Aristotle's Prior and Posterior Analytics: A Revised Text with Introduction and Commentary (Oxford University Press academic monograph reprints)

IV THE MODAL SYLLOGISM ARISTOTLE does not in the Prior Analytics tell us what he means by a 'necessary premiss'; he treats as self-evident the distinction between this and one which only professes to state a mere fact. The test he applies is simply the presence or absence of the word o.vaYK7] . But while the disti~ction between a necessary and an assertoric premiss is this purely grammatical one, as soon as the question of validity arises we must take account of the fact that a necessary proposition is true only if what it states is a neces· sary fact; and there is for Aristotle a most important distinction between a necessary fact and a mere fact. In his choice of examples, in An. Pro i.!}-II he seems sometimes to be obliterating this distinction. Consider for instance 30bS-{i. To show that. in the first figure. premisses of the form EIn warrant only an assertorle, not an apodeictic, conclusion he takes the example '(a) No animal is in movement. (b) Some white things are necessarily animals. But it is not a necessary fact that some white things are not in movement.' And then consider ib. 33--8. To show that. in the second figure. premisses of the form A nE warrant only an assertorie, not an apodeictic, conclusion he takes the example '(c) Every man is necessarily an animal. (d) Nothing white is an animal. But it is not a necessary fact that nothing white is a man.' It looks as if in (b) Aristotle were treating it as a necessary fact that some white things are animals. and in (d) treating it as a fact that nothing white is an animal. But he is not to be 1 An. Pr o 67136-7. 2 24bI9. 3 67a12-bII, An. Post. 7I124-bS, 86 1 22-9.

THE MODAL SYLLOGISM accused of inconsistency here. He is not saying that some white things are necessarily animals and then that nothing white is an animal. These are simply illustrative propositions; he is merely saying that if propositions a and b were true, it might still not he necessary that some white things should not be in movement, and that if propositions c and d were true, it might still not be necessary that nothing white should be a man. His examples, then, throw no light on the question what kinds of facts he regards as necessary, and what kinds as not necessary. But we should be justified in supposing that he draws the distinction at the point where he draws it in the Posterior Analytics, where he tells us that the connexion between a subject and any element in its definition (i.e. any of the classes to which it essentially belongs, or any of its differentiae), or again between a subject and any property which follows from its definition, is a necessary connexion. while its connexion with any other attribute is an accidental one.

The most interesting feature of Aristotle's treatment of apodeictic syllogisms is his doctrine that certain combinations of an apodeictic and an assertoric premiss warrant an apodeictic

conclusion. The rule he lays down for the first figure is that an apodeictic major and an assertoric minor may yield such a con-

clusion, while an assertoric major and an apodeictic minor cannot. The rules for the other two figures follow from those for the first (since for Aristotle the validity of these figures depends on their reducibility to the first), and need not be separately considered. We know from Alexander' that the followers of Eudemus and Theophrastus held the opposite doctrine, that if either premiss is assertoric the conclusion must be so, just as if either premiss is negative the conclusion must be so, and if either premiss is particular the conclusion must be so, and that they summed up their view by saying that the conclusion must be like the 'inferior premiss'. Nothing is really gained by the comparison; the question must be considered on its own merits. The arguments on which Theophrastus relied were two in number: (1) 'If B belongs to all C, but not of necessity, the two may be disjoined, and when B is disjoined from C, A also will be disjoined from it." Or, as the argument is put elsewhere by Alexander, since the major term is imported into the minor through the middle term, the major I

124.8-127. 16.

a

124. 18-21.

INTRODUCTION 42 cannot be more closely related to the minor than the middle is.' (2) He pointed to examples, quite comparable to those which Aristotle uses to prove his point : (a) Every man is necessarily an animal, and it might be true at some time that everything that was in movement was a man : but it could not be true that everything in movement was necessarily an animal. (b) Every literate being necessarily has scientific knowledge, and it might be true that every man was literate; but it could not be true that every man necessarily has scientific knowledge. (c) Everything that walks necessarily moves, and it might be true that every man was walking; but it could not be true that every man was necessarily in movement. 2 We need not concern ourselves with an attempt that was made to water down Aristotle's view so as to free it from these objections-an attempt which, Alexander points out, is a complete misunderstanding of what Aristotle says.' Aristotle bases his case on the general statement 'since A of necessity belongs, or does not belong, to B, and C is one of the B's, evidently to C too A will necessarily belong, or necessarily not belong' .' I.e. he takes it as self-evident that if A is necessarily true of B, it is necessarily true of everything of which B is in fact true. A further light is thrown on Aristotle's reasoning, by what he says of one of the combinations which he describes as not yielding an apodeictic conclusion-the cOn;>bination All B is A, Some C is necessarily B. This, he says, does not yield an apodeictic conclusion, OVSEV yap dSt1vo:rov aV/Jlrr{1T7'Et, 'for it cannot be established by a reductio ad impossibile'.s He clearly held that in the cases where an apodeictic conclusion does follow, it can be established by a reductio. The cases ar~ four in number; A nAA n, EnAE", A nIIn, EnIOn. In principle all four cases raise the same problem, and it is only necessary to consider A nAA "-'All B is necessarily A, All C is B, Therefore all C is necessarily A . For if some C were not necessarily A, then since all Cis B, some B would not necessarily be A.' The reductio syllogism gives a conclusion which contradicts the original major premiss, and the contradiction seems to establish the original conclusion. And, further, by using the reductio ArisI 124. 31- 12 5. 2. .. An. Pro 300.21-3.

1

AI. 124. 24- 30.

5 30bt-S .

THE MODAL SYLLOGISM 43 totle seems to get round the prima facie objection to the original syllogism, that it has a premiss 'weaker' than the conclusion it draws; for the reductio syllogism is not open to this objection. Yet Aristotle's doctrine is plainly wrong. For what he is seeking to show is that the premisses prove not only that all C is A, but also that it is necessarily A just as all B is necessarily A, i.e. by a permanent necessity of its own nature; while what they do show is only that so long as all C is B, it is A, not by a permanent necessity of its own nature, but by a temporary necessity arising from its temporarily sharing in the nature of B.' It is harder to point out the fallacy in the reductio, but it can be pointed out. What Aristotle is in effect saying is that three propositions cannot all be true-that some C is not necessarily A, that all C is B, and that all B is necessarily A ; and if 'necessarily A' meant the same in both cases this would be so. But in fact, if the argument is to prove Aristotle's point, 'necessarily' in the first proposition must mean 'by a permanent necessity of C's nature', and in the third proposition 'by a permanent necessity of B's nature', and when the propositions are so interpreted we see that the three propositions may all be true together. Thus the reductio fails, and with it what Alexander rightly recognizes as the strongest argument for Aristotle's view. 2 Aristotle's treatment of problematic syllogisms depends, of course, on his conception of the meaning of the word EVS'XE'TaL, which occurs in one or both of the premisses of a problematic syllogism. This conception we have to gather from four passages of considerable difficulty, none perhaps intelligible without assistance from one or more of the others-zsa3i-hz5. 3ZaI6-b22, 33bz533. 36b3S-37a3I. I have considered these passages in cannexion with one another in my note on 25'37-b'9; the general upshot is all that need be mentioned here. In all his treatment of problematic syllogisms Aristotle recognizes two and only two senses of Ev3EXOJLEVOV. In a loose sense it means 'not impossible'. but in its strict sense it means 'neither impossible nor necessary'. These are, indeed, the only meanings which the word could be said naturally to bear. But in each of the two senses the word has two applications. That which is Aristotle recognizes the distinction. in the words olll( ;a'7w alla.)ll(aioll «?TAWs, TO,",""V OI"7(1.1V Q.1la.YKaiov (Job 32-3), but unfortunately does not apply it impartially to all combinations of an apodeictic with an assertoric premiss. I

ilia z

12 7.3- 14.

INTRODUCTION 44 known or thought to be necessary may be said a fortiori to be possible in the loose sense; and that which, without being known or thought to be necessary, is known or thought to be not impossible, may be said to be possible in the loose sense. And again, that which has a natural tendency to be the case or to happen, and is the case or happens in most instances, may be s.aid to be possible in the strict sense; and that whose being the case or happening is a matter of pure chance may be said to be possible in the strict sense. This latter distinction is one to which Aristotle attaches much importance; he says for instance that while science may deal with that which happens for the most part, as well as with that which is necessary, it cannot profitably deal with that which is a matter of pure chance. But while this distinction is of great importance in its own place, and is mentioned in the Prior A nalytics,' it plays no part in Aristotle's treatment of the problematic syllogism ; it is in fact more pertinent to the Posterior Analytics, which is concerned with science, than to the Prior Analytics, which is concerned simply with valid syllogism. In his treatment of this, Aristotle always takes ..SIX.Ta. in a premiss as meaning 'is neither impossible nor necessary' ; where the only valid conclusion is one in which Jv8€XE'T'Qt means 'is not impossible', he is as a rule careful to point this out. For the understanding of the chapters on problematic syllogism, two further points must be kept in mind: (r) Aristotle points out a special form of &.JmUTpO"'~ (what I have called complementary conversion) which is valid for propositions that are problematic in the strict sense: 'That all B should be A is contingent' entails 'That no B should be A is contingent' and 'That some B should not be A is contingent'. 'That no B should be A is contingent' entails 'That all B should be A is contingent' and 'That some B should be A is contingent'. That some B should be A is contingent' entails That some B should not be A is contingent', and vice versa. 2 This form of conversion (whose validity follows from the strict sense of
:&

32129'-35.

3

36b3S-37a3I.

THE MODAL SYLLOGISM 4S tions stating conjunctions of subject and attribute to be possible in the stTict sense, are the same as the rules for the convertibility of assertoric and apodeictic propositions (A propositions convertible per accidens, E and I propositions simply, 0 propositions not at all), a proposition of the form 'Tllat no B should be A is contingent' does not entail 'That no A should be B is contingent'. This follows from the fact that since (i) 'For every B, being A is contingent' entails (ii) 'For every B, not being A is contingent', and (iii) 'For every A, not being B is contingent' entails (iv) 'For every A, being B is contingent', therefore if (ii) entailed (iii), (i) would entail (iv) , which plainly it does not. On the other hand, both 'For every B, not being II is contingent' and 'For some B's, not being A is contingent' entail 'For some A's, not being B is contingent'. This apparent divergence from the general principle that universal negative propositions are simply convertible, and particular negative propositions not convertible, has from early times awakened suspicion. Alexander tells us' that Theophrastus and Eudemus rejected both the dicta stated in our last paragraph and the doctrine of the complementary conversion of propositions asserting possibility in the strict sense. Maier, following Theophrastus and Eudemus, has a long passage' in which he treats the dicta of our last paragraph as an aberration on Aristotle's part, and tries to explain how he came to commit it. But Alexander defends the master against the criticism of his followers, and he is right. If Aristotle's reasoning is carefully followed, he is seen to be completely justified. Those who have criticized him have done so because they have not completely grasped his conception of strict possibility, i.e. of contingency, in which the contingency of B's being A and the contingency of its not being A are logically equivalent. This once grasped, it {ollows at once that if the statement of a universal affirmative possibility is (as everyone admits) only convertible per accidens, so must be the statement of a universal negative possibility. And this is no divergence from the general principle that while A propositions are only convertible per accidens, E propositions are convertible simply; for 'For every B, being A is contingent' and 'For every B, not being A is contingent' are, as Aristotle himself observes,' both affirmative propositions. A statement which denies the existence of a possibility is not a problematic statement at all, but a disjunctive statement asserting the existence either of necessity or of impossibility. I 159.8-13,220.9-221. 5.

a 2. a 37- 47.

3

2SbI9-24.32bl-3.

INTRODUCTION If these general features of Aristotle's theory of the problematic proposition are kept in mind, it becomes not too difficult to follow his detailed treatment of syllogisms with one or both premisses problematic, in An. Pr. i. '4-22. Of all the valid syllogisms of this type, few escape his notice; of those that do not need comple_mentary conversion for their v~lidation. none does, but of those that require such conversion several are omittedl- no doubt because, having mentioned the possibility of such validation in many cases, he does not think it necessary to mention it in all. The method of reduction of syllogisms which he adopts is in a few cases inconclusive, but these occasional flaws do not prevent the discussion from being a most remarkable piece of analysis. The fact that Theophrastus denied the convertibility of lvSlx.ra, 1TaVTl Tip B TO A inrapXELv with Ev8lXETat JL718EVI. Tip B TO A inraPXEw shows that he was ·interpreting
See instances in the table at facing p. 286.

z A1. I73. 32-174. 3.

THE MODAL SYLLOGISM 47 'Some C is not A'.' His proof of the first of these entailments (and that of the other follows suit) is as follows: 'Suppose that some C is A, and convert the major premiss. Then we have All A is necessarily not B, Some C is A, which entail Some C is necessarily not B. But ex hypothesi for all C, being B is contingent. Therefore our supposition that some C is A was false, and No C is A is true.' It will be seen that Aristotle tries to validate the inference by reductio to a syllogism with an apodeictic and an assertoric premiss. and an apodeictic conclusion; and we have already' seen reason t o deny the validity of such an inference. Aristotle is at fault, and Theophrastus' doctrine that the conclusion follows in its nature the weaker premiss is vindicated.

