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CONSPECTUS OF THE CONTENTS ANALYTICA PRIORA
BOOK I A.
STRUCTURE OF THE SYLLOGISM
I. Preliminary discussions , Subject and scope of the Analytics. Definitions of fundamental terms. 2 Conversion of pure propositions. 3 Conversion of modal propositions. 2. Exposition of the three figures 4--2'
The same, in the third figure. 3. SupPlementary discussions
23 Every syllogism is in one of the three figures, and reducible
to a universal mood of the fust figure. 24 Quality and quantity of the premisses. 2S Number of the terms, premisses, and conclusions.
26 The kinds of proposition to be proved or disproved in each figure.
B.
MODE OF DISCOVERY OF ARGUMENTS 1.
General
'7 Rilles for categorical syllogisms, applicable to all problems . • 8 Rilles for categorical syllogisms, peculiar to different prob-
lems.
CONSPECTUS OF THE CONTENTS 28r '9 Rules for reductio ad impossibile, hypothetical syllogisms, and modal syllogisms. 30 •. .Proper to the several sciences and arts 31 Division.
C. I.
RESOLUTION OF ARGUMENTS
Resolution of arguments into figures and moods of syllogism
3' Rules for the choice of premisses, middle term, and figure. 33 Error of supposing that what is true of a subject in one respect
is true of it without qualification. 34 Error due to confusion between abstract and conCIete terms.
35 Expressions for which there is no one word. 36 The nominative and the oblique cases. 37 The various kinds of attribution. 38 The difference between proving that a thing can be known, and proving that it can be known to be so-and-so. 39 Substitution of equivalent expressions. 40 The difference between proving that B is A and proving that BistheA. 4' The difference between' A belongs to all of that to which B belongs' and 'A belongs to all of that to all of which B
belongs'. The 'setting out' of terms is merely illustrative. 4' Analysis of composite syllogisms.
43 In discussing definitions, we must attend to the precise point at issue. 44 Hypothetical arguments are not reducible to the figures.
45 46
•. Resolution of syllogisms in one figure into another 3. Resolution of arguments involving the expressions 'is not A' and 'is a not-A'
BOOK II
A.
PROPERTIES OF SYLLOGISM
More than one conclusion can sometimes be drawn from the same premisses. '-4 True conclusions from false premisses, in the three figures. I
5-7 Reciprocal proof (i.e. inference of one premiss from the conclusion and the converse of the other premiss), applied to the three figures. 8-10 Conversion (i.e. inference of the opposite of one premiss from the other premiss and the opposite of the conclusion), ·applied to the three figures.
282
CONSPECTUS OF THE CONTENTS Reductio ad impossibile in the three figures. 14 The relations between ostensive proof and reductio ad impossibile. IS Reasoning from a pair of opposite premisses. 11-13
B. FALLACIES, ETC. 16 Fallacy of petitio principii. 17-18 Fallacy of false cause. 19-20
Devices to be used against an opponent in argument.
21
How ignorance of a conclusion can coexist with knowledge of the premisses.
22
Rules for the use of convertible terms and of alternative terms, and for the comparison of desirable and undesirable
objects. C.
DIALECTICAL MODES OF ARGUMENT REDUCIBLE TO THE THREE FIGURES OF SYLLOGISM
23 Induction. 24 Argument from an example.
25 Reduction of one problem to another. 26 Objection. 27 Inference from signs.
ANALYTICA POSTERIORA BOOK I A. THE ESSENTIAL NATURE OF DEMONSTRATIVE SCIENCE 1
The student's need of pre-existent knowledge. Its nature.
2
The nature of scientific knowledge and of its premisses.
3 Two errors-the view that knowledge is impossible because it involves an infinite regress, and the view that circular demonstration is satisfactory. 4 The premisses of demonstration must be such that the predicate is true of every instance of the subject, true of the subject per se, and true of it precisely qua itself. 5 How we fall into, and how we can avoid, the error of thinking our conclusion a strict universal proposition when it is not. 6 The premisses of demonstration must state necessary connexions.
CONSPECTUS OF THE CONTENTS
283
B. PROPERTIES OF DEMONSTRATIVE SCIENCE
7 The premisses of demonstration must state essential attributes of the same genus of which a property is to be proved. 8 Only eternal connexions can be demonstrated. 9 The premisses of demonstration must be peculiar to the science in question, except in the case of subaltern sciences. 10 The different kinds of ultimate premiss required by a science. I I The function of the most general axioms in demonstration. 12 Error due to assuming answers to questions inappropriate to the science distinguished from that due to assuming wrong answers to appropriate questions, or to reasoning wrongly from true and appropriate assumptions. How a science grows. '3 Knowledge of fact and knowledge of reasoned fact. '4 The first figure is the figure of scientific reasoning. IS There are negative as well as affirmative propositions that are immediate and indemonstrable. C.
ERROR AND IGNORANCE
16 Error as inference of conclusions whose opposites are im-
mediately true. 17 Error as inference of conclusions whose opposites can be
proved to be true. 18 Lack of a sense must involve ignorance of certain universal
propositions which can only be reached by induction from particular facts. D.
FURTHER PROPERTIES OF DEMONSTRATIVE SCIENCE
19 Can there be an infinite chain of premisses in a demonstra-
20
21 22
23 24 25 26 27
tion, (1) if the primary attribute is fixed, (2) if the ultimate subject is fixed, (3) if both terms are fixed? There cannot be an infinite chain of premisses if both extremes are fixed. If there cannot be an infinite chain of premisses in affirmative demonstration, there cannot in negative. There cannot be an infinite chain of premisses in affirmative demonstration if either extreme is fixed. Corollaries from the foregoing propositions. Universal demonstration is superior to particular. Affirmative demonstration is superior to negative. Ostensive demonstration is superior to reductio ad impossibile. The more abstract science is superior to the less abstract.
