for all the figures (including the fourth) there is no denying their convenience for any one who has to work out a set of problems. Here are some of the diagrams for the first figure.

The dotted lines are used to indicate doubt as to where the circle or

the part of the circle in question should fall.

CHAPTER XIV.

THE SECOND FIGURE OF THE SYLLOGISM.

In this figure each premise describes an object or set of objects, and from the nature of the two descripand general tions the conclusion tells whether or not the objects are identical with each other.

Function

cautions.

The man that came to my house was tall and thin; The man that went to your house was short and fat (ie., not tall and thin);

... The man that came to my house is not the man that

went to your house.

Crows do not sing;

This bird sings;

... This bird is not a crow.

Whales suckle their young;

Fishes do not;

... Whales are not fishes.

The second and third of these examples differ from the first in this respect: In the first, two given objects are compared, and we conclude that they are not identical; in the second a given object is compared with a class of objects, and we conclude that it does not belong to the class-that it is not the kind of thing to which the class-name applies; in the third two classes of objects are compared. In the first case we are concerned with identification in the narrowest sense of the term; in the others with classification. In the general description of the figure I have mentioned only the identification because it is the more fundamental

If we could

and the classification really depends upon it. not distinguish between individual objects, we could not distinguish between classes. To say that whales are not fishes is to say that there is not any whale which is identical with any fish. To classify is thus merely to distinguish between individuals in groups, and the principles by which we distinguish classes are nothing more than those by which we distinguish individuals.

In this figure, therefore, both premises are concerned with descriptive relations, and the conclusion with a relation of identity.*

The next thing to be noticed about the figure is that the two premises must describe their objects in the same respect. If I describe the man I saw as tall, and you describe the one you saw as agreeable, the descriptions indicate absolutely nothing about the identity of the men.

But even when both premises describe their objects in the same respect a conclusion is not always possible. If each of two persons had met a tall man named Smith, they would not necessarily have met the same man. Two Dromios or two atoms of hydrogen might have innumerable points of

* For the purposes of this figure propositions which in themselves are not strictly descriptive are treated as such. When we conclude, for example, that Newhaven and New Haven are different cities because one is on the road from Paris to London, and the other on the road from New York to Boston, the geographical or spatial relations of each of them to the adjacent cities are practically regarded as a part of the city itself. The distance between Newhaven and London or Paris is a spatial relation and belongs as much to London or Paris as to Newhaven. But when it serves to distinguish Newhaven from New Haven it is treated as though it belonged, like its size or its history, to Newhaven itself. For this reason we make the word Newhaven the subject of the sentence in which the facts are expressed. We do not say "London is a usual terminus for persons traveling from Paris and Newhaven", or "A good way to reach London from Paris is through Newhaven ", or "London is so far from Newhaven and so much farther from Paris by way of Newhaven ". What the syllogism involves is not the distance of London or Paris as such, but all of them in

so far as they characterize Newhaven.

resemblance and yet be two. As the points of resemblance between two complex things increase, the probability that the things are really identical also increases; but no amount of resemblance can supply theoretically absolute proof of such identity. The prisoner in the dock might bear every resemblance to the man who was seen reeling on the street the night before and yet possibly, though not probably, be a different man. We could be absolutely certain of their identity only if the reeling man had been arrested at the time and never lost sight of for a moment until he was placed in the dock.

The fact is that the identity of two things involves a great deal more than mere resemblance, no matter how complete the resemblance may be. Consequently, though we can often prove that things are not identical from the fact that they are dissimilar, we can never prove that they are identical from the fact that they are similar. If men are mortal and angels are not mortal, it follows that men are not angels; but if men are mortal and horses are mortal, it does not follow that men are horses. In this figure negative conclu

sions alone are valid.

There is no logical blunder more frequent than to conclude that because things are alike they are necessarily the same. Flour is white, says the child; what I see all over the ground is white; therefore what I see all over the ground is flour.

Good dollars are silvery-looking discs bearing a certain stamp;

This is a silvery-looking disc bearing that stamp; ... This is a good dollar.

Benevolent people smile affably;

This man smiles affably;

... This man is benevolent.

All P is M;

All S is M;

... All S is P.

But what the child sees on the ground is snow, not flour, and sometimes our silver disc is counterfeit, and the smiling stranger a brute. S is not always P.

The logical trouble comes when we mistake probabilities for certainties. In practical life it is usually better to take an occasional counterfeit coin than to insist upon testing them all, better to be deceived in a character occasionally than to refuse all intercourse with one's fellows until they prove their right to be trusted, better to bow to a stranger than to cut a friend. But a good rule of conduct when we must act in a hurry is not necessarily a good rule of conduct or thought when we have time to be careful. The bank teller must be on the watch for counterfeit money, the employer of a confidential clerk must look behind his face, and the sheriff should be sure of his man. In the same way, as students of deductive logic we must reject all conclusions that do not follow with absolute necessity from the premises.*

*The significance of this fallacious reasoning A A A in the second figure may become clearer if we show its relations to the first figure. In the second figure we say

All Y is Z

All X is Z

... All X is Y

Now if we could convert the first premise simply, i.e., without altering the quantity, we should get a perfectly valid syllogism in the first figure:

But we cannot convert the premise simply.

All we can say is that some Z is Y, and from this major premise no conclusion can be drawn.

If we happened to know not only that some Z is Y, but that most Z is Y, we might conclude that X is probably Y.

Most silvery looking discs bearing a certain stamp are good dollars. This is a silvery looking disc bearing that stamp.

... This is probably a good dollar.

Even as a rule for hurried action it is not wise to draw affirmative