76 ideas
| 16841 | Good inference has mechanism, precision, scope, simplicity, fertility and background fit [Lipton] |
| Full Idea: Among the inferential virtues commonly cited are mechanism, precision, scope, simplicity, fertility or fruitfulness, and fit with background beliefs. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 08 'the guiding') | |
| A reaction: [He cites Hempel, Kuhn, Quine, and Newton-Smith] I take the over-arching term 'coherence' to cover much of this, though a bolder hypothesis offers more than mere coherence. |
| 16854 | Contrary pairs entail contradictions; one member entails negation of the other [Lipton] |
| Full Idea: All pairs of contraries entail a pair of contradictories, since one member of such a pair always entails the negation of the other. P&Q and not-P are contraries, but the first entails P, which is contradictory of not-P. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 09 'Is the best') |
| 10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
| Full Idea: While truth can be defined in a relative way, as truth in one particular model, a non-relative notion of truth is implied, as truth in all models. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: [The article is actually discussing arithmetic] This idea strikes me as extremely important. True-in-all-models is usually taken to be tautological, but it does seem to give a more universal notion of truth. See semantic truth, Tarski, Davidson etc etc. |
| 10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
| Full Idea: In standard ZFC ('Zermelo-Fraenkel with Choice') set theory we deal merely with pure sets, not with additional urelements. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: The 'urelements' would the actual objects that are members of the sets, be they physical or abstract. This idea is crucial to understanding philosophy of mathematics, and especially logicism. Must the sets exist, just as the urelements do? |
| 10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
| Full Idea: In second-order logic there are three kinds of variables, for objects, for functions, and for predicates or sets. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: It is interesting that a predicate seems to be the same as a set, which begs rather a lot of questions. For those who dislike second-order logic, there seems nothing instrinsically wicked in having variables ranging over innumerable multi-order types. |
| 10165 | 'Analysis' is the theory of the real numbers [Reck/Price] |
| Full Idea: 'Analysis' is the theory of the real numbers. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: 'Analysis' began with the infinitesimal calculus, which later built on the concept of 'limit'. A continuum of numbers seems to be required to make that work. |
| 10174 | Mereological arithmetic needs infinite objects, and function definitions [Reck/Price] |
| Full Idea: The difficulties for a nominalistic mereological approach to arithmetic is that an infinity of physical objects are needed (space-time points? strokes?), and it must define functions, such as 'successor'. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: Many ontologically austere accounts of arithmetic are faced with the problem of infinity. The obvious non-platonist response seems to be a modal or if-then approach. To postulate infinite abstract or physical entities so that we can add 3 and 2 is mad. |
| 10164 | Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price] |
| Full Idea: A common formulation of Peano Arithmetic uses 2nd-order logic, the constant '1', and a one-place function 's' ('successor'). Three axioms then give '1 is not a successor', 'different numbers have different successors', and induction. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: This is 'second-order' Peano Arithmetic, though it is at least as common to formulate in first-order terms (only quantifying over objects, not over properties - as is done here in the induction axiom). I like the use of '1' as basic instead of '0'! |
| 10172 | Set-theory gives a unified and an explicit basis for mathematics [Reck/Price] |
| Full Idea: The merits of basing an account of mathematics on set theory are that it allows for a comprehensive unified treatment of many otherwise separate branches of mathematics, and that all assumption, including existence, are explicit in the axioms. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: I am forming the impression that set-theory provides one rather good model (maybe the best available) for mathematics, but that doesn't mean that mathematics is set-theory. The best map of a landscape isn't a landscape. |
| 10167 | Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price] |
| Full Idea: Structuralism has emerged from the development of abstract algebra (such as group theory), the creation of axiom systems, the introduction of set theory, and Bourbaki's encyclopaedic survey of set theoretic structures. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: In other words, mathematics has gradually risen from one level of abstraction to the next, so that mathematical entities like points and numbers receive less and less attention, with relationships becoming more prominent. |
| 10169 | Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price] |
| Full Idea: Relativist Structuralism simply picks one particular model of axiomatised arithmetic (i.e. one particular interpretation that satisfies the axioms), and then stipulates what the elements, functions and quantifiers refer to. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: The point is that a successful model can be offered, and it doesn't matter which one, like having any sort of aeroplane, as long as it flies. I don't find this approach congenial, though having a model is good. What is the essence of flight? |