284
CONSPECTUS OF THE CONTENTS 28 What constitutes the unity of a science.
29 30 31 32
How there may be several demonstrations of one connexion. Chance conjunctions are not demonstrable. . There can be no demonstration through sense-perception. All syllogisms cannot have the same first principles.
E.
STATES OF MIND TO BE DISTINGUISHED FROM SCIENTIFIC KNOWLEDGE
33 Opinion. 34 Quick wit.
BOOK II A. THE RELATION OF 'DEMONSTRATION TO DEFINITION
I
2 2.
3 4 S 6 7
1. The possible types of itl JL~ 'Trant, i.e. as expressing alternatively what A. has already expressed by T 8. 1">7 (i.e. T 8. nV, 1">7), the reference being to the combination 10 or OI. But 7j 1"-1]3' #.TEp
1l'nu... In three of the moods which A. has stated to yield a conclusion with the major term as subject and the minor as predicate (IE in all three figures) the affirmative premiss is particular. He here points out that an indefinite premiss, i.e. one in which neither 'aU' nor 'some' is attached to the subject . will produce the same result as a particular premiss. 3I-Z. fJ ya.p 8E~KnKw~ •• . 'll'"O,VTES:. An argument is said to be SHKnKos, ostensive, When the conclusion can be seen to follow either directly from the premisses (in the first figure) or from propositions that follow directly from the premisses (as when an argument in the second or third figure is reduced to the first
31 5 figure by couversion of a premiss). A reductio ad impossibile, on the other hand, uses a proposition which does not follow from the original premisses, viz. the opposite of the conclusion to be proved. A. says nothing of the proof by lK8EUL< which he has often used, because, being an appeal to our intuitive perception of certain facts (ct., for instance, 28'22.-{;), not to reasoning, it is formally less cogent. In any case it was used only as supplementing proof by conversion, or by reductio ad impossibile, or by both. b4 . 01 tJ-EV Ko,90AOU ... Q.vna'Tpa+ivTo5. The validity of Cesare and Camestres has been so established in 27'5-<J, 23). There is no passage of the A nalytics that really fulfils the promise; but 43b32-6 and A n. Post. 75b33-6, 87bl9-27, ')6'8-19 touch on the subject. 25-37. <wei ~ ......"",,"0',, The passage is a difficult one, and neither the statement with which it opens (b 25 -'7) nor the structure of the first sentence can be approved; but correct punctuation makes the passage at least coherent, and in view of the undisputed tradition by which it is supported we should hardly be justified in accepting Becker's excisions (pp. 36-7). A. starts with the statement that (I) 'For B, being A is contingent' is ambiguous, meaning either (2) 'For that to which B belongs, being A is contingent' or (3) 'For that for which B is contingent, being A is contingent'. He then (b27 - 30) supports this by the premisses (a) that (4) Ko9' oJ TO B, TO A "'8.!XETO' may mean either (2) or (3) (because it is not clear whether tnrapx£., or Ev8E'XETat is to be understood after TO B), and (b) that (I) means the same as (4); and (b31 - 2) repeats his original statement as following from these premisses. In the remainder of the passage A. applies to the syllogism the distinction thus drawn between two senses of KaO" ou 'TO B, 'TO A J",S/xn·a.t. If in the major premiss A is said to be contingent
for B, which is in th e minor premiss said to be contingent for C, we have two problematic premisses. If in the major premiss A is said to be contingent for B, which is in the minor premiss said to be true of C, we have a problematic and an assertoric premiss. A. proposes to begin with syllogisms with two similar premisses, 1Ca.8o.1T~P lCa, b Toir aAAotr, i.e. as syllogisms with two assertoric
COMMENTARY 33 0 premisses (chs. 4--J;) and those with two apodeictic premisses (ch. 8) were treated before those with an apodeictic and an assertoric premiss (chs. ELCTT'j5 8E ... EVSEXEa9a.L, i.e. when from 'B is capable of belonging to no C' we infer' B is capable of belonging to aU C': cf. 32a2g_ br.
8.
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aUTOS' OO'TrEP
TrpOTEPOV,
i.e. as in 32b38- 40.
