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All the ideas for 'Structures and Structuralism in Phil of Maths', 'The Essential Child' and 'Beyond Good and Evil'

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86 ideas

1. Philosophy / D. Nature of Philosophy / 1. Philosophy
Great philosophies are confessions by the author, growing out of moral intentions [Nietzsche]
1. Philosophy / E. Nature of Metaphysics / 2. Possibility of Metaphysics
Metaphysics divided the old unified Greek world into two [Nietzsche, by Critchley]
3. Truth / A. Truth Problems / 3. Value of Truth
Why do we want truth, rather than falsehood or ignorance? The value of truth is a problem [Nietzsche]
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 / c. Becoming
Nietzsche resists nihilism through new values, for a world of becoming, without worship [Nietzsche, by Critchley]
7. Existence / E. Categories / 2. Categorisation
Even fairly simple animals make judgements based on categories [Gelman]
Children accept real stable categories, with nonobvious potential that gives causal explanations [Gelman]
8. Modes of Existence / E. Nominalism / 6. Mereological Nominalism
A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price]
9. Objects / D. Essence of Objects / 1. Essences of Objects
In India, upper-castes essentialize caste more than lower-castes do [Gelman]
Essentialism is either natural to us, or an accident of our culture, or a necessary result of language [Gelman]
Children's concepts include nonobvious features, like internal parts, functions and causes [Gelman]
9. Objects / D. Essence of Objects / 2. Types of Essence
Essentialism: real or representational? sortal, causal or ideal? real particulars, or placeholders? [Gelman]
9. Objects / D. Essence of Objects / 5. Essence as Kind
Essentialism says categories have a true hidden nature which gives an object its identity [Gelman]
Sortals are needed for determining essence - the thing must be categorised first [Gelman]
Kind (unlike individual) essentialism assumes preexisting natural categories [Gelman]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / c. Essentials are necessary
Kinship is essence that comes in degrees, and age groups are essences that change over time [Gelman]
9. Objects / D. Essence of Objects / 14. Knowledge of Essences
Essentialism comes from the cognitive need to categorise [Gelman]
We found no evidence that mothers teach essentialism to their children [Gelman]
9. Objects / D. Essence of Objects / 15. Against Essentialism
Essentialism is useful for predictions, but it is not the actual structure of reality [Gelman]
9. Objects / E. Objects over Time / 12. Origin as Essential
Peope favor historical paths over outward properties when determining what something is [Gelman]
11. Knowledge Aims / A. Knowledge / 2. Understanding
There is intentional, mechanical, teleological, essentialist, vitalist and deontological understanding [Gelman]
12. Knowledge Sources / B. Perception / 5. Interpretation
We see an approximation of a tree, not the full detail [Nietzsche]
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
Memories often conform to a theory, rather than being neutral [Gelman]
13. Knowledge Criteria / B. Internal Justification / 2. Pragmatic justification
We shouldn't object to a false judgement, if it enhances and preserves life [Nietzsche]
13. Knowledge Criteria / E. Relativism / 4. Cultural relativism
Morality becomes a problem when we compare many moralities [Nietzsche]
14. Science / C. Induction / 1. Induction
Inductive success is rewarded with more induction [Gelman]
14. Science / C. Induction / 3. Limits of Induction
Children overestimate the power of a single example [Gelman]
Children make errors in induction by focusing too much on categories [Gelman]
14. Science / D. Explanation / 1. Explanation / a. Explanation
People tend to be satisfied with shallow explanations [Gelman]
15. Nature of Minds / C. Capacities of Minds / 10. Conatus/Striving
The ranking of a person's innermost drives reveals their true nature [Nietzsche]
16. Persons / F. Free Will / 5. Against Free Will
Wanting 'freedom of will' is wanting to pull oneself into existence out of the swamp of nothingness by one's own hair [Nietzsche]
A thought comes when 'it' wants, not when 'I' want [Nietzsche]
18. Thought / A. Modes of Thought / 4. Folk Psychology
Folk essentialism rests on belief in natural kinds, in hidden properties, and on words indicating structures [Gelman]
18. Thought / B. Mechanics of Thought / 1. Psychology
It is psychology which reveals the basic problems [Nietzsche]
18. Thought / D. Concepts / 3. Ontology of Concepts / a. Concepts as representations
Labels may indicate categories which embody an essence [Gelman]
