by Aristotle
By universal knowledge then we see the particulars, but we do not know them by the kind of knowledge which is proper to them; consequently it is possible that we may make mistakes about them, but not that we should have the knowledge and error that are contrary to one another: rather we have universal knowledge but make a mistake in regard to the particular. Similarly in the cases stated above. The [30] error in respect of the middle term is not contrary to the knowledge obtained through the deduction, nor is the belief in respect of the middle terms. Nothing prevents a man who knows both that A belongs to the whole of B, and that B again belongs to C, thinking that A does not belong to C, e.g. knowing that every mule is [35] sterile and that this is a mule, and thinking that this animal is with foal; for he does not know that A belongs to C, unless he considers the two things together. So it is evident that if he knows the one and does not know the other, he will fall into error. And this is the relation of universal knowledge to particular. For we know no sensible thing, once it has passed beyond the range of our senses, even if we happen [67b1] to have perceived it, except by means of the universal and by possessing (but not actualising) particular. For knowing is spoken of in three ways: it may be either universal knowledge or knowledge proper to the matter in hand or actualising such [5] knowledge; consequently three kinds of error also are possible. Nothing then prevents a man both knowing and being mistaken about the same thing, provided that his knowledge and his error are not contrary. And this happens also to the man who knows each proposition separately and who has not previously considered the particular question. For when he believes that the mule is with foal he does not have [10] knowledge actualised, nor on the other hand has his belief caused an error contrary to his knowledge; for the error contrary to the universal knowledge would be a deduction.
But he who believes the essence of good is the essence of bad will believe the same thing to be the essence of good and the essence of bad. Let A stand for the essence of good and B for the essence of bad, and again C for the essence of good. [15] Since then he believes B and C identical, he will believe that C is B, and similarly that B is A; consequently that C is A. For just as we saw that if B is true of all of which C is true, and A is true of all of which B is true, and A is true of all of which B [20] is true, A is true of C, similarly with believing. Similarly also with being; for we saw that if C is the same as B, and B as A, C is the same as A. Similarly therefore with opining. Perhaps then this is necessary if a man will grant the first point. But presumably that is false, that any one could think the essence of good to be the [25] essence of bad (save accidentally—for it is possible to believe this in many different ways). But we must consider this matter better.
22 · Whenever the extremes are convertible it is necessary that the middle should be convertible with both. For if A belongs to C through B, then if A and C are [30] convertible and C belongs to everything to which A belongs, B is convertible with A, and B belongs to everything to which A belongs, through C as middle; and C is convertible with B through A as middle. Similarly in the negative case, e.g. if B belongs to C, but A does not belong to B, neither will A belong to C. If then B is [35] convertible with A, C will be convertible with A. Suppose B does not belong to A; neither then will C; for ex hypothesi B belonged to every C. And if C is convertible with B, A is convertible with it too; for C is said of that of all of which B is said. And if C is convertible in relation to A as well, B also will be convertible. For C belongs to [68a1] that to which B belongs; but C does not belong to that to which A belongs. And this alone starts from the conclusion: the others differ here from the affirmative deduction.
[5] Again if A and B are convertible, and similarly C and D, and if A or C must belong to anything whatever, then B and D will be such that one or other belongs to anything whatever. For since B belongs to that to which A belongs, and D belongs to that to which C belongs, and since A or C belongs to everything, but not together, it is clear that B or D belongs to everything, but not together. For two deductions have been put together. Again if A or B belongs to everything and if C or D belongs to everything, but they do not belong together, then when A and C are convertible B and D are convertible. For if B does not belong to something to which D belongs, it is [15] clear that A belongs to it. But if A then C; for they are convertible. Therefore C and D belong together. But this is impossible. For example if that which is uncreated is incorruptible and that which is incorruptible is uncreated, it is necessary that what [10] is created should be corruptible and what is corruptible should have been created.24
When A belongs to the whole of B and to C and is affirmed of nothing else, and B also belongs to every C, it is necessary that A and B should be convertible; for since A is said of B and C only, and B is affirmed both of itself and of C, it is clear [20] that B will be said of everything of which A is said, except A itself. Again when A and B belong to the whole of C, and C is convertible with B, it is necessary that A should belong to every B; for since A belongs to every C, and C to B by conversion, A will belong to every B.
