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All the ideas for 'Structures and Structuralism in Phil of Maths', 'Ethics of the Concern for Self as Freedom' and 'Lectures on the Philosophy of (World) History'

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28 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
Critical philosophy is what questions domination at every level [Foucault]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / e. Philosophy as reason
If we look at the world rationally, the world assumes a rational aspect [Hegel]
1. Philosophy / H. Continental Philosophy / 1. Continental Philosophy
Philosophy and politics are fundamentally linked [Foucault]
2. Reason / A. Nature of Reason / 1. On Reason
The world seems rational to those who look at it rationally [Hegel]
2. Reason / A. Nature of Reason / 2. Logos
When logos controls our desires, we have actually become the logos [Foucault]
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]
13. Knowledge Criteria / E. Relativism / 1. Relativism
Saying games of truth were merely power relations would be a horrible exaggeration [Foucault]
16. Persons / E. Rejecting the Self / 2. Self as Social Construct
A subject is a form which can change, in (say) political or sexual situations [Foucault]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / b. Defining ethics
Ethics is the conscious practice of freedom [Foucault]
24. Political Theory / C. Ruling a State / 1. Social Power
The aim is not to eliminate power relations, but to reduce domination [Foucault]
25. Social Practice / A. Freedoms / 5. Freedom of lifestyle
The idea of liberation suggests there is a human nature which has been repressed [Foucault]