V INDUCTION THE chief method of argument recognized by Aristotle apart from syllogism is induction: in one passage3 he says broadly a1TaV'TG. mtTTEvojLEV 1j 3ul (1l),uoy,ap.ov ~ Jg £1raywYiis-, and in others" the same general distinction is implied. And since syllogism is the form in which demonstration is cast, a similar broad opposition between induction and demonstration is sometimess found. The general distinction is that demonstration proceeds from universals to particulars, induction from particulars to universals. 6 The root idea involved in Aristotle's usage of the words E1tI:tYEtv

and b,ay'"Y'7 is not (as Trendelenburg argued) that of adducing instances, but that of leading some one from one truth to another.' So far as this goes, ordinary syllogism might equally he described as E1TayWYJ1. and €rTaynv is occasionally used of ordinary syllogism. s And in general Aristotle clearly means by '"aywY'7 not the adducing of instances but the passage from them to a universal conclusion. But there are occasional passages in which E1TCLK'T'KOS. 9 E1TCLKTtKWS/ O and E1Tayw,qIl are used of the adducing of instances; and it seems to. be by a conflation of these two usages that £1TayW'Y"1 comes to be used habitually of leading another person on by the contemplation of instances to see a general truth. 36'7-15, 34"""'9. ::I pp. 41-3. 3 An. Pr. 68bI3. 42a3, 68b32-7; An. Post. 7IaS-II. 5 ' An. Post. 9Ib34- S, 92&3S-br. 6 SI&4o-bl, Top. 1°5&13. 1 , See introductory note to An. Pro ii. 23. 8 An. Post. ?IaU, 24. 9 nb35 and perhaps Met. I07Sb28. 10 Phys. 2lohs. b JI Cat . 13 37, Top. l08 blo, Soph. El. 174 a37, Met. I04S&36. I

4

INTRODUCTION With one exception to be mentioned presently, Aristotle nowhere offers any theory of the nature of induction, and the word braywJ'Ti cannot be said to have been with him a term of art as UVA.\OYLU,.wS' is. He uses the word to mean a variety of mental processes, having only this in common, that in all there is an advance from one or more particular jUdgements to a general one. At times the advance is from statements about species to statements about the genus they belong to;' at times it is from individuals to their species';2 and since induction starts from senseperception,3 induction from species to genus must have been preceded by induction from individuals to species. Again, where the passage is from species to genus, Aristotle sometimes' passes under review all (or what he takes to be all) the species of the genus, but more often' only some of the species. Where a statement about a whole species is based on facts about a mere selection of it.s members, or an inference about a whole genus on facts about a mere selection of its species, it cannot be reasonably supposed that there is a valid inference, and in the one passage where Aristotle discusses induction at length,- he says that induction to be valid must be from all the KaO'
INDUCTION

49

a~'\OY a~ cYrL ~p.i.1I

7"0. WpW'J'a. E7TUYWyfi yvwpl,£w avaYK'ai.ov: 'T(VV apxwv at J-I-EV E1Taywyfj 8£wpovVTa&.. at (i:' alalh}an, 0.18' E8wtJ.o/ nvl, 1((1(. ruaL S' lliwS': Elal,lI apa apxaL Jg £Lv 0 O"VAAoy'U,.,.o), WV OVK Ea'TL UV,uOYLCTJL0S' . E1ray~ apa,1 Now Aristotle considers that, in the mathematical

sciences at least, knowledge of derivative propositions can be reached, and that this can happen only if the ultimate premisses from which the proof starts are themselves known. But these are not themselves known by proof; that is implied in calling them ultimate. Here, then, under the heading of induction he clearly contemplates a mental process which is not proof, yet on which knowledge supervenes. Take the most fundamental proposition of all, that on which all proof depends, the law of contradiction. How do we come to know it? By seeing, Aristotle would say, that some particular subject B cannot both have and not have the attribute A, that some particular subject D cannot both have and not have the attribute C, and so on, until the truth of the corresponding general proposition dawns upon us. And so, too, with the a.pxalproper to a

particular science. The induction here is not proof of the principle, but the psychological preparation upon which the knowledge of the principle supervenes. The knowledge of the principle is not produced by reasoning but achieved by direct insight-vavS' av EfT} 'Twvapxwv.2 This is in fact what modem logicians call intuitive induction. And this is far the most important of the types of induction which Aristotle considers. The general principle, in such a case, being capable of being known directly on its own merits, the particular examples serve merely to direct our attention to the general principle; and for a person of sufficient intelligence one example may be enough. At the very opposite extreme to this application of induction stands the application which Aristotle considers in the one passage in which he describes induction at some length, An. Pr. ii. 23. He here studies the kind of induction which really amounts to proof and can be exhibited as a syllogism, 0 £~ £1Ta.ywyijr av,u0yw/Lor. In this all theparticulars must be studied, in order that the general principle should be proved. Induction is said to be 'the'connecting

of one extreme syllogistically with the middle term through the other extreme'. This seems at first sight inconsistent with the very notions of extreme and middle term. The explanation is not far to seek. He contemplates a situation in which certain species Ct. C2 • etc., have an attribute A because of their membership of a I

An. Post. loob3, E.N. IQ98b3,II39b29.

4985

E

':

An. Post. lOOb I2.

INTRODUCTION 50 genus B. The demonstrative syllogism would run 'All B is A; c" C" etc., are B; therefore they are A.' The inductive syllogism runs 'C" C" etc., are A; C1 , C" etc., are B, and this proposition is convertible (i.e. all B is either C1 or C" etc.); therefore all B is A.' C and A are still called the extremes and B the middle term, because that is what they are in the demonstrative syllogism, and in the nature of things. It is strange that in the one considerable passage devoted to induction Aristotle should identify it with its least valuable form, perfect induction. The reason is to be found in the remarks which introduce the chapter. Filled with enthusiasm for his new-found discovery the syllogism, he makes the bold claim that all arguments-dialectical, demonstrative, or rhetorical-are carried out in one or other of the three syllogistic figures . Not unnaturally, therefore, he selects just the type of induction which alone can be cast in the form of a valid syllogism; for it is plain that whenever the named Cs fall short of the whole extension of B, you cannot validly infer from 'C 1 , C., etc., are A ; C" C" etc., are B ' that all B is A. Nor is perfect induction entirely valueless. If you know that C" C" etc., are A, and that they are B, and that they alone are B, you have all the data required for the knowledge that all B is A ; but you have not yet that knowledge; for the drawing of the conclusion you must not only know these data, but you must also think them together (uvvO.wp"v)! and it is this, as in all syllogism, that makes a real advance in knowledge possible. To sum up, then, Aristotle uses 'induction' in three ways. He most often means by it a mode of argument from particulars which merely tends to produce belief in a general principle, without proving it. Sometimes he means by it the flash of insight by which we pass from knowledge of a particular fact to direct knowledge of the corresponding general principle. In one passage he means by it a valid argument by which we pass from seeing that certain species of a genus have a certain attribute, and that these are all the species of the genus, to seeing that the whole genus has it. We can now see why it is that Aristotle describes syllogism as 'TrpO'TEpOr Kat YVWPt/-LW'TEPO~ than induction, while induction is ~.utV £vapyE(]'7'EpoS,'J. or demonstration as being (I< 7TpOTEPWV Ka, YVWP'jLWM TEPWV a.7TAWS', induction as being EK 1TpO-r£pWV Kat YVWP~f£W-r'PWV 1\1"v.' All knowledge starts with the apprehension of particular I

An. Pro 67 1 37.

~ 68b35- 7.

3

An. Post. 72b26-30.

INDUCTION 51 facts, which are the most obvious objects of knowledge. But Aristotle is convinced that if a particular subject C has an attribute A, it has it not as being that particular subject but in virtue of some attribute B which it shares with other subjects, and that it is more really intelligible that all B is A than that C, a particular instance of B, is A. To pass ftom the particular fact that C is A to the general fact that all B is A is not to understand why all B is A ; but to pass, as we may then proceed to do, from knowing that all B is A to knowing that C, a particular B, is A, is to understand why C is A. Having in An. Pro ii. 23 shown how induction. in one of its forms, viz. perfect induction, can be reduced to syllogistic form, Aristotle proceeds in the remainder of the book to treat of other modes of argument reducible to syllogistic form--example, reduction, objection, enthymeme; but these are not of sufficient general importance to need discussion here. VI DEMONSTRATIVE SCIENCE As the Prior Analytics present Aristotle's theory of syllogism, the Posterior A nalytics present his theory of scientific knowledge. This, rather than 'knowledge' simply, is the right rendering of his word ''''C1T~I''1 ; for while he would not deny that individual facts may be known, he maintains that '''urnil''1 is of the universal. Syllogistic inference involves, no doubt, some scientific knowledge: viz. the knowledge that premisses of a certain form entail a conclusion of a certain form. But while formal logic aims simply at knowing the conditions of such entailment, a logic that aims at being a theory of scientific knowledge must do more than this; for the sciences themselves aim at knowing not only relations between propositions but also relations between things, and if the conclusions of inference are to give us such knowledge as this. they must fulfil further conditions than that of following from certain premisses. To this material logic, as we might call it in opposition to formal logic, Aristotle now turns; to the statement of these further conditions the first six chapters of A n. Post. i are devoted. Aristotle begins by pointing out that all imparting or acquisition of knowledge by reasoning starts from pre-existing knowledge; and this passage from knowledge to knowledge is what

52

INTRODUCTION occupies almost the whole of the Posterior Analytics. There remains the question whether the knowledge we start from is innate or acquired, and if acquired, how it is acquired; and to that question Aristotle turns in the last chapter of the second book. But about the nature of this original knowledge he says at once' that it is of two kinds. There is knowledge of facts and knowledge of the meaning of words. The first he illustrates by the knowledge of the law of excluded middle; the second by the knowledge that 'triangle' means so-and-so. He adds that there are certain things (e.g. the unit) about which we know not only that the word by which we designate them means so-and-so, but also that something answering to that meaning exists. And elsewhere' he expands this by observing that while we must know beforehand the meaning of all the terms we use in our science, we need know beforehand the existence of corresponding things only when these are fundamental subjects of the science in question. The instances he gives suggest-and there is much in what follows to support the suggestion-that he has mathematics in mind as furnishing the primary example of science (or rather examples, for in his view arithmetic and geometry are essentially different sciences). It was inevitable that this should be so; for the mathematical sciences were the only sciences that had been to any degree developed by the Greeks when Aristotle wrote. In Euclid, who wrote about a generation later, we find recognized the two types of preliminary knowledge that Aristotle here mentions; for Euclid's 0po, answer to Aristotle's 'knowledge of the meaning of words', and his Ko£Vat EvVOtat answer approximately to Aristotle's 'knowledge of facts'; though only approximately, as we shall see later.' Now Euclid's Elements had predecessors, and in particular it seems probable that the Elements of Theudius' existed in Aristotle's time. But we know nothing of its contents, and it would be difficult to say whether Aristotle found the distinction of two kinds of knowledge already drawn by Theudius, or whether it was Aristotle's teaching that led to the appearance of the distinction in Euclid. Aristotle turns next s to what is in fa.ct a comment on his own statement that all knowledge gained by way of reasoning is gained from pre-existing knowledge. What his comment comes to is this, that when knowledge that a particular member of a class has a I

4

7Ian-I7. .2 76a3z-6. Cf. Heath, Greek Mathematics, i. 320-1.

, PP·56-7. 5

71aI7-bS.

DEMONSTRATIVE SCIENCE 53 certain attribute is gained by way of reasoning, the major premiss must have been known beforehand, but the recognition of the particular thing as belonging to the class and the recognition of it as having that attribute may be simultaneous. 'That every triangle has its angles equal to two right angles we knew before; that this figure in the semicircle is a triangle, one grasped at the very moment at which one was led on to the conclusion.'1 This implies, of course, that the knowledge that all triangles have this property was not knowledge that each of a certain number of triangles has the property Plus the knowledge that there are no other triangles-was knowledge not of an enumerative but of a generic universal. If he did not know a thing to exist, how could he know that it has angles equal to two right angles? One has knowledge of the particular in a sense, i.e. universally, but not in the unqualified sense';<1 or, as he puts it elsewhere. 3 in knowing the major premiss one was potentially, but only potentially, knowing the conclusion. This important distinction had already been stated, in a more elaborate form, in An. Pro ii. 21. We think we have scientific knowledge of a fact, Aristotle proceeds,. when we think we know its actual cause to be its cause, and

the fact itself to be necessary. Our premisses must have two intrinsic characteristics. They must be true, and this distinguishes

the scientific syllogism from all those correct syllogisms which proceed from false premisses (for which ct. An. Pro ii. 2-4). But not all inferences from true premisses are scientific; secondly, the premisses must he primary or immediate, since a connexion that is mediable can be known only by being mediated. And besides having these intrinsic characteristics they must stand in a certain special relation to the conclusion; they must be 'more intelligible than and prior to and causes of the conclusion . .. causes because we know a fact only when we know its cause; prior, because they are causes; known before, not only in the sense that we know what the words mean but also in the sense that we khow they stand for a fact.'s These, while named as thr,ee separate conditions, are clearly connected, ·Prior'· and 'better known' state two characteristics both of which follow from the premisses' being causes, i.e. 'statements of the ground on which the fact stated in the conclusion depends. Both 'prior' and 'better known' are used in a special, non-natural sense. Aristotle would not claim that the I 7IaI9-2I.

• 7,~,6.

, lb. 2&-9. , lb. '9-33.

INTRODUCTION

54

facts stated in the premisses are necessarily prior in time; for in mathematics there is no temporal succession between ground and

consequent. Aristotle would even go farther and say that a fact (or a combination of facts) which precedes another fact can never be the complete ground of the other, since the time-lapse implies that the earlier fact can exist without the later fact's doing 50. 1 'Prior' therefore must mean 'more fundamental in the nature of things', And again 'more known' does not mean 'more familiar', nor 'foreknown' 'known earlier in time', For he goes on

to say that 'the same thing is not more known by nature and more known to us. The things that are nearer to sense are more known

to us, those that are farther from sense more known without qualification. Now the things that are most universal are farthest from sense, and individual things nearest to it.':t In ademonstratio potissima all three terms are actually of equal universality; but nevertheless wilen we say All B is A, All Cis B, Therefore all C is A, in the minor premiss we are using only the fact that all C is B, and not the fact that all B is C, so that notionally the major premiss is wider than the conclusion, and therefore (Aristotle would say) less known to us. In saying this, he is pointing to the fact that is brought out in the final chapter of the Posterior A nalytics-that the ultimate premisses of demonstration are arrived at by intuitive induction from individual facts grasped by sense; while in saying that the premisses are more known by nature he is saying that the universal fact is more intelligible than the individual fact that is deduced from it; and this is so; for if all C is A because all B is A and all C is B, we understand all C's being A only by grasping the more fundamental facts that all B is A and all C is B. Thus the two senses of 'more known' are 'more familiar', which is applicable to the conclusion, and 'more intelligible', which is applicable to the premisses. In demonstration we are not passing from familiar premisses to a less familiar con·

elusion, hut explaining a familiar fact by deducing it from less familiar but more intelligible facts. . One thing in this context that is puzzling is the statement that the premisses must' be

'TTPOYLVW(fKop.Eva,3

which clearly refers to

temporal precedence and might seem to contradict the statement that the conclusions are more familiar to us. But the two state· ments are not inconsistent: for even if the premisses have been

reached by induction from particular instances, it need not be I An. Po~t. ii. IZ.

