30 ideas
| 10528 | Definitions concern how we should speak, not how things are [Fine,K] |
| Full Idea: Our concern in giving a definition is not to say how things are by to say how we wish to speak | |
| From: Kit Fine (Precis of 'Limits of Abstraction' [2005], p.310) | |
| A reaction: This sounds like an acceptable piece of wisdom which arises out of analytical and linguistic philosophy. It puts a damper on the Socratic dream of using definition of reveal the nature of reality. |
| 15717 | Using Choice, you can cut up a small ball and make an enormous one from the pieces [Kaplan/Kaplan] |
| Full Idea: The problem with the Axiom of Choice is that it allows an initiate (by an ingenious train of reasoning) to cut a golf ball into a finite number of pieces and put them together again to make a globe as big as the sun. | |
| From: R Kaplan / E Kaplan (The Art of the Infinite [2003], 9) | |
| A reaction: I'm not sure how this works (and I think it was proposed by the young Tarski), but it sounds like a real problem to me, for all the modern assumptions that Choice is fine. |
| 15712 | 1 and 0, then add for naturals, subtract for negatives, divide for rationals, take roots for irrationals [Kaplan/Kaplan] |
| Full Idea: You have 1 and 0, something and nothing. Adding gives us the naturals. Subtracting brings the negatives into light; dividing, the rationals; only with a new operation, taking of roots, do the irrationals show themselves. | |
| From: R Kaplan / E Kaplan (The Art of the Infinite [2003], 1 'Mind') | |
| A reaction: The suggestion is constructivist, I suppose - that it is only operations that produce numbers. They go on to show that complex numbers don't quite fit the pattern. |
| 15711 | The rationals are everywhere - the irrationals are everywhere else [Kaplan/Kaplan] |
| Full Idea: The rationals are everywhere - the irrationals are everywhere else. | |
| From: R Kaplan / E Kaplan (The Art of the Infinite [2003], 1 'Nameless') | |
| A reaction: Nice. That is, the rationals may be dense (you can always find another one in any gap), but the irrationals are continuous (no gaps). |
| 15714 | 'Commutative' laws say order makes no difference; 'associative' laws say groupings make no difference [Kaplan/Kaplan] |
| Full Idea: The 'commutative' laws say the order in which you add or multiply two numbers makes no difference; ...the 'associative' laws declare that regrouping couldn't change a sum or product (e.g. a+(b+c)=(a+b)+c ). | |
| From: R Kaplan / E Kaplan (The Art of the Infinite [2003], 2 'Tablets') | |
| A reaction: This seem utterly self-evident, but in more complex systems they can break down, so it is worth being conscious of them. |
| 15715 | 'Distributive' laws say if you add then multiply, or multiply then add, you get the same result [Kaplan/Kaplan] |
| Full Idea: The 'distributive' law says you will get the same result if you first add two numbers, and then multiply them by a third, or first multiply each by the third and then add the results (i.e. a · (b+c) = a · b + a · c ). | |
| From: R Kaplan / E Kaplan (The Art of the Infinite [2003], 2 'Tablets') | |
| A reaction: Obviously this will depend on getting the brackets right, to ensure you are indeed doing the same operations both ways. |
| 10529 | If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K] |
| Full Idea: Neo-Fregeans have thought that Hume's Principle, and the like, might be definitive of number and therefore not subject to the usual epistemological worries over its truth. | |
| From: Kit Fine (Precis of 'Limits of Abstraction' [2005], p.310) | |
| A reaction: This seems to be the underlying dream of logicism - that arithmetic is actually brought into existence by definitions, rather than by truths derived from elsewhere. But we must be able to count physical objects, as well as just counting numbers. |
| 10530 | Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K] |
| Full Idea: The fundamental difficulty facing the neo-Fregean is to either adopt the predicative reading of Hume's Principle, defining numbers, but inadequate, or the impredicative reading, which is adequate, but not really a definition. | |
| From: Kit Fine (Precis of 'Limits of Abstraction' [2005], p.312) | |
| A reaction: I'm not sure I understand this, but the general drift is the difficulty of building a system which has been brought into existence just by definition. |
| 13065 | Understanding is an extremely vague concept [Salmon] |
| Full Idea: Understanding is an extremely vague concept. | |
| From: Wesley Salmon (Four Decades of Scientific Explanation [1989], 4.3) | |
| A reaction: True, I suppose, but we usually recognise understanding when we encounter it, and everybody has a pretty clear notion of an 'increase' in understanding. I suspect that the concept is perfectly clear, but we lack any scale for measuring it. |
| 13047 | It is knowing 'why' that gives scientific understanding, not knowing 'that' [Salmon] |
| Full Idea: Knowledge 'that' is descriptive, and knowledge 'why' is explanatory, and it is the latter that provides scientific understanding of our world. | |
| From: Wesley Salmon (Four Decades of Scientific Explanation [1989], Intro) | |
| A reaction: I agree, but of course, knowing 'why' may require a lot of knowing 'that'. People with extensive knowledge 'that' things are so tend to understand why something happens more readily than the rest of us ignoramuses. |
| 13054 | Correlations can provide predictions, but only causes can give explanations [Salmon] |
