### All the ideas for Michael Burke, Nicholas Rescher and M Fitting/R Mendelsohn

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54 ideas

###### 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
 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]
 13727 A 'constant' domain is the same for all worlds; 'varying' domains can be entirely separate [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
 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]
 13140 Bicon: a)if σ(X↔Y) then σ(X→Y) and σ(Y→X) b) [not biconditional, one or other fails] [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]
 13143 Universal: a) if σ ¬◊X then σ.m ¬X b) if σ □X then σ.m X [m exists] [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]
 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]
 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]
 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]
 13144 T reflexive: a) if σ □X then σ X b) if σ ¬◊X then σ ¬X [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]
 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 / A. Existence of Objects / 5. Individuation / e. Individuation by kind
 16235 Persistence conditions cannot contradict, so there must be a 'dominant sortal' [Burke,M, by Hawley]
 14753 The 'dominant' of two coinciding sortals is the one that entails the widest range of properties [Burke,M, by Sider]
###### 9. Objects / B. Unity of Objects / 1. Unifying an Object / b. Unifying aggregates
 16072 'The rock' either refers to an object, or to a collection of parts, or to some stuff [Burke,M, by Wasserman]
###### 9. Objects / B. Unity of Objects / 3. Unity Problems / b. Cat and its tail
 14751 Tib goes out of existence when the tail is lost, because Tib was never the 'cat' [Burke,M, by Sider]
###### 9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
 13278 Maybe the clay becomes a different lump when it becomes a statue [Burke,M, by Koslicki]
 16234 Burke says when two object coincide, one of them is destroyed in the process [Burke,M, by Hawley]
 16071 Sculpting a lump of clay destroys one object, and replaces it with another one [Burke,M, by Wasserman]
###### 9. Objects / B. Unity of Objects / 3. Unity Problems / d. Coincident objects
 14750 Two entities can coincide as one, but only one of them (the dominant sortal) fixes persistence conditions [Burke,M, by Sider]
###### 9. Objects / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects
 10650 In the military, persons are parts of parts of large units, but not parts of those large units [Rescher]
###### 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]
###### 27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement
 20365 We only see points in motion, and thereby infer movement [Rescher]