22 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) |
| 10688 | 'Equivocation' is when terms do not mean the same thing in premises and conclusion [Beall/Restall] |
| Full Idea: 'Equivocation' is when the terms do not mean the same thing in the premises and in the conclusion. | |
| From: JC Beall / G Restall (Logical Consequence [2005], Intro) |
| 10690 | Formal logic is invariant under permutations, or devoid of content, or gives the norms for thought [Beall/Restall] |
| Full Idea: Logic is purely formal either when it is invariant under permutation of object (Tarski), or when it has totally abstracted away from all contents, or it is the constitutive norms for thought. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 2) | |
| A reaction: [compressed] The third account sounds rather woolly, and the second one sounds like a tricky operation, but the first one sounds clear and decisive, so I vote for Tarski. |
| 10691 | Logical consequence needs either proofs, or absence of counterexamples [Beall/Restall] |
| Full Idea: Technical work on logical consequence has either focused on proofs, where validity is the existence of a proof of the conclusions from the premises, or on models, which focus on the absence of counterexamples. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 3) |
| 10695 | Logical consequence is either necessary truth preservation, or preservation based on interpretation [Beall/Restall] |
| Full Idea: Two different views of logical consequence are necessary truth-preservation (based on modelling possible worlds; favoured by Realists), or truth-preservation based on the meanings of the logical vocabulary (differing in various models; for Anti-Realists). | |
| From: JC Beall / G Restall (Logical Consequence [2005], 2) | |
| A reaction: Thus Dummett prefers the second view, because the law of excluded middle is optional. My instincts are with the first one. |
| 10689 | A step is a 'material consequence' if we need contents as well as form [Beall/Restall] |
| Full Idea: A logical step is a 'material consequence' and not a formal one, if we need the contents as well as the structure or form. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 2) |
| 10696 | A 'logical truth' (or 'tautology', or 'theorem') follows from empty premises [Beall/Restall] |
| Full Idea: If a conclusion follows from an empty collection of premises, it is true by logic alone, and is a 'logical truth' (sometimes a 'tautology'), or, in the proof-centred approach, 'theorems'. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 4) | |
| A reaction: These truths are written as following from the empty set Φ. They are just implications derived from the axioms and the rules. |
| 10693 | Models are mathematical structures which interpret the non-logical primitives [Beall/Restall] |
| Full Idea: Models are abstract mathematical structures that provide possible interpretations for each of the non-logical primitives in a formal language. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 3) |
| 10692 | Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite [Beall/Restall] |
| Full Idea: There are many proof-systems, the main being Hilbert proofs (with simple rules and complex axioms), or natural deduction systems (with few axioms and many rules, and the rules constitute the meaning of the connectives). | |
| From: JC Beall / G Restall (Logical Consequence [2005], 3) |
| 12733 | Because of the definitions of cause, effect and power, cause and effect have the same power [Leibniz] |
| Full Idea: The primary mechanical axiom is that the whole cause and the entire effect have the same power [potentia]. ..This depends on the definition of cause, effect and power. | |
| From: Gottfried Leibniz (De arcanus motus [1676], 203), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 6 | |
| A reaction: This is a useful reminder that if one is going to build a metaphysics on powers (which I intend to do), then the conservation laws in physics are highly relevant. |
| 12734 | Every necessary proposition is demonstrable to someone who understands [Leibniz] |
| Full Idea: Every necessary proposition is demonstrable, at least by someone who understands it. | |
| From: Gottfried Leibniz (De arcanus motus [1676], 203), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 6 | |
| A reaction: This kind of optimism leads to the crisis of the Hilbert Programme in the 1930s. Gödel seems to have conclusively proved that Leibniz was wrong. What would Leibniz have made of Gödel? |
| 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? |
| 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. |