rmally correct according to Barbara (or whatever the appropriate
Mood); (2) whether the premises, or the ultimate premises, are true in
fact.

Sec. 3. A Monosyllogism is a syllogism considered as standing alone or
without relation to other arguments. But, of course, a disputant may be
asking to prove the premises of any syllogism; in which case other
syllogisms may be advanced for that purpose. When the conclusion of one
syllogism is used to prove another, we have a chain-argument which,
stated at full length, is a Polysyllogism. In any Polysyllogism, again,
a syllogism whose conclusion is used as the premise of another, is
called in relation to that other a Prosyllogism; whilst a syllogism one
of whose premises is the conclusion of another syllogism, is in relation
to that other an Episyllogism. Two modes of abbreviating a
Polysyllogism, are usually discussed, the Epicheirema and the Sorites.

Sec. 4. An Epicheirema is a syllogism for one or both of whose premises a
reason is added; as--

All men are mortal, for they are animals;
Socrates is a man, for rational bipeds are men:
.'. Socrates is mortal.

The Epicheirema is called Single or Double, says Hamilton, according as
an "adscititious proposition" attaches to one or both of the premises.
The above example is of the double kind. The Single Epicheirema is said
to be of the First Order, if the adscititious proposition attach to the
major premise; if to the minor, of the Second Order. (Hamilton's
_Logic_: Lecture xix.)

An Epicheirema, then, is an abbreviated chain of reasoning, or
Polysyllogism, comprising an Episyllogism with one or two enthymematic
Prosyllogisms. The major premise in the above case, _All men are mortal,
for they are animals,_ is an Enthymeme of the First Order, suppressing
its own major premise, and may be restored thus:

All animals are mortal;
All men are animals:
.'. All men are mortal.

The minor premise, _Socrates is a man, for rational bipeds are men_, is
an Enthymeme of the Second Order, suppressing its own minor premise, and
may be restored thus:

All rational bipeds are men;
Socrates is a rational biped:
.'. Socrates is a man.

Sec. 5. The Sorites is a Polysyllogism in which the Conclusions, and even
some of the Premises, are suppressed until the arguments end. If the
chain of arguments were freed of its enthymematic character, the
suppressed conclusions would appear as premises