2 7Ib34- 72as.

l 7Ib3I; cf. 7,128.

DEMONSTRATIVE SCIENCE

55

from the instances to which the conclusion refers, and even if it is so. within the syllogism the knowledge of the conclusion appears as emerging from the knowledge of the premisses and following it in time. Aristotle adds one further qualification of the apxai of science; they must be OlKt/ta" I This must be understood as meaning not 'peculiar' to the science in question (for Aristotle includes among the apxai axioms which extend beyond the bounds of anyone science). but 'appropriate' to it. What he is excluding is the p.E'ra.f3aut~ E, c:i.\.\ou Y€lIous/' the use (as in dialectic) of premisses borrowed from here, there, and everywhere. Aristotle turns now'·to distinguish the various kinds of premiss that scientific demonstration needs. There are. first of all. dg.wp.a'Ta (also called Kowa or Kotva2 apxat), the things one must know if one is to learn anything. the principles that are true of all things that are. The only principles ever cited by Aristotle that strictly conform to this account are the laws of contradiction and of excluded middle,' but it is to be noted that he also includes under ag.wl'aTa principles of less generality than these but applying to all quantities. e.g. that if equals be taken from equals. equals remain. s Even these are Kowa as compared with assumptions peculiar to arithmetic or to geometry. Secondly, there are 8/C1£tS, necessary for the pursuit of one partiCUlar science. though not necessary presuppositions of all learning. These fall into two groups: (,) w08.".... assumptions of the existence of certain things. and (2) op'''f'oi. definitions. which, since they are co-ordinated with lmo6luns and not described as including them as elements. must be purely nominal definitions of the meaning of words. and are. indeed. so described in 7'"'4-15. The same passage adds that while with regard to some terms (e.g. triangle in geometry) only the meaning must be assumed. with regard to others (e.g. unit in arithmetic)' the existence of a corresponding entity must also be assumed. Aristotle's view is that the meaning of all the technical terms used in a science and the existence of the primary subjects of the science must be assumed. while the existence of the non-primary terms (i.e. of the attributes to be asserted of the subjects) must be proved.' I

72 '6.

.1

75'38.

4 711l14, 77.10--12, 30, 88 hz. 6

Cf. magnitude in geometry. ']6·36.

72 '14- 2 4. 76.4 1, h20, . , 76a3H . 3

5

771130-1.

INTRODUCTION With regard to these assumptions, he makes two important points elsewhere. One is that where an assumption is perfectly obvious it need not be expressly stated.' The second is that a science does not assume the axioms in all their generality. but only as applying to the subject-matter of the science'-on the principle of not employing means that are unnecessary to our end. Aristotle is not so clear as might be wished with regard to the function of the axioms in demonstration. He describes them as £; wv, starting-points. 3 In another passage he says demonstrations are achieved 8uf T€ 'TWV KOtvwV Kat £1<. nov a7To8£8Etypivwv,'" apparently distinguishing the function of the axioms from that of any previously proved propositions that form premisses for a later proposition. Their function is more obscurely hinted at in 88b3, where it is said that propositions are proved through (S
4

76bI6--2I,77I1o-12. 76b10.

z 76a37-b2.

3

5

75 1 42, 76h14, 77127, 88b28. 77"10-12.

6 On the relation of Aristotle's dpXo.l to those of Euclid cf. Heath, The Thirteen Books oj Euclid's Elenunts, i. 117-24. In referring to Euclid's axioms and postulates, I refer to the restricted list given in Heiberg's edition and Heath's translation. ' 72114-17.

DEMONSTRATIVE SCIENCE 57 all things that are (the laws of contradiction and excluded middle) or at least common to the subject-matter of arithmetic and geometry ('if equals be taken from equals, equals remain'). In Kowa, Iwota", Kotva.l means 'common to the thought of all men', and the phrase is derived not from KOLVa.L riPXat but from a phrase which Aristotle uses in the Metaphysics'----"T'us KOLVaS S6eas 19 wv a1TavTE$' S€LKVVoVaLv. Euclid's KOLVa.' mOLQL include neither of

Aristotle's axioms of supreme generality. They do include axioms common to arithmetic and geometry ('things which are equai to the same thing are also equal to one another', 'if equals be added to equals, the wholes 'are equal', 'if equals be subtracted from equals, the remainders are equal', 'the whole is greater than the part'), and one which is

KOLV7]

in the second sense but not in the

first, being limited to geometry-'things which coincide with one another (i.e. which can be superimposed on one another) are equal to one another'. . _.' Euclid's Jpo. answer exactly to Aristotle's &pwp.ol (which Aristotle elsewhere often calls Jpo,). Like Aristotle, Euclid included

definitions not only of the fundamental terms of the sciencepoint, line, surface-but also of attributes like straight, plane, rectilinear. The underlying theory is Aristotle's theory, that geometry must assume nominal definitions of all its technical terms, alike those in whose case the existence of corresponding entities is assumed, and those in whose case it must be proved. Euclid states no presuppositions answering to Aristotle's lmo8E(}EL~, assumptions of existence; it is reasonable to suppose that he silently assumes the existence of entities corresponding to the most fundamental of the terms he defines. Aristotle's treatment is in this respect preferable. He admits' that when an assumption is perfectly self-evident it need not be expressly stated; he is right in saying that even when it is not expressly stated, the presupposition of the existence of certain fundamental entities is a distinct and necessary type of presupposition. On the other hand, Euclid recognizes a type of presupposition which does not answer to anything in Aristotle-the atryp.« or postulate. The word occurs in Aristotle, but not as standing for one of the necessary presuppositions of science. When a teacher

or disputant assumes without proof something that is provable, and the learner or other disputant has no opinion or a contrary opinion on the SUbject, or indeed when anything provable is .

I

9C)6b2 8;cf. 997.zl .

INTRODUCTION assumed without proof (the alternatives show that Aristotle is not using at'"lJ1.4 as a technical tenn, but taking account of a variation in its ordinary usage). that is an a'T'I}p.a. 1 In neither case is this a proper presupposition of science. Euclid's alrrjp4Ta.

58

are a curious assemblage of two quite distinct kinds of assumption.

The first three are assumptions of the possibility of perfonning certain simple constructions-flet it be demanded to draw a straight line from any point to any point, to produce a finite straight line continuously in a straight line, to describe a circle with any centre and distance'. The last two are of qiIite a different order-'that 'alI right 'angles are equal to one another' and 'that, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than two right angles'-the famous postulate of parallels. The first three postulates are not propositions at all, but demands to be allowed to do certain things; and as such they naturally find no place among the fundamental propositions which Aristotle is seeking to classify. No doubt the demand to be allowed to do them involves a claim to be able to do them if one is allowed; an improper claim, since in fact no one can, strictly speaking, draw or produce a straight line, or describe a circle. All that the geometer really needs is pennission to reason about that which l}e has drawn, as if it were a straight line or a circle. And on this Aristotle says what is really necessary when he points out that the geometer is guilty of no falsity when he so reasons, and that the supposition, fiction if you will, that what he has drawn is a straight line or circle forms no part of his premisses but only serves to bring his reasoning home to the mind of his hearer.%

When we come to the last two of Euclid's postulates, the situation is quite different. The fourth states a self-evident proposition whose right place would be among the KOtVal. EVVOta,t.. a proposition quite analogous to the KOU..fJ €woc.a that figures which coincide are

equal. On the famous fifth postulate it would ill hecome me to dogmatize against the prevailing trend of modem mathematical theory; but 1. venture to regard this also as axiomatic. Aristotle's recognition of axioms, definitions, and hypotheses as three distinct types of assumption needed by science is sound, so far as it goes, but it needs supplementation. To begin with, he I

76b3l- 4.

a 76b39-77a3.

DEMONSTRATIVE SCIENCE 59 should have recognized the distinction between the axioms that are applicable to all things that are, and those that are applicable only to quantities, i.e. to the subject-matter of arithmetic and geometry. Secondly, he should have recognized among the principles peculiar to one science certain which are neither definitions nor assumptions of the existence of certain entities-such propositions as Euclid's fourth axiom, that things which coincide are

equal, and his fourth and fifth postulates. Among these principles he should have included such assumptions as that every number is either odd or even, every line either straight or curved, which in another passage I he inclu.des among the assumptions of science.

In recognizing the existence of such self-evident propositions as these, Aristotle is recognizing an important difference between the mathematical and the inductive sciences. In the latter the alternative attributes, one or other of which a certain subject must have, can only be discovered empirically; in the former they can be known intuitively. And finally, a closer scrutiny of the actual procedure of geometry would no doubt have shown him that it uses many other assumptions which aJ;"e involved in OUf intuition of the nature of space, e.g. (to borrow an example from Cook Wilson) that the diagonals of a quadrilateral figure which has not a fe-entrant angle must cross within the figure. It is not unusual to describe Aristotle as lacking in mathe-

matical talent; but there are at least three things which show the falsity of such a view. One is his discussion of the presuppositions of science (which means for him primarily the foundations of mathematics); this, though far from perfect, is almost certainly a great advance on anything that preceded it. Another is his masterly and completely original discussion, in the sixth book of the Physics, of the whole problem of continuity. A third is the brilliant passage in the Metaphysics' in which he anticipates Kant's doctrine that the construction of the fignre is the secret of geometrical discovery. He did not make original mathematical discoveries; but few thinkers have contributed so much as he to the philosophical theory of the nature of mathematics. Aristotle's firm insistence that there must be starting-points of proof which neither need nor admit of proof enables him' to set aside two theories that evidently had some vogue in his daytheories which assumed in common that knowledge can only be J

74bS- I2.

;!

1°51&21- 33.

l Ch.3.

60 INTRODUCTION got by proof. On this assumption some based the conclusion that knowledge is impossible since no proof proves its own premisses;1

while others held that knowledge is possible but is got by reasoning in a circle, proving a conclusion from premisses and these premisses

from the conclusion.· Aristotle refutes the latter view at some length' by pointing out in detail the futility of circular argument. He next points out' that that which is to be known scientifically must be incapable of being otherwise, and that therefore the premisses from which it is proved must also be necessary. But before drawing out the implications of this he proceeds to distinguish three relations which may exist between a predicate and

a subject, and must exist if the proposition is to be truly scientific. (I) The first is that the predicate must he Ka-rd. naY7oS', true of every instance of the subject. Universality in this merely enumerative sense is the minimum requirement. (2) The second is that the

one term must be Ka8?

a-m-o,

essential, to the other. He dis-

tinguishes four senses of KUO' aUTO, hut the last two are irrelevant

to his present inquiry and are introduced only for the sake of completeness. The first two senses have this in common, that a term A which is KQ.O'

Q.v.ro

to a term B must belong to B as an

element in its essential nature. They differ in this, that A is KaO' am-o to B in the first sense when A is an essential element in the definition 'of B. and in the second sense when B is an essential element in the definition of A. The underlying idea is that in the essential nature of anything there are two layers-a complex of fundamental attributes (genus and differentiae) which form the core of its being and by reference to which it is defined, and a complex of consequential attributes which are its properties and

can be defined only by reference to it. Propositions which are examples of the first kind of KaO' av.ro relation are definitions or partial definitions. which form suitable premisses of demonstra. tion: with regard to the second kind of KaO' am-o relation, Aristotle

no doubt means, though he fails to point out clearly, that propositions like 'every angle is either right, acute, or obtuse' occur

among the premisses of geometry, and propositions like 'the a!lgle in the semicircle is right' among its conclusions. The instances Aristotle gives of these two kinds of KaO' a.~o relation call for two comments. (a) Terms that are KaO' av.r6 in

the first sense are said to belong ("m'PXEw) to their SUbjects. inrciPX£tv is a non-technical and ambiguous word, Line belongs to I 72b7-15. 2 lb, 15- 18. ) lb. 25- 73-20. -4. 73- 21 -4_

DEMONSTRATIVE SCIENCE 61 triangle as being its boundary, point to line as being its terminus; but more often it is an attr;/;ute that he describes as being in this sense Ka.O' o.v,.o to its subject. And if we wish to express the relation of line to triangle and of point to line in terms of a relation

between an attribute and a subject, we may say that a triangle is necessarily 'bounded by lines', and a line necessarily 'terminates in points'. (b) The examples Aristotle gives here of terms that are Ko.O' am-o to others in the second sense are pairs of terms that are

alternatively predicable of their subjects (e.g. straight and curved) ; but there is no reason why he might not have cited larger groups of terms that are alternatively predicable of their subjects, or for that matter single terms that are necessarily predicable of their subjects. (3) But it is not enough that the predicate should be true, without exception and necessarily, of its subject. It must also be true of it il a.n-6, of it precisely as itseif, not of any wider whole. Aristotle applies this distinction to both kinds of Ka8' a.n-6 relation. 1 As applied to the first kind it would mean that only propositions ascribing to a subject its final differentia are suitable premisses of demonstration, for only these are simply convertible.

