set theory investigates number, order and function, showing logical foundations for mathematics [Zermelo]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZFC: Existence, Extension, Specification, Pairing, Unions, Powers, Infinity, Choice [Zermelo, by Clegg]
Zermelo published his axioms in 1908, to secure a controversial proof [Zermelo, by Maddy]
Set theory can be reduced to a few definitions and seven independent axioms [Zermelo]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
Zermelo introduced Pairing in 1930, and it seems fairly obvious [Zermelo, by Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / i. Axiom of Foundation VIII
Zermelo used Foundation to block paradox, but then decided that only Separation was needed [Zermelo, by Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / m. Axiom of Separation
Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD]
The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
For Zermelo the successor of n is {n} (rather than n U {n}) [Zermelo, by Maddy]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Zermelo, by Maddy]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR]
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 / C. Virtue Theory / 3. Virtues / a. Virtues
The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
23. Ethics / E. Utilitarianism / 1. Utilitarianism
Utilitarianism inappropriately scales up the individual willingness to make sacrifices [Rawls, by Nagel]
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 / 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]
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]