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All the ideas for '', 'Art' and 'Set Theory'

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33 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 / A. Overview of Logic / 1. Overview of Logic
11211 If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
11210 Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt]
11212 The sense of a connective comes from primitively obvious rules of inference [Rumfitt]
19. Language / F. Communication / 3. Denial
11214 We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt]
21. Aesthetics / A. Aesthetic Experience / 2. Aesthetic Attitude
23928 Good art produces exaltation and detachment [Bell,C]
21. Aesthetics / A. Aesthetic Experience / 4. Beauty
23922 The word 'beauty' leads to confusion, because it denotes distinct emotions [Bell,C]
21. Aesthetics / A. Aesthetic Experience / 5. Natural Beauty
23921 Our feeling for natural beauty is different from the aesthetic emotion of art [Bell,C]
23929 We only see landscapes as artistic if we ignore their instrumental value [Bell,C]
21. Aesthetics / A. Aesthetic Experience / 6. The Sublime
23923 Visual form can create a sublime mental state [Bell,C]
21. Aesthetics / B. Nature of Art / 1. Defining Art
23932 Art is the expression of an emotion for ultimate reality [Bell,C]
23927 Aestheticism invites artist to create beauty, but with no indication of how to do it [Bell,C]
21. Aesthetics / B. Nature of Art / 2. Art as Form
8115 Only artists can discern significant form; other people must look to art to find it [Bell,C, by Gardner]
23924 Maybe significant form gives us a feeling for ultimate reality [Bell,C]
23931 Significant form is the essence of art, which I believe expresses an emotion about reality [Bell,C]
20434 'Form' is visual relations, and it is 'significant' if it moves us aesthetically; art needs both [Bell,C, by Feagin]
21. Aesthetics / B. Nature of Art / 4. Art as Expression
23934 The only expression art could have is the emotion resulting from pure form [Bell,C]
21. Aesthetics / C. Artistic Issues / 2. Copies of Art
23925 Mere copies of pictures are not significant - unless the copies are very exact [Bell,C]
21. Aesthetics / C. Artistic Issues / 4. Emotion in Art
23926 Art is distinguished by its aesthetic emotion, which produces appropriate form [Bell,C]
21. Aesthetics / C. Artistic Issues / 6. Value of Art
23933 Aesthetic contemplation is the best and most intense mental state [Bell,C]
23935 Aesthetic experience is an exaltation which increases the possibilities of life [Bell,C]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
22691 Only artistic qualities matter in art, because they also have the highest moral value [Bell,C]
29. Religion / D. Religious Issues / 1. Religious Commitment / a. Religious Belief
23930 Religion sees infinite value in some things, and irrelevance in the rest [Bell,C]