But it is doubtful if he would have stressed this point. What he has mainly in mind is to assert that the conclusion of a demonstration Z must have terms that are equal in denotation or 'commensurately universal', though he allows that in a looser sense a proposition whose predicate is not commensurately universal may be demonstrated.' If we merely show that a subject always

and necessarily has a certain attribute, we have not yet reached the ideal of demonstration; we do this only when we show that a subject has a property ill virtue of its whole nature, so that nothing else can also have it. This is the severe ideal of demonstration which Aristotle sets up. In the next chapter< he points out various circumstances in which, while there is a 'sort of proof', there is not genuine proof because there is not a perfect fit between the subject and the predicate of our conclusion. Greek mathematics, he says. had at one time been defective because it proved that if A is to B as C is to D, A is to C as B is to D, not universally of all quantities but separately for numbers, lines, solids, and times, but had later remedied this defect.' In Euclid' we find the universal proposition actually proved. I 73b29-32. 2 74al-2. 3 lb. 2. .. i. s. s 74*17-25. Such advance from particular to general proofs is in fact constantly happening in all the sciences. 6 Bks. v I vi.

62

INTRODUCTION Aristotle has already said' that since it is the object of science to prove conclusions that state necessary facts, its premisses also must state necessary facts, but he has not supported this dictum by argument. Instead, he turned aside to state the conditions which any proposition must fulfil if it is to be necessary-viz. that it be enumeratively true, and that it state a connexion which is KaO' aUTO (for the third characteristic, that it enunciate a CODnexion which is ii aVTo, cOI:nmensurately universal, while it is a characteristic of a perfectly scientific proposition, is not a precedent condition of its being necessary). He now turns to prove the proposition stated without proof in 73'2I- 4. He supports it by a variety of probable arguments, but his most cogent argument is that stated in 74b26-32. If a proposition is provable, one cannot know it scientifically unless one knows the reason for its being true. Now if A is necessarily true of C, but B, the middle term one uses, is not necessarily true of C (or, for that matter, if A is not necessarily true of B), one cannot be knowing why C is A. For obviously C's being something which it is not necessarily cannot be the cause of its being something which it is necessarily. It is, of course, possible to infer a necessary fact from nonnecessary premisses, as it is possible to draw a true inference from" false premisses, but as in the latter case the conclusion cannot be known to be true, in the former the fact cannot be known to be necessary; but the object of science is to know just that. On the other hand, just as if the premisses are known to be true the conclusion is known to be true, so if the premisses are known to be necessary the conclusion is known to be so. Thus the requisite and sufficient condition of the conclusion's being known to be necessary is that our premisses be known to be necessary,Z or in other words that we know their predicates to be connected with their subjects by one or other of the two KaO' aUTO relations. 3 The first corollary which Aristotle deduces' from the account just given of the nature of the premisses of scientific reasoning is liA'\ov rEIIOVS', no proving of that there must be no p.£."T&j3aaLS propositions in one science by premisses drawn from another science. No science has a roving commission; each deals with a determinate genus. The subject of each of its conclusions must be an entity belonging to that genus; the predicate must be an attribute that is KaO' aUTO to such a subject; but two terms of which one is KaO' awo to the other obviously cannot be properly

le

1

73a2I- 4.

a 7Sat- t7.

3

lb. 28- 37.

.. i.7.

DEMONSTRATIVE SCIENCE linked by a middle term that is not in such a relation to them. Thus a geometrical proposition cannot be proved by arithmetic,' nor vice versa ;' for the subject of geometry is spatial magnitudes, i.e. continuous quanta, and that of arithmetic is numbers, i.e. discrete quanta.' At the same time, Aristotle allows the possibility of I'ETcf/3ClUL< from one genus to another, when the genera are 'the same in some

respect'.' What he has in mind is the possibility of using mathematical proofs in sciences that are intermediate between mathematics and physics, what he elsewhere! calls 'Tel c/JVaf.KcirrEpa 'TWV JUl-!hJJ.LaTwv, since their sUbject-matters are subordinate to those

of a mathematical science. Optics is in this sense subordinate to geometry, and harmonics to arithmetic.' He elsewhere says much the same about astronomy7 and mechanics. s Consider, for instance, optics. Optics studies rays of light, which are lines 'embodied' in certain matter ; and in virtue of their being lines they obey geometrical principles, and their properties can be studied by the aid of geometry without any improper transition being involved. But elsewhere' Aristotle adds a refinement, by distinguishing within these sciences a mathematical part and a physical or observational part, the latter being subordinate to the former as that is to geometry or arithmetic. Here it is the business of the observer to ascertain the facts, and that of the mathematician to discover the reasons for them ,10 The second corollary which Aristotle draws" from his account of the premisses of science is that there cannot, strictly speaking, be demonstration of perishable facts, i.e. of a subject's possession of an attribute at certain times. Aristotle is taking account of the fact that there are not only mathematical sciences stating eternal

and necessary connexions between subjects and attributes, but also quasi-mathematical sciences which prove and explain tem-

porary but recurring facts, as astronomy explains why the moon is at times eclipsed. There is an eternal and necessary connexion

between a body's having an opaque body interposed between it and its source of light, and its being eclipsed, and the moon someI

7S&38-9.

• 15 b&-9.

Z

7SbI3-14 .

' Phys. '94'7.

J

Cat. 4b2o-S, Mel. I020a7- 14. 6 7SbI4-I7.

Phys. 193b2S-33, Met. 10'/3b3-8. 76a22-S, 78b3S-9, Mel. 1078&14- 17. 9 78b39-79aI3. 10 For a full discussion of Aristotle's views about these intermediate sci~nces d. Mansion, Introd. a la Phys. Arislotil£cienne,94-101. I I 7Sb21- 30. 7

8

INTRODUCTION times incidentally has the one attribute because it sometimes incidentally has the other.' The proof that it has it is eternal inasmuch as its object is a recurrent type of attribute, but inasmuch as the subject does not always have this attribute the proof is particular.' The fact explained is an incidental and non-eternal example of an eternal cannexion.

The third corollary' is that the propositions of a science cannot be proved from common principles (Le. from principles which apply more widely than to the subject-matter of the science), any more than they can be proved from alien principles. For it is plain that there will be some subject to which the predicate of our conclusion applies commensurately, and that subject and not something wider must be the middle term of our proof, if our premisses are to be commensurately universal. In consequence, Aristotle rejects the ideal, adumbrated by Plato in the Republic, of a master-knowledge which will prove lbe apxa1 of the special sciences; each science, he holds, stands on its own basis, and its appropriate premisses are known by their own self-evidence. Zabarella argues' that Aristotle is not attempting to show that metaphysics cannot prove the apxa1 of the sciences, but only that they cannot prove their own tipxa1; but there is nothing here or elsewhere in Aristotle to justify this view. In the Metaphysics itself it is nowhere suggested that metaphysics can do this, and it would be inconsistent with the underlying assumption of that work, that metaphysics is the study of TO ov av, of being only in respect of its most universal characteristics. Zabarella's interpretation is, I think , only a projection of his own somewhat Platonic view into Aristotle. It is natural enough that Plato should have been scandalized by the spectacle of several sciences statting from separate apxai, and should have been fired by the ideal of a single unified system of knowledge. But it is significant that neither Plato nor anyone else has ever had any success in realizing such an ideal, while mathematics offers a clear example of a science which, starting from premisses which it holds to be self-evident, succeeds in reaching a unified body of knowledge which covers one large sphere of being. The search for a single all-explaining principle seems to be a product of the equally mistaken desire to have proof of everything. If we cannot have proof of everything (so its advocates seem to say), since the ultimate premisses of any

n

(1tIP/3~I3TJKOS 7Sb2S. % lb. 33-5. In duos Aristotelis lib. Posl. An. Comm. 44.

I ICaTcl 4

l

Ch. 9.

DEMONSTRATIVE SCIENCE proof are obviously themselves not proved, let us at least have as few unproved principles as possible, and if possible only one. But there is really nothing more scandalous in a plurality of unproved premisses than in a single one.

.

In maintaining that proof must be from the proper principles of the science in question, Aristotle might seem to be contradicting his inclusion of the KOLIla. dg,wp.aTa among the premisses of a science. In ch. 10 he meets this difficulty by pointing outl that a science does not assume the KOLVa. d(u.vp.aTa in their generality.

but only in so far as they are true of the subjects of the science in question, this being all that is necessary for its purpose. Aristotle draws an interesting distinction between three types of error which may arise in the attempt at scientific proof.' In the first place, we may sin against the principle that our premisses must be true.' In trying to prove a geometrical proposition we may use premisses that are geometrical in the sense that their terms are geometrical terms, but ungeometrical in the sense that

they connect these terms incorrectly (e.g. by assuming that the angles of a triangle are not equal to two right angles). In the second place we may sin against the principle that our proof must be syllogistically correct.' In this case our premisses may be in the full sense geometrical, but we misuse them. In the third place we may sin against the principle that proof in any science must be drawn from premisses appropriate to the science. s In this case our premisses are not geometrical at all. Aristotle adds that error of the second kind is less likely to arise in mathematics than in dialectical reasoning, because any ambiguity in terms is easily detected when we have a figure to look at. 'Is every circle a figure? If we draw one, we see that this is so. Are the epic poems a circle?' Clearly not'-i.e. not in the literal sense in which every circle is a figure.

With this distinction of three types of error we may compare a later section of the Posterior Analytics, i. 16-18. Paralogismreasoning not in accordance with the rules of syllogism-is not there mentioned, probably because it has been fully considered in the Priar A nalytics. The first kind of error discussed in the present chapter, 0: be nov av-ru(Etp.£vwv OV,uOYLup.or (e.g. reasoning from incorrect geometrical assumptions). is described in chs. 16 and 17 under the title uyvoLa 1J KaTa. 3,d8€Gw. ignorance which I 4

76a37-b2. Cf. ib. IS.

4985

2 S

77bl6-33. Cf. ch. 7.

l 6

F

Cf. 7Ibl9-2l, 25-6. They were often called & K,),cAos.

66

INTRODUCTION involves a definite though mistaken attitude towards geometrical principles. The third kind discussed in the present chapter, & O.>J.~< 7£Xvy}<, that which in the absence of even iucorrect geometrical opinions attempts to prove a geometrical proposition from premisses borrowed from another science, is by implication called aYVOta 1} Ka:r' a7Toq,aatv,I and in ch. 18 such ignorance of a whole sphere of reality is described as due to the absence of one of

'e

the senses; and this is in accordance with Aristotle's general view

that the principles of all the sciences are derived by generalization from sensuous experience.:t

The chapter with which we are dealing' contaius one further important point, not made elsewhere. A science grows, says Aristotle, not by interpolation of new middle terms, but by one or other of two methods, both of them methods of extrapolation. If we already know that C is A because B is A and C is B we can (1) add the premiss' D is C' and thus get the new conclusion that D is A, or (2) we can add the premisses that D is A and E is D, and thus get the conclusion that E is A; Le. we may extrapolate either vertically or horizontally. The dictum that a science grows by extrapolation might at first sight seem to contradict what Aristotle says elsewhere,. that 'packing' or interpolation (",;',vwa,S') is the method of science; but there is no real contradiction. We have not science at all till interpolation has been completed, till we have replaced all provable premisses by premisses that need no proof. But once this has been done, extrapolation comes by its own and provides for the growth of the science. Aristotle has pointed out' three types of error which do not yield knowledge at all. In ch. 13 he passes to consider less gross falms of error, which lead to something that may in a loose sense

be called knowledge, but falls short of demonstratio potissima. When we commit them, we may reach knowledge that a fact is so,

but not knowledge of why it is so. In the first place, we may sin against the priuciple that our premisses should be immediate' If D is A because B is A, C is B, and DisC, and we reason 'C is A, Dis C, Therefore D is A', i.e. if 'C is A' is provable and we assume it without proof, we shall not know why D is A, nor iudeed in the strict sense know that D is A, but we shall at least have reached a true opinion, and have to some extent reached it by correct means. Secondly, we may sin agaiust the principle that our I

79b23.

5 In ch. 12.

2:

ii. 19.

1

i.

12.

6 78a2J--6, d. 7IbI9-2I, 26-9.

4

84b 33- 5.

DEMONSTRATIVE SCIENCE premisses must be YVWptp.wT£pa Kat 1rpOTEpa lea! at'TtCt TOU avP.'1TEpaap.o.TOS .· Suppose we reason: 'Heavenly bodies that do not

twinkle must be relatively near to us, Planets do not twinkle, Therefore planets must be relatively near to us.' Then our premisses are true, our reasoning is syllogistically correct, and we reach a true opinion about the state of the facts. But it is not the case that because the planets do not twinkle they are near to us, but that because they are near they do not twinkle. We have clearly not reached knowledge of the actual ground of the fact we state in our conclusion. In this case the converse of OUf major premiss is true, and we can therefore replace the defective syllogism by the syllogism 'Heavenly bodies thai are near to us do not twinkle, The planets are near to us, Therefore the planets do not twinkle', and then we shall know both the fact stated in our conclusion and the ground of its truth, and our reasoning will be truly scientific. But in other cases OUf major premiss may not be convertible; then we have an unscientific syllogism which cannot be immediately re·

placed by a scientific one. Thirdly, we may sin against the principle that our premisses must be true fj au"l,. This happens when the middle term 'is placed outside', i.e. occurs as predicate of both premisses. as when

we say' All breathing things are arUmals, No wall is an animal, Therefore no wall breathes'. Here we reason as if not being an animal were the cause of not breathing, and imply that being an animal is the cause of breathing; but plainly being an animal is not the callije of breathing, since not all animals breathe. The precise or adequate cause of breathing is possession of a lung; being an animal is an inadequate cause of breathing. and not being an animal a super-adequate cause of not breathing. In saying, in effect, 'Nothing that is not an animal breathes', we have used a premiss which, while true KaTa. 1TaV'ToS' and KaO' aliTo, is not true aUTO; for it is not precisely qua not being an animal, but qua not possessing a lung, that that which does not breathe does not breathe. Having thus pointed out in ch. '3 the fallure of a second-figure argument to give the true cause of an effect, Aristotle goes on in ch. '4 to point out that in general the first figure is the figure appropriate to science. He appeals to the fact that the sciences actually use this much more than the other figures, and he gives I 7S&26-bI3, cf. 7IbI~2, 29-72&5:z 78bI3-3I, cf. 73b25-74a3.

n

68

INTRODUCTION two reasons for its superiority: (1) that it alone can establish a

definition, since the second figure cannot prove an affirmative, nor the third a universal, conclusion; and (2) that even if we start

with a syllogism in the second or third figure, if its premi"es themselves need to be proved we must fall back on the first, since the affirmative premiss which a second-figure syllogism needs cannot be proved in the second figure, and the universal premiss which a third-figure syllogism needs cannot be proved in the third. Aristotle has in ch. 3 shown, and has repeatedly thereafter assumed, that there must be immediate premisses, neither needing

nor admitting of proof. He now' makes the·important point that among these there must be negative as well as affinnative premisses, and points out clearly the kind of terms that must occur in them. If either A or B is included in a wider class in which the other is not included, the proposition No B is A cannot be immediate. For (1) if A is included in C and B is not, No B is A can be established by the premisses All A is C, No B is C. (2) If B is included in D and A is not, No B is A can be established by the premisses No A is D, All B is D. (3) If A is included in C and B in D, No B is A can be established by the premisses All A is C, No B is C, or by the premisses No A is D, All B is D. The only type of immediate negative proposition which Aristotle seems to consider is that in which one category is excluded from another, as when one says 'No substance is a quality'. The types of proposition he does not consider are those whose terms are (I) two infimae spe~ies falling under the same proximate genus, (2) two alternative differentiae, or (3) two members of the same infima species. In the first case the differentia possessed by one and not by the other can be used as middle term to prove the exclusion of one species from the other. In the second case Aristotle would have to admit that the two differentiae exclude one another directly, just as two categories do. The third case would not interest him, because in the Posterior A nalytics he is concerned only with relations between universals. His consideration of the problem is incomplete, but both his insistence that there are immediate negative premisses and his insistence that propositions

in which one category is excluded from another are immediate are important pieces of logical doctrine. He now2. embarks on a discussion, much more elaborate than any that has preceded, of the question whether there are im, Ch. IS.

