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that he is not identical with any one of them, i.e., he was not there. Similarly if we had been told that every one at the ball was tall and that there are some members of the club who are not tall, we could be sure that there are some members of the club who are not to be identified with any one who was at the ball, i.e., some members of the club were not at the ball.
Club S. At the ball = P.
Ф On the other hand we could not be sure that some of those at the ball were not members of the club. If some S's are M and no P's are M, or if some S’s are not M and all P's are M, it follows that some S’s are not P's; but it does NOT follow that some P's are not S’s, for it may be that each of the P’s is identical with one of the undescribed S's. The S's.
reasoning is valid only if you arrange your conclusion so as to have for its predicate the term which occurred in the universal premise. In the technical language of the syllogism: The major premise (i.e., the one containing the predicate of the conclusion) must be universal. The difference between concluding that some S's are not P's and that some P's are not S’s may become clearer if we remember that Proposition O cannot be converted.
When both premises are universal it is clear enough that a universal conclusion can be drawn; and of course it makes S's.
no difference which of the premises is affirmative or negative, so long as the quality of the two is different.
Putting all this together we can add another CAUTION:
6) We cannot say that any s's are not P's unless each of the S's in question is different from every P.* To put it somewhat differently, Evidence sufficient to prove that some S's are not P's may not be sufficient to prove that some P's are not s's, and vice versa.
The general principle of the figure and the caution respecting quantity are worked out together in the following formula which a student may use if he likes instead of the separate statements:
If all the members of one group differ in a given respect from all the members of another, then no member of either group is a member of the other. If some members of one group differ from all the members of another, then there are some members of the first group which are not members of the second; but it does not follow that there are members of the second which are not members of the first. The mere fact that some members of one group differ from some members of another proves that those particular individuals are not identical, but it does not prove that any member of either group is not also a member of the other.
* This caution covers the fallacy of illicit major in the second figure. Illicit minor is covered in the second figure as in the first by the first caution.
THE THIRD FIGURE OF THE SYLLOGISM.
In this figure one premise asserts that a certain object possesses (or does not possess) a given relation, and the other premise asserts that this same object possesses (or does not possess) another given relation, and on principle, the strength of these premises the conclusion as- general serts that the presence (or absence) of one of the relations sometimes coincides with the presence (or absence) of the other-e.g.:
Shakspeare was perfectly sane;
Shakspeare was a genius; ... Some geniuses (one at least) are perfectly sane, or Some perfectly sane persons are geniuses.
Sin is evil;
Sin exists; ... Something evil exists. The ancient Stoics were not enlightened by the Scrip
tures; These Stoics believed in God; .:. Some persons not enlightened by the Scriptures have
believed in God. This figure is used mainly to disprove sweeping statements or alleged general laws, by displaying cases to which they will not apply. If any one maintains that every genius is a morbid degenerate, we can disprove the statement by calling
his attention to the fact that Shakspeare or Goethe or Plato was a man of undoubted genius yet perfectly free from every trace of morbid degeneracy. If he maintains that in God's world no evil can exist, we need only point to sin. If he maintains that through the Scriptures alone can God be known, it is only necessary to remind him of the Stoics.
In this figure more than in any other the machinery of the syllogism seems very cumbersome and unnecessary. dinary speech and thought we consolidate the two premises into one statement: Shakspeare was a genius
Shakspeare was a genius and yet not morbid Sin is an evil and yet exists The Stoics believed in God 0 ° ¢, though not enlightened by the Scriptures + + +.
The PRINCIPLE on which we reason is evidently this:
A single actual case in which two positive or negative relations coincide proves that they are not incompatible.
In the examples here given Shakspeare's freedom from morbidness and the Stoics' ignorance of the Scriptures may be regarded as negative relations. As applied to these two cases the principle means that freedom from morbidness is not inconsistent with genius, and vice versa; that ignorance of the Scriptures is not inconsistent with a knowledge of God, and vice versa.
When both relations are negative a conclusion can be drawn quite as well as when one or both are positive. From the fact that stones are neither virtuous nor vicious $ $ $ we can prove that the absence of one of these qualities does not necessarily preclude the absence of the other, and thus disprove the statement that everything in the world must be one or the other.*
* The old syllogistic rule says : From two negative premises no conclusion can be drawn; but in the third figure the rule is evaded by obverting one or both premises. So that if we say “Stones aren't virtuous, and stones aren't vicious ’we cannot draw a conclusion, but if we say stones aren't virtuous and stones are not-vicious we can ! Conclusions do not depend upon the form of words in which the premises are stated, but upon the real state of affairs to which they point; yet when we consider Our conclusion in the example given does not depend upon the mere fact that there are no such things as virtuous or vicious stones, for if there were no stones at all this would still be a fact, though the conclusion would not follow; but upon the fact that there are stones which are neither virtuous nor vicious. To state the case more generally : The conclusion does not depend upon the fact that objects with the relation in question do not exist, but upon the fact that objects do exist without the relation.
This last statement suggests what is involved in the principle of the figure as I have stated it, but what cannot be too much emphasized, that the cases from which our conclusions are drawn must actually exist. We cannot prove that a good man may come to grief by Colonel Newcome, that a brave man may murder his wife by Othello, that good nature will not save us from cruelty by Arthur Donnithorne, that wounds will not destroy existence by the heroes of Valhalla, or that a pumpkin-shell may be transformed into a chariot by the adventure of Cinderella. From particular cases in one uni
we cannot prove the compatibility of relations in another.
The first CAUTION to be observed in using this figure is -put technically—that its conclusion is always particular. If all men are mortal and all men are bipeds, we can be sure that so far as men are concerned these two attributes coincide, but this does not prove that every mortal creature has two legs or that angels and all other bipeds are sure to die. In other words, the fact that certain objects possess each of several positive or negative relations does not prove that other objects may not possess one without the other or exist without either. Or more briefly:
7) Any number of coincidences between relations will not prove that they coincide always. this state of affairs there is a sense in which we can say that premises in this figure from which a conclusion can be drawn must both be affirmative in meaning, no matter what their form. See the next paragraph.