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

222 CONDITIONAL ARGUMENTS AND
NOTE B.
ARISTOTLE S DEFENCE OF THE SYLLOGISM.
The objection to the syllogistic form of inference, on
which Mill bases his charge that it is a petitio principii^
was anticipated and answered by Aristotle himself.
In his Posterior Analytics he points out that nothing
which we infer or, as he expresses it, nothing which we
discover by thought as distinct from sense-perception can
be entirely new it ; must be at least in part an application
of previous knowledge. In the case of deductive or syl
logistic reasoning, we require to know not a mere "col
lective fact," but a universal law, and also to know a
particular fact ; and the inference arises only when we
have the former in the mind and the latter is added to it
(An. Post., i. i). Consider any scientific syllogism, e.g. :
Every triangle has its three interior angles together equal
to two right angles.
This is a triangle.
Therefore this has its three interior angles together
equal to two right angles.
It would seem that some of the Sophists had brought
against the possibility of knowledge the same reproach which
Mill brought afterwards against the syllogism, that we have
no right to assert the major premise unless we already
know the conclusion. Aristotle s reply is as follows :
"Before the instance is produced or the syllogism com
pleted, 1 in one sense perhaps we must be said to know
the conclusion ; but in another sense not. For how could
any one know in the full sense of the word that this triangle,
of whose existence he is completely ignorant, has its angles
equal to two right angles ? Yet it is plain that in a sense
he does know it, inasmuch as he knouts the universal; but
in the full sense he does not know it." Aristotle then
explains how the objector puts the difficulty. He puts it
by asking,
" Do
you or do you not know that all triangles
1
By "syllogism" is meant here the two premises.