Combining Texts

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

unexpand these ideas     |    start again     |     specify just one area for these texts

75 ideas

4. Formal Logic / B. Propositional Logic PL / 3. Truth Tables
9738 Each line of a truth table is a model [Fitting/Mendelsohn]
     Full Idea: Each line of a truth table is, in effect, a model.
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.6)
     A reaction: I find this comment illuminating. It is being connected with the more complex models of modal logic. Each line of a truth table is a picture of how the world might be.
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]
     Full Idea: For modal logic we add to the syntax of classical logic two new unary operators □ (necessarily) and ◊ (possibly).
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.3)
9726 We let 'R' be the accessibility relation: xRy is read 'y is accessible from x' [Fitting/Mendelsohn]
     Full Idea: We let 'R' be the accessibility relation: xRy is read 'y is accessible from x'.
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.5)
9737 The symbol ||- is the 'forcing' relation; 'Γ ||- P' means that P is true in world Γ [Fitting/Mendelsohn]
     Full Idea: The symbol ||- is used for the 'forcing' relation, as in 'Γ ||- P', which means that P is true in world Γ.
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.6)
13136 The prefix σ names a possible world, and σ.n names a world accessible from that one [Fitting/Mendelsohn]
     Full Idea: A 'prefix' is a finite sequence of positive integers. A 'prefixed formula' is an expression of the form σ X, where σ is a prefix and X is a formula. A prefix names a possible world, and σ.n names a world accessible from that one.
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 2.2)
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]
     Full Idea: In 'constant domain' semantics, the domain of each possible world is the same as every other; in 'varying domain' semantics, the domains need not coincide, or even overlap.
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 4.5)
14684 A world is 'accessible' to another iff the first is possible according to the second [Salmon,N]
     Full Idea: A world w' is accessible to a consistent world w if and only if w' is possible in w. Being 'inaccessible to' or 'possible relative to' a consistent world is simply being possible according to that world, nothing more and nothing less.
     From: Nathan Salmon (The Logic of What Might Have Been [1989], IV)
     A reaction: More illuminating than just saying that w can 'see' w'. Accessibility is internal to worIds. It gives some connection to why we spend time examining modal logic. There is no more important metaphysical notion than what is possible according to actuality.
9734 Modern modal logic introduces 'accessibility', saying xRy means 'y is accessible from x' [Fitting/Mendelsohn]
     Full Idea: Modern modal logic takes into consideration the way the modal relates the possible worlds, called the 'accessibility' relation. .. We let R be the accessibility relation, and xRy reads as 'y is accessible from x.
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.5)
     A reaction: There are various types of accessibility, and these define the various modal logics.
9736 A 'model' is a frame plus specification of propositions true at worlds, written < G,R,||- > [Fitting/Mendelsohn]
     Full Idea: A 'model' is a frame plus a specification of which propositional letters are true at which worlds. It is written as , where ||- is a relation between possible worlds and propositional letters. So Γ ||- P means P is true at world Γ.
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.6)
9735 A 'frame' is a set G of possible worlds, with an accessibility relation R, written < G,R > [Fitting/Mendelsohn]
     Full Idea: A 'frame' consists of a non-empty set G, whose members are generally called possible worlds, and a binary relation R, on G, generally called the accessibility relation. We say the frame is the pair so that a single object can be talked about.
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.6)
9741 Accessibility relations can be 'reflexive' (self-referring), 'transitive' (carries over), or 'symmetric' (mutual) [Fitting/Mendelsohn]
     Full Idea: A relation R is 'reflexive' if every world is accessible from itself; 'transitive' if the first world is related to the third world (ΓRΔ and ΔRΩ → ΓRΩ); and 'symmetric' if the accessibility relation is mutual.
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.7)
     A reaction: The different systems of modal logic largely depend on how these accessibility relations are specified. There is also the 'serial' relation, which just says that any world has another world accessible to it.
