Return to Aristotle, Prior Analytics
If, however, one of the propositions is assumed to exist, but the other to be contingent when that which contains the greater extreme, signifies to be contingent, all the syllogisms will be perfect, and will be of the contingent, assumed according to the above-mentioned definition. But when the proposition in which the less extreme is contained, signifies to be contingent, all the syllogisms will be imperfect; and the privative syllogisms will not be of the contingent assumed according to that definition, but of that which is necessarily present with no one, or not with every individual, for if it is necessarily present with no one, or not with every individual, we say that it happens to be present with no one, or not with every individual. For let A be contingent to every B, and let B be supposed to be present with every C. Because, therefore, C is under B, but A is contingent to every B, it is evident that A also is contingent to every C. A perfect syllogism, therefore, will be produced. In like manner also, if the proposition A B is privative, but the proposition B C affirmative, and if the proposition A B is assumed to be contingent, and the proposition B C to be present with; there will be a perfect syllogism, in which it may be collected that it will happen that A is present with no C. It is evident, therefore, that when the being present with is posited to the less extreme, perfect syllogisms will be produced. But that when it subsists in a contrary mode there will also be syllogisms, may be shown by a deduction to the impossible; though at the same time it will be evident that the syllogisms will be imperfect; for the demonstration will not be from the assumed propositions. In the first place, however, it must be shown, that if when A exists, it is necessary B should exist; and that if A is possible, B will necessarily be possible. For things thus subsisting, let A be possible, but B impossible. If, therefore, the possible, when it is possible to be should be produced; the impossible, because it is impossible, will not be produced. But if at the same time A is possible, and B impossible, it will happen that A may be produced without B; and if it is produced, that it exists. For that which is generated, when it is generated, is. It is necessary, however to consider the possible and impossible, not only in that which may be generated, but also in that which may be verified, and exists in energy, and in whatever other ways the possible is said to be possible; for the reasoning is similar in all of them. Besides, when we say A is B, this ought not to be understood, as if A being one certain thing, B will be; for nothing necessarily follows from there being one thing, but from there being two things at least: for instance, when propositions subsist in syllogism, after the manner we have mentioned. For if C is predicated of D, but D of F, C also will necessarily be predicated of F. And if each proposition is possible, the conclusion also will be possible. Just, therefore, as if any one should place A as the propositions, but B the conclusion; it will not only happen that when A is necessary, at the same time also B is necessary; but, likewise, when the former is possible, the latter also will be possible. But this being demonstrated, it is evident, that when the hypothesis is false and not impossible, that also which happens on account of the hypothesis will be false and not impossible. For instance, if A is false indeed, yet not impossible, but when A is, B is; — in this case, B also will be also indeed, yet not impossible. For since it has been shown that if A is, B also is; when A is possible, B also will be possible. But it was supposed that A is possible; B, therefore, will also be possible. For if it is impossible, the same thing will be at the same time possible and impossible. These things being determined, let A be present with every B, and let B be contingent to every C. It is necessary, therefore, that A should happen to be present with every C. For let it not happen to be present; and let B be admitted to be present with every C. This is false, indeed, but not impossible. If, therefore, A is not contingent to C, but B is present with every C; A will not be contingent to every B; for a syllogism will be produced in the third figure. But it was supposed that A is present with every B. It is necessary, therefore, that A should be contingent to every C. For that which is false being supposed, and not that which is impossible, that which thence happens is impossible.
Every B is A:
It happens that every C is B:
∴ It happens that every C is A.
It is necessary that some C should not be A:
Every C is B:
∴ Not every B is A.
A deduction also to the impossible may be made in the first figure, if B is supposed to be present with C, For if B is present with every C, but A is contingent to every B, A also will be contingent to every C. It was supposed, however, that it could not be present with every C.
Every B is A:
It happens that every C is B:
∴ It happens that every C is A.
It happens that every B is A:
Every C is B:
∴ It happens that every C is A.
It is necessary, however to assume the being present with every individual, not defined by time, as now, or at this time, but simply; for we also produce syllogisms through propositions of this kind. For when a proposition is assumed according to the now, or the present time, there will not be a syllogism; since perhaps nothing hinders but that man sometime or other may be present with every thing that is moved; viz. if nothing else is moved. But that which is moved may be contingent to every horse; and man is contingent to no horse. Farther still, let the first term be animal; the middle that which is moved; and the last term, man. The propositions, therefore, will subsist similarly; but the conclusion will be necessary, and not contingent. For man is necessarily an animal.
Whatever is moved is a man:
It happens that every horse is moved:
∴ It is necessary that no horse should be a man.
Whatever is moved is an animal:
It happens that every man is moved:
∴ It is necessary that every man should be an animal.
It is evident, therefore, that the universal should be assumed simply, and not defined by time. Again, let the proposition A B be universal privative, and let A be assumed to be present with no B, but let it happen that B is present with every C. These things, therefore, being admitted, it is necessary that A should happen to be present with no C. For let it not so happen; and let B be supposed to be present with C as before. Hence it is necessary that A should be present with some B. For a syllogism will be formed in the third figure. This, however, is impossible. Hence A will be contingent to no C; for the false, and not the impossible being supposed, that which is impossible will happen.
No B is A:
It happens that every C is B:
∴ It happens that no C is A.
