"Induction, then, and the Inductive Syllogism, consists in
syllogising one extreme with the middle through the other
extreme. For example, if B is middle to A and C, to prove
through C that A belongs to B."[1]
This may be interpreted as follows: Suppose a general proposition is
in dispute, and that you wish to make it good by obtaining severally
the admission of all the particulars that it sums up. The type of a
general proposition in Syllogistic terminology is the Major Premiss,
All M is P. What is the type of the particulars that it sums up?
Obviously, the Conclusion, S is P. This particular is contained in the
Major Premiss, All M is P; its truth is accepted as contained in the
truth of All M is P. S is one of the parts of the generic whole M; one
of the individuals or species contained in the class M. If you wish,
then, to establish P of All M by Induction, you must establish P of
all the parts, species, or individuals contained in M, that is, of all
possible S_s:_ you must make good that this, that and the other S is
P, and also that this, that and the other S constitute the whole of M.
You are then entitled to conclude that All M is P: you have syllogised
one Extreme with the Middle through the other Extreme. The formal
statement of these premisses and conclusion is the Inductive
Syllogism.
This, that and the other S is P, _Major_.
This, that and the other S is all M, _Minor_.
[.'.] All M is P, _Conclusion_.
This, that and the other magnet (_i.e._, magnets individually)
attract iron.
This, that and the other magnet (_i.e._, the individuals
separately admitted) are all magnets.
[.'.] All magnets attract iron.
This, that and the other S being simply convertible with All M, you
have only to make this conversion and you have a syllogism in Barbara
where this, that and the other S figures as the Middle Term.
The practical value of this tortuous expression is not obvious.
Mediaeval logicians shortened it into what was known as the Inductive
Enthymeme: "This, that and the other, therefore all," an obvious
conclusion when this, that and the other constitute all. It is
merely an evidence of the great master's intoxication with his
grand invention. It is a proof also that Aristotle really looked
at Induction from the point of view of Interrogative Dialectic.
His question was, When is a Respondent bound to admit a general
conclusion? And his answer was, When he has admitted a certain number
of particulars, and cannot deny that those particulars constitute the
whole whose predicate is in dispute. He was not concerned primarily
with the analysis of the steps of an inquirer generalising from
Nature.
[Footnote 1: [Greek: epagoge men oun esti kai ho ex epagoges
syllogismos to dia tou eterou thateron akron to meso
syllogisasthai; Oion ei ton A G meson to B, dia tou G deixai
to A to B hyparchon.] (An. Prior., ii. 23.)]
BOOK II.
Public-domain text, read in full here on John Shaqi.
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