S' Etp1')TQ.L VpOTEPOV, in 32a29- bl. 21-3. 'Ea.v S' ... TEAELOo;. If ..,.I.AEtos be read, the statement will not be correct; for in a27-34 A. goes on to point out that when the particular premiss is negative and the universal premiss affirmative, the latter being the major premiss, there is no ·rlAHOS OlJAAoytuj.LoS'. There is no trace of 'T£'AEtOS' in Ai. (11)9. 20) or in P.'s comment (158. 13), and it is not a word they would have been likely to omit to notice if they had had it in their text. Becker (p. 75) seems to be right in wishing to omit it. 24-5 . TOliTO SE . • . EVSEXEO'OClt. Waitz reads 'TTClv-rt after Ella£'xwBat (following B's second thoughts), on the ground that it is the remark in 32b25- 32 rather than the definition of 'TO Ev8E'XEuOaL in 32"18- 20 that is referred to. But the latter may equally well be referred to, and the reading 1TClV'Tt no doubt owes its origin to the fact that one of Al.'s two interpretations (I&). 23-9) is that Ev8E'XEUOat is to be understood as if it were Ev8lXEuOat 'TTClVTt. AI., however, thinks the definition of 'TO EII8£XEuf)at in 32aI8-20 may equally well be referred to (169. 30-2) . 29. Tfi SE OeO'EL b~OlW$: EXWO'LV, i.e. 'but the universal premiss is still the major premiss'. 29-30. otov . . . ,hrapXELv. A. does not explicitly mention the case in which the premisses are EcOc. which can be dealt with on the same lines as the case mentioned, AcOc. 32. avncnpncJ.EL01'l$: Sf: Tl)$: EV ~EPEL refers not to conversion in the ordinary sense but to conversion from' B may not belong to C' to 'B may belong to C' ; ct. 32"29-bl. 33. TO «UTO ... 1fPOTE:pOV, i.e. as in aZ4. 34. tcnOa1f'E:p . .. apxi)s, i.e. as AcEc gave the same conclusion as A'A' ("5- 12). 10. 'fOUTO
332
COMMENTARY
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clauses
express alternatives falling under one main hypothesis; the fourth expresses a new main alternative. Therefore there should be a comma after &J.LOtOaxr1fLoVE~ (a37). The combinations referred to, are IcAc, OcEc, IeEe, OcAc, lele, 0'0', I 'Oe, 0'1'. Since a proposition of the form 'For all B,
not being A is contingent' is convertible with 'For all B, being A is contingent', and one of the form 'For some B, not being A is contingent' with 'For some B, being A is contingent' (avna-rPEq,OVUW at K'aTQ. TO £vSIXEu8at 7TpcrrOn€LS, b2 • d. 32a29- bI), all these combinations are reducible to the combinations 'For some
B, being A is contingent, For all C (or For some C), being B is contingent'. Now since B may extend beyond A ('38-9), we may suppose that C is the part of B which extends beyond A (i.e. for which being A is not contingent) . Then no conclusion follows; there is an undistributed middle. b3-8. ~TI. 8E . . . tll-a.T~OV. The examples given are Kotvol 'lTaV'Twv,
i.e. they are to illustrate all the combinations of premisses
mentioned in '34--S n. The reasoning therefore is as follows: The premisses It is possible for some white things to be animals (or not to be animals), It is possible for all (or no, or some) men to be white (or for some men not to be white) might both be true. But in fact it is not possible for any man not to be an animal. Therefore a negative conclusion is impossible. On the other hand, the same major premiss and the minor premiss It is possible for all (or no, or some) garments to be white (or for some garments not to be white) might both be true. But in fact it is not possible for any gannent to be an animal. Therefore an affirmative con· clusion is impossible. Therefore no conclusion is possible. 11-13. ;, JlEV ya.p ... KaTQ~a.TtKt{J. I.e., the possibility of an affirmative conclusion is precluded by the fact that sometimes, when the premisses are as supposed (i.e. the major premiss particular, in the first figure), the major term cannot be true of the minor; and the possibility of a negative conclusion is precluded by the fact that sometimes the major term cannot fail to be true of the minor. 14-16. Kal TravTl T~ Eaxa.T~ TO 1rPWTOV UVa.YK1') (sc. tnrapXEW) , i.e. in some cases (e.g. every man must be an animal). KQi. oUSlEv!. ivSEXETa~ um1pXIEW, i.e. in some cases (e.g. no garment can be an animal). 16-17. TO, ya.p civayKa.~ov •• • EVSEXO .... EVOV, d. 32aI9. :U. 1rAT)v KQT1')yOp'KWV ~f:V TEAE'O$. That AeAc yields a direct conclusion has been shown in 32b38-33aI.
O'TEP'lTLKWV
bE
333 That EcEc yields a conclusion indirectly
an"'tls.
has been shown in aI2-I7. 23.
. TOY EtP"1lJlVQV 8LOpI.0' ....6v, cf. 32&18-20. 8E Aav9a.VEL TO TOlO,iTOV, i.e., the distinction between the
Ka.Tcl.
EV(OTE
genuine &8€x0p.£vov (that which is neither impossible nor necessary) and that which is EVSEX6,.UVOll only in the sense that it is not
impossible. CHAPTER 15 Syllogisms in the first figur.e with one problematic and one assertoric premiss
33b25. (A) Both premisses universal (a) When the major premiss is problematic aaEws~ A . here explains the point made without explanation at 33b29- 3I, that arguments in the first figure with an assertoric major and a problematic minor, when they prove a negative possibility, do not prove a problematic proposition as defined in 3ZaI8-zo (.\lyw S' ivSlXEaBa, Ka, 'TO 340
I!..,
J
EVSEX0ji-El'OV,
ou ji-.ry
OV'TOS avaYKalov, n(JEV'TOS S' tnrapXE'v, ovSJv
ECJ7'a, SW TOih-' dSvva'Tov). The premisses No B is A, For all C, being B is contingent, are originally stated to justify the conclusion For all C, not being A 'iS, i.e. by the conversion of For all C, not being B is contingent into For all C, being B is contingent; cf. 32a29- br. ka.8a.VEP EY TOlS TrPOTEpOY, i.e. as with the corresponding
2,.