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]
     Full Idea: General tableau rule for negation: if σ ¬¬X then σ X
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 2.2)
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]
     Full Idea: General tableau rules for disjunctions: a) if σ ¬(X ∨ Y) then σ ¬X and σ ¬Y b) if σ X ∨ Y then σ X or σ Y
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 2.2)
13142 Existential: a) if σ ◊X then σ.n X b) if σ ¬□X then σ.n ¬X [n is new] [Fitting/Mendelsohn]
     Full Idea: General tableau rules for existential modality: a) if σ ◊ X then σ.n X b) if σ ¬□ X then σ.n ¬X , where n introduces some new world (rather than referring to a world that can be seen).
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 2.2)
     A reaction: Note that the existential rule of ◊, usually read as 'possibly', asserts something about a new as yet unseen world, whereas □ only refers to worlds which can already be seen,
13144 T reflexive: a) if σ □X then σ X b) if σ ¬◊X then σ ¬X [Fitting/Mendelsohn]
     Full Idea: System T reflexive rules (also for B, S4, S5): a) if σ □X then σ X b) if σ ¬◊X then σ ¬X
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 2.3)
13145 D serial: a) if σ □X then σ ◊X b) if σ ¬◊X then σ ¬□X [Fitting/Mendelsohn]
     Full Idea: System D serial rules (also for T, B, S4, S5): a) if σ □X then σ ◊X b) if σ ¬◊X then σ ¬□X
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 2.3)
13146 B symmetric: a) if σ.n □X then σ X b) if σ.n ¬◊X then σ ¬X [n occurs] [Fitting/Mendelsohn]
     Full Idea: System B symmetric rules (also for S5): a) if σ.n □X then σ X b) if σ.n ¬◊X then σ ¬X [where n is a world which already occurs]
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 2.3)
13147 4 transitive: a) if σ □X then σ.n □X b) if σ ¬◊X then σ.n ¬◊X [n occurs] [Fitting/Mendelsohn]
     Full Idea: System 4 transitive rules (also for K4, S4, S5): a) if σ □X then σ.n □X b) if σ ¬◊X then σ.n ¬◊X [where n is a world which already occurs]
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 2.3)
13148 4r rev-trans: a) if σ.n □X then σ □X b) if σ.n ¬◊X then σ ¬◊X [n occurs] [Fitting/Mendelsohn]
     Full Idea: System 4r reversed-transitive rules (also for S5): a) if σ.n □X then σ □X b) if σ.n ¬◊X then σ ¬◊X [where n is a world which already occurs]
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 2.3)
9740 If a proposition is possibly true in a world, it is true in some world accessible from that world [Fitting/Mendelsohn]
     Full Idea: If a proposition is possibly true in a world, then it is also true in some world which is accessible from that world. That is: Γ ||- ◊X ↔ for some Δ ∈ G, ΓRΔ then Δ ||- X.
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.6)
9739 If a proposition is necessarily true in a world, it is true in all worlds accessible from that world [Fitting/Mendelsohn]
     Full Idea: If a proposition is necessarily true in a world, then it is also true in all worlds which are accessible from that world. That is: Γ ||- □X ↔ for every Δ ∈ G, if ΓRΔ then Δ ||- X.
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.6)
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]
     Full Idea: General tableau rules for conjunctions: a) if σ X ∧ Y then σ X and σ Y b) if σ ¬(X ∧ Y) then σ ¬X or σ ¬Y
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 2.2)
13140 Bicon: a)if σ(X↔Y) then σ(X→Y) and σ(Y→X) b) [not biconditional, one or other fails] [Fitting/Mendelsohn]
     Full Idea: General tableau rules for biconditionals: a) if σ (X ↔ Y) then σ (X → Y) and σ (Y → X) b) if σ ¬(X ↔ Y) then σ ¬(X → Y) or σ ¬(Y → X)
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 2.2)
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]
     Full Idea: General tableau rules for implications: a) if σ ¬(X → Y) then σ X and σ ¬Y b) if σ X → Y then σ ¬X or σ Y
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 2.2)
13143 Universal: a) if σ ¬◊X then σ.m ¬X b) if σ □X then σ.m X [m exists] [Fitting/Mendelsohn]
     Full Idea: General tableau rules for universal modality: a) if σ ¬◊ X then σ.m ¬X b) if σ □ X then σ.m X , where m refers to a world that can be seen (rather than introducing a new world).
