Combining Texts

All the ideas for 'The Evolution of Modern Metaphysics', 'First-Order Modal Logic' and 'Art'

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64 ideas

1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
21959 Metaphysics is the most general attempt to make sense of things [Moore,AW]
4. Formal Logic / B. Propositional Logic PL / 3. Truth Tables
9738 Each line of a truth table is a model [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 2. Tools of Modal Logic / a. Symbols of ML
9727 Modal logic adds □ (necessarily) and ◊ (possibly) to classical logic [Fitting/Mendelsohn]
9726 We let 'R' be the accessibility relation: xRy is read 'y is accessible from x' [Fitting/Mendelsohn]
9737 The symbol ||- is the 'forcing' relation; 'Γ ||- P' means that P is true in world Γ [Fitting/Mendelsohn]
13136 The prefix σ names a possible world, and σ.n names a world accessible from that one [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 2. Tools of Modal Logic / b. Terminology of ML
13727 A 'constant' domain is the same for all worlds; 'varying' domains can be entirely separate [Fitting/Mendelsohn]
9734 Modern modal logic introduces 'accessibility', saying xRy means 'y is accessible from x' [Fitting/Mendelsohn]
9736 A 'model' is a frame plus specification of propositions true at worlds, written < G,R,||- > [Fitting/Mendelsohn]
9735 A 'frame' is a set G of possible worlds, with an accessibility relation R, written < G,R > [Fitting/Mendelsohn]
9741 Accessibility relations can be 'reflexive' (self-referring), 'transitive' (carries over), or 'symmetric' (mutual) [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 2. Tools of Modal Logic / c. Derivation rules of ML
13141 Negation: if σ ¬¬X then σ X [Fitting/Mendelsohn]
13138 Disj: a) if σ ¬(X∨Y) then σ ¬X and σ ¬Y b) if σ X∨Y then σ X or σ Y [Fitting/Mendelsohn]
13142 Existential: a) if σ ◊X then σ.n X b) if σ ¬□X then σ.n ¬X [n is new] [Fitting/Mendelsohn]
13144 T reflexive: a) if σ □X then σ X b) if σ ¬◊X then σ ¬X [Fitting/Mendelsohn]
13145 D serial: a) if σ □X then σ ◊X b) if σ ¬◊X then σ ¬□X [Fitting/Mendelsohn]
13146 B symmetric: a) if σ.n □X then σ X b) if σ.n ¬◊X then σ ¬X [n occurs] [Fitting/Mendelsohn]
13147 4 transitive: a) if σ □X then σ.n □X b) if σ ¬◊X then σ.n ¬◊X [n occurs] [Fitting/Mendelsohn]
13148 4r rev-trans: a) if σ.n □X then σ □X b) if σ.n ¬◊X then σ ¬◊X [n occurs] [Fitting/Mendelsohn]
9740 If a proposition is possibly true in a world, it is true in some world accessible from that world [Fitting/Mendelsohn]
9739 If a proposition is necessarily true in a world, it is true in all worlds accessible from that world [Fitting/Mendelsohn]
13137 Conj: a) if σ X∧Y then σ X and σ Y b) if σ ¬(X∧Y) then σ ¬X or σ ¬Y [Fitting/Mendelsohn]
13140 Bicon: a)if σ(X↔Y) then σ(X→Y) and σ(Y→X) b) [not biconditional, one or other fails] [Fitting/Mendelsohn]
13139 Implic: a) if σ ¬(X→Y) then σ X and σ ¬Y b) if σ X→Y then σ ¬X or σ Y [Fitting/Mendelsohn]
13143 Universal: a) if σ ¬◊X then σ.m ¬X b) if σ □X then σ.m X [m exists] [Fitting/Mendelsohn]
13149 S5: a) if n ◊X then kX b) if n ¬□X then k ¬X c) if n □X then k X d) if n ¬◊X then k ¬X [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / b. System K
9742 The system K has no accessibility conditions [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / c. System D
13114 □P → P is not valid in D (Deontic Logic), since an obligatory action may be not performed [Fitting/Mendelsohn]
9743 The system D has the 'serial' conditon imposed on its accessibility relation [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / d. System T
9744 The system T has the 'reflexive' conditon imposed on its accessibility relation [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / e. System K4
9746 The system K4 has the 'transitive' condition on its accessibility relation [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / f. System B
9745 The system B has the 'reflexive' and 'symmetric' conditions on its accessibility relation [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / g. System S4
9747 The system S4 has the 'reflexive' and 'transitive' conditions on its accessibility relation [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
9748 System S5 has the 'reflexive', 'symmetric' and 'transitive' conditions on its accessibility relation [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 4. Alethic Modal Logic
9404 Modality affects content, because P→◊P is valid, but ◊P→P isn't [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 5. Epistemic Logic
13112 In epistemic logic knowers are logically omniscient, so they know that they know [Fitting/Mendelsohn]
13111 Read epistemic box as 'a knows/believes P' and diamond as 'for all a knows/believes, P' [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 6. Temporal Logic
13113 F: will sometime, P: was sometime, G: will always, H: was always [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
13728 The Barcan says nothing comes into existence; the Converse says nothing ceases; the pair imply stability [Fitting/Mendelsohn]
13729 The Barcan corresponds to anti-monotonicity, and the Converse to monotonicity [Fitting/Mendelsohn]
5. Theory of Logic / F. Referring in Logic / 3. Property (λ-) Abstraction
9725 'Predicate abstraction' abstracts predicates from formulae, giving scope for constants and functions [Fitting/Mendelsohn]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
13730 The Indiscernibility of Identicals has been a big problem for modal logic [Fitting/Mendelsohn]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
13725 □ must be sensitive as to whether it picks out an object by essential or by contingent properties [Fitting/Mendelsohn]
13731 Objects retain their possible properties across worlds, so a bundle theory of them seems best [Fitting/Mendelsohn]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
13726 Counterpart relations are neither symmetric nor transitive, so there is no logic of equality for them [Fitting/Mendelsohn]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / b. Transcendental idealism
21958 Appearances are nothing beyond representations, which is transcendental ideality [Moore,AW]
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]