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All the ideas for 'Structures and Structuralism in Phil of Maths', 'A Philosophy of Boredom' and 'Principle Doctrines ('Kuriai Doxai') (frags)'

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40 ideas

1. Philosophy / A. Wisdom / 2. Wise People
It is a great good to show reverence for a wise man [Epicurus]
1. Philosophy / B. History of Ideas / 5. Later European Thought
Modern Western culture suddenly appeared in Jena in the 1790s [Svendsen]
1. Philosophy / D. Nature of Philosophy / 2. Invocation to Philosophy
In the study of philosophy, pleasure and knowledge arrive simultaneously [Epicurus]
1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
You can't understand love in terms of 'if and only if...' [Svendsen]
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]
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 / 5. Individuation / b. Individuation by properties
Bodies are combinations of shape, size, resistance and weight [Epicurus]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / e. Primary/secondary critique
If subjective and objective begin to merge, then so do primary and secondary qualities [Svendsen]
16. Persons / F. Free Will / 6. Determinism / a. Determinism
If everything is by necessity, then even denials of necessity are by necessity [Epicurus]
18. Thought / A. Modes of Thought / 3. Emotions / b. Types of emotion
Emotions have intentional objects, while a mood is objectless [Svendsen]
22. Metaethics / B. Value / 2. Values / e. Death
Death appears to be more frightening the less one has lived [Svendsen]
22. Metaethics / C. The Good / 2. Happiness / c. Value of happiness
What happens to me if I obtain all my desires, and what if I fail? [Epicurus]
22. Metaethics / C. The Good / 3. Pleasure / e. Role of pleasure
Pleasure and virtue entail one another [Epicurus]
23. Ethics / B. Contract Ethics / 1. Contractarianism
Justice is merely a contract about not harming or being harmed [Epicurus]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
We value our own character, whatever it is, and we should respect the characters of others [Epicurus]
23. Ethics / C. Virtue Theory / 3. Virtues / c. Justice
Justice is a pledge of mutual protection [Epicurus]
23. Ethics / F. Existentialism / 4. Boredom
We can be unaware that we are bored [Svendsen]
Boredom is so radical that suicide could not overcome it; only never having existed would do it [Svendsen]
We are bored because everything comes to us fully encoded, and we want personal meaning [Svendsen]
The profoundest boredom is boredom with boredom [Svendsen]
24. Political Theory / B. Nature of a State / 1. Purpose of a State
We have achieved a sort of utopia, and it is boring, so that is the end of utopias [Svendsen]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
A law is not just if it is not useful in mutual associations [Epicurus]
24. Political Theory / D. Ideologies / 9. Communism
The concept of 'alienation' seems no longer applicable [Svendsen]
25. Social Practice / F. Life Issues / 4. Suicide
It is small-minded to find many good reasons for suicide [Epicurus]