2;

Cbs.

15r-22.

DEMONSTRATIVE SCIENCE mediate premisses, not needing nor admitting of proof. A dialectician is satisfied if he can find two highly probable premisses of the form All B is A, All C is B; he then proceeds to infer that all Cis A. But a scientist must ask the question, 'Are All B is A, All C is B, really immediate propositions; am I not bound to look for a middle term between B and A, and one between C and B?' Aristotle divides the problem into three problems: (,) If there is a subject not predicable of anything, a predicate predicable of that subject~ and a predicate predicable of that predicate, is there an infinite chain of propositions in the upward direction, a chain in which that which is predicate in one proposition becomes subject in the next? (2) If there is a predicate of which nothing can be predicated, a subject of which it is predicable, and a subject of which that subject is predicable, is there an infinite chain in the downward direction, in which that which is subject in one proposition becomes predicate in the next? (3) Is there an infinite chain of middle terms between any two given terms?' He first' establishes that if questions (,) and (2) are to be answered in the negative, question (3) must also be so answered. This is obvious, because if between two terms in a chain leading down from a predicate, or in a chain leading up from a subject, there is ever an infinite number of middle terms, there is necessarily an infinite number of terms in the whole chain; this must be so, even if between some of the terms no middle term can be inserted. Next' Aristotle proves that if a chain having an affirmative conclusion is necessarily limited at both ends, a chain having a negative conclusion must also be limited at both ends. This follows from the fact that a negative can only be proved in one or other of the three figures: (a) No B is A, All Cis B, Therefore no C is A ; (b) All A is B, No Cis B, Therefore no C is A ; (c) No B is C (or Some B is not C) , All B is A, Therefore some A is not C. Now if in (a) we try to mediate the negative premiss, this will be by a prosyllogism: No D is A, All B is D, Therefore no B is A. Thus with each introduction of an intermediate negative premiss we introduce a new affirmative premiss; and therefore if the chain of affirmative premisses is limited, so is the chain of negative premisses; there must be a term of which A is directly deniable. A similar proof applies to cases (b) and (c). Aristotle now4 turns to his main thesis, that a chain of affirma:a Ch. 20. J Ch.21. 4 Ch. ~2.

INTRODUCTION tive premisses must be limited both in the upward and in the downward direction. He first offers arguments which he describes as dialectical,' but which we must not pass over, because they contain so much that is characteristic of his way of thinking. He starts' with the true observation that if definition is to be possible, . the elements in the definition of a thing must be limited in number. But clearly propositions other than definitions occur in scientific reasoning, and he therefore has to attempt a wider proof. He prefaces this by laying down a distinction between genuine predication and another kind of assertion. He discusses three types of assertion: (I) 'that big thing is a log', or 'that white thing is a log'; (2) 'that white thing is walking', or 'that musical thing is white'; (3) 'that log is big', or 'that log is white', or 'that man is walking'; and analyses them differently. (I) When we say 'that white thing is a log', we do not mean that 'white' is a subject of which being a log is an attribute, but that being white is an attribute of which that log is the subject. And (2) when we say 'that musical thing is white' we do not mean that 'musical' is a subject of which being white is an attribute, but that a certain man who has the attribute of being musical has also that of being white. In neither case do we think of our grammatical subject as being a metaphysical subject, or of our grammatical predicate as being a metaphysical attribute of that subject. But when (3) we say 'that log is white' we understand our subject to be a metaphysical subject underlying or possessing the attribute of being white. Aristotle recognizes oply assertions of type (3) as predications proper, and describes the others as predications Ka'Ta. aVfLfJ
DEMONSTRATIVE SCIENCE 71 metaphysical distinction of subject (or substrate) and attribute, or else, while aware of the difference, he is saying that only that is proper predication in which the metaphysical subject and attribute are made respectively logical subject and predicate; which would be just as serious an error as a confusion of the two distinctions would be. 1 It may be added that his mistake is made more easy by the Greek usage by which a phrase like 'T6 AEVKOV may stand either for 'the white thing' or for 'white colour'. For the speaker of a language in which 'TO AEUKOV £crn gvAov might mean 'white colour is a log', it becomes easy to suppose that the statement is an improper statement. It may be said too that while as a general logical doctrine what Aristotle says here is indefensible, there is some justification for his restricting predication as he does, in the present context. For the Posterior A nalytics is a study of scientific method, and he is justified in saying' that the sort of proposition which the sciences use is normally one in which an attribute is predicated of a substance. But to this it must be added that the mathematical sciences habitually assert propositions of which the subject is not a substance but an entity (such as a triangle) which is thought of as having a nature of its own in consequence of which it has the attribute that is predicated of it, as substances have attributes in consequence of their intrinsic nature. Aristotle is, in effect, recognizing this when he later describes the unit as ouO'{a a8ETO~ and the point as ovu{a OETOS'.l Among proper predications Aristotle proceeds' to distinguish definitions and partial defmitions (01T£p £KE'ivO ~ 01TEP EKE'iVO 'n OTJp.aivn) from those which assert of subjects UlJp.fJ43~K6Ta, among which he includes not only accidents but also attributes that are Ka8' atlTo in the second sense,s i.e. properties. In any case the chain of predication must be finite, since the categories. under one or other of which any predicate of a given subject must fall, are finite in number, and so are the attributes in any category,6 There is only one type of case, he points out, in which a thing is predicated of itself; viz. definition, iIi. which a thing designated by a name is identified with itself as described by a phrase. In every other case the predicate is an attribute assigned to a subject and not itself having the nature proper to a subject, i.e. not a I There is a penetrating criticism of Aristotle's doctrine in J. Cook Wilson, Statement and Inference, i. 159-66. :: 83-20-1, 34-5. 3 87a36. .. 83-24. 5 Cf. pp. 60-1. 6 83bI2-I7.

INTRODUCTION self-subsistent thing. Every chain of predication is terminated in the downward direction by such a thing, an individual substance. Upwards from this stretches a finite chain of essential attributes, terminating in a summum genus or category, and a finite chain of C1V!'f3
some of which are predicated of the subject strictly

n aVTo, just as being that subject, while others are predicated naV7"6 of some element in the nature of the subject (i.e. of some

species to which it belongs), and thus related KaO' a,lTo but not aUTO to the subject. Any chain of C1V!'f3
n

misses are.

Aristotle now' turns to the proof which he describes as analytical-analytical because it rests on a consideration not of predication in general, but of the two kinds of predication which in ch. 4 have been described as being proper to science, those in which we predicate of a subject some element in its definition, and those in which we predicate of a subject some attribute in whose definition the subject itself is included. If we had an infinite chain of predicates, each related to its subject in the second of these ways, we should have a predicate B including in its definition its subject A, a predicate C including in its definition its subject B, .. . and therefore the term at infinity would include in its definition an infinite number of elements. If, again, we had an infinite chain of predicates, each related to its subject in the first of the two ways, the original subject would include in its definition an infinite number of elements. Each of these two consequences Aristotle rejects as impossible, on the ground that, since any term is definable, no term can include an infinite number of elements in its essential nature. It would seem plausible to say that if two subjects have the 3 B4as.

DEMONSTRATIVE SCIENCE 73 same attribute, it must be by virtue of some other attribute which they have in common. But Aristotle is quick to point out' that this would involve an infinite chain of predication. If, when C and D both have the attribute A, this must be because they both have the attribute B, it will be equally true that if they both have the attribute B, this must be because they both have a further attribute in common, and so ad infinitum. The true 080S' bTl 'TaS' apxas is one that tenninates not, as Plato supposed, in a single o.pxJJ dVV1T68~TOS', but in a variety of immediate propositions, some affirmative, some negative. In seeking the ' ground of an affirmative proposition we proceed by packing the interval between our minor term and onr major, never inserting a middle term wider than our major. B is A because B is C, C is D ... y is Z, Z is A, the ultimate premisses being known not by reasoning but by intuition (voas). If the proposition we seek to prove is a ?legative one, we may proceed in either of three ways. (I) Suppose that no B is A because no C is A and all B is C; then if we want to prove that no C is A, we may do so by recognizing that no D is A and all C is D; and so on. We never take in a middle term which includes our major term A. (2) Suppose that no E is D because all D is C and no E is C ; then if we want to prove that no E is C, we may do so by recognizing that all C is F and no E is F; and so on. We never take in a middle term included within our minor, E. (3) Suppose that no E is D because no D is C and all E is C; then if we want to prove that no D is C, we may do so by recognizing that no C is F and all D is F; and so on. We never take a middle term that either includes our major, or is included in our minor.

From this consideration of the necessity for immediate premisses, Aristotle passes' to compare three pairs of types of proof in respect of 'goodness', i.e. of intellectual satisfactoriness. Is universal or particular proof the better? Is affinnative or negative proof the better ? Is ostensive proof or reductio ad impossibile the better? On the first question, he first' states various rlialectical arguments purporting to show particular proof (i.e. proof proceeding from narrower premisses) to be better than universal, then4 refutes these, and offers s dialectical arguments in favour of the opposite view, and finally" offers what he considers the most conclusive arguments in support of it, viz. (I) that if we know a z Cbs. 24-6. .5

lb.

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INTRODUCTION 74 . universal proposition such as 'Every triangle has its angles equal to two right angles', we know potentially the narrower proposition 'Every isosceles triangle has its angles equal to two right angles', while the converse is not true; and (2) that a universal proposition is apprehended by pure v6'1"'" while in approaching a particularization of it we have entered on a path which terminates in mere sensuous perception. His consideration of the merits of affinnative as compared with negative proof, I and of ostensive proof as compared with reductio,' is of less general interest.

Turning' from the comparison of particular proofs to that of whole sciences, Aristotle points out that one science is more precise than another, more completely satisfactory to the intellect, if it fulfils anyone of three conditions. In the first place, a science which knows both facts and the reasons for them is superior to a so-called science which is a mere collection of unexplained facts. In the second place; among genuine sciences a pure science, one that deals with abstract entities, is superior to an applied science, one that deals with those entities embodied in some kind of 'matter'; pure arithmetic, for instance, is superior to the applica· tion of arithmetic to the study of vibrating strings. In the third place, among pure sciences one that deals with simple entities is superior to one that deals with complex entities; arithmetic, dealing with units, which are entities without position, is superior to geometry, dealing with points, which are entities with position. It is noteworthy that, while Aristotle conceives of demonstration in the strict sense as proceeding from premisses that are necessarily true to conclusions that are necessarily true, he recognizes demonstration (in a less strict sense, of course) as capable of proceeding from premisses for the most part true to similar CODc1usions;4 That which can never be an object of scientific knowledge is a mere chance conjunction between a subject and a predicate. And, continuing in the same strain,' he points out that to grasp an individual fact by sense-perception is never to know it scientifically. Even if we could see the triangle to have its angles equal to two right angles, we should still have to look for a demonstration to show why this is so. Even if we were on the moon and could see the earth thrusting itself between the moon and the sun, we should still have to seek the cause of lunar eclipse. The function of perception is not to give us scientific knowledge but to rouse the curiosity which only demonstration I

Ch.25.

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Ch.26.

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Ch. 27.

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Ch. 30.

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Ch.31.

