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From: Philip Johnson-Laird BA PhD Psychology (UCL), Stuart Professor of Psychology Emeritus at Princeton. (Author isn't a logician.) How We Reason (1st edn 2008). p. 431, for Ch. 1.

  1. The textbook definitions of deduction and induction go back to Aristotle. In his Topics (Aristotle, 1984, Vol. 1, 105a13), he writes, “induction is a passage from particulars to universals”. He argues in his Prior Analytics (Book II, paragraph 23) that every belief comes either from deduction or induction, and that induction is from the particular to the general. Mill (1874, p. 210) writes: “Induction . . . is that operation of the mind, by which we infer that what we know to be true in a particular case or cases, will be true in all cases which resemble the former in certain assignable respects”.

Patrick Hurley PhD (Saint Louis University). A Concise Introduction to Logic (12 edn 2014). p. 39.

  A final point needs to be made about the distinction between inductive and deductive arguments. There is a tradition extending back to the time of Aristotle that holds that inductive arguments are those that proceed from the particular to the general, while deductive arguments are those that proceed from the general to the particular. (A particular statement is one that makes a claim about one or more particular members of a class, while a general statement makes a claim about all the members of a class.) It is true, of course, that many inductive and deductive arguments do work in this way; but this fact should not be used as a criterion for distinguishing induction from deduction. As a matter of fact, there are deductive arguments that proceed from the general to the general, from the particular to the particular, and from the particular to the general, as well as from the general to the particular; and there are inductive arguments that do the same.

[I pretermit two deductive arguments.]

Here is an inductive argument that proceeds from the general to the particular:

All emeralds previously found have been green.
Therefore, the next emerald to be found will be green.

If Aristotle's definition of Induction is wrong, why did he bungle? How did an egghead like him overlook inductive arguments from general to the particular, like the one that I quoted?

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    See Deductive and Inductive Arguments for clarification about the terminogy. What must be clear is that for Aristotle induction (epagôgê) is the “argument from the particular to the universal”. It is not "probabilistic reasoning": what today we often prefer to call induction. – Mauro ALLEGRANZA Jul 11 '18 at 11:05
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    In order to understand the evolution, central was the role of Francis Bacon's Novum Organon. – Mauro ALLEGRANZA Jul 11 '18 at 11:15
  • @Mauro ALLEGRANZA. You are so right. The quote and the answers all assume a Baconian version of induction, which just does not apply to Aristotle. I am doing my best to get this point across, so far without success. So you can imagine with what relief I read your intervention. – Geoffrey Thomas Jul 17 '18 at 8:01
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Arguably, it hasn't been demonstrated that Aristotle bungled, because the quoted example is an argument from the particular to the general - it's simply a matter of a contracted formulation. Here's the same argument with the unstated bits:

  1. All emeralds previously found have been green.

  2. (Unstated) Not all emeralds in existence have been found.

  3. (Unstated) All emeralds in existence are green. (from 1)

  4. Therefore, the next emerald to be found will be green. (from 2, 3)

Note that (2) is inherent in the formulation of the argument - we could not find the "next" emerald in (4) if we already found all of them - and that (3) is what actually does all the work here. Without it, there's nothing to connect (1) - what has already been found - and (4) - what will be found in the future.

It looks like it's an argument from general to particular because of the world "all" in (1), but "the next emerald found" isn't a member of the set of "all emeralds previously found". Instead, both are members of the overarching set of "all emeralds in existence" and it's this overarching set that we are reasoning about.

Compare and contrast with deductive reasoning, as in this classic example:

  1. All men are mortal. (Premise pertaining to the entire set; general.)

  2. Socrates is a man. (Premise identifying Socrates as an element of the set.)

  3. Therefore, Socrates is mortal. (Conclusion about the properties of a particular element of the set.)

  • Great answer - there are indeed several unstated elements to the argument. – Ben Jul 17 '18 at 2:02
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Aristotle did NOT define or standardly use 'induction' as inference from the particular to the general. Discussions and criticisms of him which assume that he did are just false.

There is a tradition extending back to the time of Aristotle that holds that inductive arguments are those that proceed from the particular to the general, while deductive arguments are those that proceed from the general to the particular.

