33 To repeat again the proof that both ascent and descent are finite: The subjects cannot be more in number than the constituents of a definable form, and these, we know, are not infinite in number: hence the descent is finite. The series regarded as an ascent contains subjects and ever more universal accidents, and neither subjects nor accidents are infinite in number.
34 Formal restatement of the last conclusion. [This is obscure: apparently Aristotle here contemplates a hybrid series: category, accident, further specified accident … substantial genus, subgenus … infima species, individual substance.
If this interpretation of the first portion of the chapter is at all correct, Aristotle’s first proof that the first two questions of ch. 19 must be answered in the negative is roughly as follows: The ultimate subject of all judgement is an individual substance, a concrete singular. Of such concrete singulars you can predicate substantially only the elements constituting their infima species. These are limited in number because they form an intelligible synthesis. So far, then, as substantial predicates are concerned, the questions are answered. But these elements are also the subjects of which accidents, or coincidents, are predicated, and therefore as regards accidental predicates, at any rate, the descending series of subjects terminates. The ascending series of attributes also terminates, (1) because each higher attribute in the series can only be a higher genus of the accident predicated of the ultimate subject of its genus, and therefore an element in the accident’s definition; (2) because the number of the categories is limited.
We may note that the first argument seems to envisage a series which, viewed as an ascent, starts with a concrete individual of which the elements of its definition are predicated successively, specific differentia being followed by proximate genus, which latter is the starting-point of a succession of ever more universal attributes terminating in a category; and that the second argument extends the scope of the dispute to the sum total of all the trains of accidental predication which one concrete singular substance can beget. It is, as so often in Aristotle, difficult to be sure whether he is regarding the infima species or the concrete singular as the ultimate subject of judgement. I have assumed that he means the latter.]
35 The former proof was dialectical. So is that which follows in this paragraph. If a predicate inheres in a subject but is subordinate to a higher predicate also predicable of that subject [i. e. not to a wider predicate but to a middle term giving logically prior premisses and in that sense higher], then the inherence can be known by demonstration and only by demonstration. But that means that it is known as the consequent of an antecedent. Therefore, if demonstration gives genuine knowledge, the series must terminate; i. e. every predicate is demonstrable and known only as a consequent and therefore hypothetically, unless an antecedent known per se is reached.
36 As regards type (2) [the opening of the chapter has disposed of type (1)]: in any series of such predicates any given term will contain in its definition all the lower terms, and the series will therefore terminate at the bottom in the ultimate subject. But since every term down to and including the ultimate subject is contained in the definition of any given term, if the series ascend infinitely there must be a term containing an infinity of terms in its definition. But this is impossible, and therefore the ascent terminates.
37 Note too that either type of essential attribute must be commensurate with its subject, because the first defines, the second is defined by, its subject; and consequently no subject can possess an infinite number of essential predicates of either type, or definition would be impossible. Hence if the attributes predicated are all essential, the series terminates in both directions. [This passage merely displays the ground underlying the previous argument that the ascent of attributes of type (2) is finite, and notes in passing its more obvious and already stated application to attributes of type (1).]
38 It follows that the intermediates between a given subject and a given attribute must also be limited in number.
39 Corollary: (a) demonstrations necessarily involve basic truths, and therefore (b) not all truths, as we saw [84a 32] that some maintain, are demonstrable [cf. 72b 6]. If either (a) or (b) were not a fact, since conclusions are demonstrated by the interposition of a middle and not by the apposition of an extreme term [cf. note on 78a15], no premiss would be an immediate indivisible interval. This closes the analytic argument.
40 i, ch. 7.
41 Second figure, Camestres or Baroco.
42 The distinction is that of whole and part, genus and species; not that of universal and singular.
43 And therefore also essential; cf. i, ch. 4, 73b 26 ff.
44 i. e. for no reason other than its own nature.
45 An. Pr. i, ch. 7.
46 i. e. in one syllogism and two prosyllogisms proving its premisses.