DEMONSTRATIVE SCIENCE 75 can satisfy. At the same time some of our problems are due to lack of sense-perception; for there are cases in which if we perceived a certain fact we should as an immediate consequence. without further inquiry, recognize that and why it must be so in any similar case. To quickness in divining the cause of a· fact, as

an immediate result of perceiving the fact, Aristotle assigns the name of arxlvota. t

VII THE SECOND BOOK OF THE POSTERIOR ANALYTICS THE second book of the Posterior A nalytics bears every appearance of having been originally a separate work. It begins abruptly, with no attempt to link it on to what has gone before; even the absence of a connective particle in the first sentence is significant.z

Further, there is one fact which suggests that the second book is a good deal later than the first. In the first book allusions to mathematics are very frequent, and it might almost be said that Aristotle identifies science with mathematics, as we might expect a student of the Academy to do; the only traces of a scientific interest going beyond mathematics and the semi-mathematical sciences of astronomy, mechanics, optics, and harmonics are the very cursory allusions to physics and to medical science in 77-41. b41 - 78'5, 88'14-17, bu. In the second book allusions to mathe-

matics are relatively much fewer, and references to physical and biological problems much more numerous: d. the references to the causes of thunder' and of the rising of the Nile,' to the definition of ice,' to the properties of different species of animals' and to analogical parts of animals,' to the causes of deciduousness· and of long life,' and to medical problems." The subject of the first book has been demonstration; the main subject of the second book, with which the first ten chapters are concerned, is definition. Aristotle begins by distinguishing four topics of scientific inquiry, TO on, TO 8mL, *"' 100L, Tt '(TTL. The difference between 'TO OTt and 100t turns on the difference between the copulative and the existential use of 'is'; the two

£,

• Ch·34· Apart from the Metaphysics, the only other clear cases in Aristotle of books (after the first) beginning without such a particle are Phys. 7, Pol. 3, 4. 1 93822-3, b7- 12, 94 8 3-9, b32 - 4 . .. C)8:13 I -4. 5 95116-21. (, 9883-19. 7 lb. 20--3. 8 lb. 36-bI6, b33-8, 99:123-9. I) 99bS-8. 10 94b8-2I, 97b26- 7. 2

INTRODUCTION questions are respectively of the form 'Is A B?' and of the form 'Does A exist?' If we have established that A is B, we go on to ask why it is so ; if we have established that A exists, we go on to ask what it is. Aristotle proceeds in ch. 2 to say that to ask whether A is B, or whether A exists, is to ask whether there is a middle term to account for A's being B, or for A's existing, and that to ask why A is B, or what A is, is to ask what this middle term is. But there are reasons for supposing that this is an over-statement of Aristotle's meaning. He never, so far as I know, makes the question whether a certain substance exists tum on the question whether there is a middle tenn to account for its existence, nor the question what a certain substance is tum on the question what that middle tenn is; and it would be strange if he did so. The question whether a certain substance exists is to be decided simply by observation; the question what it is is to be answered by a definition stating simply the genus to which the substance belongs, and the differentia or differentiae that distinguish it from other species of the genus. It is really of attributes that Aristotle is speaking when he says that to ask whether they exist is to ask whether there is a cause to account for them, and that to ask what they are is to ask what that cause is. And when we are considering an attribute, the question whether it exists is identified with the question whether this, that, or the other substance possesses it, and the question what it is is identified with the question why this, that, or the other substance possesses it. 'What is eclipse? Deprivation of light from the moon by the interposition of the earth. Why does eclipse occur, or why does the moon suffer eclipse? Because its light fails through the earth's blocking it off." In ch. 3 Aristotle passes to pose certain questions regarding the relation between demonstration and definition. How is a definition proved? How is the method of proof to be put into syllogistic form? What is definition? What things can be defined? Can the same thing be known, in the same respect, by definition and by demonstration? In a passage which is clearly only dialectical' he argues that not everything that can be demonstrated can be defined, that not everything that can be defined can be demonstrated, and, indeed, that nothing can be both demonstrated and defined. Dialectical arguments directed against various possible methods of attempting to prove a definition, and tending to

SECOND BOOK OF POSTERIOR ANALYTICS 77 show the complete impossibility of definition, are offered in chs. 4-'1. In ch. 8 Aristotle turns to examining critically these dialectical arguments. As a clue to the discovery of the true method of definition, he adopts the thesis already laid down,' that to know the cause of a substance's possessing an attribute is to know the essence of the attribute. Suppose that we know that a certain event. say, eclipse, exists. We may know this merely KdTa. uvp.{3€f3"rJKO< (e.g. by hearsay) without knowing anything of what is meant by the word. and in that case we have not even a starting-

point for definition. But suppose we have some knowledge of the nature of the event, e.g. that eclipse is a loss of light. Then to ask whether the moon suffers eclipse is to ask whether a cause capable of producing it (e.g. interposition of the earth between the moon and the sun) exists. If, starting with a subject C and an attribute (or event) A, we can establish a connexion between C and A by a series of intermediate propositions such as 'that which has the attribute B, necessarily has the attribute A, that which has the attribute B, necessarily has the attribute B, . . . that which has the attribute B. necessarily has the attribute B._" C necessarily has the attribute B.', then we know both that and why C has the attribute A. If at some point we fail to reach immediacy, e.g. if we have to be content with saying 'C actually (not necessarily) has the attribute B,;, we know that C has the attribute A but not why it has it. Aristotle illustrates the latter situation by this example: A heavenly body which produces no shadow, though there is nothing between us and it to account for this, must be in eclipse, The moon is thus failing to produce a shadow, Therefore the moon is in eclipse. Here the middle term by the use of which we infer the existence of eclipse plainly cannot be the cause of eclipse, being instead a necessary consequence of it; it does not help us to explain why the moon is in eclipse, and therefore does not help us to know what eclipse is. But the discovery, by this means, that eclipse exists may set us on inquiring what cause does exist that would explain the existence of eclipse, whether it is the interposition of an opaque body between the moon and its source of light, or a divergence of the moon from its usual path, or the extinction of fire in it. If we find such a cause to exist, it becomes the definition of eclipse; eclipse is the interposition of the earth between the moon and the sun. And if we can in time discover the presence of a cause which J

90-14-23.

INTRODUCTION will account for the earth's coming between the moon and the sun, that will serve as a further, even more satisfactory. definition

of eclipse. I We never get a syllogism having as its conclusion 'eclipse is so-and-so', but we get a sorites by which it becomes clear what eclipse is-a sorites of the form 'What has B. suffers eclipse, What has B. has B• ... What has Bn has B n_I , The moon has B n , Therefore the moon suffers eclipse'. Our final definition would then be 'eclipse is loss of light by the moon in consequence of the sequence of attributes B n , B n_., . . . B., B1 '. This type of definition can of course be got only when A is an attribute that has a cause or series of causes. But there are also things that have no cause other than themselves, and of these we must simply assume, or make known by some other means (e.g. by pointing to an example) both that they exist and what they are. This is what every science does with regard to its primary . subjects, e.g. arithmetic with regard to the unit.' There are thus three types of definition:' (1) A verbal definition stating the nature of an attribute or event by naming its generic nature and the substance in which it occurs, e.g. 'eclipse is a loss of light by a heavenly body'-a definition which sets us on to search for a causal definition of the thing in question. (2) A causal definition of such a thing, e.g. 'eclipse of the moon is a deprivation of light from the moon by the interposition of the earth between the moon and the sun'. Such a definition is 'a sort of demonstration of the essence, differing in form from the demonstration',. I.e., the definition packs into a phrase the substance of the demonstration 'What has an opaque body interposed hetween it and its sou;ce of light is eclipsed. The moon has an opaque body so 'interposed, Therefore the moon suffers eclipse: A definition of type (1), on the other hand, contains a restatement only of the conclusion of the demonstration. (g) A definition of a term that needs no mediation, i.e. of one of the primary subjects of a science.

Aristotle now passes from the subject of definition to consider a number of special questions relating to demonstration. s It is unnecessary to enter here into the difficulties of ch. II, one of the most difficult chapters in the whole of Aristotle. He introduces here a list of types of a17ia. which differs from. his usual list by containing, in addition to the formal, the efficient, and the final I

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SECOND BOOK OF POSTERIOR ANALYTICS 79 cause, not the material cause but ore) 'Tlvwv OV'TWV Q.VclYInJ 'TO;;" Elva~. That this is not another name for the material cause is shown by two things. For one thing, the material cause could not be so described; for Aristotle frequently insists that the material cause does not necessitate its effect, but is merely a necessary precondition of it. And secondly, the example given is as remote as possible from the typical examples of the material cause which he gives elsewhere. How, then, is this departure from his usual list of causes to be explained? We may conjecture that it was due to Aristotle's recognition of the difference between the type 01 explanation that is appropriate in the writing of history or the pursuit of natural science and that which is appropriate in mathematics. In history and in natural science we are attempting to explain events, and an event is to be explained (in Aristotle's view) by reference either to an event that precedes it (an efficient cause) or to one that follows it (a final cause). In mathematics we are dealing with eternal attributes of eternal subjects, and neither an efficient nor a final cause is to be looked for, but only another eternal attribute of the same eternal subject, some attribute the possession of which by the subject can be more directly apprehended than its possession of the attribute to be explained. This eternal ground of an eternal consequent is thus introduced here instead of the material cause which we find elsewhere in Aristotle's account of causation. A reference to the material cause would indeed be out of place here; for the analysis of the individual thing into matter and form is a purely metaphysical one of which logic need take no account, and in fact the word ~>''1 and that for which it stands are entirely absent from the Organon. It is not easy to see how the efficient cause, the final cause, and the eternal ground are related, in Aristotle's thought, to the formal cause. But we have already found him stating the definition or formal cause of eclipse to be 'deprivation of light from the moon by the interposition of the earth', where the efficient cause becomes an element in the formal cause and is by an overstatement said to be the formal cause.' And similarly here he identifies the formal cause of the rightness of the angle in the semicircle. with its being equal to the half of two right angles, i.e. with the ground on which it is inferred" And again, where an event is to be explained by a final cause, he would no doubt be prepared to identify the formal cause of the event with its final cause. We 1

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INTRODUCTION have here in fact the doctrine that is briefly adumbrated in Metaphysics I04IaZ7 - 3o--avEpov 'Totvvv 07£ '7'JTEi 'TO arnov' 'Toiho 8' Ecrrt 'TO 'Tl -ryv Elvat , W~ El1TE'iV AO)'tKWS'. 8 E'fr' t.vtwv p.£v Eun TlvOfi EVEKa, olov wwS' al'TtoV

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EKlVT}UE trpC¥rov'

The doctrine is that the cau'se of the inherence

of a ,,0.90s in a substratum (e.g. of noise in clouds) or of a quality in certain materials (e.g. of the shape characteristic of a house in bricks and timber) is always-to state the matter abstractly (AOYLKws)- the 'Tl1}v Elva, or definition of the union of substratum and 1Ta.f)OS', or of materials and shape. But in some cases this definition expresses the final cause-e.g. a house is defined as a shelter for living things and goods;' in other cases the definition expresses the efficient cause--e.g. thunder is a noise in clouds produced by the quenching of fire.' In yet other cases, he here adds, the formal cause expresses the eternal ground of an eternal attribute. In other words, the fannal cause is not a distinct cause over and above the final or efficient cause or the eternal ground, but is one of these when considered as forming the definition of the thing in question. The one type of cause that can never be identical with the formal cause is the material, and hence the material cause is silently omitted from the present passage. Aristotle goes on in ch. 12 to point out a difficulty which arises with regard to efficient causation. Here, he maintains, we can infer from the fact that an event has occurred that its cause must have occurred previously, but we cannot infer from the fact that a cause has occurred that its effect must have occurred. For between an efficient cause and its effect there is always an interval of time, and within that interval it would not be true to say that the effect has occurred. Similarly we cannot infer that since a certain efficient cause has taken place, its effect will take place. For it does not take place in the interval, and we can neither say how long the interval will last, nor even whether it will ever end. Aristotle is clearly conscious of the difficulty which everyone must feel if he asks the question why a cause precedes its effect; for it is hard to see how a mere lapse of time can be necessary for the occurrence of an event when the other conditions are already present; this is a mystery which has never been explained. Aristotle confesses his sense of the mystery when he says E"" UK€7TTEOV S~ -rl 'TO UVllEXOV WO"7'E P.E'To. 'TO yeyov£va, 'TO ylvEu8a, irrrapx€w EV 'ToiS' 7rpayp.auw. 3 This much" he adds, is clear, that the cam8 I Met. 1043aI6,33. Z An. Post. 93b8, 94 5. 3 9Sbl-S.

SECOND BOOK OF POSTERIOR ANALYTICS 8I pletion of one process, being momentary, cannot be contiguous to the completion of another, which is also momentary, any more than one point can be contiguous to another, nor one continuous process contiguous to the completion of another, any more than

a line can be contiguous to a point. For the fuller treatment of this subject he refers to the Physics, where it is in fact treated much more fully.' It is reasonable to infer that this chapter either was written after that .part of the Physics, or at least belongs to about the same period of Aristotle's life. It being impossible to infer from the occurrence of a past event that a later past event has occurred, Aristotle concludes that we can only infer that an earlier past event must have occurred; and similarly, it being impossible to infer that if a future event occurs a later future event must occur also, we can only infer that if a future event is to occur an earlier future event must occur. In either case the implied assumption is that for the occurrence of an event there are needed both a set of particular circumstances and a lapse of time whose length we cannot determine, so that we can reason from 't he occurrence of an event to the previous occurrence of its particular conditions but not vice versa. In ch. 13 Aristotle returns to the subject of definition. He has

stated his theory of definition; he now gives practical advice as to how definitions are to be arrived at. But here he is concerned

not with the definition of events, like eclipse or thunder, but with the definition of the primary subjects of a science. If we wish to define the number three, for instance, we collect the various attributes each of which is applicable to all sets of three and to certain other things as well, but all of which together belong only to sets of three. Three is (I) a number, (2) odd, (3) prime, (4) not formed by the addition of other numbers.' It is noticeable that Aristotle does not follow the prescription laid down in the Metaphysics,' that each differentia must be a further differentiation of the previous differentia, SO that a definition is complete when the genus and the final differentia have been stated; and in fact the number two satisfies conditions (3) and (4) but not condition (2). The present passage may be compared with that in the De Partibus' in which he rejects, so far as biology is concerned, the Platonic method of definition by successive dichotomies, as failing to correspond to the complexity of nature. J

In Bk. 6.

