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All the ideas for 'Structures and Structuralism in Phil of Maths', 'Review: Meinong 'Untersuchungen zur..'' and 'Works (refs to 8 vol Colli and Montinari)'

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47 ideas

1. Philosophy / D. Nature of Philosophy / 1. Philosophy
Nietzsche thinks philosophy makes us more profound, but not better [Nietzsche, by Ansell Pearson]
1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
How many mediocre thinkers are occupied with influential problems! [Nietzsche]
1. Philosophy / E. Nature of Metaphysics / 6. Metaphysics as Conceptual
Nietzsche has a metaphysics, as well as perspectives - the ontology is the perspectives [Nietzsche, by Richardson]
1. Philosophy / F. Analytic Philosophy / 6. Logical Analysis
We can't sharply distinguish variables, domains and values, if symbols frighten us [Russell]
2. Reason / A. Nature of Reason / 7. Status of Reason
Reason is just another organic drive, developing late, and fighting for equality [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 / D. Theories of Reality / 5. Naturalism
First see nature as non-human, then fit ourselves into this view of nature [Nietzsche]
8. Modes of Existence / C. Powers and Dispositions / 1. Powers
Storms are wonderful expressions of free powers! [Nietzsche]
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 / A. Existence of Objects / 4. Impossible objects
Common sense agrees with Meinong (rather than Russell) that 'Pegasus is a flying horse' is true [Lackey on Russell]
I prefer to deny round squares, and deal with the difficulties by the theory of denoting [Russell]
9. Objects / D. Essence of Objects / 3. Individual Essences
We begin with concepts of kinds, from individuals; but that is not the essence of individuals [Nietzsche]
20. Action / A. Definition of Action / 1. Action Theory
Nietzsche classified actions by the nature of the agent, not the nature of the act [Nietzsche, by Foot]
20. Action / C. Motives for Action / 4. Responsibility for Actions
Nietzsche failed to see that moral actions can be voluntary without free will [Foot on Nietzsche]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
Each person has a fixed constitution, which makes them a particular type of person [Nietzsche, by Leiter]
Nietzsche could only revalue human values for a different species [Nietzsche, by Foot]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / f. Übermensch
The superman is a monstrous oddity, not a serious idea [MacIntyre on Nietzsche]
Nietzsche's higher type of man is much more important than the idealised 'superman' [Nietzsche, by Leiter]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / g. Will to power
The 'will to power' is basically applied to drives and forces, not to people [Nietzsche, by Richardson]
22. Metaethics / B. Value / 2. Values / g. Love
Friendly chats undermine my philosophy; wanting to be right at the expense of love is folly [Nietzsche]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / c. Particularism
Moral generalisation is wrong, because we should evaluate individual acts [Nietzsche, by Foot]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / d. Virtue theory critique
Nietzsche thought our psychology means there can't be universal human virtues [Nietzsche, by Foot]
23. Ethics / F. Existentialism / 1. Existentialism
Nietzsche tried to lead a thought-provoking life [Safranski on Nietzsche]
23. Ethics / F. Existentialism / 2. Nihilism
Initially nihilism was cosmic, but later Nietzsche saw it as a cultural matter [Nietzsche, by Ansell Pearson]
Nietzsche urges that nihilism be active, and will nothing itself [Nietzsche, by Zizek]
23. Ethics / F. Existentialism / 4. Boredom
Flight from boredom leads to art [Nietzsche]
23. Ethics / F. Existentialism / 7. Existential Action
Nietzsche was fascinated by a will that can turn against itself [Nietzsche, by Safranski]
23. Ethics / F. Existentialism / 8. Eternal Recurrence
Reliving life countless times - this gives the value back to life which religion took away [Nietzsche]
24. Political Theory / B. Nature of a State / 1. Purpose of a State
Individual development is more important than the state, but a community is necessary [Nietzsche]
24. Political Theory / B. Nature of a State / 4. Citizenship
Nietzsche thinks we should join a society, in order to criticise, heal and renew it [Nietzsche, by Richardson]
24. Political Theory / B. Nature of a State / 5. Culture
Every culture loses its identity and power if it lacks a major myth [Nietzsche]