The Organon, Or Logical Treatises, of Aristotle

CHAP. XII. A comparison of pure with necessary Syllogisms.'

* i. e. pure

between an ab

1. Distinction solute and necessary concluthe latter's dependence upon the premises; their connexion also with it.

sion as regards

It appears then, that there is not a syllogism de inesse unless both propositions signify the being present with,2 but that a necessary conclusion follows, even if one alone is necessary. But in both,* the syllogisms and modal. being affirmative, or negative, one of the propositions must necessarily be similar to the conclusion; I me n by similar, that if (the conclusion) be (simply) that a thing is present with, (one of the propositions also signifies simply) the being present with, but if necessarily, (that is, in the conclusion, one of the propositions is also) necessary. Wherefore this also is evident, that there will neither be a conclusion necessary nor simple de inesse, unless one proposition be assumed as necessary, or purely categorical, and concerning the necessary, how it arises, and what difference it has in regard to the de inesse, we have almost said enough.

1. Definition of

the contingent

(τοῦ ἐνδεχομέ Vov) given and

CHAP. XIII.-Of the Contingent, and its concomitant Propositions. LET us next speak of the contingent, when, and how, and through what (propositions) there will be a syllogism; and to be contingent, and the contingent, I define to be that which, not being necessary, but being assumed to exist, nothing impossible will on this account arise, for we say that the necessary is contingent equivocally. But, that such

confirmed.

(Vide Metaph.

lib. v. 2,) also Interpret. 13.

' Vide the previous notes on the subject of modals. The reader who wishes to ascertain how far logic is conversant with the expressed matter of modal proposition, will find arguments ad rem, "" and "ad nauseam both, in relation to the various views of the question, in Ed. Review, No. 118; Kant, Logik, sec. 30; St. Hilaire's preface. In both modals and pure categoricals, the formal consequence alone is really the legitimate object of consideration to the logician, with the material he has strictly nothing to do. Whately has shown that a modal may be stated as a pure proposition, by attaching the mode to one of the terms; this being done, the rule of consequence applies to both equally.

2 i. e. in categoricals both premises must be affirmative for the con. clusion to be so.

is the contingent, is evident from opposite negatives and affirmatives, for the assertions-"it does not happen to be," and, "it is impossible to be," and, "it is necessary not to be," are either the same, or follow each other; wherefore also the contraries to these, "it happens to be," "it is not impossible to be," and, "it is not necessary not to be," will either be the same, or follow each other; for of every thing, there is either affirmation or negation, hence the contingent will be not necessary, and the not-necessary will be contingent. It hap

2. Contingent προτάσεις capable of conversion.

happens to

* i. e. is conver

sion effected.

pens, indeed, that all contingent propositions are convertible with each other. I do not mean the affirmative into the negative, but as many as have an affirmative figure, as to opposition; e. g. "it exist," (is convertible into) "it happens not to exist," and, "it happens to every," into "it happens to none," or, "not to every," and, "it happens to some," into "it happens not to some.' In the same manner also with the rest,* for since the contingent is non-necessary, and the non-necessary may happen not to exist, it is clear that if A happens to be with any B, it may also happen not to be present, and if it happens to be present with every B, it may also happen not to be present with every B. There is the same reasoning also in particular affirmatives, for the demonstration is the same, but such propositions are affirmative and not negative, for the verb "to be contingent," is arranged similarly to the verb "to be," as we have said before.†

+ Vide c. 3.

3. The contin

gent predicated

in two ways

finite-the me

same to each.

These things then being defined, let us next remark, that to be contingent is predicated in two the one general, ways, one that which happens for the most part the other inde- and yet falls short of the necessary—(for instance, thod of conver- for a man to become hoary, or to grow, or to sion not the waste, or in short whatever may naturally be, for this has not a continued necessity, for the man may not always exist, but while he does exist it is either of necessity or for the most part)—the other way (the contingent is) indefinite, and is that which may be possibly thus and not thus; as for an animal to walk, or while it is walking for an earthquake to happen, or in short whatever occurs casually, for

i. e. that he is subject to these things.

nothing is more naturally produced thus, or in a contrary way. Each kind of contingent however is convertible according to opposite propositions, yet not in the same manner, but what may naturally subsist is convertible into that which does not subsist of necessity; thus it is possible for a man not to become hoary, but the indefinite is converted into what cannot more subsist in this than in that way. Science however and demonstrative syllogism do not belong to indefinites, because the middle is irregular, but to those things which may naturally exist; and arguments and speculations are generally conversant with such contingencies, but of the indefinite contingent we may make a syllogism, though it is not generally investigated. These things however will be more defined in what follows, at present let us show when and how and what will be a syllogism from contingent propositions.

