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

THE VALIDITY OF THE SYLLOGISM. 215
effect, of resemblance and difference, seem to involve
distinct laws of thought, to create for themselves special
elements and functions of language, and to require
special canons of logic. In all these spheres there is
room for such a necessary nexus of conceptions as
demonstration requires ; yet the rules of class-reasoning
[the syllogism] have no natural application. Such
maxims as that a body cannot be in two places at once,
that causa causa causa causati, that two things, of
which the first is like and the second unlike a third, are
unlike each other, are not less really the basis of
frequent reasoning than the dictum
the is genus true of the species."
that what is true of
Mr Bradley, in his
Principles of Logic,
has worked out a classification of
the most important types of relation which ordinary
judgments express, among which the syllogism takes
its place, as dealing with propositions that express the
relation of subject and attribute. Against this doctrine
the following remarks must be made. One may put the
matter as a question of verbal definition, or as a question
of the meaning of the dictum de omni. (i) If by a syl
logism we mean a piece of
"
class-reasoning," formulated
in such a way as always to conform to the type :
Each of the individuals which make up
M, is P ;
A is one of these ;
. . A is P ;
the class
then there are inferences, scientifically certain, which
are not
"
syllogisms," and the syllogism is what Mill con
sidered it to be (see below, 8 ad finem). But (2) if we
interpret the dictum as Aristotle does, for, when stating
it (see p. 139, note), Aristotle says nothing about classes,
genera, or species; and if we regard the "wording" or