18. Thought / D. Concepts / 4. Structure of Concepts / a. Conceptual structure
Causal properties are seen as more central to category concepts [Gelman]
18. Thought / D. Concepts / 4. Structure of Concepts / d. Concepts as prototypes
Categories are characterized by distance from a prototype [Gelman]
18. Thought / D. Concepts / 4. Structure of Concepts / f. Theory theory of concepts
Theory-based concepts use rich models to show which similarities really matter [Gelman]
18. Thought / D. Concepts / 5. Concepts and Language / c. Concepts without language
Prelinguistic infants acquire and use many categories [Gelman]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / a. Idealistic ethics
The most boring and dangerous of all errors is Plato's invention of pure spirit and goodness [Nietzsche]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / d. Biological ethics
Nietzsche felt that Plato's views downgraded the human body and its brevity of life [Nietzsche, by Roochnik]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / f. Übermensch
Noble people see themselves as the determiners of values [Nietzsche]
Nietzsche's judgement of actions by psychology instead of outcome was poisonous [Foot on Nietzsche]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
That which is done out of love always takes place beyond good and evil [Nietzsche]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / k. Ethics from nature
Nature is totally indifferent, so you should try to be different from it, not live by it [Nietzsche]
22. Metaethics / C. The Good / 1. Goodness / c. Right and good
Morality originally judged people, and actions only later on [Nietzsche]
22. Metaethics / C. The Good / 1. Goodness / g. Consequentialism
In the earliest phase of human history only consequences mattered [Nietzsche]
23. Ethics / A. Egoism / 1. Ethical Egoism
The noble soul has reverence for itself [Nietzsche]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / c. Particularism
Moralities extravagantly address themselves to 'all', by falsely generalising [Nietzsche]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / d. Virtue theory critique
Virtue has been greatly harmed by the boringness of its advocates [Nietzsche]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
The four virtues are courage, insight, sympathy, solitude [Nietzsche]
23. Ethics / C. Virtue Theory / 3. Virtues / f. Compassion
In ancient Rome pity was considered neither good nor bad [Nietzsche]
23. Ethics / D. Deontological Ethics / 4. Categorical Imperative
The idea of the categorical imperative is just that we should all be very obedient [Nietzsche]
23. Ethics / E. Utilitarianism / 3. Motivation for Altruism
The morality of slaves is the morality of utility [Nietzsche]
23. Ethics / F. Existentialism / 1. Existentialism
The greatest possibilities in man are still unexhausted [Nietzsche]
23. Ethics / F. Existentialism / 3. Angst
The thought of suicide is a great reassurance on bad nights [Nietzsche]
The freedom of the subject means the collapse of moral certainty [Nietzsche, by Critchley]
23. Ethics / F. Existentialism / 6. Authentic Self
Man is the animal whose nature has not yet been fixed [Nietzsche]
Nietzsche thinks the human condition is to overcome and remake itself [Nietzsche, by Ansell Pearson]
23. Ethics / F. Existentialism / 8. Eternal Recurrence
The great person engages wholly with life, and is happy to endlessly relive the life they created [Nietzsche]
24. Political Theory / C. Ruling a State / 2. Leaders / d. Elites
Only aristocratic societies can elevate the human species [Nietzsche]
A healthy aristocracy has no qualms about using multitudes of men as instruments [Nietzsche]
24. Political Theory / D. Ideologies / 5. Democracy / f. Against democracy
Democracy diminishes mankind, making them mediocre and lowering their value [Nietzsche]
26. Natural Theory / B. Natural Kinds / 3. Knowing Kinds
One sample of gold is enough, but one tree doesn't give the height of trees [Gelman]
26. Natural Theory / B. Natural Kinds / 5. Reference to Natural Kinds
Nouns seem to invoke stable kinds more than predicates do [Gelman]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism
Essentialism doesn't mean we know the essences [Gelman]
Essentialism encourages us to think about the world scientifically [Gelman]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / d. Knowing essences
Essentialism starts from richly structured categories, leading to a search for underlying properties [Gelman]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / e. Anti scientific essentialism
A major objection to real essences is the essentialising of social categories like race, caste and occupation [Gelman]
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
Christianity is Platonism for the people [Nietzsche]