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 2.2)
     A reaction: Note that the universal rule of □, usually read as 'necessary', only refers to worlds which can already be seen, whereas possibility (◊) asserts some thing about a new as yet unseen world.
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]
     Full Idea: Simplified S5 rules: 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. 'n' picks any world; in a) and b) 'k' asserts a new world; in c) and d) 'k' refers to a known world
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 2.3)
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / b. System K
9742 The system K has no accessibility conditions [Fitting/Mendelsohn]
     Full Idea: The system K has no frame conditions imposed on its accessibility relation.
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.8)
     A reaction: The system is named K in honour of Saul Kripke.
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]
     Full Idea: System D is usually thought of as Deontic Logic, concerning obligations and permissions. □P → P is not valid in D, since just because an action is obligatory, it does not follow that it is performed.
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.12.2 Ex)
9743 The system D has the 'serial' conditon imposed on its accessibility relation [Fitting/Mendelsohn]
     Full Idea: The system D has the 'serial' condition imposed on its accessibility relation - that is, every world must have some world which is accessible to it.
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.8)
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]
     Full Idea: The system T has the 'reflexive' condition imposed on its accessibility relation - that is, every world must be accessible to itself.
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.8)
14669 For metaphysics, T may be the only correct system of modal logic [Salmon,N]
     Full Idea: Insofar as modal logic is concerned exclusively with the logic of metaphysical modality, ..T may well be the one and only (strongest) correct system of (first-order) propositional logic.
     From: Nathan Salmon (The Logic of What Might Have Been [1989], Intro)
     A reaction: This contrasts sharply with the orthodox view, that S5 (or at the very least S4) is the correct system for metaphysics.
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]
     Full Idea: The system K4 has the 'transitive' condition imposed on its accessibility relation - that is, if a relation holds between worlds 1 and 2 and worlds 2 and 3, it must hold between worlds 1 and 3. The relation carries over.
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.8)
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]
     Full Idea: Even the conventionally accepted system B, which is weaker than S5 and independent of S4, has not been adequately justified as a fallacy-free system of reasoning about what might have been.
     From: Nathan Salmon (The Logic of What Might Have Been [1989], Intro)
14668 In B it seems logically possible to have both p true and p is necessarily possibly false [Salmon,N]
     Full Idea: The characteristic of B has the form φ⊃□◊φ. ...Even if these axioms are necessarily true, it seems logically possible for p to be true while the proposition that p is necessarily possible is at the same time false.
     From: Nathan Salmon (The Logic of What Might Have Been [1989], Intro)
14692 System B implies that possibly-being-realized is an essential property of the world [Salmon,N]
     Full Idea: Friends of B modal logic commit themselves to the loaded claim that it is logically true that the property of possibly being realized (or being a way things might have been) is an essential property of the world.
     From: Nathan Salmon (The Logic of What Might Have Been [1989], V)
     A reaction: I think this 'loaded' formulation captures quite nicely the dispositional view I favour, that the possibilities of the actual world are built into the actual world, and define its nature just as much as the 'categorial' facts do.
9745 The system B has the 'reflexive' and 'symmetric' conditions on its accessibility relation [Fitting/Mendelsohn]
     Full Idea: The system B has the 'reflexive' and 'symmetric' conditions imposed on its accessibility relation - that is, every world must be accessible to itself, and any relation between worlds must be mutual.
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.8)
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]
     Full Idea: We can say of a wooden table that it would have been possible for it to have originated from some different matter, even though it is not actually possible. So what is necessary fails to be necessarily necessary, and S4 modal logic is fallacious.
     From: Nathan Salmon (The Logic of What Might Have Been [1989], I)
     A reaction: [compressed]
9747 The system S4 has the 'reflexive' and 'transitive' conditions on its accessibility relation [Fitting/Mendelsohn]
     Full Idea: The system S4 has the 'reflexive' and 'transitive' conditions imposed on its accessibility relation - that is, every world is accessible to itself, and accessibility carries over a series of worlds.
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.8)
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
14686 S5 modal logic ignores accessibility altogether [Salmon,N]
     Full Idea: When we ignore accessibility altogether, we have finally zeroed in on S5 modal logic.