| 10179 | There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price] |
| Full Idea: The term 'structure' has two uses in the literature, what can be called 'particular structures' (which are particular relational systems), but also what can be called 'universal structures' - what particular systems share, or what they instantiate. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §6) | |
| A reaction: This is a very helpful distinction, because it clarifies why (rather to my surprise) some structuralists turn out to be platonists in a new guise. Personal my interest in structuralism has been anti-platonist from the start. |
| 10181 | Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price] |
| Full Idea: According to 'pattern' structuralism, what we study are not the various particular isomorphic models of arithmetic, but something in addition to them: a corresponding pattern. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §7) | |
| A reaction: Put like that, we have to feel a temptation to wield Ockham's Razor. It's bad enough trying to give the structure of all the isomorphic models, without seeking an even more abstract account of underlying patterns. But patterns connect to minds.. |
| 10182 | There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price] |
| Full Idea: There are four main variants of structuralism in the philosophy of mathematics - formalist structuralism, relativist structuralism, universalist structuralism (with modal variants), and pattern structuralism. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §9) | |
| A reaction: I'm not sure where Chihara's later book fits into this, though it is at the nominalist end of the spectrum. Shapiro and Resnik do patterns (the latter more loosely); Hellman does modal universalism; Quine does the relativist version. Dedekind? |
| 10168 | Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price] |
| Full Idea: Formalist Structuralism endorses structural methodology in mathematics, but rejects semantic and metaphysical problems as either meaningless, or purely formal, or as inference relations. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §3) | |
| A reaction: [very compressed] I find the third option fairly congenial, certainly in preference to rather platonist accounts of structuralism. One still needs to distinguish the mathematical from the non-mathematical in the inference relations. |
| 10178 | Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price] |
| Full Idea: It is tempting to take a modal turn, and quantify over all possible objects, because if there are only a finite number of actual objects, then there are no models (of the right sort) for Peano Arithmetic, and arithmetic is vacuously true. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: [compressed; Geoffrey Hellman is the chief champion of this view] The article asks whether we are not still left with the puzzle of whether infinitely many objects are possible, instead of existent. |
| 10176 | Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price] |
| Full Idea: Universalist Structuralism is a semantic thesis, that an arithmetical statement asserts a universal if-then statement. We build an if-then statement (using quantifiers) into the structure, and we generalise away from any one particular model. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: There remains the question of what is distinctively mathematical about the highly generalised network of inferences that is being described. Presumable the axioms capture that, but why those particular axioms? Russell is cited as an originator. |
| 10177 | Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price] |
| Full Idea: Universalist Structuralism is eliminativist about abstract objects, in a distinctive form. Instead of treating the base element (say '1') as an ambiguous referring expression (the Relativist approach), it is a variable which is quantified out. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: I am a temperamental eliminativist on this front (and most others) so this is tempting. I am also in love with the concept of a 'variable', which I take to be utterly fundamental to all conceptual thought, even in animals, and not just a trick of algebra. |
| 10171 | The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price] |
| Full Idea: Relativist Structuralism must first assume the existence of an infinite set, otherwise there would be no model to pick, and arithmetical terms would have no reference. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: See Idea 10169 for Relativist Structuralism. They point out that ZFC has an Axiom of Infinity. |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| Full Idea: One way for a nominalist to reject appeal to all abstract objects, including sets, is to only appeal to nominalistically acceptable objects, including mereological sums. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: I'm suddenly thinking that this looks very interesting and might be the way to go. The issue seems to be whether mereological sums should be seen as constrained by nature, or whether they are unrestricted. See Mereology in Ontology...|Intrinsic Identity. |
| 16814 | Understanding is not mysterious - it is just more knowledge, of causes [Lipton] |
| Full Idea: On the causal model of explanation, understanding is unmysterious and objective; it is not some sort of super-knowledge, but simply more knowledge; knowledge of causes. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 03 'Fact') | |