47 i. e. the impossibility of A–C, the conclusion of the hypothetical syllogism.
48 Protagoras is perhaps referred to.
49 i. e. demonstration through the commensurate universal.
50 Cf. e. g. 100b 12.
51 A theory of the concentration of rays through a burning-glass which was not Aristotle’s.
BOOK II
1 The kinds of question we ask are as many as the kinds of things which we know. They are in fact four:—(1) whether the connexion of an attribute with a thing is a fact, (2) what is the reason of the connexion, (25) (3) whether a thing exists, (4) what is the nature of the thing. Thus, when our question concerns a complex of thing and attribute and we ask whether the thing is thus or otherwise qualified—whether, e. g., the sun suffers eclipse or not—then we are asking as to the fact of a connexion. That our inquiry ceases with the discovery that the sun does suffer eclipse is an indication of this; and if we know from the start that the sun suffers eclipse, we do not inquire whether it does so or not. On the other hand, when we know the fact we ask the reason; as, for example, when we know that the sun is being eclipsed and that an earthquake is in progress, (30) it is the reason of eclipse or earthquake into which we inquire.
Where a complex is concerned, then, those are the two questions we ask; but for some objects of inquiry we have a different kind of question to ask, such as whether there is or is not a centaur or a God. (By ‘is or is not’ I mean ‘is or is not, without further qualification’; as opposed to ‘is or is not (e. g.) white’.) On the other hand, when we have ascertained the thing’s existence, we inquire as to its nature, asking, for instance, ‘what, then, is God?’ or ‘what is man?’
2 These, (35) then, are the four kinds of question we ask, and it is in the answers to these questions that our knowledge consists.
Now when we ask whether a connexion is a fact, or whether a thing without qualification is, we are really asking whether the connexion or the thing has a ‘middle’; and when we have ascertained either that the connexion is a fact or that the thing is—i. e. ascertained either the partial or the unqualified being of the thing—and are proceeding to ask the reason of the connexion or the nature of the thing, then we are asking what the ‘middle’ is. [90a]
(By distinguishing the fact of the connexion and the existence of the thing as respectively the partial and the unqualified being of the thing, I mean that if we ask ‘does the moon suffer eclipse?’, or ‘does the moon wax?’, the question concerns a part of the thing’s being; for what we are asking in such questions is whether a thing is this or that, i. e. has or has not this or that attribute: whereas, if we ask whether the moon or night exists, the question concerns the unqualified being of a thing.)
We conclude that in all our inquiries we are asking either whether there is a ‘middle’ or what the ‘middle’ is: for the ‘middle’ here is precisely the cause, (5) and it is the cause that we seek in all our inquiries. Thus, ‘Does the moon suffer eclipse?’ means ‘Is there or is there not a cause producing eclipse of the moon?’, and when we have learnt that there is, our next question is, ‘What, then, is this cause?’; for the cause through which a t
hing is—not is this or that, i. e. has this or that attribute, but without qualification is—and the cause through which it is—not is without qualification, (10) but is this or that as having some essential attribute or some accident—are both alike the ‘middle’. By that which is without qualification I mean the subject, e. g. moon or earth or sun or triangle; by that which a subject is (in the partial sense) I mean a property, e. g. eclipse, equality or inequality, interposition or non-interposition. For in all these examples it is clear that the nature of the thing and the reason of the fact are identical: the question ‘What is eclipse?’ and its answer ‘The privation of the moon’s light by the interposition of the earth’ are identical with the question ‘What is the reason of eclipse?’ or ‘Why does the moon suffer eclipse?’ and the reply ‘Because of the failure of light through the earth’s shutting it out’. (15) Again, for ‘What is a concord? A commensurate numerical ratio of a high and a low note’, (20) we may substitute ‘What reason makes a high and a low note concordant? Their relation according to a commensurate numerical ratio.’ ‘Are the high and the low note concordant?’ is equivalent to ‘Is their ratio commensurate?’; and when we find that it is commensurate, we ask ‘What, then, is their ratio?’.
