CHAPTER XV.

THE THIRD FIGURE OF THE SYLLOGISM.

Purpose,

and

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;

caution.

... 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 Scriptures;

Lat 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. In ordinary speech and thought we consolidate the two premises into one statement: Shakspeare was a genius and yet not morbid Sin is an evil ● and yet exists The Stoics believed in God, 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 universe 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,

The briefer statement is less comprehensive, but it will cover any case that is likely to arise.*

Negative relations.

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In this figure as in the second we must be careful not to be confused by negative relations. From the fact that all M's are P, and that no M's are S, we can infer that some P's are not S; but we cannot infer that some S's are not P.†t From the Pope we may perhaps prove that there are infallible mortals, but not that there are fallible immortals. It takes the Devil for that. The sixth .caution or its corollary--- 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"-is one which we tend to ignore or misunderstand continually. Altogether the best way to observe it without confusion, whether we are reasoning in the third figure or in one of the others, is to put our premises affirmatively, with the negative element, when there is one, in the predicate (ie., to obvert negative premises and conclusions). When we say that there are infallible mortals or that there are fallible immortals, our meaning is much clearer and the distinction between the two statements is much more obvious

This caution covers illicit minors in the third figure. Put in terms of causal relations the caution is this:

A single coincidence proves the compatibility of relations, but no number of coincidences can prove their necessary connection.

This caution covers illicit majors in the third figure as well as in the second.

The statement in this form has moreover the advantage of directing attention to the fact that we are talking about real things. (See top of p. 173.) The diagrams in the text seem to me to accent the affirmative

M

S

O

element which reasoning in the third figure particularly involves, as well as to guard against the confusion referred to in the text better than Euler's. Students always find it difficult to see why this figure does not mean that some P's are not S as well as that some S's are not P. But if we represent S by a vertical stroke and P by a horizontal

the distinction between M which is S but not P

and M which is P

but not S is obvious, and with it the distinction between S not-P + and P not-S

than when we say that some mortals are not fallible or that some fallible beings are not mortal.

By the coincidence of two relations we mean that they both belong to the same individual. Whether they do or not is

primarily, of course, a matter of observation in

Quantity

premises.

each particular case; but when the coincidence of the of the relations must be inferred by putting together statements about the existence of each we must remember one more CAUTION:

8) Two different relations can belong to individuals of the same class without belonging to the same individual, unless at least one of them belongs to every individual in the class.*

If we know that this particular X is both Y and Z, we know of course that Y and Z coexist. If we know that every X is Y and every X is Z, we can be sure that each X is both Y and Z; if we know that every X is Y and that some X is Z, we can be sure that some X or other is both Y and Z; but if we only know that some X's or other are Y and that some X's or other are Z, we cannot be sure that Y and Z ever belong to the same X. This is what is meant in this figure by the technical rule that from two particular premises no conclusion can be drawn. The technical rule should have added that from a particular premise and a singular premise in the third figure no conclusion can be drawn; for it does no good to know which particular X's are Y so long as we do not know which are Z.

The principle and all the cautions can be put together in such a general statement as this:

The coincidence of relations-whether positive or negativeproves that they are compatible, but it does not prove that either of them involves the other, or that the absence of one is compatible either with the presence or with the absence of the other. Moreover the fact that two relations belong to objects of the same class will not prove that they belong to the same objects unless at least one of them belongs to all the objects in the class.

* This covers undistributed middles in the third figure,