| A reaction: There seems to be some distinction between revealing some causes, and revealing a cause which 'makes the light dawn'. |
| 16825 | How do we distinguish negative from irrelevant evidence, if both match the hypothesis? [Lipton] |
| Full Idea: How can Best Explanation distinguish negative evidence from irrelevant evidence, when the evidence is logically consistent with the hypothesis? | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 05 'A case') | |
| A reaction: There seems no answer to this other than to assess batches of evidence by their coherence, rather than one at a time. Anomalies can be conclusive, or pure chance. |
| 16851 | The inference to observables and unobservables is almost the same, so why distinguish them? [Lipton] |
| Full Idea: The inferential path to unobservables is often the same as to unobserved observables. In these two sorts of case, the reason for belief can be equally strong, so the suggestion that we infer truth in one case but not the other seems perverse. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 09 'Voltaire's') | |
| A reaction: [Van Fraassen 1980 is the target of this] Van F seems to be in the grip of some sort of verificationism, which I always disliked on the grounds that speculation can be highly meaningful. Why embrace something because it 'could' be observed? |
| 16799 | Inductive inference is not proof, but weighing evidence and probability [Lipton] |
| Full Idea: Inductive inference is a matter of weighing evidence and judging probability, not of proof. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 01 'Underd') | |
| A reaction: This sounds like a plausible fallibilist response to the optimistic view of Aristotle. |
| 16798 | We infer from evidence by working out what would explain that evidence [Lipton] |
| Full Idea: Explanatory considerations are an important guide to inference, …we work out what to infer from our evidence by thinking about what would explain that evidence. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], Pref 2nd ed) | |
| A reaction: I take this to be inferences about the physical world, rather than of pure logic. The thesis sounds a bit thin, since there is no logical sense of 'infer' here, so all it could mean is 'what caused that?'. |
| 16856 | It is more impressive that relativity predicted Mercury's orbit than if it had accommodated it [Lipton] |
| Full Idea: We are more impressed by the fact that the special theory of relativity was used to predict the shift in the perihelion of Mercury than we would have been if we knew that the theory was constructed in order to account for that effect. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 10 'The fudging') | |
| A reaction: Lipton has a nice discussion of the relative merits of predicting data and accommodating it. He invites astrologers to predict events, rather than accommodate past ones. |
| 16857 | Predictions are best for finding explanations, because mere accommodations can be fudged [Lipton] |
| Full Idea: Accommodations are often worth less than predictions, because only they have to face the possibility that the best explanation of the fit between the theory and data is that the theoretical system was fudged. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 11 'Circularity') | |
| A reaction: Lipton illuminatingly explores the discovery by Semmelweiss of the cause of childbed fever. He predicted various explanations, and tested them out in a hospital. It clicks when the prediction occurs. |
| 16827 | If we make a hypothesis about data, then a deduction, where does the hypothesis come from? [Lipton] |
| Full Idea: The cost of the hypothetico-deductive method …is that we are left in the dark about the source of the hypotheses themselves. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 05 'Explanation') | |
| A reaction: How do we distinguish a wild hypothesis from a plausible one? It can only be from patterns in the data, rather than mere accumulations of data. If water causes cholera, or smoking causes cancer, the hypothesis guides the data search. |
| 16804 | Induction is repetition, instances, deduction, probability or causation [Lipton] |
| Full Idea: Five attempts to describe induction are 'more of the same', the instantial model, the hypothetico-deductive model, the Bayesian approach …and causal inference. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 01 'Descr') | |
| A reaction: This interesting list totally fails to mention the best answer, which is essentialism! If you observe some instances, you only begin to think that there will be more of the same if you think you have discerned the essence. Ravens are black things! |
| 16823 | Standard induction does not allow for vertical inferences, to some unobservable lower level [Lipton] |
| Full Idea: One of the problems of the extrapolation and instantial models of confirmation is that they do not cover vertical inferences, where we infer from what we observe to something at a different level that is often unobservable. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 04 'Attractions') | |
| A reaction: This is my preferred essentialist view of induction, that we don't just infer that future swans will be white, but also that whiteness is built into the biology of swans. There seems to be predictive induction and explanatory induction. |
| 16800 | An inductive inference is underdetermined, by definition [Lipton] |
| Full Idea: If an inference is inductive, then by definition it is underdetermined by the evidence and the rules of deduction. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 01 'Underd') |
| 16858 | We can argue to support our beliefs, so induction will support induction, for believers in induction [Lipton] |
