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Aristotle on Induction

How did induction get started? Where did it come from? What was it like, then? Here is the original argument that has, apparently, impressed the world. It's by Aristotle.

http://classics.mit.edu/Aristotle/prior.mb.txt
It is clear then how the terms are related in conversion, and in respect
of being in a higher degree objects of aversion or of desire. We must
now state that not only dialectical and demonstrative syllogisms are
formed by means of the aforesaid figures, but also rhetorical syllogisms
and in general any form of persuasion, however it may be presented.
For every belief comes either through syllogism or from induction.

Now induction, or rather the syllogism which springs out of induction,
consists in establishing syllogistically a relation between one extreme
and the middle by means of the other extreme, e.g. if B is the middle
term between A and C, it consists in proving through C that A belongs
to B. For this is the manner in which we make inductions. For example
let A stand for long-lived, B for bileless, and C for the particular
long-lived animals, e.g. man, horse, mule. A then belongs to the whole
of C: for whatever is bileless is long-lived. But B also ('not possessing
bile') belongs to all C. If then C is convertible with B, and the
middle term is not wider in extension, it is necessary that A should
belong to B. For it has already been proved that if two things belong
to the same thing, and the extreme is convertible with one of them,
then the other predicate will belong to the predicate that is converted.
But we must apprehend C as made up of all the particulars. For induction
proceeds through an enumeration of all the cases.

Such is the syllogism which establishes the first and immediate premiss:
for where there is a middle term the syllogism proceeds through the
middle term; when there is no middle term, through induction. And
in a way induction is opposed to syllogism: for the latter proves
the major term to belong to the third term by means of the middle,
the former proves the major to belong to the middle by means of the
third. In the order of nature, syllogism through the middle term is
prior and better known, but syllogism through induction is clearer
to us.

We have an 'example' when the major term is proved to belong to the
middle by means of a term which resembles the third. It ought to be
known both that the middle belongs to the third term, and that the
first belongs to that which resembles the third. For example let A
be evil, B making war against neighbours, C Athenians against Thebans,
D Thebans against Phocians. If then we wish to prove that to fight
with the Thebans is an evil, we must assume that to fight against
neighbours is an evil. Evidence of this is obtained from similar cases,
e.g. that the war against the Phocians was an evil to the Thebans.
Since then to fight against neighbours is an evil, and to fight against
the Thebans is to fight against neighbours, it is clear that to fight
against the Thebans is an evil. Now it is clear that B belongs to
C and to D (for both are cases of making war upon one's neighbours)
and that A belongs to D (for the war against the Phocians did not
turn out well for the Thebans): but that A belongs to B will be proved
through D. Similarly if the belief in the relation of the middle term
to the extreme should be produced by several similar cases. Clearly
then to argue by example is neither like reasoning from part to whole,
nor like reasoning from whole to part, but rather reasoning from part
to part, when both particulars are subordinate to the same term, and
one of them is known. It differs from induction, because induction
starting from all the particular cases proves (as we saw) that the
major term belongs to the middle, and does not apply the syllogistic
conclusion to the minor term, whereas argument by example does make
this application and does not draw its proof from all the particular
cases.
Notice how he says induction differs than argument by example because in induction one starts from every possible particular case, not just a limited set of examples. But when does anyone analyze every possible case? There are unlimited cases to consider. So no one performs induction up to the standard Aristotle sees is necessary for it to work.

Aristotle wasn't very consistent or clear about what induction is. He mentions in frequently. That passage was the closest thing I could find to an attempt to explain it.