| Full Idea: Various kinds of correlations exist that provide excellent bases for prediction, but because no suitable causal relations exist (or are known), these correlations do not furnish explanation. | |
| From: Wesley Salmon (Four Decades of Scientific Explanation [1989], 2.3) | |
| A reaction: There may be problem cases for the claim that all explanations are causal, but I certainly think that this idea is essentially right. Prediction can come from induction, but inductions may be true and yet baffling. |
| 13067 | For the instrumentalists there are no scientific explanations [Salmon] |
| Full Idea: There is a centuries-old philosophical tradition, sometimes referred to by the name of 'instrumentalism', that has denied the claim that science has explanatory power. For the instrumentalists there are no scientific explanations. | |
| From: Wesley Salmon (Four Decades of Scientific Explanation [1989], 4.3) | |
| A reaction: [He quotes Coffa] Presumably it is just a matter of matching the world to the readings on the instruments, aiming at van Fraassen's 'empirical adequacy'. If there are no scientific explanations, does that mean that there are no explanations at all? Daft! |
| 15713 | The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan] |
| Full Idea: The claim that no number is greater than a million is confirmed by the first million test cases. | |
| From: R Kaplan / E Kaplan (The Art of the Infinite [2003], 2 'Intro') | |
| A reaction: Extrapolate from this, and you can have as large a number of cases as you could possibly think of failing to do the inductive job. Love it! Induction isn't about accumulations of cases. It is about explanation, which is about essence. Yes! |
| 13055 | Good induction needs 'total evidence' - the absence at the time of any undermining evidence [Salmon] |
| Full Idea: Inductive logicians have a 'requirement of total evidence': induction is strong if 1) it has true premises, 2) it has correct inductive form, and 3) no additional evidence that would change the degree of support is available at the time. | |
| From: Wesley Salmon (Four Decades of Scientific Explanation [1989], 2.4.2) | |
| A reaction: The evidence might be very close at hand, but not quite 'available' to the person doing the induction. |
| 13046 | Scientific explanation is not reducing the unfamiliar to the familiar [Salmon] |
| Full Idea: I reject the view that scientific explanation involves reduction of the unfamiliar to the familiar. | |
| From: Wesley Salmon (Four Decades of Scientific Explanation [1989], Pref) | |
| A reaction: Aristotle sometimes seems to imply this account of explanation, and I would have to agree with Salmon's view of it. Aristotle is also, though, aware of real explanations, definitions and essences. People are 'familiar' with some peculiar things. |
| 13058 | Why-questions can seek evidence as well as explanation [Salmon] |
| Full Idea: There are evidence-seeking why-questions, as well as explanation-seeking why-questions. | |
| From: Wesley Salmon (Four Decades of Scientific Explanation [1989], 3.2) | |
| A reaction: Surely we would all prefer an explanation to mere evidence? It seems to me that they are all explanation-seeking, but that we are grateful for some evidence when no full explanation is available. Explanation renders evidence otiose. |
| 13050 | The 'inferential' conception is that all scientific explanations are arguments [Salmon] |
| Full Idea: The 'inferential' conception of scientific explanation is the thesis that all legitimate scientific explanations are arguments of one sort or another. | |
| From: Wesley Salmon (Four Decades of Scientific Explanation [1989], 1.1) | |
| A reaction: This seems to imply that someone has to be persuaded of something, and hence seems a rather too pragmatic view. I presume an explanation might be no more than dumbly pointing at conclusive evidence of a cause. Man with smoking gun. |
| 13059 | Ontic explanations can be facts, or reports of facts [Salmon] |
| Full Idea: Proponents of the ontic conception of explanation can say that explanations exist in the world as facts, or that they are reports of such facts (as opposed to the view of explanations as arguments, or as speech acts). | |
| From: Wesley Salmon (Four Decades of Scientific Explanation [1989], 3.2) | |
| A reaction: [compressed] I am strongly drawn to the ontic approach, but not sure whether we want facts, or reports of them. The facts are the causal nexus, but which parts of the nexus provide the main aspect of explanation? I'll vote for reports, for now. |
| 13064 | The three basic conceptions of scientific explanation are modal, epistemic, and ontic [Salmon] |
| Full Idea: There are three basic conceptions of scientific explanation - modal, epistemic, and ontic - which can be discerned in Aristotle, and that have persisted down the ages. | |
| From: Wesley Salmon (Four Decades of Scientific Explanation [1989], 4.1) |
| 13049 | We must distinguish true laws because they (unlike accidental generalizations) explain things [Salmon] |
| Full Idea: The problem is to distinguish between laws and accidental generalizations, for laws have explanatory force while accidental generalizations, even if they are true, do not. | |
| From: Wesley Salmon (Four Decades of Scientific Explanation [1989], 1.1) | |
| A reaction: [He is discussing Hempel and Oppenheim 1948] This seems obviously right, but I can only make sense of the explanatory power if we have identified the mechanism which requires the generalisation to continue in future cases. |
