very one of its parts," is really a sufficient statement of the
principle: the whole being the Middle Term, and the Minor being a
part of it, the Major is predicable of the Minor affirmatively or
negatively if it is predicable similarly of the Middle.

This Axiom, as the name imports, is indemonstrable. As Aristotle
pointed out in the case of the Axiom of Contradiction, it can be
vindicated, if challenged, only by reducing the challenger to a
practical absurdity. You can no more deny it than you can deny that
if a leaf is in a book and the book is in your pocket, the leaf is in
your pocket. If you say that you have a sovereign in your purse and
your purse is in your pocket, and yet that the sovereign is not in
your pocket: will you give me what is in your pocket for the value of
the purse?

II.--THE MINOR FIGURES OF THE SYLLOGISM, AND THEIR REDUCTION TO THE
FIRST.

The word Figure ([Greek: schema]) applies to the form or figure of
the premisses, that is, the order of the terms in the statement of the
premisses, when the Major Premiss is put first, and the Minor second.

In the First Figure the order is

M P
S M

But there are three other possible orders or figures, namely:--

Fig. ii. Fig. iii. Fig. iv.
PM MP PM
SM MS MS.

It results from the doctrines of Conversion that valid arguments may
be stated in these forms, inasmuch as a proposition in one order of
terms may be equivalent to a proposition in another. Thus No M is in P
is convertible with No P is in M: consequently the argument

No P is in M
All S is in M,

in the Second Figure is as much valid as when it is stated in the
First--

No M is in P
All S is in M.

Similarly, since All M is in S is convertible into Some S is in M, the
following arguments are equally valid:--

Fig. iii. Fig. i.
All M is in P All M is in P
=
All M is in S Some S is in M.

Using both the above Converses in place of their Convertends, we
have--

Fig. iv. Fig. i.
No P is in M No M is in P
=
All M is in S Some S is in M.

It can be demonstrated (we shall see presently how) that altogether
there are possible four valid forms or moods of the Second Figure, six
of the Third, and five of the Fourth. An ingenious Mnemonic of
these various moods and their reduction to the First