When, of two opposites A and B, A is preferable to B, and similarly D is [25] preferable to C, then if A and C together are preferable to B and D together, A is preferable to D. For A is as much to be pursued as B is to be avoided, since they are opposites; and C is similarly related to D, since they also are opposites. If then A is as desirable as D, B is as much to be avoided as C (since each is to the same extent as [30] each—the one an object of aversion, the other an object of desire). Therefore A and C together will be as much to be desired or avoided as B and D together. But since A and C are preferable to B and D, A cannot be as desirable as D; for then B along with D would be as desirable as A along with C. But if D is preferable to A, then B must be less to be avoided than C; for the less is opposed to the less. But the greater [35] good and lesser evil are preferable to the lesser good and greater evil: the whole BD, then, is preferable to the whole AC. But ex hypothesi this is not so. A then is preferable to D, and C consequently is less to be avoided than B. If then every lover in virtue of his love would prefer A, viz. that the beloved should be such as to grant a [68b1] favour, and yet should not grant it (for which C stands), to the beloved’s granting the favour (represented by D) without being such as to grant it (represented by B), it is clear that A (being of such a nature) is preferable to granting the favour. To receive affection then is preferable in love to sexual intercourse. Love then aims at affection rather than at intercourse. And if it aims most at affection, then this is its end. Intercourse then either is not an end at all or is an end relative to the receiving [5] of affection. And indeed the same is true of the other desires and arts.
23 · It is clear then how the terms are related in conversion, and in respect of being preferable or more to be avoided. We must now state that not only dialectical and demonstrative deductions are formed by means of the aforesaid [10] figures, but also rhetorical deductions and in general any form of persuasion, however it may be presented. For every belief comes either through deduction or from induction.
Now induction, or rather the deduction which springs out of induction, consists [15] in deducing a relation between one extreme and the middle by means of the other extreme, e.g. if B is the middle term between A and C, it consists in proving through C that A belongs to B. For this is the manner in which we make inductions. For example, let A stand for long-liver, B for bileless, and C for the particular long-lived [20] animals, e.g. man, horse, mule. A then belongs to the whole of C; [for whatever is bileless is long-lived].25 But B also (not possessing bile) belongs to every C. If then C is convertible with B, and the middle term is not wider in extension, it is necessary that A should belong to B. For it has already been proved that if two things belong to [25] the same thing, and the extreme is convertible with one of them, then the other predicate will belong to one that is converted. But we must apprehend C as made up of all the particulars. For induction proceeds through an enumeration of all the cases.
[30] Such i
s the deduction which establishes primary and immediate propositions; for where there is a middle term the deduction proceeds through the middle term; when there is no middle term, through induction. And in a way induction is opposed to deduction; for the latter proves the extreme to belong to the third term by means of the middle, the former proves the extreme to belong to the middle by means of the [35] third. In the order of nature, deduction through the middle term is prior and more familiar, but deduction through induction is clearer to us.
24 · We have an example when the extreme is proved to belong to the middle by means of a term which resembles the third. It must be familiar both that the middle belongs to the third term, and that the first belongs to that which resembles the third. For example let A be evil, B making war against neighbours, C [69a1] Athenians against Thebans, D Thebans against Phocians. If then we wish to prove that to fight with the Thebans is an evil, we must assume that to fight against neighbours is an evil. Conviction of this is obtained from similar cases, e.g. that the [5] war against the Phocians was an evil to the Thebans. Since then to fight against neighbours is an evil, and to fight against the Thebans is to fight against neighbours, it is clear that to fight against the Thebans is an evil. Now it is clear that B belongs to C and to D (for both are cases of making war upon one’s neighbours) and that A [10] belongs to D (for the war against the Phocians did not turn out well for the Thebans); but that A belongs to B will be proved through D. Similarly if the conviction in the relation of the middle term to the extreme should be produced by several similar cases. Clearly then an example stands neither as part to whole, nor [15] as whole to part, but rather as part to part, when both are subordinate to the same term, and one of them is familiar. It differs from induction, because induction starting from all the particular cases proves (as we saw) that the extreme belongs to the middle, and does not connect the deduction to the extreme, whereas argument by example does make this connexion and does not draw its proof from all the particular cases.
[20] 25 · By reduction we mean an argument in which the first term clearly belongs to the middle, but the relation of the middle to the last term is uncertain though equally or more convincing than the conclusion; or again an argument in which the terms intermediate between the last term and the middle are few. For in any of these cases it turns out that we approach more nearly to knowledge. For [25] example let A stand for what can be taught, B for knowledge, C for justice. Now it is clear that knowledge can be taught; but it is uncertain whether virtue is knowledge. If now BC is equally or more convincing than AC, we have a reduction; for we are nearer to knowledge, since we have made an extra assumption, being before without knowledge that A belongs to C.26 Or again suppose that the terms intermediate between B and C are few; for thus too we are nearer knowledge. For example let D [30] stand for squaring, E for rectilinear figure, F for circle. If there were only one term intermediate between E and F (viz. that the circle is made equal to a rectilinear figure by the help of lunules), we should be near to knowledge. But when BC is not more convincing than AC, and the intermediate terms are not few, I do not call this [35] reduction; nor again when BC is immediate—for such a statement is knowledge.
26 · An objection is a proposition contrary to a proposition. It differs from a proposition, because it may be particular, but a proposition either cannot be particular at all or not in universal deductions. An objection is brought in two ways [69b1] and through two figures; in two ways because every objection is either universal or particular, by two figures because objections are brought in opposition to the proposition, and opposites can be proved only in the first and third figures. When a [5] man claims that something belongs to all of a given subject, we object either that it belongs to none or that it does not belong to some; and of these, the former is proved from the first figure, the latter from the third. For example let A stand for there being a single science, B for contraries. If a man proposes that contraries are subjects of a single science, the objection may be either that opposites are never [10] subjects of a single science, and contraries are opposites, so that we get the first figure; or that the knowable and the unknowable are not subjects of a single science—this is the third figure; for it is true of C (the knowable and the unknowable) that they are contraries, and it is false that they are the subjects of a single science.
Similarly if the proposition is negative. For if a man claims that contraries are [15] not subjects of a single science, we reply either that all opposites or that certain contraries, e.g. what is healthy and what is sickly, are subjects of the same science: the former argument issues from the first, the latter from the third figure.
In general, in all cases if a man urges a universal objection he must frame his contradiction with reference to the universal of the terms proposed, e.g. if a man [20] claims that contraries are not subjects of the same science, his opponent must reply that there is a single science of all opposites. Thus we must have the first figure; for the term which is universal relative to the original subject becomes the middle term.
If the objection is particular, the objector must frame his contradiction with reference to a term relatively to which the subject of the proposition is universal, e.g. he will point out that the knowable and the unknowable are not subjects of the same [25] science; for contraries are universal relatively to these. And we have the third figure; for the particular term assumed is middle, e.g. the knowable and the unknowable. Premisses from which it is possible to draw the contrary conclusion are what we start from when we try to make objections. Consequently we bring objections in these figures only; for in them only are opposite deductions possible, [30] since the second figure cannot produce an affirmative conclusion.
