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All the ideas for 'Structures and Structuralism in Phil of Maths', 'Model Theory for Modal Logic I' and 'Thus Spake Zarathustra'

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42 ideas

1. Philosophy / A. Wisdom / 3. Wisdom Deflated
But what is the reasoning of the body, that it requires the wisdom you seek? [Nietzsche]
1. Philosophy / D. Nature of Philosophy / 8. Humour
Reject wisdom that lacks laughter [Nietzsche]
3. Truth / A. Truth Problems / 7. Falsehood
To love truth, you must know how to lie [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 / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
S5 provides the correct logic for necessity in the broadly logical sense [Fine,K]
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]
16. Persons / B. Nature of the Self / 7. Self and Body / a. Self needs body
The powerful self behind your thoughts and feelings is your body [Nietzsche]
16. Persons / D. Continuity of the Self / 3. Reference of 'I'
Forget the word 'I'; 'I' is performed by the intelligence of your body [Nietzsche]
20. Action / B. Preliminaries of Action / 2. Willed Action / a. Will to Act
The will is constantly frustrated by the past [Nietzsche]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / d. Biological ethics
We created meanings, to maintain ourselves [Nietzsche]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / f. Übermensch
The noble man wants new virtues; the good man preserves what is old [Nietzsche]
22. Metaethics / B. Value / 2. Values / g. Love
We only really love children and work [Nietzsche]
22. Metaethics / C. The Good / 2. Happiness / c. Value of happiness
I want my work, not happiness! [Nietzsche]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
Virtues can destroy one another, through jealousy [Nietzsche]
23. Ethics / C. Virtue Theory / 4. External Goods / c. Wealth
People now find both wealth and poverty too much of a burden [Nietzsche]
23. Ethics / C. Virtue Theory / 4. External Goods / d. Friendship
If you want friends, you must be a fighter [Nietzsche]
23. Ethics / F. Existentialism / 2. Nihilism
The greatest experience possible is contempt for your own happiness, reason and virtue [Nietzsche]
24. Political Theory / A. Basis of a State / 1. A People / c. A unified people
An enduring people needs its own individual values [Nietzsche]
24. Political Theory / B. Nature of a State / 3. Constitutions
The state coldly claims that it is the people, but that is a lie [Nietzsche]
25. Social Practice / A. Freedoms / 5. Freedom of lifestyle
Saints want to live as they desire, or not to live at all [Nietzsche]
25. Social Practice / D. Justice / 3. Punishment / b. Retribution for crime
Whenever we have seen suffering, we have wanted the revenge of punishment [Nietzsche]
25. Social Practice / F. Life Issues / 5. Sexual Morality
Man and woman are deeply strange to one another! [Nietzsche]
28. God / A. Divine Nature / 2. Divine Nature
I can only believe in a God who can dance [Nietzsche]
28. God / C. Attitudes to God / 5. Atheism
Not being a god is insupportable, so there are no gods! [Nietzsche]
29. Religion / D. Religious Issues / 2. Immortality / d. Heaven
Heaven was invented by the sick and the dying [Nietzsche]
We don't want heaven; now that we are men, we want the kingdom of earth [Nietzsche]