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

I2O MEDIATE INFERENCE
We shall first examine particular instances of the
syllogism, and thus arrive at the rules of their com
bination. We shall then sum up the results in a form
in which they may easily be remembered. In all
essentials, we shall follow the Aristotelian exposition.
The syllogism is composed of logical propositions,
which can only have four forms, A, E, I, O. We
have to find the different ways in which these may be
combined so as to lead to correct conclusions, and
to show that no other combinations yield correct
conclusions.
Suppose that we have to prove
conclusion,
"
"
All S is P
a universal affirmative
; how may this most com
pendiously be done ? It is required to prove something
of a whole class, to prove that the quality P is pos
sessed by a whole class S. Is P admitted to be a
quality of any higher class to which S undoubtedly
belongs? Suppose that M is admitted to be such
a class i.e., that the qualities of M are predicated
of all S, and that the quality P is predicated of all M.
Then it follows at once that the quality P must be
predicated
of all S :
is predicated of all M.
M is predicated of all S.
is predicated of all S.
;P
. . P
This statement of the syllogism is based on the predi
cative view of propositions, and is usually adopted by
Aristotle. Expressed according to the Class view, the
argument
is :
( All of M is in P.
I All of S is in M.
/. All of S is in P.