It is necessary that some C should be A:
Every C is B:
∴ Some B is A.
This syllogism, therefore, is not of that contingent which is according to the definition above given, but of that which is necessarily present with no individual. For this is a contradiction of the given hypothesis; because it was supposed that A is necessarily present with some C. But the syllogism which is through the impossible is of an opposite contradiction. Again, it is also evident from the terms, that the conclusion is not contingent. For let A be a crow; B, that which is intelligent; and C, man. A, therefore, is present with no B; for nothing intelligent is a crow. But B is contingent to every C; for it happens to every man to be intelligent. A, however, is necessarily present with no C. The conclusion, therefore is not contingent.
Nothing intelligent is a crow:
It happens that every man is intelligent:
∴ It is necessary that no man should be a crow.
The conclusion, however, is not always necessary. For let A be that which is moved; B be science; and C be man. A, therefore, will be present with no B; but B is contingent to every C; and the conclusion will not be necessary. For it is not necessary that no man should be moved, but it also is not necessary, that a certain man should be moved. It is evident, therefore, that the conclusion is of that which is necessarily present with no individual. Hence the terms must be assumed in a better manner. But if the privative is joined to the less extreme, and signifies to be contingent; from the assumed propositions, indeed, there will be no syllogism; but the contingent proposition being converted there will be a syllogism, as in the former instances. For let A be present with every B, but let B be contingent to no C. The terms, therefore, thus subsisting, nothing necessary will be collected. But if the proposition B C is converted, and B is assumed to be contingent to every C, a syllogism will be produced as before. For the terms will have a similar position. The like will also take place when both the intervals are privative, if the interval A B signifies the not being present with, but B C signifies the being contingent to no individual. For through the assumed propositions nothing necessary will be collected; but the contingent proposition being converted, there will be a syllogism. For let it be assumed that A is present with no B, and let B be contingent to no C. Through these, therefore, nothing necessary will be collected. But if it is assumed that B is contingent to every C, which is true, and the proposition A B subsists similarly; again there will be the same syllogism. If, however, it is assumed that B is not present with C, but not that it happens not to be present with it; there will by no means be a syllogism, neither when the proposition A B is privative, nor when it is affirmative. But let the common terms of being present with from necessity be, white, animal, snow; and of not being contingent, white, animal, pitch.
It happens that every/no animal is white:
No snow is an animal:
∴ It is necessary that all snow should be white.
It happens that every/no animal is white:
No pitch is an animal;
∴ It is necessary that no pitch should be white.
It is evident, therefore, that when the terms are universal, and one of the propositions is assumed to exist, (i.e. is assumed pure), but the other contingent; when the proposition which contains the less extreme is assumed to be contingent, a syllogism will always be produced; except that it will sometimes be produced from the propositions themselves, and sometimes from the proposition being converted. When, however, each of these takes place, and from what cause we have already shown. But if one of the intervals is assumed to be universal, and the other partial; when, indeed, a universal contingent is joined to the greater extreme, whether it be affirmative or negative; but the partial interval is affirmative and pure, there will be a perfect syllogism, just as when the terms are universal. The demonstration, however, is the same as before. But when the interval in which the greater extreme is contained, is pure and not contingent; but the other is partial and contingent; whether both the propositions are posited affirmative or negative; or whether the one is affirmative, but the other negative, there will entirely be an imperfect syllogism. Some, however, will be confirmed through the impossible; but others, through a conversion of the contingent proposition, as in the former syllogisms. But there will be a syllogism through conversion, and when the universal proposition being joined to the greater extreme signifies the being present with, or the not being present with; but the partial proposition being privative assumes the contingent: as, for instance, if A is present indeed, or is not present with every B, but B happens not to be present with a certain C; for the proposition B C being converted according to the being contingent, a syllogism will be produced. But when the particular proposition assumes the not being present with, there will not be a syllogism. Let the terms of being present with be white, animal, snow; but of not being present with be white, animal, pitch. For the demonstration is to be assumed through the indefinite.
It happens that every/no animal is white:
Some snow is not an animal:
∴ It is necessary thatall snow should be white.
It happens that every/no animal is white: Some pitch is not an animal: It is necessary that no pitch should be white. But if universal is joined to the less extreme, and particular to the greater; whether privative, or affirmative, contingent, or pure, there will by no means be a syllogism. Nor will there then be a syllogism, when the propositions are posited in a part, or indefinite; whether they assume the being contingent, or the being present with, or whether the one is contingent, but the other present with. But the demonstration is the same as in the former syllogisms. Let, however, the common terms of being present with from necessity be animal, white, man; but of not being contingent be animal, white, garment.
It happens that something/not everything white is an animal:
Every/No/Some/Not every man is white:
∴ It is necessary that every man should be an animal.
It happens that something/not everything white is an animal:
Every/No/Some/Not every garment is white:
∴ It is necessary that no garment should be an animal.
Something/Not everything white is an animal:
It happens that every/no/some/not every man is white:
∴ It is necessary that every man should be an animal.
Something/Not everything white is an animal:
It happens that every/no/some/not every garment is white:
∴ It is necessary that no garment should be an animal.
It is evident, therefore, that if the major proposition is posited universal, a syllogism will always be produced: but if the minor, that nothing can ever thence be collected.
Return to Aristotle, Prior Analytics
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