| 13051 | Deductive-nomological explanations will predict, and their predictions will explain [Salmon] |
| Full Idea: The deductive-nomological view has an explanation/prediction symmetry thesis - that a correct explanation could be a scientific prediction, and that any deductive prediction could serve as a deductive-nomological explanation. | |
| From: Wesley Salmon (Four Decades of Scientific Explanation [1989], 1.1) | |
| A reaction: Of course, not all predictions will explain, or vice versa. Weird regularities become predictable but remain baffling. Good explanations may be of unrepeatable events. It is the 'law' in the account that ties the two ends together. |
| 13053 | A law is not enough for explanation - we need information about what makes a difference [Salmon] |
| Full Idea: To provide an adequate explanation of any given fact, we need to provide information that is relevant to the occurrence of that fact - information that makes a difference to its occurrence. It is not enough to subsume it under a general law. | |
| From: Wesley Salmon (Four Decades of Scientific Explanation [1989], 2.2) | |
| A reaction: [He cites Bromberger for this idea] Salmon is identifying this idea as the beginnings of trouble for the covering-law account of explanation, and it sounds exactly right. |
| 13061 | Flagpoles explain shadows, and not vice versa, because of temporal ordering [Salmon] |
| Full Idea: The height of the flagpole explains the length of the shadow because the interaction between the sunlight and the flagpole occurs before the interaction between the sunlight and the ground. | |
| From: Wesley Salmon (Four Decades of Scientific Explanation [1989], 3.6) | |
| A reaction: [Bromberger produced the flagpole example] This seems to be correct, and would apply to all physical cases, but there may still be cases of explanation which are not causal (in mathematics, for example). |
| 13045 | Explanation at the quantum level will probably be by entirely new mechanisms [Salmon] |
| Full Idea: My basic feeling about explanation in the quantum realm is that it will involve mechanisms, but mechanisms that are quite different from those that seem to work in the macrocosm. | |
| From: Wesley Salmon (Four Decades of Scientific Explanation [1989], Pref) | |
| A reaction: Since I take most explanation to be by mechanisms (or some abstraction analogous to mechanisms), then I think this is probably right (rather than being by new 'laws'). |
| 13062 | Does an item have a function the first time it occurs? [Salmon] |
| Full Idea: In functional explanation, there is a disagreement over whether an item has a function the first time it occurs. | |
| From: Wesley Salmon (Four Decades of Scientific Explanation [1989], 3.8) | |
| A reaction: This question arises particularly in evolutionary contexts, and would obviously not generally arise in the case of human artefacts. |
| 13063 | Explanations reveal the mechanisms which produce the facts [Salmon] |
| Full Idea: I favour an ontic conception of explanation, that explanations reveal the mechanisms, causal or other, that produce the facts we are trying to explain. | |
| From: Wesley Salmon (Four Decades of Scientific Explanation [1989], 4.1) | |
| A reaction: [He also cites Coffa and Peter Railton] A structure may explain, and only be supported by causal powers, but it doesn't seem to be the causal powers that do the explaining. Is a peg fitting a hole explained causally? |
| 13060 | Can events whose probabilities are low be explained? [Salmon] |
| Full Idea: Can events whose probabilities are low be explained? | |
| From: Wesley Salmon (Four Decades of Scientific Explanation [1989], 3.6) | |
| A reaction: I take this to be one of the reasons why explanation must ultimately reside at the level of individual objects and events, rather than residing with generalisations and laws. |
| 13056 | Statistical explanation needs relevance, not high probability [Salmon] |
| Full Idea: Statistical relevance, not high probability, is the key desideratum in statistical explanation. | |
| From: Wesley Salmon (Four Decades of Scientific Explanation [1989], 2.5) | |
| A reaction: I suspect that this is because the explanation will not ultimately be probabilistic at all, but mechanical and causal. Hence the link is what counts, which is the relevance. He notes that relevance needs two values instead of one high value. |
| 13057 | Think of probabilities in terms of propensities rather than frequencies [Salmon] |
| Full Idea: Perhaps we should think of probabilities in terms of propensities rather than frequencies. | |
| From: Wesley Salmon (Four Decades of Scientific Explanation [1989], 3.2) | |
| A reaction: [He cites Coffa 1974 for this] I find this suggestion very appealing, as it connects up with dispositions and powers, which I take to be the building blocks of all explanation. It is, of course, easier to render frequencies numerically. |
| 10527 | An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K] |
| Full Idea: If an abstraction principle is going to be acceptable, then it should not 'inflate', i.e. it should not result in there being more abstracts than there are objects. By this mark Hume's Principle will be acceptable, but Frege's Law V will not. | |
| From: Kit Fine (Precis of 'Limits of Abstraction' [2005], p.307) | |
| A reaction: I take this to be motivated by my own intuition that abstract concepts had better be rooted in the world, or they are not worth the paper they are written on. The underlying idea this sort of abstraction is that it is 'shared' between objects. |