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

THE VALIDITY OF THE SYLLOGISM.
1 99
premise applies it to a matter of fact. The principle of
the hypothetical syllogism is that of the Aristotelian first
figure, expressed in the general Canon of Reasoning
(ch. V. 6).
The minor premise may affirm or deny the antecedent
hence there are four arith
or consequent of the major ;
metically possible forms :
(a) IfSisP, QisR; (b) If S is P, Q is R SisnotP; Q
;
is Rj
no conclusion.
no conclusion.
(c)
If S is P, Q is R; (0 If S is P, Q is S is P ;
R;
Q is not R ;
.-. Qis R. S is not P.
There is no conclusion in (a) and (b) ;
if we deny the
antecedent, we cannot therefore deny the consequent,
for the latter may be true for other reasons ; and if we
affirm the consequent, we cannot therefore affirm the
antecedent, for the consequent may result from other
reasons.
We will now give concrete examples of each of the four
cases.
"
(a) If the study of Logic furnished the mind with a
multitude of useful facts, like other sciences, it would deserve
to be cultivated ; but it does not furnish the mind with a
multitude of useful facts ; therefore it does not deserve
cultivation." [Jevons.]
This conclusion does not follow from the premises for
;
the acquiring of a multitude of useful facts is not the only
ground on which the study of a science can be recommended.
To correct and exercise the powers of judgment and reason
ing may be regarded, for example, as a sufficient justification
of logical study.
"
(b)
If a man s character is avaricious, he will refuse to
this man refuses money for
give money for useful purposes ;
such purposes ; therefore this man s character is avaricious."
But we are not entitled to infer this from the premises ;