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

2O2 CONDITIONAL ARGUMENTS AND
The student will find that, when the hypothetical is
expressed as a categorical syllogism, the fallacy of
affirming the consequent appears as Undistributed
Middle; and the fallacy of denying
the antecedent
appears as Illicit Major.
Hamilton maintained that the hypothetical proposi
tion is not more complex than the ordinary one, and the
syllogism may be expressed
thus :
If A is B, C is D ;
Therefore, A being B, C is D.
He considered that the hypothetical syllogism is an
immediate inference. It is true that no new term is
introduced in the minor premise ; but the major and
the minor are distinct propositions, and the conclusion is
the result not of either proposition by itself but only of
the two together. To say that the conclusion could be
obtained from either premise singly, is to misunderstand
the whole nature and construction of the hypothetical
syllogism.
(a) The major premise affirms only that the relation
of Reason and Consequence holds between two judg
ments or concepts. It does not expressly refer to
instances where the relation actually occurs and about
;
any particular instance it tells us nothing at all. We
may know that A is
"if B, then C is without know
D,"
ing that "A is B, therefore C is D." To say that "if
the barometer falls, the weather will be bad," is not the
same thing as to say that "the barometer is falling, and
so the weather will be bad." But when, independently
" A is B,"
of the major, we know the truth of the minor,
"the barometer is falling," then we may
assert the con
clusion. And we cannot assert it unless both premises
are conceded ; that is to say, the inference is mediate.