mood (AE'AP) treated of in the last chapter (35'3- lI). 28-31. ouS' ils. A. says here that premisses of the form E'Ee can be made to yield a conclusion 'by converting the premisses', i.e. by complementary conversion (d. 3zazg-bI). By this means we pass from EcEe to AeAc, the combination already seen in aq- I9 to be valid. In a27 Waitz reads, with n, lav jL€Ta),71rp8fj TO EVSEx€u8at jL~ ,hrapx£tv, assuming that jL£'Ta>..7J~8fj means 'is changed'; and this derives some support from Al.'s commentary (243. 23)- jL€'Ta),1Jrp8€{u1JS Si rijs EAa'T'Tovos £ls T~V KaTar/>aTtK~V EVS£xojLEV7Jv-and the corresponding remark in P. 229. 26. But the usual sense of I'ETaAUI'j3o.VEtV in A. is 'to substitute' (d. Bonitz, Index), and 1'>1
is therefore not wanted. 28-3I. Et 8' ... aUAAoytaJ-Los, i.e. 'the valid syllogisms in this figure with two problematic premisses of different quantity correspond to the valld syllogisms with two asseTtoTic premisses of different quantity'. Thus we have AcIe, IcAc, Eele, and OcAe corresponding to Datisi, Disamis, Ferison, Bocardo. But in addition, owmg to the possibility of complementary conversion of problematic premisses (32'29-br), A. allows EeOe and O'Ee to be valid ('38-b2). He says nothing of AeO' and I'Ee, but these he would regard as valid for the same reason. 36-8. ol'o,,,,S 8•••. uvn<J'Tpo4>ils. The validity of Eele would
COMMENTARY be proved thus: By conversion of the minor premiss, 'For all C, not being A is contingent, For some C, being B is contingent' becomes 'For all C, not being A is contingent, For some B, being C is contingent', from which it follows that for some B not being A is contingent. The validity of O'A' would be proved thus: By complementary conversion, followed by simple conversion, of the major premiss, and by changing the order of the premisses, 'For some C, not being A is contingent, For all C, being B is contingent' becomes 'For all C, being B is contingent, For some A, being C is contingent', from which it follows that for some A being B is contingent, and therefore that for some B being A is contingent. bI. ku9a,1rEP Ev 1'oi~ 1TpOTEPOV, i.e. in the case of EcEc, OcAc ('23--8, 36--8). 3-4. ka.l yelp ... Jol11SEvi. lnrapXELv, i.e. there are cases in which A must belong to B, and cases in which it cannot, so that neither a negative nor an affinnative problematic conclusion can follow
from premisses of this form . 4-6. OPOL TOU UTJ'a.PXEW .......eaov A'UKOV. I.e. it is possible that some white things should be, and that some should not be, animals, it is possible that some white things should be, and that some should not be, men; and in fact every man is necessa.rily an
animal. On the. other hand, it is possible that some white things should be, and that some should not be, horses, it is possible that some white things should be, and that some should not be, men; but in fact it is necessary that no man should be a horse. Thus 1'1', 1'0', 0'1', 0'0' in the third figure prove nothing.
CHAPTER 21 SyUogisms in the third figure with one problematic and one assertoric premiss 39b,. If one premiss is assertoric, one problematic, the con· elusion is problematic. The same combinations are valid as were
named in the last chapter. (A) Both premisses universal
10.
(a) Both premisses affirmative: AA'lp valid, by conversion. 16. A'AI' valid, by conversion. (b) Major premiss negative, minor affirmative: EA'Op, EeAOe valid, by conversion .
I,.
•
1"
r~
;
I. 20. 39bI-21. 39b22 23. (d) Both premisses negative lVTwv
0' Eenat, bZ3 - S). 25. Ko,8a.1TEP EV TOtS 1TpchEPOV J i.e. by complementary con-
version AEc, EEe are reduced to the valid moods AAe, EAe, as
EeEc was reduced to AcAc in a26-8. 2~39. Et S' • • • "1rciPXELV. A. considers here premisses differing in quantity. (I) If both premisses are affirmative, the conclusion is validated by reduction to the first figure ('>27-31). This covers AI', loA, A'l, lAo. (2) So too if the universal premiss is negative, the particular premiss affirmative (ib.). Prima facie
this covers EI', l'E, E'l, IE'. But of these l'E (though A. does not say so) is invalidated by the fact that in the third figure the minor premiss must (to avoid illicit major) be affirmative (IE' escapes this objection by complementary conversion of Ee). (3) If the universal premiss is affirmative, the particular premiss negative, the conclusion will be got (so A. says) by reductio ad impossibile (b31 - 3). Prima facie this covers the cases AO', O'A, A'O, OA'. But the ouly case specifically mentioned is O'A (b33-.iM.{3T)KE, and other instances cited in Denniston, The Greek
Particles, 6!J-70. 23-5. aTE ya.p .•. civ8EX0j.1EvOV, The combination in question, EcAn, reduces. by conversion of the minor premiss, to EeIn in the first figure, which was in 36'39-bZ shown to yield only a problematic conclusion. 3&-2. OTE 8" ... l'TJ UTra.pxuv. The combination in question, EnAc, reduces, by conversion of the minor premiss, to Enlc in the first figure, which was in 36'34-9 shown to yield an assertoric conclusion, and a fortiori yields a conclusion of the form It is not impossible that some 5 shonld not be P. dvaYKTJ here ('3Z) only means 'it follows' ; the conclusion is not apodeictic; d. 36aIO n. 34-5 . .,ETah'lOE''''lS ....... p6TEpOV, i.e. by complementary conversion of the minor premiss (d. 32129- bI). bz-8. Kai. OTQ.V ..• au}'Wt1l"'rEW. The first rule stated here (1'2-3) prima facie includes InEe; but the rule in b8-IO also prima facie includes it. Again. the rule in h3-8 prima facie approves ICE", which the rule in bIo-II condemns; and in fact IcED proves nothing, since in the third figure the minor premiss cannot be
negative unless it is problematic and therefore convertible by complementary conversion into an affirmative. Finally, AeOn, which prima facie falls under the rule in b 3-8, is invalid for the same reason. Clearly, then, b2- 3, 3-8 are not meant to cover so much as they appear to cover. Now in bg A. expressly passes to the cases in which the major premiss is affirmative, the minor
I.