     From: Nathan Salmon (The Logic of What Might Have Been [1989], IV)
14691 S5 believers say that-things-might-have-been-that-way is essential to ways things might have been [Salmon,N]
     Full Idea: Believers in S5 as a correct system of propositional reasoning about what might have been must claim that it is an essential property of any way things might have been that things might have been that way.
     From: Nathan Salmon (The Logic of What Might Have Been [1989], V)
     A reaction: Salmon is working in a view where you are probably safe to substitute 'necessary' for 'essential' without loss of meaning.
14693 The unsatisfactory counterpart-theory allows the retention of S5 [Salmon,N]
     Full Idea: Counterpart-theoretic modal semantics allows for the retention of S5 modal propositional logic, at a considerable cost.
     From: Nathan Salmon (The Logic of What Might Have Been [1989], V n18)
     A reaction: See the other ideas in this paper by Salmon for his general attack on S5 as the appropriate system for metaphysical necessity. He favours the very modest System T.
9748 System S5 has the 'reflexive', 'symmetric' and 'transitive' conditions on its accessibility relation [Fitting/Mendelsohn]
     Full Idea: The system S5 has the 'reflexive', 'symmetric' and 'transitive' conditions imposed on its accessibility relation - that is, every world is self-accessible, and accessibility is mutual, and it carries over a series of worlds.
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.8)
     A reaction: S5 has total accessibility, and hence is the most powerful system (though it might be too powerful).
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]
     Full Idea: Metaphysical modal logic concerns metaphysical (or alethic) necessity and metaphysical (alethic) possibility, or necessity and possibility tout court - as opposed to such other types of modality as physical necessity, epistemic necessity etc.
     From: Nathan Salmon (The Logic of What Might Have Been [1989], Intro n2)
9404 Modality affects content, because P→◊P is valid, but ◊P→P isn't [Fitting/Mendelsohn]
     Full Idea: P→◊P is usually considered to be valid, but its converse, ◊P→P is not, so (by Frege's own criterion) P and possibly-P differ in conceptual content, and there is no reason why logic should not be widened to accommodate this.
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.2)
     A reaction: Frege had denied that modality affected the content of a proposition (1879:p.4). The observation here is the foundation for the need for a modal logic.
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]
     Full Idea: In epistemic logic the knower is treated as logically omniscient. This is puzzling because one then cannot know something and yet fail to know that one knows it (the Principle of Positive Introspection).
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.11)
     A reaction: This is nowadays known as the K-K Problem - to know, must you know that you know. Broadly, we find that externalists say you don't need to know that you know (so animals know things), but internalists say you do need to know that you know.
13111 Read epistemic box as 'a knows/believes P' and diamond as 'for all a knows/believes, P' [Fitting/Mendelsohn]
     Full Idea: In epistemic logic we read Υ as 'KaP: a knows that P', and ◊ as 'PaP: it is possible, for all a knows, that P' (a is an individual). For belief we read them as 'BaP: a believes that P' and 'CaP: compatible with everything a believes that P'.
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.11)
     A reaction: [scripted capitals and subscripts are involved] Hintikka 1962 is the source of this. Fitting and Mendelsohn prefer □ to read 'a is entitled to know P', rather than 'a knows that P'.
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]
     Full Idea: We introduce four future and past tense operators: FP: it will sometime be the case that P. PP: it was sometime the case that P. GP: it will always be the case that P. HP: it has always been the case that P. (P itself is untensed).
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.10)
     A reaction: Temporal logic begins with A.N. Prior, and starts with □ as 'always', and ◊ as 'sometimes', but then adds these past and future divisions. Two different logics emerge, taking □ and ◊ as either past or as future.
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]
     Full Idea: The Converse Barcan says nothing passes out of existence in alternative situations. The Barcan says that nothing comes into existence. The two together say the same things exist no matter what the situation.
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 4.9)
     A reaction: I take the big problem to be that these reflect what it is you want to say, and that does not keep stable across a conversation, so ordinary rational discussion sometimes asserts these formulas, and 30 seconds later denies them.
