| 5854 | Nobody fears a disease which nobody has yet caught [Aristotle] |
| Full Idea: Nobody is on his guard against a disease that nobody has yet caught. | |
| From: Aristotle (The Art of Rhetoric [c.350 BCE], 1372a27) | |
| A reaction: A beautifully simple indication of one problem with induction. In a dangerous situation, you can't wait around for a few experiences in order to learn the regularities and rules. Either you are doomed, or you must explain using related experiences. |
| 12271 | Induction is the progress from particulars to universals [Aristotle] |
| Full Idea: Induction is the progress from particulars to universals; if the skilled pilot is the best pilot and the skilled charioteer the best charioteer, then, in general, the skilled man is the best man in any particular sphere. | |
| From: Aristotle (Topics [c.331 BCE], 105a15) | |
| A reaction: It is a bit unclear whether we are deriving universal concepts, or merely general truths. Need general truths be absolute or necessary truths? Presumably occasionally the best person is not the most skilled, as in playing a musical instrument. |
| 5714 | Even simple facts are hard to believe at first hearing [Lucretius] |
| Full Idea: No fact is so simple that it is not harder to believe than to doubt at the first presentation. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], II.1022) | |
| A reaction: Hence induction is just 'drumming it in' until you come to believe it. There are good evolutionary reasons why we should be like this, because we would otherwise believe all sorts of silly half-perceptions in the gloaming. |
| 17027 | Science deduces propositions from phenomena, and generalises them by induction [Newton] |
| Full Idea: In experimental philosophy, propositions are deduced from the phenomena and are made general by induction. | |
| From: Isaac Newton (Principia Mathematica [1687], Bk 3 Gen Schol) | |
| A reaction: Sounds easy, but generalising by induction requires all sorts of assumptions about the stability of natural kinds. Since the kinds are only arrived at by induction, it is not easy to give a proper account here. |
| 7446 | The idea of inductive evidence, around 1660, made Hume's problem possible [Hume, by Hacking] |
| Full Idea: Hume's sceptical problem of induction could not have arisen much before 1660, for there was no concept of inductive evidence in terms of which to raise it. | |
| From: report of David Hume (Treatise of Human Nature [1739]) by Ian Hacking - The Emergence of Probability Cont 19 | |
| A reaction: Hacking is the expert, but Ideas 1683 and 1886 suggest there was some thinking on the problem in the ancient world. The worry about whether the future would be like the past must occasionally have bothered someone. |
| 16845 | The whole theory of induction rests on causes [Mill] |
| Full Idea: The notion of cause is the root of the whole theory of induction. | |
| From: John Stuart Mill (System of Logic [1843], 3.05.2), quoted by Peter Lipton - Inference to the Best Explanation (2nd) 08 'From cause' | |
| A reaction: This sounds much better to me than the Humean view that it rests on the psychology of regularity and habit. However, maybe Hume describes induction, and Mill is adding abduction (inference to the best explanation). |
| 16843 | Mill's methods (Difference,Agreement,Residues,Concomitance,Hypothesis) don't nail induction [Mill, by Lipton] |
| Full Idea: The Method of Difference, and even the full four 'experimental methods' (Difference, Agreement, Residues and Concomitant Variations) are agreed on all sides to be incomplete accounts of inductive inference. Mill himself added the Method of Hypothesis. | |
| From: report of John Stuart Mill (System of Logic [1843], 3.14.4-5) by Peter Lipton - Inference to the Best Explanation (2nd) 08 'Improved' | |
| A reaction: If induction is just 'learning from experience' (my preferred definition) then there is unlikely to be a precise account of its methods. Mill seems to have done a lovely job. |
| 8624 | Induction is merely psychological, with a principle that it can actually establish laws [Frege] |
| Full Idea: Induction depends on the general proposition that the inductive method can establish the truth of a law, or the probability for it. If we deny this, induction becomes nothing more than a psychological phenomenon. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §03 n) | |
| A reaction: The problem is that we can't seem to 'establish' the requisite proposition, even for probability, since probability is in part subjective. I think induction needs the premiss that nature has underlying uniformity, which we then tease out by observation. |
| 8626 | In science one observation can create high probability, while a thousand might prove nothing [Frege] |
| Full Idea: The procedure of the sciences, with its objective standards, will at times find a high probability established by a single confirmatory instance, while at others it will dismiss a thousand as almost worthless. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §10) | |
