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All the ideas for 'Structures and Structuralism in Phil of Maths', 'Buddhacarita' and 'Justice: What's the right thing to do?'

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40 ideas

3. Truth / A. Truth Problems / 3. Value of Truth
Speak truth only to those who deserve the truth [Sandel]
Careful evasions of truth at least show respect for it [Sandel]
3. Truth / F. Semantic Truth / 2. Semantic Truth
While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
'Analysis' is the theory of the real numbers [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
Mereological arithmetic needs infinite objects, and function definitions [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Set-theory gives a unified and an explicit basis for mathematics [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism
Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price]
There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price]
Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price]
There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price]
Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price]
Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price]
8. Modes of Existence / E. Nominalism / 6. Mereological Nominalism
A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price]
16. Persons / E. Rejecting the Self / 4. Denial of the Self
When the Buddha reached the highest level of insight, he could detect no self in the world [Ashvaghosha]
23. Ethics / B. Contract Ethics / 1. Contractarianism
Not all deals are fair deals [Sandel]
Does consent create the obligation, or must there be some benefit? [Sandel]
Moral contracts involve both consent and reciprocity; making the deal, and keeping it [Sandel]
23. Ethics / B. Contract Ethics / 2. Golden Rule
The categorical imperative is not the Golden Rule, which concerns contingent desires [Sandel]
23. Ethics / D. Deontological Ethics / 5. Persons as Ends
Man cannot dispose of himself, because he is not a thing to be owned [Sandel]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
Just visiting (and using roads) is hardly ratifying the Constitution [Sandel]
24. Political Theory / B. Nature of a State / 3. Constitutions
A ratified constitution may not be a just constitution [Sandel]
A just constitution harmonises the different freedoms [Sandel]
24. Political Theory / D. Ideologies / 6. Liberalism / d. Liberal freedom
Liberal freedom was a response to assigned destinies like caste and class [Sandel]
25. Social Practice / B. Equalities / 4. Economic equality
Libertarians just want formal equality in a free market; the meritocratic view wants fair equality [Sandel]
25. Social Practice / D. Justice / 1. Basis of justice
We can approach justice through welfare, or freedom, or virtue [Sandel]
Justice concerns how a society distributes what it prizes - wealth, rights, power and honours [Sandel]
Should we redress wrongs done by a previous generation? [Sandel]
Distributive justice concern deserts, as well as who gets what [Sandel]
Justice is about how we value things, and not just about distributions [Sandel]
Work is not fair if it is negotiated, even in a fair situation, but if it suits the nature of the worker [Sandel]
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / b. Limited purposes
Teleological thinking is essential for social and political issues [Sandel]
29. Religion / C. Spiritual Disciplines / 3. Buddhism
The first stage of trance is calm amidst applied and discursive thinking [Ashvaghosha]
The Buddha sought ultimate reality and the final goal of existence in his meditations [Ashvaghosha]