| Full Idea: There is nothing illegitimate about giving arguments for beliefs one already holds. …So inductive justification of induction, while impotent against the skeptic, is legitimate for those who already rely on induction. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 11 'Circularity') | |
| A reaction: Not so fast! The first sentence is generally right, but if the 'beliefs one already holds' are beliefs about methods of argument, that is a different case. Compare 'this book is the word of God, because it says so in the book'. Can logic prove logic? |
| 16832 | If something in ravens makes them black, it may be essential (definitive of ravens) [Lipton] |
| Full Idea: We are considering that there is something in ravens, a gene perhaps, that makes them black, and this cause is part of the essence of ravens. Birds lacking this cause could not interbreed with ravens. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 05 'Unsuitable') | |
| A reaction: At last, the essentialist approach to induction! Of course, it is tricky to decide a priori whether there could be albino ravens. It only takes one white (interbreeding) raven to ruin a nice essentialist story. Individuals matter. |
| 16836 | My shoes are not white because they lack some black essence of ravens [Lipton] |
| Full Idea: The reason my shoe is white is not that it lacks some feature essential to ravens that makes them black. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 06 'The Method') | |
| A reaction: Good, but not totally true. If my shoes were made to grow from genes, and then had some raven spliced into them, we might manage it. That is an explanation, but a long way from the best one. Enquiry is explanations, not deductions. |
| 16831 | A theory may explain the blackness of a raven, but say nothing about the whiteness of shoes [Lipton] |
| Full Idea: Explanatory considerations help with the raven paradox since, while the raven hypothesis may provide an explanation for the blackness of a particular raven, neither the original hypothesis nor its contrastive explanation explain why the shoe is white. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 06 'Unsuitable') | |
| A reaction: For me, the examination of ravens is a search for the essence of ravenhood, which is why non-ravens don't help. Of course, if you eliminate all culprits except one, you have your culprit, but will your evidence stand up in court? |
| 16833 | We can't turn non-black non-ravens into ravens, to test the theory [Lipton] |
| Full Idea: We cannot transform a non-black non-raven into a raven to see whether we get a simultaneous transformation from non-black to black, in the way we can transform a flame without sodium into a flame with sodium. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 06 'Unsuitable') | |
| A reaction: A white shoe would be an example of a non-black non-raven. People mesmerised by the raven paradox are too concerned with investigation being a 'logical' process. Lipton makes a nice point. We need to know the nature of ravens. |
| 16834 | To pick a suitable contrast to ravens, we need a hypothesis about their genes [Lipton] |
| Full Idea: Without something like a hypothesis about the genes of ravens, we simply do not know what would count as a relevantly similar bird for comparison. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 06 'Unsuitable') | |
| A reaction: Lipton is endorsing the view that explanation should be 'contrastive', as well as aiming to discover the inner nature of ravens. He makes a good case for the contrastive approach. |
| 16802 | Bayes seems to rule out prior evidence, since that has a probability of one [Lipton] |
| Full Idea: Old evidence seems to provide some confirmation, but Bayesianism does not allow for this, since old evidence will have a prior probability of one, and so have no effect on the posterior probability of the hypothesis. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 01 'Descr') |
| 16803 | Bayes is too liberal, since any logical consequence of a hypothesis confirms it [Lipton] |
| Full Idea: Since the Bayesian account says a hypothesis is confirmed by any of its logical consequences …it seems to inherit the over-permissiveness of the hypothetico-deductive model. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 01 'Descr') | |
| A reaction: This sounds like Hempel's Raven Paradox, where the probability of some logical consequences seems impossible to assess. |
| 16801 | A hypothesis is confirmed if an unlikely prediction comes true [Lipton] |
| Full Idea: In English, Bayes's Theorem says that there is a high confirmation when your hypothesis entails an unlikely prediction that turns out to be correct - a very plausible claim. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 01 'Descr') | |
| A reaction: Presumably the simple point is that a likely prediction could have been caused by many things, but an unlikely prediction will probably only be caused by that thing. |
| 16837 | Bayes involves 'prior' probabilities, 'likelihood', 'posterior' probability, and 'conditionalising' [Lipton] |
| Full Idea: In p(H|E) = p(E|H)p(H)/p(E), the left side is the 'posterior' probability of H given E, p(E|H) is the 'likelihood' of E given H, and the others are the 'priors' of H and E. Moving from right to left is known as 'conditionalization'. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 07 'The Bayesian') |
| 16839 | Explanation may be an important part of implementing Bayes's Theorem [Lipton] |
| Full Idea: Explanatory considerations may play an important role in the actual mechanisms by which inquirers 'realize' Bayesian reasoning. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 07 'The Bayesian') | |
