s, 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_:--

The cost of labour depends on the efficiency of labour;
The rate of profits depends on the cost of labour;
The investment of capital depends on the rate of profits;
Wages depend on the investment of capital:
.'. Wages depend on the efficiency of labour.

Had it occurred to Mill to construct this Sorites, he would have
modified his doctrine of the wages-fund, and would have spared many
critics the malignant joy of refuting him.

Sec. 6. The Antinomy is a combination of arguments by which contradictory
attributes are proved to be predicable of the same subject. In symbols,
thus:

All M is P; All N is p;
All S is M: All S is N:
.'. All S is P. .'. All S is p.

Now, by the principle of Contradiction, S cannot be P and p (not-P):
therefore, if both of the above syllogisms are sound, S, as the subject
of contradictory attributes, is logically an impossible thing. The
contradictory conclusions are called, respectively, Thesis and
Antithesis.

To come to particulars, we may argue: (1) that a constitution which is
at once a