13729 The Barcan corresponds to anti-monotonicity, and the Converse to monotonicity [Fitting/Mendelsohn]
     Full Idea: The Barcan formula corresponds to anti-monotonicity, and the Converse Barcan formula corresponds to monotonicity.
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 6.3)
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]
     Full Idea: If a designated conclusion follows from the premisses, but the argument involves two howlers which cancel each other out, then the moral is that the path an argument takes from premisses to conclusion does matter to its logical evaluation.
     From: Ian Rumfitt ("Yes" and "No" [2000], II)
     A reaction: The drift of this is that our view of logic should be a little closer to the reasoning of ordinary language, and we should rely a little less on purely formal accounts.
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]
     Full Idea: If 'and' and 'but' really are alike in sense, in what might that likeness consist? Some philosophers of classical logic will reply that they share a sense by virtue of sharing a truth table.
     From: Ian Rumfitt ("Yes" and "No" [2000])
     A reaction: This is the standard view which Rumfitt sets out to challenge.
11212 The sense of a connective comes from primitively obvious rules of inference [Rumfitt]
     Full Idea: A connective will possess the sense that it has by virtue of its competent users' finding certain rules of inference involving it to be primitively obvious.
     From: Ian Rumfitt ("Yes" and "No" [2000], III)
     A reaction: Rumfitt cites Peacocke as endorsing this view, which characterises the logical connectives by their rules of usage rather than by their pure semantic value.
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]
     Full Idea: 'Predicate abstraction' is a key idea. It is a syntactic mechanism for abstracting a predicate from a formula, providing a scoping mechanism for constants and function symbols similar to that provided for variables by quantifiers.
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], Pref)
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]
     Full Idea: By admitting possible worlds of unlimited variation and recombination, I simply abandon true metaphysical essentialism. By my lights, any property is attached to anything in some possible world or other. I am a closet radical anti-essentialist.
     From: Nathan Salmon (The Logic of What Might Have Been [1989], II)
     A reaction: Salmon includes impossible worlds within his scheme of understanding. It strikes me that this is metaphysical system which tells us nothing about how things are: it is sort of 'logical idealist'. Later he talks of 'we essentialists'.
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
13730 The Indiscernibility of Identicals has been a big problem for modal logic [Fitting/Mendelsohn]
     Full Idea: Equality has caused much grief for modal logic. Many of the problems, which have struck at the heart of the coherence of modal logic, stem from the apparent violations of the Indiscernibility of Identicals.
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 7.1)
     A reaction: Thus when I say 'I might have been three inches taller', presumably I am referring to someone who is 'identical' to me, but who lacks one of my properties. A simple solution is to say that the person is 'essentially' identical.
10. Modality / A. Necessity / 3. Types of Necessity
14680 Logical possibility contains metaphysical possibility, which contains nomological possibility [Salmon,N]
     Full Idea: Just as nomological possibility is a special kind of metaphysical possibility, so metaphysical possibility is a special kind of logical possibility.
     From: Nathan Salmon (The Logic of What Might Have Been [1989], III)
     A reaction: This is the standard view of how the three types of necessity are nested. He gives a possible counterexample in footnote 7.
10. Modality / A. Necessity / 5. Metaphysical Necessity
14690 In the S5 account, nested modalities may be unseen, but they are still there [Salmon,N]
     Full Idea: The S5 theorist's miscontrual of English (in the meaning of 'possibly possible') makes nested modality unseen, but it does not make nested modality vanish. Inaccessible worlds are still worlds.
     From: Nathan Salmon (The Logic of What Might Have Been [1989], IV)
14677 Metaphysical necessity is said to be unrestricted necessity, true in every world whatsoever [Salmon,N]
     Full Idea: It is held that it is the hallmark of metaphysical necessity is that it is completely unrestricted, the limiting case of restricted necessity, with no restrictions whatever. A proposition is necessary only if it is true in absolutely every world whatever.
     From: Nathan Salmon (The Logic of What Might Have Been [1989], II)
     A reaction: This is the standard picture which leads to the claim that S5 modal logic is appropriate for metaphysical necessity, because there are no restrictions on accessibility. Salmon raises objections to this conventional view.