The existence of a tradition and its veracity to Aristotle's texts are two different matters. Aristotle uses 'epagoge', generally translated 'induction', in too many different ways for any such clear and simple contrast between deduction and induction, as formulated above, to be recoverable from his work.

Look at the texts

I draw on the work of John Milton - the present-day scholar, not the 17the century poet.

Aristotle's theory of science has a place for both deduction and induction. Scientific knowledge is obtained by demonstration from undemonstrable first principles, and knowledge of these first principles is in turn obtained by induction. One might expect therefore that Aristotle would have discussed deduction and induction at something like equal length. In fact his remarks about induction are fairly brief and in many respects very obscure.

There are two main places in which Aristotle discusses the theory of inductive reasoning. The first, in Prior Analytics 11.23, is not very illuminating. It is concerned purely with induction by complete enumeration, and provides a good example of Aristotle's intermittent but regrettable tendency to use Procrustean methods in forcing other kinds of inference into syllogistic.

The most important other place in Aristotle's writings in which the nature of induction is discussed is Posterior Analytics 11.19. This chapter is notoriously one of the most obscure in all Aristotle's writings, and its interpretation is far from straightforward. A considerable part of its obscurity derives from the fact that Aristotle appears to slide without explanation from an account of how we acquire universal concepts (I00a3-b3) to an account of how we acquire knowledge of universal truths (100b3ff). Sir David Ross assumed that Aristotle was concerned both with concept formation and with induction, and passes from the one to the other because of a close analogy between the two (Ross [1949], p. 675). Jonathan Barnes on the other hand supposes that only concept formation is involved, and that Aristotle uses epagoge 'in a weak sense, to refer to any cognitive progress from the less to the more general' (Barnes [1975], p. 256). This problem and others closely related to it have recently been the subject of much discussion among specialists in ancient philosophy (Barnes [1975], Hamlyn [1976], Engberg-Pedersen [1980], Upton [1981], Kahn [1981]). Like most really well established disputes in ancient philosophy, this one is unlikely ever to be finally and definitively resolved. All the less transient interpretations have at least something to be said for them, and we have no final assurance that Aristotle ever formulated a single coherent, or even approximately coherent theory. Further minute analysis of Aristotle's Greek text is unlikely to produce much further enlightenment, indispensable as such analysis certainly is. I would therefore wish to excuse myself from attempting any direct contribution to this debate (except to note a broad agreement with Kahn's approach). Instead it would seem to me useful to look first at the uses to which epagoge was put by Aristotle, and then at the subsequent history of epagoge and of non-deductive inferences generally. By doing this we can hope to gain insight, not so much into what was in Aristotle's mind when he was writing the Posterior Analytics, as into the problems and possible solutions characteristic of any broadly Aristotelian system of philosophy.

Aristotle uses the word epagoge and its derivatives with what seems at least to us to be a large variety of senses. Sometimes the meaning seems to be experience or observation (Physics, 185a14; De Caelo, 276a14), or example (Physics, 229b3). More commonly some element of generalisation is involved, but the content of the generalisations is likely to appear strange to someone familiar only with the modern tradition of inductive logic stemming from Bacon. Sometimes we have the kind of argument familiar from the Socratic dialogues: 'If the skilled pilot is the best pilot and the skilled charioteer is the best charioteer, then in general the skilled man is the best in any particular sphere' (Topics, 105a15-7). In the majority of cases however what is established by induction has even less claim to be considered as an empirical generalisation. Among the truths which Aristotle describes as being reached by induction we have the principle that non- accidental changes occurs only between contraries, between their intermediaries and between contradictories (Physics, 224b30); the principle that whatever is posterior in the order of development is prior in the order of nature (De Partibus Animalium, 646a30); the principle that contrariety is the greatest difference (Metaphysics, 10055a6); and the principle that excellence is the best position, state or capacity of anything that has some employment or function (Eudemian Ethics, I219a1). What we do not find are what we are accustomed to think of as empirical generalisations. Aristotle uses the word epagoge and its derivatives over fifty times in his various writings, and the only example of a proposition derived by epagoge which could reasonably be described as an empirical generalisation is the discussion example of all bileless animals being long-lived which appears in Prior Analytics, 11.23. (On the background to this example, see Guthrie [1981], pp. 194-5.) It is noteworthy that in this case Aristsotle states explicitly that the induction requires a survey of all the particular instances.

