Neither of us could detect this until we were told to mark the position of B, or the middle term in the premisses, and then we saw that B was subject in the major premiss (top proposition) of syllogism (i), but predicate of major premiss of syllogism (ii).

Here, then, is another point in which these triplets of propositions, called syllogisms, may differ. And as syllogisms differ in mood according to the arrangement of their propositions, so they differ in figure according to the position of the middle term in those propositions. There can only be four figures. Where the middle term is subject in the major and predicate in the minor premiss, where it is predicate in both, where it is subject in both, and where it is predicate and subject; e.g., take the mood A A A in all the four figures:

A. All B is A

We know there can be only four figures; the question is, how many moods can we have in those four figures. The four figures may be remembered by the front of a collar. As to moods, it is clear that out of the four forms or propositions AEIO a large number of different triplets can be made. We

1 See next page. The figures are thus easily remembered;\, these lines being taken from the position of the middle term as marked above. For further remarks upon the figures see Appendix A (i.).

may have A A A in all the four figures, and AAE, AE E, and so on; these will be all syllogisms, i.e. triplets of propositions comparing two terms through

a third; but whether they will be all valid syllogisms is another question. Supposing we act upon the conclusion we get from a syllogism and fall into error, we should at once turn upon Logic and abuse it. But Logic does not warrant as valid every combination of the propositions AEIO in syllogistic triplets.'

'I don't quite understand,' said I.

'Take the mood A A A in the second figure, and tell me whether its conclusion is true :

'It seems right, as far as I can judge,' said I.

'By this syllogism a man might pray for a dissolution of his marriage on the ground that his wife was married to a crocodile; for

"All crocodiles are animals,

All men are animals,

Therefore all men are crocodiles."

'In this shape it certainly sounds wrong,' said I. 'Of course; and there are many other of the possible moods which will be found to be not valid in the same way. A mood not valid in one figure may be valid in another. There are sixty-four possible moods. How many of them can we admit into the four figures as valid syllogisms? That all the moods are not valid in all the figures is clear from the above instance, where the mood A A A in the second figure is found to produce an unheard-of conclusion. By what test shall we try pretenders to the name of valid syllogisms? The answer is, by applying certain rules to them; and if they do not violate these rules, they are valid; and if they do, they are not. These rules are eight. Do not be alarmed; they are all eight wrapped up in four lines easily learnt. To explain these rules :

once.

'(1) The middle term must be distributed at least For unless it be used in its full extent once, it may be used first for one part of itself, and secondly for another part of itself; e.g.

This whole figure represents the class "women; parts of this class are cooks and 66

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وو

دو

queens."

Hence :

All queens are women,

All female cooks are women,

... all female cooks are queens.

دو

Had the middle term " women been once used in its full extent, this false conclusion could not have been drawn.

'(2) You must only have three terms, otherwise the principle of the syllogism is violated, "things which are equal to the same," &c. An ambiguous middle term is the same as two terms, thus :-

All chests are boxes,

Part of me is a chest,

.. part of me is a box,

where "chest" means "box" in the major premiss, and "breast" in the minor.

(3) Two negative premisses prove nothing. For if we wish to compare two things through a third, and neither of these two things is connected with the third, we can draw no conclusion. From "Socrates is not an elephant," and "Pugilists are not elephants," I should be in no way helped as to the question whether Socrates was a pugilist or not.

(4) Two particular premisses prove nothing. For they would be O, 0, which violates (3), or I, I, which violates (1), or I, O, which will be found to violate (5).1

(5) If either premiss be negative, the conclusion must be negative. For if, after taking our middle 1 For further explanation see Appendix A (ii.).

term as a medium of comparison, we say that one of the two things to be compared is equal to the middle term and the other is not, it follows that the two things to be compared cannot be equal to one another. If we want to compare "Socrates " and "stone" through the medium "animal," we say "Socrates is animal, stone is not animal," and the conclusion must be negative, "... Socrates is not stone."

(6) If either premiss be particular, the conclusion1 must be particular. I will prove this rule afterwards.1

(7) Let no term be distributed in the conclusion, unless it has been already distributed in the premisses. Otherwise we argue from part to whole. Violation of this rule, if it be in the case of the minor term, is called "illicit process of the minor," or, if it be in the case of the major term, "illicit process of the major."

(8) Let not the conclusion be negative, unless one1 of the premisses is negative. For we could not say, "Socrates is not stone" as a conclusion, unless we had a " in one of our premisses; e.g., "Stone is not animal," "Socrates is animal."1

"not"

'Further explanation of these rules I do not think to be necessary, but you can find it in the books of Mr. Jevons or Mr. Fowler. For our purpose it will be enough to remember them by heart, and this you do by learning off these four hexameter lines:

For further explanation see Appendix A (ii.).