(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. |
This suffices to show that the Protosyllogism of a Goclenian Sorites is an Enthymeme of the Third Order; after which the argument is a chain of Enthymemes of the First Order, or of the First and Third combined, since the conclusions as well as the major premises are omitted, except in the last one.
Lest it should be thought that the Sorites is only good for arguments so frivolous as the above, I subjoin an example collected from various parts of Mill's Political Economy:—