of Episyllogisms.

Two varieties of Sorites are recognised, the Aristotelian (so called,
though not treated of by Aristotle), and the Goclenian (named after its
discoverer, Goclenius of Marburg, who flourished about 1600 A.D.). In
order to compare these two forms of argument, it will be convenient to
place side by side Hamilton's classical examples of them.

Aristotelian. Goclenian.
Bucephalus is a horse; An animal is a substance;
A horse is a quadruped; A quadruped is an animal;
A quadruped is an animal; A horse is a quadruped;
An animal is a substance: Bucephalus is a horse:
.'. Bucephalus is a substance. .'. Bucephalus is a substance.

The reader wonders what is the difference between these two forms. In
the Aristotelian Sorites the minor term occurs in the first premise, and
the major term in the last; whilst in the Goclenian the major term
occurs in the first premise, and the minor in the last. But since the
character of premises is fixed by their terms, not by the order in which
they are written, there cannot be a better example of a distinction
without a difference. At a first glance, indeed, there may seem to be a
more important point involved; the premises of the Aristotelian Sorites
seem to proceed in the order of Fig. IV. But if that were really so the
conclusion would be, _Some Substance is Bucephalus_. That, on the
contrary, every one writes the conclusion, _Bucephalus is a substance_,
proves that the logical order of the premises is in Fig. I. Logically,
therefore, there is absolutely no difference between these two forms,
and pure reason requires either that the "Aristotelian Sorites"
disappear from the text-books, or that it be regarded as in Fig. IV.,
and its conclusion converted. It is the shining merit of Goclenius to
have restored the premises of the Sorites to the usual order of Fig. I.:
whereby he has raised to himself a monument more durable than brass, and
secured indeed the very cheapest immortality.

The common Sorites, then, being in Fig. I., its rules follow from those
of Fig. I:

(1) Only one premise can be particular; and, if any, only that in which
the minor term occurs.

For, just as in Fig I., a particular premise anywhere else involves
undistributed Middle.

(2) Only one premise can be negative; and, if any, only that in which
the major term occurs.

For if there were two negative premise