Combining Texts

All the ideas for 'Set Theory', 'The Trouble with Being Born' and 'Introduction to Virtue Ethics'

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38 ideas

1. Philosophy / A. Wisdom / 3. Wisdom Deflated
So-called wisdom is just pondering things instead of acting [Cioran]
1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
Systems are the worst despotism, in philosophy and in life [Cioran]
1. Philosophy / H. Continental Philosophy / 3. Hermeneutics
A text explained ceases to be a text [Cioran]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
Extensionality: ∀x ∀y (∀z (z ∈ x ↔ z ∈ y) → x = y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
Pairing: ∀x ∀y ∃z (x ∈ z ∧ y ∈ z) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / d. Axiom of Unions III
Union: ∀F ∃A ∀Y ∀x (x ∈ Y ∧ Y ∈ F → x ∈ A) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
Infinity: ∃x (0 ∈ x ∧ ∀y ∈ x (S(y) ∈ x) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
Power Set: ∀x ∃y ∀z(z ⊂ x → z ∈ y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
Replacement: ∀x∈A ∃!y φ(x,y) → ∃Y ∀X∈A ∃y∈Y φ(x,y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / i. Axiom of Foundation VIII
Foundation:∀x(∃y(y∈x) → ∃y(y∈x ∧ ¬∃z(z∈x ∧ z∈y))) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
Choice: ∀A ∃R (R well-orders A) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / k. Axiom of Existence
Set Existence: ∃x (x = x) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / n. Axiom of Comprehension
Comprehension: ∃y ∀x (x ∈ y ↔ x ∈ z ∧ φ) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L
Constructibility: V = L (all sets are constructible) [Kunen]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not
Negation doesn't arise from reasoning, but from deep instincts [Cioran]
7. Existence / A. Nature of Existence / 3. Being / i. Deflating being
The word 'being' is very tempting, but in fact means nothing at all [Cioran]
7. Existence / D. Theories of Reality / 4. Anti-realism
People who really believe anti-realism don't bother to prove it [Cioran]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
Convictions are failures to study anything thoroughly [Cioran]
Opinions are fine, but having convictions means something has gone wrong [Cioran]
16. Persons / F. Free Will / 5. Against Free Will
If people always acted without words we would take them for robots [Cioran]
18. Thought / D. Concepts / 5. Concepts and Language / a. Concepts and language
If only we could write like a reptile, of endless sensations and no concepts! [Cioran]
20. Action / C. Motives for Action / 4. Responsibility for Actions
We could only be responsible if we had consented before birth to who we are [Cioran]
We may still admire a person's character even if the traits are involuntary [Statman]
21. Aesthetics / A. Aesthetic Experience / 6. The Sublime
We morally dissolve if we spend time with excessive beauty [Cioran]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / d. Ethical theory
There is a new sort of moral scepticism, about the possibility of moral theories [Statman]
22. Metaethics / C. The Good / 2. Happiness / b. Eudaimonia
With a broad concept of flourishing, it might be possible without the virtues [Statman]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / d. Virtue theory critique
Virtue theory isn't a genuine ethical theory, because it doesn't have universal application [Statman]
Promises create moral duties that have nothing to do with character [Statman]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / d. Teaching virtue
Moral education is better by concrete example than abstract principle [Statman]
23. Ethics / C. Virtue Theory / 4. External Goods / d. Friendship
Friends express friendship even when no utility is involved [Statman]
23. Ethics / D. Deontological Ethics / 2. Duty
Behaviour may be disgusting or inhumane, but violate no duty [Statman]
The ancients recognised imperfect duties, but we have added perfect duties like justice [Statman]
23. Ethics / F. Existentialism / 3. Angst
In anxiety people cling to what reinforces it, because it is a deep need [Cioran]
23. Ethics / F. Existentialism / 4. Boredom
Fear cures boredom, because it is stronger [Cioran]
It is better to watch the hours pass, than trying to fill them [Cioran]
25. Social Practice / F. Life Issues / 3. Abortion
Abortion issues focus on the mother's right over her body, and the status of the foetus [Statman]
25. Social Practice / F. Life Issues / 4. Suicide
Suicide is pointless, because it always comes too late [Cioran]
29. Religion / D. Religious Issues / 2. Immortality / d. Heaven
The first man obviously found paradise unendurable [Cioran]