Combining Texts

All the ideas for 'Structures and Structuralism in Phil of Maths', 'Law,Liberty and Morality' and 'The Myth of Sisyphus'

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42 ideas

1. Philosophy / A. Wisdom / 3. Wisdom Deflated
Life will be lived better if it has no meaning [Camus]
1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
Suicide - whether life is worth living - is the one serious philosophical problem [Camus]
1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
To an absurd mind reason is useless, and there is nothing beyond reason [Camus]
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 / A. Overview of Logic / 3. Value of Logic
Logic is easy, but what about logic to the point of death? [Camus]
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 / F. Free Will / 1. Nature of Free Will
Whether we are free is uninteresting; we can only experience our freedom [Camus]
16. Persons / F. Free Will / 6. Determinism / b. Fate
The human heart has a tiresome tendency to label as fate only what crushes it [Camus]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / d. Ethical theory
Discussing ethics is pointless; moral people behave badly, and integrity doesn't need rules [Camus]
22. Metaethics / B. Value / 2. Values / g. Love
The more one loves the stronger the absurd grows [Camus]
22. Metaethics / C. The Good / 1. Goodness / g. Consequentialism
Conduct is not isolated from its effect on the moral code [Hart,HLA]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
One can be virtuous through a whim [Camus]
23. Ethics / F. Existentialism / 2. Nihilism
Happiness and the absurd go together, each leading to the other [Camus]
If we believe existence is absurd, this should dictate our conduct [Camus]
23. Ethics / F. Existentialism / 7. Existential Action
Essential problems either risk death, or intensify the passion of life [Camus]
Danger and integrity are not in the leap of faith, but in remaining poised just before the leap [Camus]
24. Political Theory / D. Ideologies / 5. Democracy / e. Democratic minorities
The great danger of democracy is that the oppression of the minority becomes unobjectionable [Hart,HLA]
24. Political Theory / D. Ideologies / 6. Liberalism / a. Liberalism basics
In an organised society all actions have some effect on other people [Hart,HLA]
25. Social Practice / A. Freedoms / 5. Freedom of lifestyle
The value of liberty allows freedom of action, even if that distresses other people [Hart,HLA]
25. Social Practice / D. Justice / 2. The Law / a. Legal system
The principle of legality requires crimes to be precisely defined in advance of any action [Hart,HLA]
Some private moral issues are no concern of the law [Hart,HLA]
Do morals influence law? Is morality an aspect of law? Can law be morally criticised? [Hart,HLA]
Is the enforcement of morality morally justifiable? [Hart,HLA]
Modern law still suppresses practices seen as immoral, and yet harmless [Hart,HLA]
25. Social Practice / D. Justice / 3. Punishment / b. Retribution for crime
Moral wickedness of an offence is always relevant to the degree of punishment [Hart,HLA]
25. Social Practice / F. Life Issues / 4. Suicide
It is essential to die unreconciled and not of one's own free will [Camus]