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 monarchy, an aristocracy and a democracy, must comprise the best elements of all three forms; and must, therefore, be the best of all forms of government:  the British Constitution is, therefore, the best of all.  But (2) such a constitution must also comprise the worst elements of monarchy, aristocracy and democracy; and, therefore, must be the worst of all forms.  Are we, then, driven to conclude that the British Constitution, thus proved to be both the best and worst, does not really exist at all, being logically impossible?  The proofs seem equally cogent; but perhaps neither the best nor the worst elements of the simpler constitutions need be present in our own in sufficient force to make it either good or bad.

Again: 

    (1) Every being who is responsible for his actions is free;
        Man is responsible for his actions: 
      .’.  Man is free.

    (2) Every being whose actions enter into the course of nature is not free;
        Man is such a being: 
      .’.  Man is not free.

Does it, then, follow that ‘Man,’ as the subject of contradictory attributes, is a nonentity?  This doctrine, or something like it, has been seriously entertained; but if to any reader it seem extravagant (as it certainly does to me), he will no doubt find an error in the above arguments.  Perhaps the major term is ambiguous.