| A reaction: This thought is presumably what pushes theorists away from traditional induction and towards Bayes's Theorem (Idea 2798). The remark is a great difficulty for anyone trying to defend traditional induction. |
| 22200 | If you eliminate the impossible, the truth will remain, even if it is weird [Conan Doyle] |
| Full Idea: When you have eliminated the impossible, whatever remains, however improbable, must be the truth. | |
| From: Arthur Conan Doyle (The Sign of Four [1890], Ch. 6) | |
| A reaction: A beautiful statement, by Sherlock Holmes, of Eliminative Induction. It is obviously not true, of course. Many options may still face you after you have eliminated what is actually impossible. |
| 16941 | Induction relies on similar effects following from each cause [Quine] |
| Full Idea: Induction expresses our hopes that similar causes will have similar effects. | |
| From: Willard Quine (Natural Kinds [1969], p.125) | |
| A reaction: Some top philosophers are also top teachers, and Quine was one of them, in his writings. He boils it down for the layman. Once again, he is pointing to the fundamental role of the similarity relation. |
| 16940 | Induction is just more of the same: animal expectations [Quine] |
| Full Idea: Induction is essentially only more of the same: animal expectation or habit formation. | |
| From: Willard Quine (Natural Kinds [1969], p.125) | |
| A reaction: My working definition of induction is 'learning from experience', but that doesn't disagree with Quine. Lipton has a richer account of different types of induction. Quine's point is that it rests on resemblance. |
| 6955 | Enumerative induction is inference to the best explanation [Harman] |
| Full Idea: We might think of enumerative induction as inference to the best explanation, taking the generalization to explain its instances. | |
| From: Gilbert Harman (Rationality [1995], 1.5.2) | |
| A reaction: This is a helpful connection. The best explanation of these swans being white is that all swans are white; it ceased to be the best explanation when black swans turned up. In the ultimate case, a law of nature is the explanation. |
| 7369 | Brains are essentially anticipation machines [Dennett] |
| Full Idea: All brains are, in essence, anticipation machines. | |
| From: Daniel C. Dennett (Consciousness Explained [1991], 7.2) | |
| A reaction: This would necessarily, I take it, make them induction machines. So brains will only evolve in a world where induction is possible, which is one where there a lot of immediately apprehensible regularities. |
| 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! |
| 9163 | If we only use induction to assess induction, it is empirically indefeasible, and hence a priori [Field,H] |
| Full Idea: If some inductive rule is basic for us, in the sense that we never assess it using any rules other than itself, then it must be one that we treat as empirically indefeasible (hence as fully a priori, given that it will surely have default status). | |
| From: Hartry Field (Apriority as an Evaluative Notion [2000], 4) | |
| A reaction: This follows on from Field's account of a priori knowledge. See Ideas 9160 and 9164. I think of induction as simply learning from experience, but if experience goes mad I will cease to trust it. (A rationalist view). |
| 6352 | Enumerative induction gives a universal judgement, while statistical induction gives a proportion [Pollock/Cruz] |
| Full Idea: Enumerative induction examines a sample of objects, observes they all have a property, and infers that they all have that property; statistical induction observes a proportion of the objects having the property, and infers that proportion in general. | |
| From: J Pollock / J Cruz (Contemporary theories of Knowledge (2nd) [1999], §1.4.6) | |
| A reaction: There is also induction by elimination, where it is either p or q, and observation keeps saying it isn't p. A small sample is very unreliable, but a huge sample (e.g. cigarettes and cancer) is almost certain, so where is the small/huge boundary? |
| 15708 | Inductive success is rewarded with more induction [Gelman] |
| Full Idea: Inductive success is rewarded with more induction. | |
| From: Susan A. Gelman (The Essential Child [2003], 11 'Broadening') | |
| A reaction: I love this one. Neat, accurate, and central to how we understand the world. I take inductive success to be stored as labels, concepts, categories, words and general truths, which are then our resource for further attempts. |
| 16254 | Induction leaps into the unknown, but usually lands safely [Maudlin] |
| Full Idea: Induction is always a leap beyond the known, but we are constantly assured by later experience that we have landed safely. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 2.5) | |
| A reaction: Not philosophically very interesting, but a nice remark for capturing the lived aspect of inductive thought, as practised by the humblest of animals. |
