Combining Texts

All the ideas for 'works', 'Works (refs to 8 vol Colli and Montinari)' and 'Investigations in the Foundations of Set Theory I'

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41 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]
2. Reason / A. Nature of Reason / 7. Status of Reason
Reason is just another organic drive, developing late, and fighting for equality [Nietzsche]
2. Reason / D. Definition / 8. Impredicative Definition
Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
We take set theory as given, and retain everything valuable, while avoiding contradictions [Zermelo]
Set theory investigates number, order and function, showing logical foundations for mathematics [Zermelo]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZFC: Existence, Extension, Specification, Pairing, Unions, Powers, Infinity, Choice [Zermelo, by Clegg]
Zermelo published his axioms in 1908, to secure a controversial proof [Zermelo, by Maddy]
Set theory can be reduced to a few definitions and seven independent axioms [Zermelo]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
Zermelo introduced Pairing in 1930, and it seems fairly obvious [Zermelo, by Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / i. Axiom of Foundation VIII
Zermelo used Foundation to block paradox, but then decided that only Separation was needed [Zermelo, by Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / m. Axiom of Separation
Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD]
The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
For Zermelo the successor of n is {n} (rather than n U {n}) [Zermelo, by Maddy]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Zermelo, by Maddy]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR]
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]
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 / C. Virtue Theory / 3. Virtues / a. Virtues
Unlike us, the early Greeks thought envy was a good thing, and hope a bad thing [Hesiod, by Nietzsche]
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]