An introductory text-book of logic - Mellone, Sydney - Rare Books at ...

THE GENERAL NATURE OF INDUCTION. 22Q
Thus, to take one of Aristotle s examples,
if we see
that the skilful steersman is best, and the skilful driver,
and so on, we realise that the man who is skilful is
best in every occupation. In other words, we illustrate
a statement about a whole class by reference to par
ticular cases of it.
The following is Aristotle s most complete account of the
"
process to which he limits the name of Induction" (An.
Prior., ii. 23). It consists in
"proving the major of the
middle by means of the minor." To understand this, we
must first state a syllogism in Barbara:
All B is A,
All C is B ;
. . All C is A.
Here, as usual, the major term, A, is proved of the minor,
C, by means of the middle, B. But in the inductive syl
logism we prove A of B by means of C :
All C is A,
AU_C_is_Bj
. . All B is A.
This is a syllogism in fig. iii. and is formally invalid ; but it
is a cogent argument if we know not only that all C is B
but that B and C are convertible, so that all B is C also ;
for if we then substitute "all B is C" for the old minor
premise, we have a valid syllogism
in Barbara. The
possibility of the inductive syllogism depends on our finding,
by exhaustive observation, that B and C are convertible.
Thus, to take a concrete example, let A = ductile, B = metal,
C= particular ductile kinds of metal, gold, copper, lead,
&c. Then the inductive syllogism is :
Gold, copper, lead, c., are ductile ;
Gold, copper, lead, &c., are metals ;
. .All metals are ductile.
This argument is cogent if we know not only that these
metals are ductile but that they are all the existing metals.
The minor premise must give a complete enumeration of all
the instances.