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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 conclusions 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 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 :
All Z is Y
All X is Z
... All X is Y 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. φο0
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
We have seen that in this figure no affirmative conclusion can be drawn—similar things are not necessarily identical. But how about the negative conclusion ? Can we say with any more certainty that dissimilar things are not identical ? Is not the tadpole of last summer identical with this summer's frog, the bright-winged bird of the spring with the sober-looking one of the summer, the grub of one month with the butterfly of the next, Saul the persecutor with Paul the apostle ? On the other hand, no one can suppose that the tadpole is identical with the later bird, or the grub with Paul, or even that a tadpole seen this morning is identical with a perfect frog seen this noon. The fact is that objects can be distinguished from each other by their qualities or relations only when these are different at one and the same instant; so that if the objects are not observed simultaneously we cannot distinguish them by their qualities or relations unless we believe these latter to be so permanent that they cannot be wholly changed in the time which has elapsed between the two observations. What qualities or relations are relatively permanent and what are not we can learn only through experience, without a constant appeal to which logic is perfectly helpless.*
To sum up, the PRINCIPLE on which we reason in the second figure is that Dissimilar objects are not identical; and these are the CAUTIONS:
3) Similarity does not prove identity. †
4) Dissimilarity does not prove non-identity if the object might have changed. conclusions in the second figure unless we have reason to believe that the converse of the major premise is usually true. In other words, the only possible justification for such reasoning in the second figure is found in the fact that it sometimes represents a fairly good induction in the first figure.
* Of course it is only things that change and still retain their identity. Blue is not like yellow now, and never will be.
† This caution covers the fallacy of undistributed middle as it occurs in the second figure.
5) Different descriptions do not imply dissimilarity unless the relations described are incompatible.
So far our examples have all dealt with universal or singular propositions, and no difficulties have arisen from questions of quantity. It is clear that from Quantity universal or singular premises a universal or
figure. singular conclusion can be drawn; but can we draw any conclusion at all from particular premises ?
First, when both premises are particular. If some members of Congress have blue eyes and some lovers of literature have brown eyes, i.e., have not blue eyes, what inference can be drawn ?
It is clear enough that certain members of Congress, namely, those with blue eyes, are not identical with certain lovers of literature, namely, those with brown eyes. Using the sign = to indicate identity and # to indicate nonidentity, we can make such a diagram as this:
Congressmen. Lovers of Literature.
meaning that no one of the described congressmen is identical with any one of the described lovers of literature. But for all we know, each one of the described congressmen may be identical with one of the undescribed lovers of literature, and vice versa, e.g., the first in one column with the third in the other, and so on. It might be that every congressman was a lover of literature and every lover of literature a congressman, in spite of the fact that a blue-eyed congressman is not a brown-eyed lover of literature.
To put the matter somewhat differently. From the fact that certain S’s are not identical with certain P's, it by no means follows that certain S’s are not P's at all. Suppose every S to be a P as indicated below:
The first S is identical with the first P, but for that very reason it cannot possibly be identical with the second or the third. If there are in all one hundred different S's and one hundred different P's, and if each of the S’s is identical with one of the P's, then there are ninety-nine different P's with which that particular S is not identical. Jones the congressman is identical with Jones the literary man, but not with Smith or Brown.
As long as there are two or more S's it must necessarily be true that certain S's and certain P's are not identical, and it does not make any difference whether every S is a P, or no S is a P, or some S's are P and some are not. Hence the inference we seem to draw from two particular premises in the second figure—that certain S’s are not identical with certain P's—does not follow from these premises any more than from any others in which several S’s are mentioned. It is equivalent to the mere truism that no one S can be identical with more than one P. It is something we might have known long before we knew anything about the special facts stated in the premises. It is practically no inference whatever from these premises and we may as well say that from such premises no inference can be drawn.
When one premise is particular and the other singular the case is much the same. If we have been told that some of the masqueraders at a ball were tall and if we know that John is short, we can be sure that John was not one of these tall masqueraders. We can say if we like that there were certain persons there with whom John was not identical; but we know that already if we happen to know that there were more persons than one present. It doesn't depend at all upon the question of height. This inference is thus worthless; and no other can be drawn.
When one premise is universal the case is different. If everybody at the ball was tall and John is short, we know