14679 Bizarre identities are logically but not metaphysically possible, so metaphysical modality is restricted [Salmon,N]
     Full Idea: Though there is a way things logically could be according to which I am a credit card account, there is no way things metaphysically might be according to which I am a credit card account. This illustrates the restricted nature of metaphysical modality.
     From: Nathan Salmon (The Logic of What Might Have Been [1989], III)
     A reaction: His drift is that metaphyical modality is restricted, but expressing it in S5 modal logic (where all worlds see one another) makes it unrestricted, so S5 logic is wrong for metaphysics. I'm impressed by his arguments.
14688 Without impossible worlds, the unrestricted modality that is metaphysical has S5 logic [Salmon,N]
     Full Idea: If one confines one's sights to genuinely possible worlds, disavowing the impossible worlds, then metaphysical modality emerges as the limiting case - the 'unrestricted' modality that takes account of 'every' world - and S5 emerges as its proper logic.
     From: Nathan Salmon (The Logic of What Might Have Been [1989], IV)
     A reaction: He observes that this makes metaphysical modality 'restricted' simply because you have restricted what 'all worlds' means. Could there be non-maximal worlds? Are logical and metaphysical modality coextensive? I think I like the S5 view.
14685 Metaphysical necessity is NOT truth in all (unrestricted) worlds; necessity comes first, and is restricted [Salmon,N]
     Full Idea: A mythology gave us the idea that metaphysical necessity is truth in every world whatsoever, without restriction. But the notion of metaphysical modality comes first, and, like every notion of modality, it is restricted.
     From: Nathan Salmon (The Logic of What Might Have Been [1989], IV)
10. Modality / A. Necessity / 6. Logical Necessity
14681 Logical necessity is free of constraints, and may accommodate all of S5 logic [Salmon,N]
     Full Idea: With its freedom from the constraint of metaphysical possibility, logical necessity may be construed as accommodating all the axioms and rules of S5.
     From: Nathan Salmon (The Logic of What Might Have Been [1989], III)
     A reaction: He goes on to raise problems for this simple thought. The big question: what are the limits of what is actually possible? Compare: what are the limits of what is imaginable? what are the limits of what is meaningfully sayable?
10. Modality / A. Necessity / 7. Natural Necessity
14676 Nomological necessity is expressed with intransitive relations in modal semantics [Salmon,N]
     Full Idea: Intransitive relations are introduced into modal semantics for the purposes of interpreting various 'real' or restricted types of modalities, such as nomological necessity.
     From: Nathan Salmon (The Logic of What Might Have Been [1989], II)
     A reaction: The point here is that the (so-called) 'laws of nature' are held to change from world to world, so necessity in one could peter out in some more remote world, rather than being carried over everywhere. A very Humean view of such things.
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]
     Full Idea: The real meanings of the simple modal terms 'necessary' and 'possible' are not the same as the concepts of actual necessity and actual possibility, necessity and possibility according to the actual world.
     From: Nathan Salmon (The Logic of What Might Have Been [1989], IV)
     A reaction: If you were an 'actualist' (who denies everything except the actual world) then you are unlikely to agree with this. In unrestricted possible worlds, being true in one world makes it possible in all worlds. So actual necessity is possible everywhere.
10. Modality / E. Possible worlds / 1. Possible Worlds / b. Impossible worlds
14674 Impossible worlds are also ways for things to be [Salmon,N]
     Full Idea: Total ways things cannot be are also 'worlds', or maximal ways for things to be. They are impossible worlds.
     From: Nathan Salmon (The Logic of What Might Have Been [1989], I)
     A reaction: This unorthodox view doesn't sound too plausible to me. To think of a circular square as a 'way things could be' sounds pretty empty, and mere playing with words. The number 7 could be the Emperor of China?
14682 Denial of impossible worlds involves two different confusions [Salmon,N]
     Full Idea: Every argument I am aware of against impossible worlds confuses ways for things to be with ways things might have been, or worse, confuses ways things cannot be with ways for things to be that cannot exist - or worse yet, commits both errors.
