Combining Texts

All the ideas for 'Set Theory', 'Existentialism and Humanism' and 'Proof of an External World'

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28 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
13030 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
13032 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
13033 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
13037 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
13038 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
13034 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
13039 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
13036 Choice: ∀A ∃R (R well-orders A) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / k. Axiom of Existence
13029 Set Existence: ∃x (x = x) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / n. Axiom of Comprehension
13031 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
13040 Constructibility: V = L (all sets are constructible) [Kunen]
11. Knowledge Aims / B. Certain Knowledge / 2. Common Sense Certainty
6349 I can prove a hand exists, by holding one up, pointing to it, and saying 'here is one hand' [Moore,GE]
16. Persons / A. Concept of a Person / 4. Persons as Agents
3847 Man is nothing else but the sum of his actions [Sartre]
16. Persons / F. Free Will / 1. Nature of Free Will
3846 Man IS freedom [Sartre]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
3843 There is no human nature [Sartre]
22. Metaethics / B. Value / 1. Nature of Value / a. Nature of value
20762 There are no values to justify us, and no excuses [Sartre]
22. Metaethics / B. Value / 1. Nature of Value / d. Subjective value
3852 If values depend on us, freedom is the foundation of all values [Sartre]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
20764 In becoming what we want to be we create what we think man ought to be [Sartre]
23. Ethics / C. Virtue Theory / 3. Virtues / d. Courage
3848 Cowards are responsible for their cowardice [Sartre]
23. Ethics / D. Deontological Ethics / 3. Universalisability
20763 When my personal freedom becomes involved, I must want freedom for everyone else [Sartre]
23. Ethics / F. Existentialism / 1. Existentialism
22229 Existentialists says that cowards and heroes make themselves [Sartre]
23. Ethics / F. Existentialism / 5. Existence-Essence
3842 Existence before essence (or begin with the subjective) [Sartre]
6868 'Existence precedes essence' means we have no pre-existing self, but create it through existence [Sartre, by Le Poidevin]
23. Ethics / F. Existentialism / 6. Authentic Self
3844 Existentialism says man is whatever he makes of himself [Sartre]
20754 It is dishonest to offer passions as an excuse [Sartre]
23. Ethics / F. Existentialism / 7. Existential Action
6571 When a man must choose between his mother and the Resistance, no theory can help [Sartre, by Fogelin]
3851 If I do not choose, that is still a choice [Sartre]
28. God / A. Divine Nature / 6. Divine Morality / d. God decrees morality
3845 Without God there is no intelligibility or value [Sartre]