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
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 , 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 , p. 256). This problem
and others closely related to it have recently been the subject of much
discussion among specialists in ancient philosophy (Barnes , Hamlyn
, Engberg-Pedersen , Upton , Kahn ). 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
, 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
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' :
All A applies to all B
All B applies to all C
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.
Barnes, J. . Aristotle's Posterior Analytics. Oxford: Clarendon Press.
Engberg-Pederson, T. [I980]: 'More on Aristotelian Epagoge', Phronesis, 24, pp. 301-19.
Hamlyn, D. W. : 'Aristotelian Epagoge', Phronesis, 21, pp. 167-84.
Kahn, C. H. : '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. 'Induction before Hume', The British Journal for the Philosophy of Science, Vol. 38, No. 1, pp. 49-74
Ross, W. D. : Aristotle's Prior and Posterior Analytics. Oxford: Clarendon Press.
Upton, T: V. : 'A note on Aristotelian epagoge', Phronesis, 26, pp. 172-6.