22. 40aI5-bI2
negative. All is made clear by realizing that in b2-8 A. has in mind only the cases in which the major premiss is negative. the minor affirmative; thus A. is not there thinking of the cases InEc, IcEn, AeOn. 4-6. ;, ya.p a.UTO§ TP01l'OS ••• bVTWV. EnleO is in fact validated just as EDAoO was ('25-32). by conversion; but OnA'O is validated by reductio ad impossibile. 8-11. OTQ.V 8E •.• EaTo,L, KuOoAov 'A'rJcfoOI.II is unnecessary, since AnOc is valid, as well as InEc, and AeOn invalid, as well as IeEn, But /Ca06Aov A~4>OIv has the support of AI. and P .• and of all the MSS. 11-12. 8E,x8~aETa.L 8E: . . . 8pwv, cf. '35-8. It is contingent that some men should be asleep. no man can be a sleeping horse; but every sleeping horse must be asleep. On the other hand. it is contingent that some men should be asleep, no man can be a waking horse; and in fact no waking horse can be asleep. Therefore IcEn cannot prove either a negative or an affirmative conclusion.
CHAPTER 23 Every syllogism is in one of the three figures. and reducible to a universal mood of the first figure 40b17. We have seen that the syllogisms in all three figures are reducible to the universal moods of the first figure; we have now to show that every syllogism must be so reducible. by showing that it is proved by one of the three figures. 23. Every proof must prove either an affinnative or a negative, either universal or particular. either ostensively or from a hypothesis (the latter including reductio ad impossibile). If we can prove our point about ostensive proof, it will become clear also about proof from an hypothesis. lO. If we have to prove A true, or untrue, of B, we must assume something to be true of something. To assume A true of B would be to beg the question. If we assume A true of C. but not C true of anything. nor anything other than A true of C. nor anything other than A true of A, there will be no inference; nothing follows from the assumption of one thing about one other. 37 . If in addition to'C is A' we assume that A is true of something other than B. or something other than B of A. or something other than B of C. there may be a syllogism. but it will not prove A true of B ; nor if C be assumed true of something other than B. and that of something else. and that of something else. without establishing connexion with B. 4985 B b
COMMENTARY 41'2. For we stated that nothing can be proved of anything else without taking a middle term related by way of predication to each of the two. For a syllogism is from premisses, and a syllogism relating to this term from premisses relating to this term, and a syllogism connecting this term with that term from premisses connecting this term with that; and you cannot get premisses leading to a conclusion about B without affirming or denying something of B, or premisses proving A of B if you do not take something common to A and B but affirm or deny separate things of each of them. 13. You can get something common to them, only by predicating either A of C and C of B. or C of both, or both of C, and these are the figures we have named; therefore every syllogism must be in one of these figures. If more terms are used connecting A with B, the figure will be the same.
37 0
21.
Thus all ostensive inferences are in the aforesaid figures;
it follows that reductio ad impossiOile will be so too. For all such arguments consist of (a) a syllogism leading to a false conclusion, and (b) a proof of the original conclusion by means of a hypothesis, viz. by showing that something impossible follows from assuming the contradictory of the original conclusion. 26. E.g. we prove that the diagonal of a square is incommensurate with the side by showing that if the opposite be assumed odd numbers must be equal to even numbers. 32. Thus reductio uses an ostensive syllogism to prove the false conclusion; and we have seen that ostensive syllogisms must be in one of the three figures; so that reductio is achieved by means of
the three figures. 37. So too with all arguments from an hypothesis; in all of them there is a syllogism leading to the substituted conclusion, and the original conchision is proved by means of a conceded premiss or of some further hypothesis. hI. Thus all proof must be by the three figures; and therefore all must be reducible to the universal moods of the first figure.
40bd~I9. 8ul. TWV ..• o,UhhoyLO'.... WV. In 29bI-25 A. has shown that all the valid moods of the three figures can be reduced to the universal moods of the first figure (Barbara, Celarent). Maier (2 a. 217 n.) objects that it is only the moods of the pure syllogism that were dealt with there, and that A. could not claim that all the moods of the modal syllogism admit of such reduction; he wishes to reject KaDoAO" here and in 41 hS. But throughout the treatment of the modal syllogism A. has consistently maintained
37 I that the modal syllogisms are subject to the same conditions, mutatis mutandis, as the pure, and there can be no doubt that he would claim that they, like pure syllogisms, are all reducible to Barbara or Celarent. Both AI. and P. had Ko86>.ov, and it would be perverse to reject the word in face of their agreement with the MSS. 25· ETL i] OELKTtKW5 11 E~ ll1f09EO'EWS. Cf. 29a31- 2 n. A. describes an argument as E.g tnro(Uuf;w3 when besides assuming the premisses one supposes something else, in order to see what conclusion follows when it is combined with one or both of the premisses. Reductio ad impossibile is a good instance of this. For A.'s analysis of ordinary reasoning ;.g lJ7ToOlaEw 3 (other than reductio) ct. 50'16-28. 33-41'1 . .t BE • • • QuAAOYLQ!"OS. A. Jays down (1) ('33-7) what we must have in addition to 'C is A', in order to get a syllogism at all. We must have another premiss containing either C or A. He mentions the cases in which C is asserted or denied of something, or something of C, or something of A, but omits by inadvertence the remaining case in which A is asserted or denied