Cases in which the ‘middle’ is sensible show that the object of our inquiry is always the ‘middle’: we inquire, (25) because we have not perceived it, whether there is or is not a ‘middle’ causing e. g. an eclipse. On the other hand, if we were on the moon we should not be inquiring either as to the fact or the reason, but both fact and reason would be obvious simultaneously. For the act of perception would have enabled us to know the universal too; since, the present fact of an eclipse being evident, perception would then at the same time give us the present fact of the earth’s screening the sun’s light, (30) and from this would arise the universal.
Thus, as we maintain, to know a thing’s nature is to know the reason why it is; and this is equally true of things in so far as they are said without qualification to be as opposed to being possessed of some attribute, and in so far as they are said to be possessed of some attribute such as equal to two right angles, or greater or less.
3 It is clear, (35) then, that all questions are a search for a ‘middle’. Let us now state how essential nature is revealed, and in what way it can be reduced to demonstration;1 what definition is, and what things are definable. And let us first discuss certain difficulties which these questions raise, beginning what we have to say with a point most intimately connected with our immediately preceding remarks, namely the doubt that might be felt as to whether or not it is possible to know the same thing in the same relation, both by definition and by demonstration. [90b] It might, I mean, be urged that definition is held to concern essential nature and is in every case universal and affirmative; whereas, (5) on the other hand, some conclusions are negative and some are not universal; e. g. all in the second figure are negative, none in the third are universal. And again, not even all affirmative conclusions in the first figure are definable, e. g. ‘every triangle has its angles equal to two right angles’. An argument proving this difference between demonstration and definition is that to have scientific knowledge of the demonstrable is identical with possessing a demonstration of it: hence if demonstration of such conclusions as these is possible, (10) there clearly cannot also be definition of them. If there could, one might know such a conclusion also in virtue of its definition without possessing the demonstration of it; for there is nothing to stop our having the one without the other.
Induction too will sufficiently convince us of this difference; for never yet by defining anything—essential attribute or accident—did we get knowledge of it. (15) Again, if to define is to acquire knowledge of a substance, at any rate such attributes are not substances.
It is evident, then, that not everything demonstrable can be defined. What then? Can everything definable be demonstrated, or not? There is one of our previous arguments which covers this too. (20) Of a single thing qua single there is a single scientific knowledge. Hence, since to know the demonstrable scientifically is to possess the demonstration of it, an impossible consequence will follow:—possession of its definition without its demonstration will give knowledge of the demonstrable.
Moreover, the basic premisses of demonstrations are definitions, and it has already been shown2 that these will be found indemonstrable; either the basic premisses will be demonstrable and will depend on prior premisses, (25) and the regress will be endless; or the primary truths will be indemonstrable definitions.
But if the definable and the demonstrable are not wholly the same, may they yet be partially the same? Or is that impossible, because there can be no demonstration of the definable? There can be none, because definition is of the essential nature or being of something, (30) and all demonstrations evidently posit and assume the essential nature—mathematical demonstrations, for example, the nature of unity and the odd, and all the other sciences likewise. Moreover, every demonstration proves a predicate of a subject as attaching or as not attaching to it, but in definition one thing is not predicated of another; we do not, (35) e. g., predicate animal of biped nor biped of animal, nor yet figure of plane—plane not being figure nor figure plane. Again, to prove essential nature is not the same as to prove the fact of a connexion. [91a] Now definition reveals essential nature, demonstration reveals that a given attribute attaches or does not attach to a given subject; but different things require different demonstrations—unless the one demonstration is related to the other as part to whole. [91a] I add this because if all triangles have been proved to possess angles equal to two right angles, then this attribute has been proved to attach to isosceles; for isosceles is a part of which all triangles constitute the whole. (5) But in the case before us the fact and the essential nature are not so related to one another, since the one is not a part of the other.