| 4584 | The problem of induction is how to justify our belief in the uniformity of nature [Baggini /Fosl] |
| Full Idea: At its simplest, the problem of induction can be boiled down to the problem of justifying our belief in the uniformity of nature. | |
| From: J Baggini / PS Fosl (The Philosopher's Toolkit [2003], §1.03) | |
| A reaction: An easy solution to the problem of induction: we treat the uniformity of nature as axiomatic, and then induction is all reasoning which is based on that axiom. The axiom is a working hypothesis, which may begin to appear false. Anomalies are hard. |
| 18690 | Induction is said to just compare properties of categories, but the type of property also matters [Murphy] |
| Full Idea: Most theories of induction claim that it should depend primarily on the similarity of the categories involved, but then the type of property should not matter, yet research shows that it does. | |
| From: Gregory L. Murphy (The Big Book of Concepts [2004], Ch. 6) | |
| A reaction: I take this to be good empirical support for Gilbert Harman's view that induction is really inference to the best explanation. The thought (which strikes me as obviously correct) is that we bring nested domains of knowledge to bear in induction. |
| 14953 | Induction is reasoning from the observed to the unobserved [Ladyman/Ross] |
| Full Idea: Induction is any form of reasoning that proceeds from claims about observed phenomena to claims about unobserved phenomena. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 4.5) | |
| A reaction: Most accounts of induction seem to imply that they lead to generalisations, rather than just some single unobserved thing. This definition is in line with David Lewis's. |
| 22176 | Induction is inferences from examined to unexamined instances of a given kind [Okasha] |
| Full Idea: Some philosophers use 'inductive' to just mean not deductive, …but we reserve it for inferences from examined to unexamined instances of a given kind. | |
| From: Samir Okasha (Philosophy of Science: Very Short Intro (2nd ed) [2016], 2) | |
| A reaction: The instances must at least be comparable. Must you know the kind before you start? Surely you can examine a sequence of things, trying to decide whether or not they are of one kind? Is checking the uniformity of a kind induction? |
| 18609 | Psychologists use 'induction' as generalising a property from one category to another [Machery] |
| Full Idea: Typically, psychologists use 'induction' to refer to the capacity to generalise a property from a category (the source) to another category (the target). | |
| From: Edouard Machery (Doing Without Concepts [2009], 7.1.1) | |
| A reaction: This is because psychologists are interested in the ongoing activities of thought. Philosophers step back a bit, to ask how the whole thing could get started. Philosophical induction has to start with individuals and single observations. |
| 18610 | 'Ampliative' induction infers that all members of a category have a feature found in some of them [Machery] |
| Full Idea: Induction is 'ampliative' when it infers that all or most members of a category possess a property from the fact that some of its members have this property. | |
| From: Edouard Machery (Doing Without Concepts [2009], 7.1.1) | |
| A reaction: This sounds like a simple step in reasoning, but actually it is more like explanation, and will involve overall coherence and probability, rather than a direct conclusion. This invites sceptical questions. The last one observed may be the exception. |
| 14551 | If causation were necessary, the past would fix the future, and induction would be simple [Mumford/Anjum] |
| Full Idea: If there were necessity to be found in causation, then the problem of induction would seem to be dissolved. The future would indeed proceed like the past if it were for all time necessitated what caused what. | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 3.14) | |
| A reaction: My working hypothesis is that the essences of nature necessitate their interactions, and that the problem of induction is solved in that way. We can allow causation to be a process in this action, the transmitter of necessities. Or it could drop out. |
| 14571 | The only full uniformities in nature occur from the essences of fundamental things [Mumford/Anjum] |
| Full Idea: There is indeed natural uniformity in the negative charge of electrons, but the reason for this is that it is an essential property of being an electron that something be negatively charged. It would not be an electron otherwise. | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 6.6) | |
| A reaction: See Idea 14570 for the first part of this thought. This doesn't feel right. The behaviour of gravity according to the inverse square law, or General Relativity, seems to be a uniformity that extends beyond the essences of the ingredients. |