It appears therefore that although Aristotle's formal position was that first principles of the sciences are obtained by induction, he was not an inductivist after the manner of Bacon, or Herschel, or Mill. Drawing up empirical generalisations from a wide and varied range of particular instances played little part in his scientific practice.

Aristotle's examples of inductive inferences can therefore be divided into two classes. First we have broadly common-sense arguments, usually appearing in rhetorical contexts, whose purpose is to establish some general thesis about human life and conduct. The argument about skilled pilots and charioteers in the Topics is an example, and there are other specimens in the Rhetoric (e.g., 1398b5-18). These may be termed rhetorical inductions. Secondly there are more abstract arguments which are intended to establish some theoretical point within philosophy. These may be called philosophical inductions.

Conclusion

I cannot see from this survey of examples that at least on the inductive side the thesis that 'inductive arguments are those that proceed from the particular to the general, while deductive arguments are those that proceed from the general to the particular' can be plausibly attributed to Aristotle. The Aristotelian account of induction or epagoge is far too complex or, if you prefer, miscellaneously varied to support any short-formula distinction between deduction and induction. (J. R. Milton, 'Induction before Hume', The British Journal for the Philosophy of Science, Vol. 38, No. 1 (Mar., 1987), pp. 49-74 : 51-3.

Endote on deduction

As a matter of fact, there are deductive arguments that proceed from the general to the general, from the particular to the particular, and from the particular to the general, as well as from the general to the particular.

Aristotle recognised syllogistic arguments that proceed from the general to the general. The First Figure allows the 'mood' :

  1. All A applies to all B

  2. All B applies to all C

  3. Therefore : All A applies to all C

This proceeds from general to general.

I cite this example just to make the point that in talking about Aristotle on deduction (and induction) we really do need to know what Aristotle actually says and not rely on what Medieval Scholasticism or the body of logical theory that later accreted itself around 'Aristotelian logic' attributed to him.

Endnote on history

Aristotle's contribution to philosophy was made two millenia and more ago. One might well expect errors in the work of a theorist who was clearing the ground and could know nothing of the Stoic, Scholastic, let alone post-Fregean developments in logic.

But that is not the problem here. Aristotle distinguishes between sullogismos and epagoge. The first is, without regard for historical nicety, translated as 'deduction', the second as 'induction'. My whole point is that Aristotelian epagoge is not induction in the sense which the question 'How did Aristotle define induction so incorrectly?' assumes. The question and accompanying text employ 'induction' in a post-Baconian sense. Compare the Aristotlian references above with Francis Bacon's Novum Organon (1620) and the fact is patent.

References

Barnes, J. [1975]. Aristotle's Posterior Analytics. Oxford: Clarendon Press.

Engberg-Pederson, T. [I980]: 'More on Aristotelian Epagoge', Phronesis, 24, pp. 301-19.

Hamlyn, D. W. [1976]: 'Aristotelian Epagoge', Phronesis, 21, pp. 167-84.

Kahn, C. H. [1981]: 'The Role of nous in the Cognition of First Principles in the Posterior Analytics', in E. Berti (ed.), Aristotle on Science: the Posterior Analytics. Padua: Editrice Antenore.

Milton, J.R. [1987]'Induction before Hume', The British Journal for the Philosophy of Science, Vol. 38, No. 1, pp. 49-74

Ross, W. D. [1949]: Aristotle's Prior and Posterior Analytics. Oxford: Clarendon Press.

Upton, T: V. [1981]: 'A note on Aristotelian epagoge', Phronesis, 26, pp. 172-6.

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The value of labels

Deductive and inductive labels of two sets applied to certain arguments. It appears they overlap, and you can choose in these cases which label you wish to apply depending on where you are coming from and the conclusion you are drawing.

So Aristotle was describing the two sets. Whether he defined the overlap or not does not mean he was wrong.

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In general, the answer to questions of the form "Why was Aristotle so wrong about X" is that Aristotle was not a modern logician, scientist, aesthetician, or political theorist, etcetera, and he didn't have the benefit of the successive 2000+ years of development of the field.

For a lot of these topics, Aristotle was the first person in the Western world to identify them and think about them systematically. So it's not surprising that he got most of the fine details "wrong." His version was the raw version, our version is the one that has gone through generations of refinements.

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