ormer example: _All authors
are vain_ is the same as--Vanity is predicated of all authors; _Cicero
is an author_ is the same as--Cicero is identified as an author;
therefore _Cicero is vain_, or--Vanity may be predicated of Cicero. The
_Dictum_ then requires: (1) three propositions; (2) three terms; (3)
that the middle term be distributed; (4) that one premise be
affirmative, since only by an affirmative proposition can one term be
identified with another; (5) that if one premise be negative the
conclusion shall be so too, since whatever is predicated of the middle
term is predicated _in like manner_ of the minor.

Thus far, then, the _Dictum_ is wholly analytic or verbal, expressing no
more than is implied in the definitions of 'Syllogism' and 'Middle
Term'; since (as we have seen) all the General Canons (except the third,
which is a still more general condition of formal proof) are derivable
from those definitions. However, the _Dictum_ makes a further statement
of a synthetic or real character, namely, that _when these conditions
are fulfilled an inference is justified_; that then the major and minor
terms are brought into comparison through the middle, and that the major
term may be predicated affirmatively or negatively of all or part of the
minor. It is this real assertion that justifies us in calling the
_Dictum_ an Axiom.

Sec. 4. Whether the Laws of Thought may not fully explain the Syllogism
without the need of any synthetic principle has, however, been made a
question. Take such a syllogism as the following:

All domestic animals are useful;
All pugs are domestic animals:
.'. All pugs are useful.

Here (an ingenious man might urge), having once identified pugs with
domestic animals, that they are useful follows from the Law of Identity.
If we attend to the meaning, and remember that what is true in one form
of words is true in any other form, then, all domestic animals being
useful, of course pugs are. It is merely a case of subalternation: we
may put it in this way:

All domestic animals are useful:
.'. Some domestic animals (e.g., pugs) are useful.

The derivation of negative syllogisms from the Law of Contradiction (he
might add) may be shown in a similar manner.

But the force of this ingenious argument depends on the participial
clause--'having once identified pugs with domestic animals.' If this is
a distinct step of the reasoning, the above syllogism cannot be reduced