Combining Texts

All the ideas for 'A Short History of Ethics', 'Difference and Repetition' and 'Structures and Structuralism in Phil of Maths'

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34 ideas

1. Philosophy / B. History of Ideas / 4. Early European Thought
In the Reformation, morality became unconditional but irrational, individually autonomous, and secular [MacIntyre]
1. Philosophy / B. History of Ideas / 5. Later European Thought
The Levellers and the Diggers mark a turning point in the history of morality [MacIntyre]
1. Philosophy / H. Continental Philosophy / 1. Continental Philosophy
'Difference' refers to that which eludes capture [Deleuze, by May]
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]
7. Existence / A. Nature of Existence / 3. Being / a. Nature of Being
Ontology can be continual creation, not to know being, but to probe the unknowable [Deleuze]
'Being' is univocal, but its subject matter is actually 'difference' [Deleuze]
7. Existence / A. Nature of Existence / 3. Being / i. Deflating being
Ontology does not tell what there is; it is just a strange adventure [Deleuze, by May]
Being is a problem to be engaged, not solved, and needs a new mode of thinking [Deleuze, by May]
8. Modes of Existence / E. Nominalism / 6. Mereological Nominalism
A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price]
15. Nature of Minds / A. Nature of Mind / 2. Psuche
When Aristotle speaks of soul he means something like personality [MacIntyre]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
Sophists don't distinguish a person outside one social order from someone outside all order [MacIntyre]
22. Metaethics / B. Value / 1. Nature of Value / b. Fact and value
The value/fact logical gulf is misleading, because social facts involve values [MacIntyre]
22. Metaethics / C. The Good / 2. Happiness / b. Eudaimonia
'Happiness' is a bad translation of 'eudaimonia', which includes both behaving and faring well [MacIntyre]
23. Ethics / C. Virtue Theory / 3. Virtues / c. Justice
'Dikaiosune' is justice, but also fairness and personal integrity [MacIntyre]
23. Ethics / D. Deontological Ethics / 2. Duty
My duties depend on my identity, which depends on my social relations [MacIntyre]
24. Political Theory / A. Basis of a State / 3. Natural Values / a. Natural freedom
I am naturally free if I am not tied to anyone by a contract [MacIntyre]
25. Social Practice / C. Rights / 1. Basis of Rights
Fans of natural rights or laws can't agree on what the actual rights or laws are [MacIntyre]
29. Religion / B. Monotheistic Religion / 5. Bible
The Bible is a story about God in which humans are incidental characters [MacIntyre]