Combining Texts

All the ideas for 'Set Theory', 'Sketch for a Theory of the Emotions' and 'The Runabout Inference Ticket'

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21 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]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
17896 We need to know the meaning of 'and', prior to its role in reasoning [Prior,AN, by Belnap]
17898 Prior's 'tonk' is inconsistent, since it allows the non-conservative inference A |- B [Belnap on Prior,AN]
11021 Prior rejected accounts of logical connectives by inference pattern, with 'tonk' his absurd example [Prior,AN, by Read]
13836 Maybe introducing or defining logical connectives by rules of inference leads to absurdity [Prior,AN, by Hacking]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / b. Essence of consciousness
24016 Consciousness always transcends itself [Sartre]
18. Thought / A. Modes of Thought / 3. Emotions / a. Nature of emotions
24013 An emotion and its object form a unity, so emotion is a mode of apprehension [Sartre]
24017 Emotion is one of our modes of understanding our Being-in-the-World [Sartre]
18. Thought / A. Modes of Thought / 3. Emotions / c. Role of emotions
24014 Emotions are a sort of bodily incantation which brings a magic to the world [Sartre]
24015 Emotions makes us believe in and live in a new world [Sartre]
24. Political Theory / B. Nature of a State / 1. Purpose of a State
20491 States have a monopoly of legitimate violence [Sartre, by Wolff,J]