     From: Nathan Salmon (The Logic of What Might Have Been [1989], III)
     A reaction: He is claiming that 'ways for things to be' allows impossible worlds, whereas 'ways things might have been' appears not to. (I think! Read the paragraph yourself!)
14687 Without impossible worlds, how things might have been is the only way for things to be [Salmon,N]
     Full Idea: If one ignores impossible worlds, then ways things might have been are the only ways for things to be that are left.
     From: Nathan Salmon (The Logic of What Might Have Been [1989], IV)
     A reaction: Impossible worlds are included in 'ways for things to be', but excluded from 'ways things might have been'. I struggle with a circle being square as a 'way for circles to be'. I suppose being the greatest philosopher is a way for me to be.
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]
     Full Idea: On my conception, the notions of metaphysical necessity and possibility are not defined or analyzed in terms of the apparatus of possible worlds. The order of analysis is just the reverse: possible worlds rely on the notion of what might have been.
     From: Nathan Salmon (The Logic of What Might Have Been [1989], IV)
     A reaction: This view seems to be becoming the new orthodoxy, and I certainly agree with it. I have no idea how you can begin to talk about possible worlds if you don't already have some idea of what 'possible' means.
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]
     Full Idea: I conceive of possible worlds as certain sorts of maximal abstract entities according to which certain things (facts, states of affairs) obtain and certain other things do not obtain. They are total ways things might have been.
     From: Nathan Salmon (The Logic of What Might Have Been [1989], I)
14675 Possible worlds just have to be 'maximal', but they don't have to be consistent [Salmon,N]
     Full Idea: As far as I can tell, worlds need not be logically consistent. The only restriction on worlds is that they must be (in some sense) 'maximal' ways for things to be.
     From: Nathan Salmon (The Logic of What Might Have Been [1989], I)
     A reaction: The normal idea of a maximal model is that it must contain either p or ¬p, and not both, so I don't think I understand this thought, but I pass it on.
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]
     Full Idea: It is not a good idea to think of possible worlds as sets of propositions, and at the same time to think of propositions as sets of possible worlds.
     From: Nathan Salmon (The Logic of What Might Have Been [1989], I n3)
     A reaction: Salmon favours thinking of worlds as sets of propositions, and hence rejects the account of propositions as sets of worlds. He favours the 'Russellian' view of propositions, which seem to me to be the same as 'facts'.
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]
     Full Idea: If □ is to be sensitive to the quality of the truth of a proposition in its scope, then it must be sensitive as to whether an object is picked out by an essential property or by a contingent one.
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 4.3)
     A reaction: This incredibly simple idea strikes me as being powerful and important. ...However, creating illustrative examples leaves me in a state of confusion. You try it. They cite '9' and 'number of planets'. But is it just nominal essence? '9' must be 9.
13731 Objects retain their possible properties across worlds, so a bundle theory of them seems best [Fitting/Mendelsohn]
     Full Idea: The property of 'possibly being a Republican' is as much a property of Bill Clinton as is 'being a democrat'. So we don't peel off his properties from world to world. Hence the bundle theory fits our treatment of objects better than bare particulars.
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 7.3)
     A reaction: This bundle theory is better described in recent parlance as the 'modal profile'. I am reluctant to talk of a modal truth about something as one of its 'properties'. An objects, then, is a bundle of truths?
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]
     Full Idea: The main technical problem with counterpart theory is that the being-a-counterpart relation is, in general, neither symmetric nor transitive, so no natural logic of equality is forthcoming.
     From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 4.5)
     A reaction: That is, nothing is equal to a counterpart, either directly or indirectly.
19. Language / F. Communication / 3. Denial
11214 We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt]
     Full Idea: The standard view is that affirming not-A is more complex than affirming the atomic sentence A itself, with the latter determining its sense. But we could learn 'not' directly, by learning at once how to either affirm A or reject A.
     From: Ian Rumfitt ("Yes" and "No" [2000], IV)
     A reaction: [compressed] This seems fairly anti-Fregean in spirit, because it looks at the psychology of how we learn 'not' as a way of clarifying what we mean by it, rather than just looking at its logical behaviour (and thus giving it a secondary role).