Here's another mention:

http://classics.mit.edu/Aristotle/posterior.mb.txt
Knowledge of the fact differs from knowledge of the reasoned fact.
To begin with, they differ within the same science and in two ways:
(1) when the premisses of the syllogism are not immediate (for then
the proximate cause is not contained in them-a necessary condition
of knowledge of the reasoned fact): (2) when the premisses are immediate,
but instead of the cause the better known of the two reciprocals is
taken as the middle; for of two reciprocally predicable terms the
one which is not the cause may quite easily be the better known and
so become the middle term of the demonstration. Thus (2, a) you might
prove as follows that the planets are near because they do not twinkle:
let C be the planets, B not twinkling, A proximity. Then B is predicable
of C; for the planets do not twinkle. But A is also predicable of
B, since that which does not twinkle is near--we must take this truth
as having been reached by induction or sense-perception.
What is he talking about? We know that things which are near don't twinkle via induction or sense perception? No we don't. Near things can twinkle. And even if we didn't have any modern flashing lights or paintings of Santa's eyes, there's no way to perceive that nothing that is near could ever twinkle. And if it could have been induced in Aristotle's time, as he seems to claim, that would prove that induction can reach false conclusions, since near things can and do twinkle sometimes.

Here's a relevant passage:
It is also clear that the loss of any one of the senses entails the
loss of a corresponding portion of knowledge, and that, since we learn
either by induction or by demonstration, this knowledge cannot be
acquired. Thus demonstration develops from universals, induction from
particulars; but since it is possible to familiarize the pupil with
even the so-called mathematical abstractions only through induction-i.e.
only because each subject genus possesses, in virtue of a determinate
mathematical character, certain properties which can be treated as
separate even though they do not exist in isolation-it is consequently
impossible to come to grasp universals except through induction. But
induction is impossible for those who have not sense-perception. For
it is sense-perception alone which is adequate for grasping the particulars:
they cannot be objects of scientific knowledge, because neither can
universals give us knowledge of them without induction, nor can we
get it through induction without sense-perception.
It tells us induction requires sense-perception for input, but that's about it.

In this next passage, as I read it, Aristotle says that induction is fallbile:
Nor, as was said in my formal logic, is the method of division a process
of inference at all, since at no point does the characterization of
the subject follow necessarily from the premising of certain other
facts: division demonstrates as little as does induction. For in a
genuine demonstration the conclusion must not be put as a question
nor depend on a concession, but must follow necessarily from its premisses,
even if the respondent deny it. The definer asks 'Is man animal or
inanimate?' and then assumes-he has not inferred-that man is animal.
Next, when presented with an exhaustive division of animal into terrestrial
and aquatic, he assumes that man is terrestrial. Moreover, that man
is the complete formula, terrestrial-animal, does not follow necessarily
from the premisses: this too is an assumption, and equally an assumption
whether the division comprises many differentiae or few. (Indeed as
this method of division is used by those who proceed by it, even truths
that can be inferred actually fail to appear as such.) For why should
not the whole of this formula be true of man, and yet not exhibit
his essential nature or definable form? Again, what guarantee is there
against an unessential addition, or against the omission of the final
or of an intermediate determinant of the substantial being?
Next, here's Aristotle commenting on a limit of induction. Aristotle says induction can only tell us whether a thing has some attribute or not.
we
may not proceed as by induction to establish a universal on the evidence
of groups of particulars which offer no exception, because induction
proves not what the essential nature of a thing is but that it has
or has not some attribute. Therefore, since presumably one cannot
prove essential nature by an appeal to sense perception or by pointing
with the finger, what other method remains?
Here's a final passage. In it Aristotle says that scientific knowledge is the truest type of knowledge, except for one superior type: intuition.
Thus it is clear that we must get to know the primary premisses by
induction; for the method by which even sense-perception implants
the universal is inductive. Now of the thinking states by which we
grasp truth, some are unfailingly true, others admit of error-opinion,
for instance, and calculation, whereas scientific knowing and intuition
are always true: further, no other kind of thought except intuition
is more accurate than scientific knowledge, whereas primary premisses
are more knowable than demonstrations, and all scientific knowledge
is discursive. From these considerations it follows that there will
be no scientific knowledge of the primary premisses, and since except
intuition nothing can be truer than scientific knowledge, it will
be intuition that apprehends the primary premisses
Perhaps I've searched the wrong books. If anyone knows another passage, let me know.

Elliot Temple on November 14, 2009

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