J I038~2I. 1985

2

For the Greeks, one was not a number but an cipx;' &p,8p.ofi. .. i. 2- 3. G

82

INTRODUCTION This passage is, however, followed by onel in which he assumes that each of the differentiae included in a definition will be a differentiation of the previous differentia. .The latter passage must almost certainly date back to an earlier period in which Aristotle was still accepting the Platonic method of definition. He concludes with a passage in which he points out the danger of assuming that a single term necessarily stands for a single species, and recommends that, since wider terms are more likely to be ambiguous than narrower ones, we should move cautiously up through the definition of narrower terms to that of wider. Aristotle assumes' that. generally speaking. ordinary language will provide us with names for the genera and species which form the subjects of a science. When we have established the existence of such a chain of gen~ra and species, the right order (he continues) of attacking the problem of discovering the properties of the genus and of its species is to discover first the properties of the whole genus, for then we shall know both that and why the species possess these properties, and need only consider what peculiar properties they have and why they have them. But we must be prepared to find that sometimes common language fails to provide us with names for the species. Greek has no name for the class of horned animals, but we must be prepared to find that they form a real class, whose possession of certain other attributes depends on their having homB. Or again we may find that the possession of certain common attributes by different species of animals depends on their having parts which without being the same have an analogous character, as the spine in fishes and the pounce in squids are analogous to bone in other animals. We may find that problems apparently different find their solution in a single middle term, e.g. in d.VTL7TEp{a'Ta(n~, reciprocal replacement, which in fact Aristotle uses as the explanation not only of different problems but of problems in different sciences. Or again we may find that the solution of one problem gives us part of the solution of another, by providing us with one of two or more middle terms. 3 Aristotle now' turns to the problem of plurality of causes. We may find a complete coincidence between two attributes, e.g. (in trees) the possession of broad leaves and deciduousness, or between two events, e.g. the interposition of the earth between the sun and the moon and lunar eclipse, and in such a case the presence of r

96bI5-97b6.

2

Ch. 14.

3'

Ch. 15.

.. Ch. 16.

SECOND BOOK OF POSTERIOR ANALYTICS 83 either attribute or event may be inferred from that of the otherthough, since two things cannot be causes of one another, only one of the two inferences will explain the fact it establishes. But may there not be cases of the following type-such that attribute A belongs to D because of its possession of attribute B, and to E because of its possession of attribute C, A being directly and separately entailed both by B and by C? Then, while the possession of B or of C entails the possession of A, the possession of A will not presuppose the possession of B nor the possession of C, but only the possession of either B or C. Or must there be for each type of phenomenon a single commensurate subject, all of which and nothing but which suffers that phenomenon, and a single commensurate middle term, which must be present wherever the phenomenon is present? Aristotle offers his solution in an admirable chapter' in which he does justice both to the general principle that a single effect must have a single cause, and of the facts that seem to point to a plurality of causes. He distinguishes various cases in which a plurality of things have or seem to have an attribute in cornmon. At one extreme is the case in which there is not really a single attribute but different attributes are called by the same name; we must not look for a common cause of similarity between colours and between figures, for similarity in the one case is sensible similarity and in the other is proportionality of sides and equality of angles. Next there is the case in which the SUbjects, and again the attributes, are analogically the same; i.e. in which a certain attribute is to a certain subject as a second attribute is to a second

subject. In this case the two middle terms are also analogically related. Thirdly there is the case in which the two subjects fall within a single genus. Suppose we ask, for instance, why, if A is to B as C is to D, A must be to C as B is to D, alike when the terms are lines and when they are numbers; we may say that the proportion between lines is convertible because of the nature of lines and that between numbers because of the nature of numbers. thus assigning different causes. But we can also say that in both cases the proportion is convertible because in both cases we have a proportion between quantities, and then we are assiguing an identical cause. The attribute, the possession of which is to be explained, is always wider than each of the subjects that possess it, but commensurate with all of them together, and so is the I

Ch. 17.

INTRODUCTION middle term. When subjects of more than one species have a common attribute there is always a middle term next to each subject and different for each subject, and a middle term next to the attribute and the same for all the subjects, being in fact the definition of the attribute. The deciduousness of the various deciduous trees has one common cause, the congelation of the sap, but this is mediated to the different kinds of tree by different proximate causes. Any given attribute will have ODe immediate cause A ; but things of the class D may have A because they have B, and things of the class E may have it because they have e; because of the difference of nature between class D and class E they may require different causes of their possession of A and of the consequent attribute. But things of the same species, having no essential difference of nature, require no such differing causes of their possession of A and of its consequent. Leaving aside the question of the possession of a common attribute by different species, and considering only the possession of an attribute by a single species, we may say that when species D possesses an attribute e, which entails B, which entails A, e is the cause of D's having B, and therefore of its having A, that B is the cause of e's entailing A, and that B's own nature is the cause of its entailing A.' Aristotle now' comes to his final problem; how do we come to know the first principles, which as we have seen cannot be known by demonstration, being presupposed by it? The questions he propounds are· (I) whether they are objects of ""crnip.'1 or of some other state of mind, and (.) whether the knowledge of them is acquired or inborn; and he attacks the second question first. It would be strange if we had had from birth such a state of mind, superior to scientific knowledge (of which it is the foundation), without knowing that we had it; and it is equally difficult to see how we could have acquired such a state if we had no knowledge to start with. We must therefore have from birth some faculty of apprehension, but not one superior either to knowledge by demonstration or to knowledge of first principles. Now in fact all animals have in sense-perception an innate discriminative faculty. In some, no awareness of the object survives the moment of perception; in others such awareness persists, in the form of memory; and of those that have memory, some as a result of 1

Ch. 18.

Z

Ch. 19.

SECOND BOOK OF POSTERIOR ANALYTICS

85

repeated memories of the same object acquire (experience', From

experience-from the 'resting' in the mind of the universal, the identical element present in a number of similar objects but distinct from them-art and science take their origin, art concerned with bringing things into being, and science with that which is. Thus the apprehension of universals neither is present from the start nor comes from any state superior to itself; it springs from sense--perception. In a famous simile I Aristotle likens the passage from individual objects to universals, and to wider universals, to the rallying of a routed army by one stout fighter who gradually gathers to him others. The process is made possible by the fact that while the object of perception is always an individual, it is the universal in the individual that is perceived, 'man, not the man Callias·. 2

The discussion started from the question how we come to know the universal propositions which lie at the basis of science: it has diverged to the question how we come to apprehend universal

concepts like 'animal'. Aristotle now returns to his main theme by saying that just as we reach universal concepts by induction from sense-perception, so we come to know the first principles of science. Just as the perception of one man, while we still remember perceiving another, leads to the grasping o~ the universal 'man', so by perceiving that this thing, that thing, and the other thing are never white and black in the same part of themselves, we come to grasp the law of contradiction; and so with the other fTPW'TQ. of science.

Aristotle now' turns to the other main question propounded in the chapter; what is the state of mind by which we grasp the "pw7a? The only states of mind that are infallible are scientific knowledge and intuitive reason; the first principles of science must be more completely apprehended than the conclusions from them, and intuitive reason is the only state of 'm ind that is superior to scientific knowledge . . Therefore it must be intuitive reason that grasps the first principles. This is the faculty which is the starting-point of knowledge, and it is it that grasps the startingpoint of the knowable, while the combination of it and scientific knowledge (the combination which is in the Ethics called "o.pta) grasps the whole of the knowable.' This chapter is concerned only with the question how we come I 100-12- 13.

z lb. I7-bI.

" With this chapter should be compared Met. A.

3

I.

qb

s.

86

INTRODUCTION to know the first principles on which science is based. Aristotle's answer does justice both to the part played by sense-perception and to that played by intuitive reason. Sense-perception supplies the particular infonnation without which general principles could never be reached: but it does not explain our reaching them; for that a distinct capacity possessed by man alone among the animals is needed, the power of intuitive induction which sees the general principle of which the particular fact is but one exemplification. Aristotle is thus neither an empiricist nor a rationalist, but recognizes that sense and intellect are mutually complementary. The same balance is found in the account which he gives of the way in which science proceeds from its first principles to its conclusions. Sense-perception, he says, supplies us with the facts to be explained, and without it science could not even make a beginning.' Its problem is that of bridging the gulf between the particular facts of which sense-perception informs us and the general principles by which they are to be explained. He is often charged with having proceeded too much a priori in his pursuit of natural science, and he cannot be acquitted of the charge, but his fault lay not in holding wrong general views on the subject, but in a failure to apply correctly his own principles. His theory is that it is the business of sense-perception to supply science with its data; the O'rt must be known before we begin the search for the 8wn,' and d,,68,,[tS is thought of by him not as the arriving by reasoning at knowledge of particular facts, but as the explanation by reasoning of facts already known by senseperception. This is no doubt the true theory. But he failed in two respects, as anyone in the infancy of science was bound to fail. The 'facts' with which he started were not always genuine facts; they were often unjustifiable though natural interpretations of the facts which our senses really give us. And, on the other hand, some of the first principles on which he relied as being selfevident were not really so. His physics and his biology yield many examples of both these errors. Yet he must be given the credit for having at least seen the general position in its true light-that it is the role of science to wait on experience for the facts to be explained, and use reason as the faculty which can explain them. Of the further function of reason-that of reasoning from facts known by experience to those not yet experienced-he has little conception. z

&)bZ9-3 I •

THE TEXT OF THE ANALYTICS VIII THE TEXT OF THE AN ALYTICS FOR the purpose of establishing the text I have chosen the five oldest of the MSS. cited by Waitz. These are (I) Urbinas 35 (Bekker's and Waitz's A), of the ninth or early tenth century; (2) Marcianus 201 (Bekker's and Waitz's B), written in 955; (3) Coislinianus 330 (Bekker's and Waitz's C), of the eleventh century; (4) Laurentianus 72.5 (Waitz's d), of the eleventh century; (5) Ambrosianus 490 (formerly L 93) (Waitz's n), of the ninth century. Where we have so unusual an array of old MSS., it is unlikely that very much would be gained by exploring the vast field of later MSS. We may look, in the first place, at the relative frequency of agreements between the readings of these five MSS. There are two long passages for which the original hand of all the five is extant, and I have made a count of the agreements in these passages, 31218- 49az6 and

~b4-82a2,

which together amount to

between a third and a half of the whole of the Analytics. The figures for the groupings of consentient readings are as follows: ABCd 399, ABCn 173, ABdn 199, ACdn 78, BCdn 70. ABC 18, ABd 68, ABn '9, ACd '3, ACn 6, Adn 12, BCd 4, BCn '7, Bdn II, Cdn 19. AB 20, AC 7, Ad 26, An 5, BC 8, Bd 5, Bn '7, Cd 14, Cn 60, dn 14. A alone 78, B alone 88, C alone 235, d alone 185, n alone 416. Summing the agreements of MSS. two at a time we get: ~~,~~M~hW,OC~M~,&~~m,

Cn 423, dn 403. We notice first that the agreements of four MSS. are much more numerous than the agreements of three only, or of two only. Either the variations are due to casual errors in single MSS., or

there is a family of four MSS. and a family of only one, or there is a combination of these two circumstances. The fact that all the groups of four are large, compared with the groups of three or of two, shows that casual errors in single MSS. playa large part in the situation. But when we look more closely at the groups of four, we find that one group, ABCd, is twice as large as that which is nearest to it in size, and more than five times as large as the smallest. Either, then, n is particularly careless, or it represents a separate tradition, or both these things are true. Now individual variations in one MS. from the others may. when they are wrong.

INTRODUCTION 88 imply either carelessness in the writing of the MS. or careful following of a different tradition. But when they are right this must be due to the following of a different, and a right, tradition. We must 'therefore look next to see how our MSS. compare in respect of correctness, in passages where the true reading can be established on grounds of sense or grammar or of Aristotelian usage. Within the two long passages already mentioned I have found B to have the right reading 40' times, A 389 times,C 363 times, n 339 times, d 337 times; the earlier editors Bekker and Waitz are evidently justified in considering A and B the most reliable MSS. Bekker gives the preference to A; Waitz gives it to B, and his opinion is endorsed by Strache in his edition of the Topics . At the same time it is noteworthy that the other three MSS. fall so little behind A and B in respect of accuracy. The value of a MS., however, does not depend only on the number of times in which it gives an evidently correct reading. but also on the number of times it is alone in doing so. I have made a note of the passages, throughout the Analytics, in which a certainly (or almost certainly) correct reading is found in one MS. only (ignoring the very numemus insertions by later hands). The results are as follows: A alone has the right reading in 92'32, 94'7, 95'35, '00"; B alone in 3I332, 441 34-5, 4Sb3, 46bz8, 47a2l, 59126, 65129. 67118, 70b " 75 b34, 87 b38 , 94b30, 35, 99'33; C alone in 28b31, '29b28, 30b31, 32'5, 47'14, 5,'8, 52b8, 19, 54b35, 56b29, 65 b3, 66'14, 67 b37, 69b20, 73", 33, 74'8, 81"; d alone in 2t'9. 33125. 48bI2, 49b36. 70b32. 72%,88127.94-322, b16; n ala'ne in 34138, bI8. 31. 35aI3. 39bzz, 44a4. 6, 46139, 4712, II. 19. 49129. 52ar. 54a37. 57bz4, 58a25, b33 , 62 bro, z3, 64b30' 73120, 74122. 38, 7SbI9. 28, 77br, 78b2- 3. 31, 35. 8014, 8z br, 10, 841J9. 32 , b33 • 85'5. 26, 28, b8, IS. 86a20, 37, 39. b 17 . 87118, 88a7. 10. 15, 20, ZI. bII , 16, 89127, 90119, 24, 27, bI . 91b3, 921II, 27. 34, b27 , 93131, 35. 36, bu , 13,31,36. 95a16. b6, 25.

Util

g6'15, 98'II, '2, 26, 32, 38 (specially important because n comes to our aid where there is a lacuna in A. B, and d, and the original hand of C is lacking), b20, '3, 38, 99'5, 25, bI I, '9. Thus, while there are only four passages in which A alone has the true reading. there are fourteen in which B has it. eighteen in which C has it, nine in which d has it, and no fewer than eighty& ~!1,e in which n has it. It follows, then, that the very numerous

~%Ei'8~~i~ ~u,""'\'\;""',

;::: ,\

__

12, 24. 30, 37,

It!' .."."

L. ...

.