| A reaction: Lipton's strategy for making peace between IBE and Bayesians. Explanations give likeliness. The background question for Bayesians always seems to be how the initial probabilities are assigned. Pure logic won't do that job. |
| 16850 | Explanation may describe induction, but may not show how it justifies, or leads to truth [Lipton] |
| Full Idea: Explanation is a partial answer to the descriptive problem of induction, …but the justificatory problem is recalcitrant, since it may seem particularly implausible that explanatory considerations should be a reliable guide to truth. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 09 'Voltaire's') | |
| A reaction: His claim that explanation is a guide to inference is intended to bridge the gap. One might say that a good explanation has to be true, so just make sure your explanation is 'good', according to a few criteria. |
| 16807 | An explanation gives the reason the phenomenon occurred [Lipton] |
| Full Idea: According to the reason model of explanation, to explain a phenomenon is to give a reason to believe that the phenomenon occurs. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 02 'Reason') | |
| A reaction: [He cites Hempel 1965] Put like that, it doesn't sound very promising. Personally I believe things occur if my wife tells me they do, because I trust her. Lipton says knowing that it occurs is not understanding why it occurs. |
| 16808 | An explanation is what makes the unfamiliar familiar to us [Lipton] |
| Full Idea: On the 'familiarity' model of explanation, unfamiliar phenomena call for explanation, and good explanations somehow make them familiar. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 02 'Reason') | |
| A reaction: Lipton notes that his encourages explanation by analogy, but that may not add to understanding. A better version is that an explanation makes a phenomenon less surprising (but that sounds rather relative and subjective). |
| 16806 | An explanation is what is added to knowledge to yield understanding [Lipton] |
| Full Idea: The question about explanation can be put this way: What has to be added to knowledge to yield understanding? | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 02 'Underst') | |
| A reaction: In the spirit of Aristotle, I take 'understanding' to be the end of all enquiry, even if it's rather open-ended, relative and vague. Presumably there are lots of true explanations which don't deliver understanding, because baffling ingredients are cited. |
| 16822 | Seaching for explanations is a good way to discover the structure of the world [Lipton] |
| Full Idea: One of the points of our obsessive search for explanations is that this is a peculiarly effective way of discovering the structure of the world. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 04 'Attractions') | |
| A reaction: This remark is a nice corrective to the sceptical view that explanations are entirely subjective, pragmatic, and even conventional. Whether this means that there are 'real' and 'objective' explanations is another matter. |
| 16816 | In 'contrastive' explanation there is a fact and a foil - why that fact, rather than this foil? [Lipton] |
| Full Idea: In a 'contrastive' explanation what gets explained is not 'Why this?', but 'Why this rather than that?'. There is a fact and a foil, and one fact may have several foils. Why do leaves turn yellow in November rather than in January? | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 03 'Fact') | |
| A reaction: Lipton really likes this, and builds his story around it. Maybe, but it looks to me like an easier step towards a proper explanation. The foils are infinite. Why turn yellow rather than radioactive, insincere, divisible by three, or expensive? |
| 16826 | With too many causes, find a suitable 'foil' for contrast, and the field narrows right down [Lipton] |
| Full Idea: The class of possible causes is often too big, …but if we are lucky or clever enough to find or produce a contrast where fact and foil have similar histories, most potential explanations are immediately 'cancelled out', and we have a research programme. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 05 'A case') | |
| A reaction: He has a nice example of a triumph in 19th century German epidemiology. Once you get a good hypothesis, you can set up comparisons, based on a possible fact and a good foil. Genius is spotting hypothesis and foil. Nice. |
| 16811 | An explanation unifies a phenomenon with our account of other phenomena [Lipton] |
| Full Idea: According to the 'unification' model of explanation, we come to understand a phenomenon when we see how it fit together with other phenomena into unified whole. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 02 'Reason') | |
| A reaction: [He cites Kitcher 1989] This works quite well for a lot of explanation, but a revolutionary explanation might involve a completely new theory. Lipton says it is rather linguistic, and has no room for a regress of causes, or for singular explanations. |
| 16810 | Deduction explanation is too easy; any law at all will imply the facts - together with the facts! [Lipton] |
| Full Idea: Deduction models of explanation make it far too easy to explain. You can explain that planets move in an ellipse from the conjunction of the fact that they do, together with any law you please, say a law in economics. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 02 'Reason') |
| 16829 | We reject deductive explanations if they don't explain, not if the deduction is bad [Lipton] |