of something). (2) (b37 - 41 '2) he points out what we must have in addition to 'C is A', to prove that B is A. We cannot prove this if the other premiss is of the form 'D is A', 'A is D', 'Cis D', or 'D isC'. 4182-4. OAW~ yap .. . KaT1')yoptaL~ . A. has not made this general statement before, but it is implied in the account he gives in chs. 4-6 of the necessity of a middle term in each of the three figures. TatS KUTrrY0PLUtS is to be explained by reference to 814- 16. zz_b 3 . OTt 8£ !Cui. ot EtS 'TO a.8uvaTov . . . CTX"li-'CtTWV. For the understanding of A.'s conception of reductio ad impossibile, the present passage must be compared with 50'16-38. In both passages reductio is compared with other forms of proof ,~ tJ7To(UO€WS, The general nature of such proof is that, desiring to prove a certain proposition, we first extract from our opponent the admission that if a certain other proposition can be proved, the original proposition follows, and then we proceed to prove the substituted proposition (TO P.ETUAup./3UJlOp.£JlOJl, 4Ia39). The substituted proposition is said to be proved syllogistically, the other not syllogistically but .g iYrr08'Clew..af'f3dvt:w is used in a sense which is explained in AI. 263. 26-36, (taking a proposition in another sense than that in which it was put forward', or (more strictly) 'substituting a proposition of the form "A is B" for one of the form "If A is B, C is D" '. AI. ascribes this sense not to A. but to ot apxa'io£, the older Peripatetics, and it is (as Maier points out, 2 a. 250 n.) a Theophrastean, not an Aristotelian, usage. According to regular Aristotelian usage I'E7aJ.OI'/3a.wv means 'to substitute' (cf. 48'9, 49b 3) , and what A. is saying is this: In all proofs starting from an hypothesis, the syllogism proceeds to the substituted proposition, while the proposition originally put forward to be proved is established (I) by an agreement between the speakers or (2) by some other hypothesis. Let the proposition to be proved be 'A is B'. The speaker who wants to prove this says to his opponent 'Will you agree that if C is D, A is B?' (1) If the opponent agrees, the first speaker proves syllogistically that C is D, and infers nonsyllogistically that A is B. (2) If the opponent does not agree, the first speaker falls back on another hypothesis: 'Will you agree that if E is F, then if C is D, A is B?' , and proceeds to establish syllogistically that E is F and that C is D, and nonsyllogistically that A is B. The procedure is familiar in Plato; cf., for example, Meno, 86 e-87 c, Prot. 355 e. Shorey in '1:vAAol'wf'Ol .g {m08luEw, in A: (A.J.P. x (1889), 462) points out that A. had the M eno rather specially in mind when he wrote the Analytics; cf. 67'21, 69'24-9, An. Post. 71'29 . bS' EtS TOUS EV TOUT~ tca96Aou O'UAAoyt.a'I-'0US, d. 4obr8- 19 n. CHAPTER 24 Quality and quantity of the premisses 41b6. Every syllogism must have an affirmative premiss and a
universal premiss; without the latter either there will be no syllogism, or it will not prove the point at issue, or the question will be begged. For let the point to be proved be tlrat the pleasure given by music is good. If we take as a premiss that pleasure is good without adding 'all', there is no syllogism; if we specify one particular pleasure. then if it is some other pleasure that is
COMMENTARY 374 specified, that is not to the point; if it is the pleasure given by music, we are begging the question. 13. Or take a geometrical example. Suppose we want to prove the angles at the base of an isosceles triangle equal. If we assume the two angles of the semicircle to be equal, and again the two angles of the same segment to be equal, and again that, when we take the equal angles from the equal angles, the remainders are equal, without making the corresponding universal assumptions.
we shall be begging the question. zz. Clearly then in every syllogism there must be a universal premiss, and a universal conclusion requires all the premisses to be universal, while a particular conclusion does not require this. 2.7. Further, either both premisses or one must be like the conclusion, in respect of being affirmative or negative, and apodeictic, assertoric, or problematic. The remaining qualifications of premisses must be looked into. 3%. It is clear, too, when there is and when there is not a syllogism, when it is potential and when perfect, and that if there
is to be a syllogism the terms must be related in one of the aforesaid ways. 41b6. "E" TE , • ,Etv".. A. offers no proof of this point; he treats it as proved by the inductive examination of syllogisms in chs. 4-22. The apparent exceptions, in which two negative premisses, one or both of which are problematic, give a conclusion, are not real exceptions. For a proposition of the form "oytCTJ1.0V. AI. noticed that this point has been made already with regard to rand Ll ('22-4), and therefore, to avoid repetition, suggested (280. 21-4) that AB
should be read for
rLl.