So it emerges that not all the definable is demonstrable nor all the demonstrable definable; and we may draw the general conclusion that there is no identical object of which it is possible to possess both a definition and a demonstration. (10) It follows obviously that definition and demonstration are neither identical nor contained either within the other: if they were, their objects would be related either as identical or as whole and part.
4 So much, then, for the first stage of our problem. The next step is to raise the question whether syllogism—i. e. demonstration—of the definable nature is possible or, as our recent argument assumed, impossible.
We might argue it impossible on the following grounds:—(a) syllogism proves an attribute of a subject through the middle term; on the other hand (b) its definable nature is both ‘peculiar’ to a subject and predicated of it as belonging to its essence. (15) But in that case (1) the subject, its definition, and the middle term connecting them must be reciprocally predicable of one another; for if A is ‘peculiar’ to C, obviously A is ‘peculiar’ to B and B to C—in fact all three terms are ‘peculiar’ to one another: and further (2) if A inheres in the essence of all B and B is predicated universally of all C as belonging to C’s essence, (20) A also must be predicated of C as belonging to its essence.
If one does not take this relation as thus duplicated—if, that is, A is predicated as being of the essence of B, but B is not of the essence of the subjects of which it is predicated—A will not necessarily be predicated of C as belonging to its essence. So both premisses will predicate essence, and consequently B also will be predicated of C as its essence. (25) Since, therefore, both premisses do predicate essence—i. e. definable form—C’s definable form will appear in the middle term before the conclusion is drawn.
We may generalize by supposing that it is possible to prove the essential nature of man. Let C be man, A man’s essential nature—two-footed animal, or aught else it may be. Then, if we are to syllogize, A must be predicated of all B. But this premiss will be mediated by a fresh definition, which consequently will also be the essential nature of man.3
(30) Therefore the argument assumes what it has to prove, since B too is the essential nature of man. It is, however, the case in which there are only the two premisses—i. e. in which the premisses are primary and immediate—which we ought to investigate, because it best illustrates the point under discussion.
Thus they who prove the essential nature of soul or man or anything else through reciprocating terms beg the question. (35) It would be begging the question, for example, to contend that the soul is that which causes its own life, and that what causes its own life is a self-moving number; for one would have to postulate that the soul is a self-moving number in the sense of being identical with it. [91b] For if A is predicable as a mere consequent of B and B of C, A will not on that account be the definable form of C: A will merely be what it was true to say of C. Even if A is predicated of all B inasmuch as B is identical with a species of A, still it will not follow: being an animal is predicated of being a man—since it is true that in all instances to be human is to be animal, (5) just as it is also true that every man is an animal—but not as identical with being man.
We conclude, then, that unless one takes both the premisses as predicating essence, one cannot infer that A is the definable form and essence of C: but if one does so take them, in assuming B one will have assumed, before drawing the conclusion, what the definable form of C is; so that there has been no inference, for one has begged the question. (10)
5 Nor, as was said in my formal logic, is the method of division a process of inference at all, since at no point does the characterization of the subject follow necessarily from the premising of certain other facts: division demonstrates as little as does induction. (15) For in a genuine demonstration the conclusion must not be put as a question nor depend on a concession, but must follow necessarily from its premisses, even if the respondent deny it. The definer asks ‘Is man animal or inanimate?’ and then assumes—he has not inferred—that man is animal. Next, when presented with an exhaustive division of animal into terrestrial and aquatic, he assumes that man is terrestrial. Moreover, (20) that man is the complete formula, terrestrial-animal, does not follow necessarily from the premisses: this too is an assumption, and equally an assumption whether the division comprises many differentiae or few. (Indeed as this method of division is used by those who proceed by it, even truths that can be inferred actually fail to appear as such.) (25) For why should not the whole of this formula be true of man, and yet not exhibit his essential nature or definable form? Again, what guarantee is there against an unessential addition, or against the omission of the final or of an intermediate determinant of the substantial being?
The Basic Works of Aristotle (Modern Library Classics) Page 24