| Full Idea: The hypothetico-deductive model does not account for the negative impact of explanatory failure. We reject hypotheses because they fail to explain contrasts, not because they are logically incompatible with them. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 05 'Explanation') | |
| A reaction: The general move in modern accounts of investigation is away from an excessive emphasis on logic that used to be favoured. The underpinning of this is that science concerns mechanisms more than equations. |
| 16809 | Good explanations may involve no laws and no deductions [Lipton] |
| Full Idea: Many ordinary explanations include no laws and allow no deduction, yet are not incomplete or mere sketches. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 02 'Reason') | |
| A reaction: The simplest sort of explanation simply shows the underlying cause. |
| 16812 | An explanation shows why it was necessary that the effect occurred [Lipton] |
| Full Idea: According to the 'necessity' model of explanation, an explanation shows that the phenomenon in question had to occur. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 02 'Reason') | |
| A reaction: [He cites Glymour 1980] Lipton objects that the sort of necessity involved is too uncertain, can't account for the 'why-regress', and doesn't fit everyday explanation, like why we abandoned the football match. |
| 16846 | A cause may not be an explanation [Lipton] |
| Full Idea: I take it that we may think about causes without thinking especially about explanations, and so we might judge likeliest cause without considering loveliest explanation. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 08 'From cause') |
| 16813 | To explain is to give either the causal history, or the causal mechanism [Lipton] |
| Full Idea: According to the causal model of explanation, to explain a phenomenon is simply to give information about its causal history, or, where the phenomenon is itself a causal regularity, to give information about the mechanism linking cause and effect. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 03 'Fact') | |
| A reaction: [He cites Lewis's 1986 paper] Simply citing causal regularity seems to me to explain nothing. It happened because it always happens. Mechanism, on the other hand, is just what we are after. |
| 16815 | Mathematical and philosophical explanations are not causal [Lipton] |
| Full Idea: Mathematical explanations are never causal, and philosophical explanations seldom are. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 03 'Fact') | |
| A reaction: There may still be a 'direction' of explanation in mathematics, as when the nature of the triangle explains the Pythagoras Theorem, but the theorem may not give you the basic nature of triangles. Lipton suggests 'determination' for 'causation'. |
| 16849 | Explanations may be easier to find than causes [Lipton] |
| Full Idea: It is often easier to say what a factor would explain than it is to say what it would cause. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 08 'From cause') | |
| A reaction: Presumably the presence of some factor might explain something, but the factor itself might have mysterious causal powers. A catalyst, for example. We don't need to understand the factor that explains. |
| 16848 | Causal inferences are clearest when we can manipulate things [Lipton] |
| Full Idea: Our most secure basis for causal inference is manipulation, as when flicking the switch causes the light to go on. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 08 'From cause') | |
| A reaction: Correct, but Woodward elevates this into an entire theory of causation, which does not convince me. |
| 16842 | We want to know not just the cause, but how the cause operated [Lipton] |
| Full Idea: We understand a phenomenon better when we know not just what caused it, but how the cause operated. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 08 'the guiding') | |
| A reaction: This is the key point behind the desire for 'mechanism' in explanation. It strikes me as undeniable. |
| 16840 | To maximise probability, don't go beyond your data [Lipton] |
| Full Idea: If all we wanted was to maximise probability, we would never venture beyond our data. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 07 'friends') |
| 16824 | Is Inference to the Best Explanation nothing more than inferring the likeliest cause? [Lipton] |
| Full Idea: A suspicion is that Inference to the Best Explanation is nothing more than Inference to the Likeliest Cause in fancy dress, and so fails to account for the symptoms of likeliness. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 04 'Attractions') | |
| A reaction: In a lot of cases the cause is the explanation. An explanation might be the absence of a cause (as in 'you forgot to switch it on'). Lipton's 'lovely' explanations go further, and reveal a network of causes. |
| 16817 | Best Explanation as a guide to inference is preferable to best standard explanations [Lipton] |
| Full Idea: The core idea of Inference to the Best Explanation (IBE) is that explanatory considerations are a guide to inference. …Inserting one of the standard models of explanation yields disappointing results, because of their backward state. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 04 'Spelling') | |
| A reaction: Inferences tend to come one at a time, but I see best explanations as the formation of coherent pictures. The tricky bit is when to decide the coherence makes it acceptable. Lipton has that problem too, with his inferences. 'Working explanations'. |
| 16818 | The 'likeliest' explanation is the best supported; the 'loveliest' gives the most understanding [Lipton] |