THE TEXT OF THE ANALYTICS 89 variations of n from the other MSS. are not always due to carelessness on the part of the writer of the MS. or of one of its ancestors, but are often the result of its following a different, and a right, tradition; we have clear evidence of there being two families of MSS. represented by ABCd and by n. Next, we note that A and B agree a good deal more often than any other pair of MSS., and we may infer that they are the most faithful representatives of their .family. B is both more often right, and more often alone in being right. than A; and n agrees more often with B than with any of the other three MSS.; we may therefore infer that B is the best representative of its family. B and n, then, are the most important MSS. It follows, too, that any agreement of n with any of the other MSS. is prima-facie evidence of the correctness of the reading in which they agree. Much new light has recently been cast on the text of the Prior Analytics by the researches of Mr. L. Minio into two ancient Syriac translations. The older of these (which he denotes by the symbol II) is a translation of i. 1-7, not improbably by Proba, a writer of the middle of the fifth century; it is extant in eight MSS., of which the oldest belongs to the eighth or ninth century. The other (denoted by F) is a complete translation by George, Bishop of the Arabs, and belongs to the end of the seventh or the beginning of the eighth century; it is found in one MS. of the eighth or ninth century. Minio's critical apparatus shows only the divergences of rand II from the text of Waitz, and since Waitz's text is based mainly on A and B, the comparative rarity of the appearance of A and B in his apparatus does not prove that the Syriac translations agree less with them than with the other MSS.; it is quite likely that a complete apparatus would show that they agree more closely with these two Greek MSS. than with any others. Further, the translation II covers ouly a part of the Prior A nalytics for which we have not the original hand of n, hut a text in a later hand. What Minio's collation does show, however, is two things: (1) the large measure of agreement of both translations with C, (2) the large measure of their agreement with the late Greek MS. m. From the point at which the original hand of n begins (31'18), the most striking feature of Minio's collation is the very large numher of agreements of r with n. Its correspondences with C, though not so numerous as those with n, are fairly numerous. Minio ranks the MSS. ABCmn in the order nBCAm as regards

INTRODUCTION their affinity, and with this I agree, except that it would seem that if Waitz's citations of m were complete, it might he seen to have more affinity with r than any of the other MSS. The readings of r and II, when they do not agree with any of the best Greek MSS., do not seem to me very important; in many cases the apparent divergences may be due simply to a certain freedom in translation, or to errors in translation. For · this reason, and to avoid overburdening the apparatus, I have abstained from recording such readings. In passages in which no Greek MS. affords a tenable reading, I have not found that r or II comes to our aid. Again, I have refrained from recording the readings of r and II where Minio expresses some doubt about them. But where there is no doubt about their readings, and where these agree with any of the chief Greek MSS., I have recorded them, as providing evidence that the reading of the Greek MS. goes back to a period some centuries earlier than itself. it is particularly interesting to note that n, which on its own merits I had come to consider as representing a good independent tradition, is very often supported by the evidence of r. I may add Minio's summary of the position as regards the Categories, which he has very carefully studied: '(a) The Greek copies current 'in the Vth to VIIth centuries' agreed between themselves and with the later Greek tradition on most essential features; '(b) they varied hetween themselves in many details; most of these old variants are preserved also in one or more later Greek MSS, and a large proportion of the variants which differentiate these later copies go hack to the older texts; '(c) Wait,'s choice of B ... as the best Greek MS is confirmed to be on the whole right; but '(d) other MSS appear to represent a tradition going back at least to the Vth-VIth century, especially n . . " and in a smaller degree C and e .. .; '(e) iu a few instances the older tradition stands unanimous against the Greek MSS; and '(f) in the instances coming under (d) and (e) there is no apparent reason to prder the later to the older evidence.' 'The frequent coincidence', continues Minio, 'between the Greek

MS nand Boethius confirms what had already been pointed out by S. Schuler, K. Kalbfleisch and G. Furl.ni on the importance of I

i.e. those on which Boethius' translation was based.

THE TEXT OF THE ANALYTICS 91 this MS, which is perhaps the oldest we possess. They even exaggerated the extent of its similarity to the older texts. It is true that it agrees with them on many points against the other Greek MSS, but it is not true that it is nearer to them than B is, since it has a great number of variants differentiating it from all older texts. It is, however, interesting to notice tbat the importance of n as preserving old features was emphasized also in regard to the De Interpret. by K. Meiser and J. G. E. Hoffmann who found striking examples of this fact while examining the Latin and Syriac versions of this treatise: I have still to consider the contribution of the Greek commentators to the establishment of the text. Alexander is more than 600 years nearer to Aristotle than the earliest Greek MS. of the Analytics, Themistius 500, Ammonius about 400, Simplicius 300; it might perhaps be expected that the commentators should be of primary importance for the text of Aristotle. But we must be careful. Support for a reading derived from the commentaries is of very different degrees: (I) Sometimes the course of the commentary makes it clear what reading the commentator had before him. Such support I designate by AI (Alexander), Am (Ammonius), An (Anonymus), E (Eustratius), P (Philoponus), T (Themistius). (.) Sometimes the commentator introduces a citation which is evidently meant to be exact. But even so he may not be quoting quite exactly, or the citation as it reaches us may pave been influenced by the text of Aristotle used by the copyist from the commentator's MS. Such support I designate by Ale, etc. (3) Sometimes the commentator introduces a careless citation, paraphrasing the sense of the text he had before him. (4) The lemmata I designate by Ai1, etc.

It is agreed among scholars that the lemmata were written not by the commentators, but by copyists; and the copyists responsible for our MSS. of the commentators are as a rule later than the writers of our five old MSS. The lemmata are therefore almost valueless as support for a reading against the evidence of our MSS., and not worth very much as support for one variant as against another. For obvious reasons the loose quotations also have little importance. I have included lemmata in the apparatus only to show that there is some support for a reading found in only one,

INTRODUCTION

92

or in none, of our MSS. To make more mention of them than this would be to overload 'the apparatus with n~edIess infonnation. The first two of the four kinds of evidence, on the other hand, have great importance, and the first kind has much more than the second, because it can hardly have been influenced by the MSS. of Aristotle used by the copyists of the commentaries. But even when we know that a commentator had a certain reading, it by no means follows that that reading is what Aristotle wrote; in many places the commentators plainly had an inferior text. Nevertheless, of the '34 places cited above in which the plainly right reading is found in only one MS., there are 69 in which that reading finds support in one or more of the commentators. In addition, there is a certain number of passages in which the first hands of all our five MSS. go astray, while one or more of the commentators has the right reading. Those that I have noted will be found at 30b'4, 36"3, 44b38, 45 b'4, 46'17, 82b'7, 83b'4, 86'8, b'7, 88b29, 89'13, 90b10, 16, 92'24, 30 (bis) , 31, b9, 93'24, 94'34, 35, 95b34, 97bI4, 33, 98b6. In addition there are a few passages in which a commentator has a reading that has claims on our acceptance not by reason of intrinsic superiority but because the commentator is a much earlier authority than many of our MSS .. These are found at 24b29. 26 a2, 38b2I. In our two test passages (31'18- 49'z6, 6gb4-S Z" ) the following agreements occur : A B

=

AI

20

times

=

Aleg

22

9

C

29

II

d

17 30

9 12

=

P

21

z9 32 27 29

=

.pc 5

~

4

T4 2

Total 5S 66

II

5

88

8

4

65

il9 It is surprising that the two MSS. hitherto reckoned the best show the least agreement with the commentators; but the total number n

9

9

of agreements is probably too small to warrant any very definite conclusion, and the agreements throug/wut the Analytics should be taken as the basis for any conclusions to be drawn. It is interesting, however, to find some confirmation of the possession of an old and good tradition by n. Our original hypothesis that, with five MSS. of so early a date, we have little need to take account of later MSS. is confinned if we consider the .very small number of passages in which a clearly right reading is found only in a later MS. or MSS., or in a later hand in one of the old MSS. The only instances I have

THE TEXT OF THE ANALYTICS 93 noted will be found at 26'32 (f). 66b,o (mn'). 82 b'7 (MP). 83b'4 (DM). 84 b33 (D). 87'24 (c'). 88b22 (DM). 89'13 (DP). 90b10 (c'P'). 16 (Mn'E), 92'31 (B'E). b9 (DAn'E). 94'3 (D). 34 (c'P). 35 (DP).

LIST OF MANUSCRIPTS NOT INCLUDED IN THE SIGLA A

I, '.2

= An. Pro I, IT; A 3, 4 = An. Post. I, II

Ambrosianus 124 (B 103), sacco xiii 231 (D 43) u xiv (A I, mutilus) " 237 (D 54) "xiii (A I (pars), 2, 3 (pars»

"

255 (D 82)

"xiii

344 (F 67) "xvi (A 3, 4) 525 (M 71, Waitzii q), saec. xiv and xv Bodleianus, Baroccianus 87. saee. xv " "

" " "

" Laudianus " Seldenianus

177 u 45" 46" 35 "

xiii ineuntis xv xiv xiv xv (A I. 1"""'9)

" Miscellaneus 261 " Bononiensis (Bib!. Univ.) 3637, saec. xiv (A I, mutilus) Escurialis

Gennensis F VI. 9, saec. xv-xvi (A I) Gudianus gr 24. saec. xiii Laurentianus 72, 3 (Waitzii e), :mni 1383 (palimpsestus) 72, 4, saec. xiii " 72, ·10 " xiv (A I, 2) " 72, 12 (Waitzii T), saee. xiii " 72,19, saec. xiv (A I. 1-7) " 87,16" xiii (A I (pars» " 89, 77 " xvi " Suppl. 55 (88. 39), saec. xiv (A I, mutilus) " Conventi suppressi 192, saec. xiv (A I, 2) Lipsiensis (Bib!. Sanataria) 7, saec. xv (A I, 2) Marcianus 202, saec. xiv-xv " 203" xiv " 204 (Waitzii a), saec. xiv " App IV. 53 (Bekkeri Nb, Waitzii L), saec. xii Manacensis 222, saec. xiv (A 2- 4) " 234" xvi (A 3, 4) Mutinensis uB (II D 19), anni 1400 " 149 (II E 16), saec. xv (A 3, 4) " 189 (III F II) " xiv-xv-xvi Neapolitanus III D 30, saec. xv " III D 31 " xiv " In D 32 " xv (A 4)

INTRODUCTION

94

Neapolitanus III D 37 saec. xiv (A I) Oxoniensis, Coll. Corporis Christi 104, saec. xv (A 3, 4) " CoIl. Novi 225, saec. xiv " Coll. Novi 299 " xv Parisinus I&i3, saec. xiii I&i5 " xiv r&i6 " xiv (A I, 2) " IB47 " xvi (A 3, 4) " I8g7 A, saec. xiii " 1919, anni 1442 (A I, 2, 4) " 1971, saec. xiii xiv 1972 1974 " xv

" " " " " " " "

2020 2030

" " " "

XV

xvi (A I, 2) xiv (A 1, 2) 2051 2086 xiv 2120 " xvi " 167, saec. xiv Coislinianus xiv (A I, 2) 323 " xiv " 327 " Suppl. 141, saec. xvi " xiv 245 " " 644 " xiv " " " Toletanus 95-8 Vaticanus 110, saec. xiii-xiv (A I, 2) " 199" xiv (A I, 2) " 241 (Bekkeri I, Waitzii K), saec. xiii " 242, saec. xiii-xiv xiii-xiv 243 " 244 " xiii " 245 " xiii (A 1- 4 (A 4 mutilus» " 247 (Waitzii E), saec. xiii- xiv (A I) " 1018, saec. xv-xvi (A I, 2) " 1294

" " " " " "

" " " " " " "

14<)8 16<)3 Ottobonianus ,386, saec. xv (A 1) Palatinus 34 saec. xiv A I, 2 (A 2 mutilus) " 74" xv JJ 78 " . xvexeuntis 159, anni 1442 "" 255, saec. xv Reginensis 10'/, saec. xiv " u 6 " xiv " 190" xvi (A 1-4 (A 2 mutilus» Urbinas 56, saec. xvi (A r, 2, mutili)

MANUSCRIPTS NOT INCLUDED IN THE SIGLA Vindobonensis 41 , saec. xv-xvi (A I, mutilus) "

" "

..

94

155.. xvi exeuntis (A 3, 4) 230 (A I, .2) Suppl. 59. saee. xiv (A 1,2, mutili) ,.

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SIGLA An.P" 24&10-310.17 31aI8- 49a26

codices

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(Bekkeri atque Waitzii) = Urbinas 35. saec. ix vel x ineuntis (Bekkeri atque Waitzii) = Marcianus 201, anni 955 (Bekkeri atque Waitzii) = Coislinianus 330, saec. xi (Waitzii) = Laurentianus 72. 5, saec. xi (Waitzii) = Ambrosianus 490 (olim L 93), saec. ix

r n Al Am An E P T Ale, All,

= Georgii traductio Syriaca = Probae traductio Syriaca

= Alexander in An. Pro i = Ammonius in An. Pr.. i = Anonymus in A". Post. ii = Eustratius in An. Post. ii = Philoponus in An. Pro et Post. = Themistius in An. Post.

Arne, Anc, Ee, pc = Alexandri, etc., citatio Ami, Ani, EI, pi = Alexandri, etc" lemma

RARO CITANTUR D (Bekkcri atque Waitzii) = Coislinianus IS7, saec. xiv medii F (Waitzii) = Vatieanus 209~ saee. xiv M (Waitzii) = Mareianus App. iv. 51 a (Waitzii) = Angelieus 42 (olim C 3. 13), saee. xiv e (Waitzii) = Vatieanus 1024, vetustus f (Waitzii) = Mareianus App. iv. 5, saee. xiv i (Waitzii) = Laurcntianus 72. IS, sacco xiv m (Waitz.ii) = Ambrosianus 687 (olim Q 87), saee. xv p {Waitzii) ,.", Ambrosianus 535 (olim M 89), saee. xiv u (Waitzii) = Basileensis 54 (F ii. 21), saee. ~i

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