60 ideas
17070 | Coherence is consilience, simplicity, analogy, and fitting into a web of belief [Smart] |
Full Idea: I shall make use of the admittedly imprecise notions of consilience, simplicity, analogy and fitting into a web of belief, or in short of 'coherence'. | |
From: J.J.C. Smart (Explanation - Opening Address [1990], p.06) | |
A reaction: Coherence sounds like a family of tests, rather than a single unified concept. I still like coherence, though. |
17072 | We need comprehensiveness, as well as self-coherence [Smart] |
Full Idea: Not mere self-coherence, but comprehensiveness belongs to the notion of coherence. | |
From: J.J.C. Smart (Explanation - Opening Address [1990], p.07) |
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. |
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) |
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) |
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 |
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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 |
|
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. |
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) |
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. |
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. |
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) |
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) |
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) |
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) |
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) |
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). |
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. |
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'. |
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. |
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) |
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. |
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. |
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) |
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. |
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? |
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. |
17073 | I simply reject evidence, if it is totally contrary to my web of belief [Smart] |
Full Idea: The simplest way of fitting the putative observed phenomena of telepathy or clairvoyance into my web of belief is to refuse to take them at face value. | |
From: J.J.C. Smart (Explanation - Opening Address [1990], p.07-8) | |
A reaction: Love it. It is very disconcerting for the sceptical naturalist to be faced with adamant claims that the paranormal has occurred, but my response is exactly the same as Smart's. I reject the reports, no matter how passionately they are asserted. |
17077 | The height of a flagpole could be fixed by its angle of shadow, but that would be very unusual [Smart] |
Full Idea: You could imagine a person using the angle from a theodolite to decide a suitable spot to cut the height of the flagpole, …but since such circumstances would be very unusual we naturally say the flagpole subtends the angle because of its height. | |
From: J.J.C. Smart (Explanation - Opening Address [1990], p.14) | |
A reaction: [compressed; he mentions Van Fraassen 1980:132-3 for a similar point] As a response this seems a bit lame, if the direction is fixed by what is 'usual'. I think the key point is that the direction of explanation is one way or the other, not both. |
17078 | Universe expansion explains the red shift, but not vice versa [Smart] |
Full Idea: The theory of the expansion of the universe renders the red shift no longer puzzling, whereas he expansion of the universe is hardly rendered less puzzling by facts about the red shift. | |
From: J.J.C. Smart (Explanation - Opening Address [1990], p.15) | |
A reaction: The direction of explanation is, I take it, made obvious by the direction of causation, with questions about what is 'puzzling' as mere side-effects. |
17061 | Explanation of a fact is fitting it into a system of beliefs [Smart] |
Full Idea: I want to characterise explanation of some fact as a matter of fitting belief in this fact into a system of beliefs. | |
From: J.J.C. Smart (Explanation - Opening Address [1990], p.02) | |
A reaction: Sounds good to me. Simple facts slot straight into daily beliefs, and deep obscure facts are explained when we hook them up to things we have already grasped. Quark theory fits into prior physics of forces, properties etc. |
17074 | Explanations are bad by fitting badly with a web of beliefs, or fitting well into a bad web [Smart] |
Full Idea: An explanation may be bad if it fits only into a bad web of belief. It can also be bad if it fits into a (possibly good) web of belief in a bad sort of way. | |
From: J.J.C. Smart (Explanation - Opening Address [1990], p.09) | |
A reaction: Nice. If you think someone has an absurd web of beliefs, then it counts against some belief (for you) if it fits beautifully into the other person's belief system. Judgement of coherence comes in at different levels. |
17076 | Deducing from laws is one possible way to achieve a coherent explanation [Smart] |
Full Idea: The Hempelian deductive-nomological model of explanation clearly fits in well with the notion of explanation in terms of coherence. One way of fitting a belief into a system is to show that it is deducible from other beliefs. | |
From: J.J.C. Smart (Explanation - Opening Address [1990], p.13) | |
A reaction: Smart goes on to reject the law-based deductive approach, for familiar reasons, but at least it has something in common with the Smart view of explanation, which is the one I like. |
17071 | An explanation is better if it also explains phenomena from a different field [Smart] |
Full Idea: One explanation will be a better explanation that another if it also explains a set of phenomena from a different field ('consilience'). | |
From: J.J.C. Smart (Explanation - Opening Address [1990], p.07) | |
A reaction: This would count as 'unexpected accommodation', rather than prediction. It is a nice addition to Lipton's comparison of mere accommodation versus prediction as criteria. It sounds like a strong criterion for a persuasive explanation. |
17062 | If scientific explanation is causal, that rules out mathematical explanation [Smart] |
Full Idea: I class mathematical explanation with scientific explanation. This would be resisted by those who, unlike me, regard the notion of causation as essential to scientific explanation. | |
From: J.J.C. Smart (Explanation - Opening Address [1990], p.02-3) | |
A reaction: I aim to champion mathematical explanation, in terms of axioms etc., so I am realising that my instinctive attraction to exclusively causal explanation won't do. What explanation needs is a direction of dependence. |
17075 | Scientific explanation tends to reduce things to the unfamiliar (not the familiar) [Smart] |
Full Idea: The history of science suggests that most often explanation is reduction to the unfamiliar. | |
From: J.J.C. Smart (Explanation - Opening Address [1990], p.11) | |
A reaction: Boyle was keen to reduce things to the familiar, but that was early days for science, and some nasty shocks were coming our way. What would Boyle make of quantum non-locality? |
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). |
17063 | Unlike Newton, Einstein's general theory explains the perihelion of Mercury [Smart] |
Full Idea: Newtonian celestial mechanics does not explain the advance of the perihelion of Mercury, while Einstein's general theory of relativity does. | |
From: J.J.C. Smart (Explanation - Opening Address [1990], p.03) | |
A reaction: A perfect example of why explanation is the central concept in science, and probably in all epistemological activity. The desire to know is the desire for an explanation. Once the explanation is obvious, we know. |