But in fact this sentence is no mere
COMMENTARY repetition. In '14--24 A. was examioing his first main alternative, that the conclusion from A and B is E. Under this, he examioes various hypotheses as to the conclusion from rand LI, and the last of these is that they have no conclusion. In '24-30 he is examining his other main alternative, that the conclusion from A and B is something other than E, and here also he has to examine, in connexion with this hypothesis, the various hypotheses about the conclusion from rand LI, and again the last of these is that they have no conclusion. 3"-5. TOUTOU 8' •. • au)'Aoy,al'w., From the fact that there are three and only three terms it follows that there are two and only two premisses-unless we bring in a new premiss, by converting one of the original premisses, to reduce the argument from the second or third figure to the first (cf. 24b22--anKov .......ovaxwS', i .e. by Barbara (2S b37- 40). 34-5. TO SE C7TElO7J~ Ta.VnJ~ rijs 7rPOTo.UEWS, h6) (i.e. to assume that some C is B), and combine with it the other original datum (No B is A), and we get an ostensive syllogism in Ferio proving that some C is not A. 12-13. T a.iha. lLEV o~v • . . hEYWlJ.EV i.e. in ii. 14. 15-19. ~ of: TO'S a.AAo~S . . . ETrLrJAEtltEWS. Arguments Ka-ra. 1""7&'>''1''''" are those in which the possession of an attribute by a term is proved by proving its possession of a substituted attribute (TO fLE'Ta,Aap,pav6p.EIJOV, 4Ia39). Arguments KaTa. 1TOtO'T1]'Ta., says AI. (324. 19-325. 24), are those that proceed cr".. TOU (1) ~OV Kat (2) >iTTOV Kat (3) o!'-olov, all of which 'accompany quality'. (1) may be illustrated thus: Suppose we wish to prove that happiness does not consist in being rich. We argue thus: 'If something that would be thought more sufficient to produce happiness than wealth is not sufficient, neither is that which would be thought less sufficient. Health, which seems more sufficient than wealth, is not sufficient. Therefore wealth is not.' And we prove that health is not sufficient by saying 'No vicious person is happy, Some vicious people are healthy, Therefore some healthy people are not happy' . A corresponding proof might be given in mode (2). (3) May be illustrated thus: 'If noble birth, being equally desirable with wealth, is good, so is wealth. Noble birth, being equally desirable with wealth, is good' (which we prove by saying 'Everything desirable is good, Noble birth is desirable, Therefore noble birth is good'). 'Therefore wealth is good.' Arguments Ka-ra 1TOtOn],ra are thus one variety of arguments KaTa. fLETdA7]IjJW, since a substituted term is introduced. In all such arguments, says A. (if the text be sound), the i.e. the search for subjects and predicates of the major and minor term, and for attributes incompatible with the major or minor term (43 b39- 44'17), takes place with regard not to the terms of the proposition we want to prove, but to the terms of the proposition substituted for it (as something to be proved as a means to proving
394
1
UK'' ' '
395 it). The reason for this is that, whereas the logical connexion between the new term and that for which it is substituted is established 8,,' 6JLOAoylas .;;
'TWOS'
lli'1S' inroOluEw!;, the substituted
proposition is established by syllogism (4x'38.J>x). Maier (2 a. 282- 4) argues that the expressions KaT"
iUTc!.)"~"',V,
are quite unknown in A,'s writings, and that olav . . . is an interpolation by a Peripatetic familiar with
Ka'Ta 7TOW'T7}'TU
1row'T't}'TU
Theophrastus' theory of the hypothetical syllogism, in which, as we rna y learn from AI., these expressions were technical terms (for a full account of Theopbrastus' theory see Maier, 2 a. 263-87). But since A. here uses the phrase £V 'TOtS' fLETaAaiJ'fJavopivoLS'. it can hardly be said that he could not have used the phrase KaT" fwrcfA7]if;tv, and it would be rash to eject olov .. . 7TOt6TrJTa in face of the unanimous testimony of the MSS., AI., and P. 19-20. €'ft'U7KE"'a.a9a.L
SE ...
U1r08EO'EWt;.
A. nowhere discusses
this topic in general, but reductio ad impossibile is examined in ii. 11- 14. 2.2-8. Ean SE . ' , ' E1TL~AE'fTEOV. I.e. the assumption that rn (a subject of the major term A) is identical with Hn (a subject of the minor term E), which in 44'X9-2X proved that some E is A, will, if we add the hypothesis that only Hn's are E, justify the conclusion All E is A. ((x) All rn is A, All Hn is r n, Therefore all Hn is A; (2) All Hn is A, All E is H n, Therefore all E is A.) And the assumption that LIn (an attribute incompatible with A) is identical with H n , which in 44'28- 30 proved that Some E is not A , will, if we add the hypothesis that only Hn's are E, justify the conclusion No E is A. ((x) NoLIn is A, All Hn is LIn' Therefore no Hn is A; (2) No Hn is A, All E is H n, Therefore no E is A.) Therefore it is useful to examine _whether only the Hn's are E. in addition to the connexions of terms mentioned in 44aI2-35 (Kal. oUrws £mfiAE7T7'EOII, 45b28). 28-31. TO" aUTOV OE Tp(hTOV . . . O'uAAoy~a .... os. This refers to the method prescribed in ch. 28, i.e. to the use of the terms designated A- a in 44a12- 17. 32-4. SESEU(Ta~ ya.p . •. auAAoY'O'll-0s. This was shown in the chapters on syllogisms with at least one problematic premiss (chs. 14- 22). 34. o~o'ws of: ... kQ,T1lYOpu;'v, i.e. propositions asserting that it is SVVa7'Oll, OV Swa-roll, OVK EIISEX0P.£VOII, ci3vlla-rov, OVK dSvlla-roll, OVK allaYKatoll, aA."O£s, OVK ciA1']O£s, that E is A (De Int. 22aU- I3). Such propositions are to be established, says A., op.olws, i.e. by the same scrutiny of the antecedents and consequents of E and A, and of the terms incompatible with E or A (43 b3!f-44'3S).