| Full Idea: There is a distinction between the explanation best supported by the evidence, and the explanation that would provide the most understanding: in short, between the 'likeliest' and the 'loveliest' explanation. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 04 'Spelling') | |
| A reaction: A very nice, very real and very illuminating distinction. Presumably truth must play an important role in both likelihood and loveliness. |
| 16819 | IBE is inferring that the best potential explanation is the actual explanation [Lipton] |
| Full Idea: According to Inference to the Best Explanation we do not infer the best actual explanation; rather we infer that the best of the available potential explanations is an actual explanation. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 04 'Spelling') | |
| A reaction: Clearly to say that you should just accept the best available explanation is asking for trouble, if all the available explanations are absurd. But what are the criteria for saying the best one is the actual one? |
| 16820 | Finding the 'loveliest' potential explanation links truth to understanding [Lipton] |
| Full Idea: We should considere Inference to the Loveliest Potential Explanation, …which links the search for truth and the search for understanding in a fundamental way. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 04 'Spelling') |
| 16828 | IBE is not passive treatment of data, but involves feedback between theory and data search [Lipton] |
| Full Idea: The slogan 'Inference to the Best Explanation' may bring to mind an excessively passive picture of scientific enquiry, …but there is the feedback between hypothesis formation and data acquisition that characterises actual enquiry. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 05 'Explanation') | |
| A reaction: Perhaps it should be renamed 'Search for the Best Explanation'. |
| 16844 | A contrasting difference is the cause if it offers the best explanation [Lipton] |
| Full Idea: We are to infer that a difference marks a cause just in case the difference would provide the best explanation of the contrast. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 08 'Improved') | |
| A reaction: Lipton's offers this as his distinctive contribution to Mill's methods of enquiry. His point is that we draw inferences for explanatory reasons. He rests on Mill, and on contrastive explanation. It sounds rightish, but a bit optimistic. |
| 16853 | We select possible explanations for explanatory reasons, as well as choosing among them [Lipton] |
| Full Idea: Explanatory considerations can play a role in the generation of potential explanations as well as in the subsequent selection from among them. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 09 'The two-stage') | |
| A reaction: Lipton offers this to meet an obvious objection to Inference to the Best Explanation - that compiling the possible explanations seems to need guidance. Seems a good reply. |
| 16821 | Must we only have one explanation, and must all the data be made relevant? [Lipton] |
| Full Idea: Two problems for IBE are that only one explanation can be inferred from any set of data, and that the only data that are relevant to a hypothesis are data the hypothesis explains. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 04 'Spelling') | |
| A reaction: I don't see why the theory prohibits a tie for what is 'best', given that you don't have to commit. The second one is partly to do with what observers should do about anomalies, and it is sometimes right to ignore them. |
| 16838 | Bayesians say best explanations build up an incoherent overall position [Lipton] |
| Full Idea: Bayesians object to inference to the best explanation, because someone who favoured powerful ('lovely') explanations would end up with an incoherent distribution of states of belief. They would be persuaded by loss-making wagers (a 'dutch book'). | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 07 'The Bayesian') | |
| A reaction: [compressed; he cites Van Fraassen 1989 Ch.7] Lipton's Ch. 7 tries to address this issue. |
| 16855 | The best theory is boring: compare 'all planets move elliptically' with 'most of them do' [Lipton] |
| Full Idea: The best theory is almost always boring. …The claim that all planets move in ellipses is interesting, and the claim that some do not is not interesting. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 09 'Is the best') | |
| A reaction: This applies to any extraction of a universal 'law' by induction. The best theory just affirms what has been observed. How could generalising about what you haven't observed be 'better'? Answer: because it goes via the essence. |
| 16852 | Best explanation can't be a guide to truth, because the truth must precede explanation [Lipton] |
| Full Idea: Inference to the best explanation cannot be epistemically effective, since an actual explanation must be true, so one would have to know the truth before one could infer an explanation. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 09 'Voltaire's') | |
| A reaction: Lipton rests on 'contrastive' explanation, so that the one that explains more is more likely to be true. If true, it explains. That seems to me correct, even though it could occasionally go horribly wrong. Approach explanation cautiously. |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 16847 | Counterfactual causation makes causes necessary but not sufficient [Lipton] |
| Full Idea: The counterfactual conception of causation makes causes necessary but not sufficient conditions for their effects. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 08 'From cause') | |
| A reaction: Interesting. Then causes would be necessary, but would not necessitate. So what makes a cause sufficient? |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |