13 Knowledge of the fact differs from knowledge of the reasoned fact. To begin with, they differ within the same science and in two ways: (1) when the premisses of the syllogism are not immediate (for then the proximate cause is not contained in them—a necessary condition of knowledge of the reasoned fact): (2) when the premisses are immediate, (25) but instead of the cause the better known of the two reciprocals is taken as the middle; for of two reciprocally predicable terms the one which is not the cause may quite easily be the better known and so become the middle term of the demonstration. Thus (2) (a) you might prove as follows that the planets are near because they do not twinkle: let C be the planets, (30) B not twinkling, A proximity. Then B is predicable of C; for the planets do not twinkle. But A is also predicable of B, since that which does not twinkle is near—we must take this truth as having been reached by induction or sense-perception. Therefore A is a necessary predicate of C; so that we have demonstrated that the planets are near. (35) This syllogism, then, proves not the reasoned fact but only the fact; since they are not near because they do not twinkle, but, because they are near, do not twinkle. The major and middle of the proof, however, may be reversed, and then the demonstration will be of the reasoned fact. (40) Thus: let C be the planets, B proximity, A not twinkling. [78b] Then B is an attribute of C, and A—not twinkling—of B. Consequently A is predicable of C, and the syllogism proves the reasoned fact, since its middle term is the proximate cause. Another example is the inference that the moon is spherical from its manner of waxing. Thus: since that which so waxes is spherical, and since the moon so waxes, (5) clearly the moon is spherical. Put in this form, the syllogism turns out to be proof of the fact, but if the middle and major be reversed it is proof of the reasoned fact; since the moon is not spherical because it waxes in a certain manner, but waxes in such a manner because it is spherical. (Let C be the moon, B spherical, and A waxing.) (10) Again (b), in cases where the cause and the effect are not reciprocal and the effect is the better known, the fact is demonstrated but not the reasoned fact. This also occurs (1) when the middle falls outside the major and minor, for here too the strict cause is not given, and so the demonstration is of the fact, not of the reasoned fact. For example, (15) the question ‘Why does not a wall breathe?’ might be answered, ‘Because it is not an animal’; but that answer would not give the strict cause, because if not being an animal causes the absence of respiration, then being an animal should be the cause of respiration, according to the rule that if the negation of x causes the non-inherence of y, (20) the affirmation of x causes the inherence of y; e. g. if the disproportion of the hot and cold elements is the cause of ill health, their proportion is the cause of health; and conversely, if the assertion of x causes the inherence of y, the negation of x must cause y’s non-inherence. But in the case given this consequence does not result; for not every animal breathes. A syllogism with this kind of cause takes place in the second figure. Thus: let A be animal, B respiration, (25) C wall. Then A is predicable of all B (for all that breathes is animal), but of no C; and consequently B is predicable of no C; that is, the wall does not breathe. Such causes are like far-fetched explanations, which precisely consist in making the cause too remote, (30) as in Anacharsis’ account of why the Scythians have no flute-players; namely because they have no vines.
Thus, then, do the syllogism of the fact and the syllogism of the reasoned fact differ within one science and according to the position of the middle terms. But there is another way too in which the fact and the reasoned fact differ, and that is when they are investigated respectively by different sciences. (35) This occurs in the case of problems related to one another as subordinate and superior, as when optical problems are subordinated to geometry, (40) mechanical problems to stereometry, harmonic problems to arithmetic, the data of observation to astronomy. [79a] (Some of these sciences bear almost the same name; e. g. mathematical and nautical astronomy, mathematical and acoustical harmonics.) Here it is the business of the empirical observers to know the fact, of the mathematicians to know the reasoned fact; for the latter are in possession of the demonstrations giving the causes, and are often ignorant of the fact: just as we have often a clear insight into a universal, (5) but through lack of observation are ignorant of some of its particular instances. These connexions16 have a perceptible existence though they are manifestations of forms. For the mathematical sciences concern forms: they do not demonstrate properties of a substratum, since, even though the geometrical subjects are predicable as properties of a perceptible substratum, it is not as thus predicable that the mathematician demonstrates properties of them. As optics is related to geometry, (10) so another science is related to optics, namely the theory of the rainbow. Here knowledge of the fact is within the province of the natural philosopher, knowledge of the reasoned fact within that of the optician, either qua optician or qua mathematical optician. Many sciences not standing in this mutual relation enter into it at points; e. g. medicine and geometry: it is the physician’s business to know that circular wounds heal more slowly, the geometer’s to know the reason why. (15)
14 Of all the figures the most scientific is the first. Thus, it is the vehicle of the demonstrations of all the mathematical sciences, such as arithmetic, geometry, and optics, and practically of all sciences that investigate causes: for the syllogism of the reasoned fact is either exclusively or generally speaking and in most cases in this figure—a second proof that this figure is the most scientific; for grasp of a reasoned conclusion is the primary condition of knowledge. (20) Thirdly, the first is the only figure which enables us to pursue knowledge of the essence of a thing. In the second figure no affirmative conclusion is possible, (25) and knowledge of a thing’s essence must be affirmative; while in the third figure the conclusion can be affirmative, but cannot be universal, and essence must have a universal character: e. g. man is not two-footed animal in any qualified sense, but universally. Finally, the first figure has no need of the others, (30) while it is by means of the first that the other two figures are developed, and have their intervals close-packed until immediate premisses are reached. Clearly, therefore, the first figure is the primary condition of knowledge.
15 Just as an attribute A may (as we saw) be atomically connected with a subject B, so its disconnexion may be atomic. I call ‘atomic’ connexions or disconnexions which involve no intermediate term; since in that case the connexion or disconnexion will not be mediated by something other than the terms themselves. (35) It follows that if either A or B, or both A and B, have a genus, their disconnexion cannot be primary. Thus: let C be the genus of A. Then, if C is not the genus of B—for A may well have a genus which is not the genus of B—there will be a syllogism proving A’s disconnexion from B thus: (40)
all A is C,
no B is C,
no B is A.
[79b] Or if it is B which has a genus D, we have
all B is D,
no D is A,
no B is A, by syllogism;
and the proof will be similar if both A and B have a genus. (5) That the genus of A need not be the genus of B and vice versa, is shown by the existence of mutually exclusive co-ordinate series of predication. If no term in the series ACD … is predicable of any term in the series BEF …, and if G—a term in the former series—is the genus of A, (10) clearly G will not be the genus of B; since, if it were, the series would not be mutually exclusive. So also if B has a genus, it will not be the genus of A. If, on the other hand, neither A nor B has a genus and A does not inhere in B, this disconnexion must be atomic. If there be a middle term, one or other of them is bound to have a genus, (15) for the syllogism will be either in the first or the second figure. If it is in the first, B will have a genus—for the premiss containing it must be affirmative;17 if in the second, either A or B indifferently, since syllogism is possible if either is contained in a negative premiss,18 but not if both premisses are negative. (20)
Hence it is clear that one thing may be atomically disco
nnected from another, and we have stated when and how this is possible.
16 Ignorance—defined not as the negation of knowledge but as a positive state of mind—is error produced by inference.
(1) Let us first consider propositions asserting a predicate’s immediate connexion with or disconnexion from a subject. (25) Here, it is true, positive error may befall one in alternative ways; for it may arise where one directly believes a connexion or disconnexion as well as where one’s belief is acquired by inference. The error, however, that consists in a direct belief is without complication; but the error resulting from inference—which here concerns us—takes many forms. Thus, let A be atomically disconnected from all B: then the conclusion inferred through a middle term C, (30) that all B is A, will be a case of error produced by syllogism. Now, two cases are possible. Either (a) both premisses, or (b) one premiss only, may be false. (a) If neither A is an attribute of any C nor C of any B, whereas the contrary was posited in both cases, both premisses will be false. (C may quite well be so related to A and B that C is neither subordinate to A nor a universal attribute of B: for B, (35) since A was said to be primarily disconnected from B, cannot have a genus, and A need not necessarily be a universal attribute of all things. Consequently both premisses may be false.) On the other hand, (b) one of the premisses may be true, (40) though not either indifferently but only the major A–C; since, B having no genus, the premiss C–B will always be false, while A–C may be true. [80a] This is the case if, for example, A is related atomically to both C and B; because when the same term is related atomically to more terms than one, neither of those terms will belong to the other. It is, of course, equally the case if A–C is not atomic. (5)
Error of attribution, then, occurs through these causes and in this form only—for we found that no syllogism of universal attribution was possible in any figure but the first. On the other hand, an error of non-attribution may occur either in the first or in the second figure. Let us therefore first explain the various forms it takes in the first figure and the character of the premisses in each case. (10)
(c) It may occur when both premisses are false; e. g. supposing A atomically connected with both C and B, if it be then assumed that no C is A, and all B is C, both premisses are false.
(d) It is also possible when one is false. This may be either premiss indifferently. A–C may be true, C–B false—A–C true because A is not an attribute of all things, (15) C–B false because C, which never has the attribute A, cannot be an attribute of B; for if C–B were true, the premiss A–C would no longer be true, and besides if both premisses were true, the conclusion would be true. Or again, C–B may be true and A–C false; e. g. if both C and A contain B as genera, (20) one of them must be subordinate to the other, so that if the premiss takes the form No C is A, it will be false. This makes it clear that whether either or both premisses are false, (25) the conclusion will equally be false.
In the second figure the premisses cannot both be wholly false; for if all B is A, no middle term can be with truth universally affirmed of one extreme and universally denied of the other: but premisses in which the middle is affirmed of one extreme and denied of the other are the necessary condition if one is to get a valid inference at all. (30) Therefore if, taken in this way, they are wholly false, their contraries conversely should be wholly true. But this is impossible. On the other hand, there is nothing to prevent both premisses being partially false; e. g. if actually some A is C and some B is C, then if it is premised that all A is C and no B is C, (35) both premisses are false, yet partially, not wholly, false. The same is true if the major is made negative instead of the minor. Or one premiss may be wholly false, and it may be either of them. Thus, supposing that actually an attribute of all A must also be an attribute of all B, then if C is yet taken to be a universal attribute of all A but universally non-attributable to B, (40) C–A will be true but C–B false. [80b] Again, actually that which is an attribute of no B will not be an attribute of all A either; for if it be an attribute of all A, it will also be an attribute of all B, which is contrary to supposition; but if C be nevertheless assumed to be a universal attribute of A, (5) but an attribute of no B, then the premiss C–B is true but the major is false. The case is similar if the major is made the negative premiss. For in fact what is an attribute of no A will not be an attribute of any B either; and if it be yet assumed that C is universally non-attributable to A, but a universal attribute of B, (10) the premiss C–A is true but the minor wholly false. Again, in fact it is false to assume that that which is an attribute of all B is an attribute of no A, for if it be an attribute of all B, it must be an attribute of some A. If then C is nevertheless assumed to be an attribute of all B but of no A, C–B will be true but C–A false.
It is thus clear that in the case of atomic propositions erroneous inference will be possible not only when both premisses are false but also when only one is false. (15)
17 (2) In the case of attributes not atomically connected with or disconnected from their subjects, (a) (i) as long as the false conclusion is inferred through the ‘appropriate’ middle, (20) only the major and not both premisses can be false. By ‘appropriate middle’ I mean the middle term through which the contradictory—i. e. the true—conclusion is inferrible. Thus, let A be attributable to B through a middle term C: then, since to produce a conclusion the premiss C–B must be taken affirmatively, it is clear that this premiss must always be true, (25) for its quality is not changed. But the major A–C is false, for it is by a change in the quality of A–C that the conclusion becomes its contradictory—i. e. true. Similarly (ii) if the middle is taken from another series of predication; e. g. suppose D to be not only contained within A as a part within its whole but also predicable of all B. Then the premiss D–B must remain unchanged, (30) but the quality of A–D must be changed; so that D–B is always true, A–D always false. Such error is practically identical with that which is inferred through the ‘appropriate’ middle. On the other hand, (b) if the conclusion is not inferred through the ‘appropriate’ middle—(i) when the middle is subordinate to A but is predicable of no B, (35) both premisses must be false, because if there is to be a conclusion both must be posited as asserting the contrary of what is actually the fact, and so posited both become false: e. g. suppose that actually all D is A but no B is D; then if these premisses are changed in quality, a conclusion will follow and both of the new premisses will be false. (40) When, however, (ii) the middle D is not subordinate to A, A–D will be true, D–B false—A–D true because A was not subordinate to D, D–B false because if it had been true, the conclusion too would have been true; but it is ex hypothesi false. [81a]
When the erroneous inference is in the second figure, (5) both premisses cannot be entirely false; since if B is subordinate to A, there can be no middle predicable of all of one extreme and of none of the other as was stated before.19 One premiss, however, may be false, and it may be either of them. Thus, if C is actually an attribute of both A and B, but is assumed to be an attribute of A only and not of B, (10) C–A will be true, C–B false: or again if C be assumed to be attributable to B but to no A, C–B will be true, C–A false.
We have stated when and through what kinds of premisses error will result in cases where the erroneous conclusion is negative. (15) If the conclusion is affirmative, (a) (i) it may be inferred through the ‘appropriate’ middle term. In this case both premisses cannot be false since, as we said before,20 C–B must remain unchanged if there is to be a conclusion, and consequently A–C, the quality of which is changed, will always be false. This is equally true if (ii) the middle is taken from another series of predication, (20) as was stated to be the case also with regard to negative error;21 for D–B must remain unchanged, while the quality of A–D must be converted, and the type of error is the same as before.
(b) The middle may be inappropriate. Then (i) if D is subordinate to A, (25) A–D will be true, but D–B false; since A may quite well be predicable of several
terms no one of which can be subordinated to another. If, however, (ii) D is not subordinate to A, obviously A–D, since it is affirmed, will always be false, while D–B may be either true or false; for A may very well be an attribute of no D, (30) whereas all B is D, e. g. no science is animal, all music is science. Equally well A may be an attribute of no D, and D of no B. It emerges, then, that if the middle term is not subordinate to the major, not only both premisses but either singly may be false.
Thus we have made it clear how many varieties of erroneous inference are liable to happen and through what kinds of premisses they occur, (35) in the case both of immediate and of demonstrable truths.
18 It is also clear that the loss of any one of the senses entails the loss of a corresponding portion of knowledge, and that, since we learn either by induction or by demonstration, this knowledge cannot be acquired. (40) Thus demonstration develops from universals, induction from particulars; but since it is possible to familiarize the pupil with even the so-called mathematical abstractions only through induction—i. e. only because each subject genus possesses, in virtue of a determinate mathematical character, certain properties which can be treated as separate even though they do not exist in isolation—it is consequently impossible to come to grasp universals except through induction. [81b] (5) But induction is impossible for those who have not sense-perception. For it is sense-perception alone which is adequate for grasping the particulars: they cannot be objects of scientific knowledge, because neither can universals give us knowledge of them without induction, nor can we get it through induction without sense-perception.
The Basic Works of Aristotle (Modern Library Classics) Page 20