4. The indefinite contingent of less use in syllogism.

Since then that this happens to be present with that may be assumed in a twofold respect,-(for it either signifies that with which this is present, or that with which it may be present, thus the assertion, A is contingent to that of which B is predicated, signifies one of these things, either that of which B is predicated, or that of which it may be predicated; but the assertion that A is contingent to that of which there is B, and that A may be present with every B, do not differ from each other, whence it is evident that A may happen to be present with every B in two ways,)-let us first show if B is contingent to that of which there is C, and if A is contingent to that of which there is B, what and what kind of syllogism there will be, for thus both propositions are contingently assumed. When however A is contingent to that with which B is present, one proposition is de in- into the conesse, but the other of that which is contingent, so that we must begin from those of similar character, as we began elsewhere.2

5. An inquiry

struction of contingent syllogisms prepared.

In the Post Analytics, i. c. 8. In Rhetoric, b. ii. c. 24, he admits ac cident to be an element of apparent argument, but in Metap. lib. v. c. 3, denies that there is any science of it, and regards it as a onμetov.

That is, from syllogisms, each of whose propositions is contingent.

CHAP. XIV.-Of Syllogisms with two contingent Propositions in

1. With the

contingent premises both uni

versal there

will be a perfect syllogism.

2nd case.

gent, this under B.

3rd case.

* Vide ch. 13.

the first Figure.

WHEN A is contingent to every B, and B to every C, there will be a perfect syllogism, so that A is contingent to every C, which is evident from the definition, for thus we stated the universal contingent (to imply). So also if A is contingent to no B, but B to every C, (it may be concluded) that A is contingent to no C, for to affirm that A is contingent in respect of nothing to which B is continwere to leave none of the contingents which are But when A is contingent to every B, but B contingent to no C, no syllogism arises from the assumed propositions, but B C1 being converted according to the contingent, the same syllogism arises as existed before, as since it happens that B is present with no C, it may also happen to be present with every C, which was shown before,* wherefore if B may happen to every C, and A to every B, the same syllogism will again arise. The like will occur also if negation be added with the contingent (mode) to both propositions, I mean, as if A is contingent to no B, and B to no C, no syllogism arises through the assumed propositions, but when they are converted there will be the same as before. is evident then that when negation is added to the minor extreme, or to both the propositions, there is either no syllogism, or an incomplete one, syllogism or an for the necessity (of consequence) is completed by conversion. If however one of the propositions be universal, and the other be assumed as partiminor particu- cular, the universal belonging to the major exlar, different. treme there will be a perfect syllogism, for if A is contingent to every B, but B to a certain C, A is also contingent to a certain C, and this is clear from the definition of universal contingent. Again, if A is contingent to no B, but B happens to be present with some C, it is necessary that A should happen not to be present with some C, since the de

4th case.

2 When the premises are ooth negative or the minor negative, there is either no

incomplete one -case of the major universal with the

1 That is, the minor negative being made affirmative.

2. Vice versa.

monstration is the same; but if the particular proposition be assumed as negative, and the universal affirmative, and retain the same position as if A happens to be present to every B, but B happens not to be present with some C, no evident syllogism arises from the assumed propositions, but the particular being converted and B being assumed to be contingently present with some C, there will be the same conclusion as before in the first syllogisms. Still if the major proposition be taken as particular, but the minor as universal, and if both be assumed affirmative or negative, or of different figure, or both indefinite or particular, there will never be a syllogism; for there is nothing to prevent B from being more widely extended than A, and from not being equally predicated. Now let that by which B exceeds A, be assumed to be C, to this it will happen2 that A is present neither to every, nor to none, nor to a certain one, nor not to a certain one, since contingent propositions are convertible, and B may happen to be present to more things than A. Besides, this is evident from the terms, for when the propositions are thus, the first is contingent to the last, and to none, and necessarily present with every individual, and let the common terms of all be these; of being present necessarily 3 "animal," "white," "man," but of not being con* Example (1.) tingent, "animal," "white," "garment."* Therefore it is clear that when the terms are thus there is no syllo

In the universal imperfect syllogisms mentioned towards the beginning of this chapter.

Because C is necessarily not present, and the necessary is distinguished from the contingent.

That is, of the major being with the minor.

Ex 1. It happens that something white {is not