xm0 † my′1x′y′1

i.e. “Some persons, who are not philosophers, are not gamblers.”

[§ 9.]
My Method of treating Syllogisms and Sorites.

Of all the strange things, that are to be met with in the ordinary text-books of Formal Logic, perhaps the strangest is the violent contrast one finds to exist between their ways of dealing with these two subjects. While they have elaborately discussed no less than nineteen different forms of Syllogisms——each with its own special and exasperating Rules, while the whole constitute an almost useless machine, for practical purposes, many of the Conclusions being incomplete, and many quite legitimate forms being ignored——they have limited Sorites to two forms only, of childish simplicity; and these they have dignified with special names, apparently under the impression that no other possible forms existed!

As to Syllogisms, I find that their nineteen forms, with about a score of others which they have ignored, can all be arranged under three forms, each with a very simple Rule of its own; and the only question the Reader has to settle, in working any one of the 101 Examples given at [p. 101] of this book, is “Does it belong to Fig. I., II., or III.?”

[pg184]As to Sorites, the only two forms, recognised by the text-books, are the Aristotelian, whose Premisses are a series of Propositions in A, so arranged that the Predicate of each is the Subject of the next, and the Goclenian, whose Premisses are the very same series, written backwards. Goclenius, it seems, was the first who noticed the startling fact that it does not affect the force of a Syllogism to invert the order of its Premisses, and who applied this discovery to a Sorites. If we assume (as surely we may?) that he is the same man as that transcendent genius who first noticed that 4 times 5 is the same thing as 5 times 4, we may apply to him what somebody (Edmund Yates, I think it was) has said of Tupper, viz., “here is a man who, beyond all others of his generation, has been favoured with Glimpses of the Obvious!”

These puerile——not to say infantine——forms of a Sorites I have, in this book, ignored from the very first, and have not only admitted freely Propositions in E, but have purposely stated the Premisses in random order, leaving to the Reader the useful task of arranging them, for himself, in an order which can be worked as a series of regular Syllogisms. In doing this, he can begin with any one of them he likes.

I have tabulated, for curiosity, the various orders in which the Premisses of the Aristotelian Sorites

1. All a are b;
2. All b are c;
3. All c are d;
4. All d are e;
5. All e are h.
∴ All a are h.