Combining Texts

All the ideas for 'Set Theory', 'The Trouble with Being Born' and 'The Condemnation of 1277'

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33 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]
10. Modality / B. Possibility / 1. Possibility
In future, only logical limits can be placed on divine omnipotence [Anon (Par), by Boulter]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
Opinions are fine, but having convictions means something has gone wrong [Cioran]
Convictions are failures to study anything thoroughly [Cioran]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / f. Foundationalism critique
It is heresy to require self-evident foundational principles in order to be certain [Anon (Par)]
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]
21. Aesthetics / A. Aesthetic Experience / 6. The Sublime
We morally dissolve if we spend time with excessive beauty [Cioran]
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 / E. Policies / 5. Education / d. Study of history
It is heresy to teach that history repeats every 36,000 years [Anon (Par)]
25. Social Practice / F. Life Issues / 4. Suicide
Suicide is pointless, because it always comes too late [Cioran]
28. God / A. Divine Nature / 3. Divine Perfections
It is heresy to teach that natural impossibilities cannot even be achieved by God [Anon (Par)]
28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
It is heresy to teach that we can know God by his essence in this mortal life [Anon (Par)]
29. Religion / D. Religious Issues / 2. Immortality / d. Heaven
The first man obviously found paradise unendurable [Cioran]