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 premises, at the point where the second entered the chain of argument there must be a syllogism with two negative premises, which is contrary to Rule 5; whilst if one premise be negative it must be that which contains the major term, for the same reason as in Fig.  I., namely, that the conclusion will be negative, and that therefore only a negative major premise can prevent illicit process of the major term.

If we expand a Sorites into its constituent syllogisms, the conclusions successively suppressed will reappear as major premises; thus: 

    (1) An animal is a substance;
        A quadruped is an animal: 
      .’.  A quadruped is a substance.

    (2) A quadruped is a substance;
        A horse is a quadruped: 
      .’.  A horse is a substance.

    (3) A horse is a substance: 
        Bucephalus is a horse: 
      .’.  Bucephalus is a substance.