Besides, an objection in the middle figure would require a fuller argument, e.g. if it should not be granted that A belongs to B, because C does not follow B. This can [35] be made clear only by other propositions. But an objection ought not to turn off into other things, but have its other proposition quite clear immediately. [For this reason also this is the only figure from which proof by signs cannot be obtained.]27
We must consider too the other kinds of objection, namely the objection from contraries, from similars, and from common opinion, and inquire whether a [70a1] particular objection cannot be elicited from the first figure or a negative objection from the second.28
27 · A probability and a sign are not identical, but a probability is a reputable proposition: what men know to happen or not to happen, to be or not to be, [5] for the most part thus and thus, is a probability, e.g. envious men hate, those who are loved show affection. A sign is meant to be a demonstrative proposition either necessary or reputable; for anything such that when it is another thing is, or when it has come into being the other has come into being before or after, is a sign of the [10] other’s being or having come into being. An enthymeme is a deduction starting from probabilities or signs,29 and a sign may be taken in three ways, corresponding to the position of the middle term in the figures. For it may be taken as in the first figure or the second or the third. For example the proof that a woman is with child because she has milk is in the first figure: for to have milk is the middle term. Let A [15] represent to be with child, B to have milk, C woman. The proof that wise men are good, since Pittacus is good, comes through the last figure. Let A stand for good, B for wise men, C for Pittacus. It is true then to predicate both A and B of C—only men do not say the latter, because they know it, though they state the former. The [20] proof that a woman is with child because she is pale is meant to come through the middle figure; for since paleness follows women with child and is a concomitant of this woman, people suppose it has been proved that she is with child. Let A stand for paleness, B for being with child, C for woman.
Now if the one proposition is stated, we have only a sign, but if the other is [25] stated as well, a deduction, e.g. Pittacus is generous; for ambitious men are generous and Pittacus is ambitious. Or again: Wise men are good; for Pittacus is
not only good but wise. In this way then deductions are formed, only that which [30] proceeds through the first figure is irrefutable if it is true (for it is universal), that which proceeds through the last figure is refutable even if the conclusion is true, since the deduction is not universal nor relevant to the matter in question; for though Pittacus is good, it is not therefore necessary that all other wise men should be good. But the deduction which proceeds through the middle figure is always [35] refutable in any case; for a deduction can never be formed when the terms are related in this way; for though a woman with child is pale, and this woman also is pale, it is not necessary that she should be with child. Truth then may be found in signs whatever their kind, but they have the differences we have stated.
We must either divide signs in the way stated, and among them designate the [70b1] middle term as the evidence (for people call that the evidence which makes us know, and the middle term above all has this character), or else we must call the arguments derived from the extremes signs, that derived from the middle term the evidence; for that which is proved through the first figure is most reputable and [5] most true.
It is possible to infer character from physical features, if it is granted that the body and the soul are changed together by the natural affections (No doubt by learning music a man has made some change in his soul, but this is not one of those affections which are natural to us; but rather such natural motions as anger and [10] desire.) If then this were granted and also that there is one sign for one affection, and if we could state the affection and sign proper to each kind of animal, we shall be able to infer character from physical features. For if there is an affection which belongs properly to an individual genus, e.g. courage to lions, it is necessary that [15] there should be a sign of it; for ex hypothesi body and soul are affected together. Suppose this sign is the possession of large extremities: this may belong to other genera also though not universally. For the sign is proper in the sense that it is proper to the whole genus, though not proper to it alone, according to our usual manner of speaking. This then will be found in other genera too, and man may be [20] brave, and some other genera of animal as well. They will then have the sign; for ex hypothesi there is one sign for one affection. If then this is so, and we can collect signs of this sort in these animals which have only one affection proper to them, and each affection has its sign, since it is necessary that it should have a single sign, we [25] shall then be able to infer character from physical features. But if the genus as a whole has two properties, e.g. if the lion is both brave and generous, how shall we know which of the signs which are its proper concomitants is the sign of which affection? Perhaps if both belong to some other genus though not to the whole of it, and if, in those genera in which each is found though not in the whole of their members, some members possess one of the affections and not the other: e.g. if a man is brave but not generous, but possesses, of the two signs, this one, it is clear [30] that this is the sign of courage in the lion also.