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All the ideas for '', 'First-Order Modal Logic' and 'The Logic of What Might Have Been'

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75 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
13727 A 'constant' domain is the same for all worlds; 'varying' domains can be entirely separate [Fitting/Mendelsohn]
14684 A world is 'accessible' to another iff the first is possible according to the second [Salmon,N]
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]
14669 For metaphysics, T may be the only correct system of modal logic [Salmon,N]
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
14667 System B has not been justified as fallacy-free for reasoning on what might have been [Salmon,N]
14668 In B it seems logically possible to have both p true and p is necessarily possibly false [Salmon,N]
14692 System B implies that possibly-being-realized is an essential property of the world [Salmon,N]
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
14671 What is necessary is not always necessarily necessary, so S4 is fallacious [Salmon,N]
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
14686 S5 modal logic ignores accessibility altogether [Salmon,N]
14691 S5 believers say that-things-might-have-been-that-way is essential to ways things might have been [Salmon,N]
14693 The unsatisfactory counterpart-theory allows the retention of S5 [Salmon,N]
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
14670 Metaphysical (alethic) modal logic concerns simple necessity and possibility (not physical, epistemic..) [Salmon,N]
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 / 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]
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 / D. Essence of Objects / 15. Against Essentialism
14678 Any property is attached to anything in some possible world, so I am a radical anti-essentialist [Salmon,N]
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 / A. Necessity / 3. Types of Necessity
14680 Logical possibility contains metaphysical possibility, which contains nomological possibility [Salmon,N]
10. Modality / A. Necessity / 5. Metaphysical Necessity
14690 In the S5 account, nested modalities may be unseen, but they are still there [Salmon,N]
14677 Metaphysical necessity is said to be unrestricted necessity, true in every world whatsoever [Salmon,N]
14679 Bizarre identities are logically but not metaphysically possible, so metaphysical modality is restricted [Salmon,N]
14688 Without impossible worlds, the unrestricted modality that is metaphysical has S5 logic [Salmon,N]
14685 Metaphysical necessity is NOT truth in all (unrestricted) worlds; necessity comes first, and is restricted [Salmon,N]
10. Modality / A. Necessity / 6. Logical Necessity
14681 Logical necessity is free of constraints, and may accommodate all of S5 logic [Salmon,N]
10. Modality / A. Necessity / 7. Natural Necessity
14676 Nomological necessity is expressed with intransitive relations in modal semantics [Salmon,N]
10. Modality / C. Sources of Modality / 5. Modality from Actuality
14689 Necessity and possibility are not just necessity and possibility according to the actual world [Salmon,N]
10. Modality / E. Possible worlds / 1. Possible Worlds / b. Impossible worlds
14674 Impossible worlds are also ways for things to be [Salmon,N]
14682 Denial of impossible worlds involves two different confusions [Salmon,N]
14687 Without impossible worlds, how things might have been is the only way for things to be [Salmon,N]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
14683 Possible worlds rely on what might have been, so they can' be used to define or analyse modality [Salmon,N]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
14672 Possible worlds are maximal abstract ways that things might have been [Salmon,N]
14675 Possible worlds just have to be 'maximal', but they don't have to be consistent [Salmon,N]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / c. Worlds as propositions
14673 You can't define worlds as sets of propositions, and then define propositions using worlds [Salmon,N]
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]
19. Language / F. Communication / 3. Denial
11214 We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt]