| 1683 | We learn universals from many particulars [Aristotle] |
| Full Idea: It is from many particulars that the universal becomes plain. Universals are valuable because they make the explanation plain. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 88a05) |
| 16576 | Science is based on induction, for general truths about fire, rhubarb and magnets [Buridan] |
| Full Idea: Induction should be regarded as a principle of natural science. For otherwise you could not prove that every fire is hot, that all rhubarb is purgative of bile, that every magnet attracts iron. | |
| From: Jean Buridan (Questions on Aristotle's Physics [1346], I.15 f. 18vb), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 02.3 | |
| A reaction: He is basing this on Aristotle, and refers to 'Physics' 190a33-b11. |
| 19387 | Hypotheses come from induction, which is comparison of experiences [Leibniz] |
| Full Idea: We construct a hypothesis on the basis of an induction, that is on the basis of a comparison of experiences. | |
| From: Gottfried Leibniz (Elements of Law and Justice [1669], p.2) | |
| A reaction: This fits the traditional positivist picture of science (observe-hypothesise-predict-observe). I like the definition of induction as 'comparison of experiences', because it doesn't reduce it to sequences of objects, and points to coherence. |
| 2198 | We assume similar secret powers behind similar experiences, such as the nourishment of bread [Hume] |
| Full Idea: We always presume, when we see like sensible qualities, that they have like secret powers, and expect that effects, similar to those which we have experienced, will follow from them. …Thus, we expect bread to nourish us, from previous experience. | |
| From: David Hume (Enquiry Conc Human Understanding [1748], IV.II.29) |
| 19234 | 'Induction' doesn't capture Greek 'epagoge', which is singulars in a mass producing the general [Peirce] |
| Full Idea: The word 'inductio' is Cicero's imitation of Aristotle's term 'epagoge'. It fails to convey the full significance of the Greek word, which implies the examples are arrayed and brought forward in a mass. 'The assault upon the generals by the singulars'. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], II) | |
| A reaction: Interesting, thought I don't think there is enough evidence in Aristotle to get the Greek idea fully clear. |
| 17631 | Induction is inferring premises from consequences [Russell] |
| Full Idea: The inferring of premises from consequences is the essence of induction. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.274) | |
| A reaction: So induction is just deduction in reverse? Induction is transcendental deduction? Do I deduce the premises from observing a lot of white swans? Hm. |
| 2941 | Induction accepts the simplest law that fits our experiences [Wittgenstein] |
| Full Idea: The procedure of induction consists in accepting as true the simplest law that can be reconciled with our experiences. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 6.363) |
| 5190 | The induction problem is to prove generalisations about the future based on the past [Ayer] |
| Full Idea: The problem of induction is (roughly) finding a way to prove that certain empirical generalisations which are derived from past experience will hold good also in the future. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.2) | |
| A reaction: This doesn't seem to be the only problem. It seems self-evident (since Hume) that you cannot use deductive reasoning to prove that the future will be like the past. In fact, we should obviously be cautious, as things could easily change. |
| 19462 | Induction passes from particular facts to other particulars, or to general laws, non-deductively [Ayer] |
| Full Idea: Inductive reasoning covers all cases in which we pass from a particular statement of fact, or set of them, to a factual conclusion which they do not formally entail. The inference may be to a general law, or by analogy to another particular instance. | |
| From: A.J. Ayer (The Problem of Knowledge [1956], 2.viii) | |
| A reaction: My preferred definition is 'learning from experience' - which I take to be the most rational behaviour you could possibly imagine. I don't think a definition should be couched in terms of 'objects' or 'particulars'. |
| 21748 | More careful inductions gradually lead to the hypothetico-deductive method [Quine] |
| Full Idea: Our inductions become increasingly explicit and deliberate, and in the fulness of time we even rise above induction, to the hypothetico-deductive method. | |
| From: Willard Quine (On the Nature of Moral Values [1978], p.57) | |
| A reaction: This seems to defer to Hempel's account of scientific theorising. I wander what exactly 'rising above' means? |
| 3095 | Induction is an attempt to increase the coherence of our explanations [Harman] |
| Full Idea: Induction is an attempt to increase the explanatory coherence of our view, making it more complete, less ad hoc, more plausible. | |
| From: Gilbert Harman (Thought [1973], 10.2) |
| 9661 | Induction is just reasonable methods of inferring the unobserved from the observed [Lewis] |
| Full Idea: I use the word 'induction' broadly, to cover all the methods we deem reasonable for forming beliefs about the unobserved parts of our world on the basis of experience with the observed parts. | |
| From: David Lewis (On the Plurality of Worlds [1986], 2.5) | |
| A reaction: Good. Attempts to be precise about it seem to be hopeless and invite paradoxes. Personally I just define it as 'learning from experience', because that makes what we do continuous with the behaviour of other sensible animals. |
| 3709 | Induction must go beyond the evidence, in order to explain why the evidence occurred [Bonjour] |
| Full Idea: Inductive explanations must be conceived of as something stronger than mere Humean constant conjunction; …anything less than this will not explain why the inductive evidence occurred in the first place. | |
| From: Laurence Bonjour (In Defence of Pure Reason [1998], §7.7) |
| 6775 | Induction is inference to the best explanation, where the explanation is a law [Bird] |
| Full Idea: Induction can be seen as inference to the best explanation, where the explanation is a law. | |
| From: Alexander Bird (Philosophy of Science [1998], Ch.3) | |
| A reaction: I like this. I increasingly think of explanation as central to rational thought, as the key route for empiricists to go beyond their immediate and verifiable experience. Laws can be probabilistic. |