COMMENTARY CHAPTER 30 Rules proper to the several sciences and arts 46'3. The method described is to be followed in the establishment of all propositions, whether in philosophy or in any science; we must scrutinize the consequents and antecedents of our two terms, we must have an abundance of these, and we must proceed by way of three terms; if we want to establish the truth we must scrutinize the antecedents and consequents really connected with our subject and our predicate, while for dialectical syllogisms we must have premisses that command general assent. 10, We have described the nature of the starting-points and how to hunt for them, to save ourselves from looking at all that can be said about the given terms, and limit ourselves to what is appropriate to the proof of A, E, I, or 0 propositions. 17. Most of the suitable premisses state attributes peculiar to the science in question; therefore it is the task of experience to supply the premisses suitable to each subject. E.g. it was only when the phenomena of the stars had been sufficiently collected that astronomical proofs were discovered; if we have the facts we can readily exhibit the proofs. If the facts were fully discovered by our research we should be able to prove whatever was provable, and, when proof was impossible, to make this plain. 28. This, then, is our general account of the selection of premisses; we have discussed it more in detail in our work on dialectic. 46"5. 1fEpl EKQ.TEPOV, i.e. about the subject and the predicate between which we wish to establish a connexion. 8. £1< TWV 1..1JAwv S' o~ A£yETat means 'the major is not predicable of the middle term, nor the middle term of the minor'. A. makes a mistake here. The major tenn is predicated not ouly of the minor but also of the middle term ('that of which there is knowledge is a genus'). A. has carelessly treated not 'that of which there is knowledge' but 'knowledge' as if it were the tenn that occurs in the major premiss. 33-5, 61'0'''', yEvO" This refers to arguments in the second figure (like the two arguments in Cesare in b 30-2, 32-3) in which 'the problem is cancelled', i.e. the proposed proposition is negated. or in other words a negative conclusion is reached, on the strength of the special relation (a relation involving the use
S' ...
COMMENTARY 408 of an oblique case) in which the genus, i.e. the middle term (which in the second figure is the predicate in both premisses), stands to the extreme terms. aU1"6 (sc. 70 1Tp6{JA'1/La) is used carelessly for the terms of the proposed proposition. 41. Ta.e; KAiJUElC; T(;W OVO ....a.TWV, i.e. their nominatives. Cf. Sopko El. 173b40 EX6v'TWV Or/AEtas ~ d.PPEvoS KAfjaLv (cf. 182:;1.18). 49a z-S. f) ya.p ... 1Tpcha.atv, 'for one of the two things may appear in the dative, as when the other is said to be equal to it, or in the genitive, as when the other is said to be the double of it, or in the accusative, as when the other is said to hit it or se-e it, or in the nominative, as when a man is said to be an animalor in whatever other way the word may be declined in accordance with the premiss in which it occurs'.
CHAPTER 37 The various kinds of attribution 49'6. That this belongs to that, or that this is true of that, has a variety of meanings corresponding to the diversity of the categories; further, the predicates in this or that category may be predicated of the subject either in a particular respect or absolutely, and either simply or compounded; so too in the case of negation. This demands further inquiry.
49a6-8. To 8" lJ1'l'apXEtV ... ~h:nPTJVT(U, i.e. in saying' A belongs to B' we may mean that A is the kind of substance B is, a quality B has, a relation B is in, etc. 8. KaL Ta.uTas il 1TTI il «1TAWS, i.e. in saying 'A belongs to B' we mean that A belongs to B in some respect, or without qualification. En 11 «vACis 11 O'U}.I.1TETrAEY}.I.EVa.S I e.g. (to take Al.'s examples) we may say 'Socrates is a man' or 'Socrates is white', or we may say 'Socrates is a white man'; we may say 'Socrates is talking' or 'Socrates is sitting', or we may say 'Socrates is sitting talking'. 9-10. E1T~O'KEVTEOV SE: ... ~EAnov. This probably refers to all the matters dealt with in this chapter. The words do not amount to a promise; they merely say that these questions demand further study.
CHAPTER 38
The difference between promng that a thing can be known, and promng that it can be known to be so-and-so 49'11 . A word that is repeated in the premisses should be attached to the major, not to the middle, term. E.g., if we want to prove that 'of justice there is knowledge that it is good', 'that it is good' must be added to the major term. The correct analysis is: Of the good there is knowledge that it is good, Justice is good, Therefore of justice there is knowledge that it is good. If we say 'Of the good, that it 'is good, there is knowledge', it would be false and silly to go on to say 'Justice is good, that it is good'. 2:0. Similarly if we wanted to prove that the healthy is knowable qua good, or the goat-stag knowable qua non-existent, or man perishable qua sensible object. 27. The setting out of the terms is not the same when what is proved is something simple and when it is qualified by some attribute or condition, e.g. when the good is proved to be knowable and when it is proved to be capable of being known to be good. In the former case we put as middle term 'existing thing'; in the latter, 'that which is some particular thing'. Let A be knowledge that it is some particular thing, B some particular thing, C good. Then we can predicate A of B ; for of some particular thing there is knowledge that it is that particular thing. And we can predicate B of C ; for the good is some particular thing. Therefore of the gMd there is knowledge that it is good. If 'existing thing' were made middle term we should not have been able to infer that of the good there is knowledge that it is good, but only that there is knowledge that it exists. 49aII-22.
To
S' ''ft'aVa8Ln-Xoul'EVOY
auvETov,
'That the
good is good can be known' is in itself as proper an expression as
'The good can be known to be good', and A. does not deny this. What he points out is that only the latter forro is available as a premiss to prove that justice can be known to be good. To treat the former expression as a premiss would involve having as the other premiss the absurd statement 'Justice is that the good is good'. 14. Ii 6.y"Oc\v. A. is here anticipating. The whole argument in "2-22 deals with the question in which term of the syllogism (to prove that there is knowledge of the goodness of justice) 'that it is good' must be included. 'There is knowledge of justice in so
n
4IO
COMMENTARY
far as it is good' is a different proposition, belonging to the type dealt with in "'-5. But here also A.'s point is sound. If we want to prove that justice in so far as it is good is knowable, we must put our premisses in the form What is good is knowable in so far as it is good, Justice is good. For if we begin by saying The good in so far as it is good is knowable. we cannot go on to say Justice is good in so far as it is good. This, if not o/2. But if A belongs to everything of which B is truly stated,
412
COMMENTARY
A will be true of all of that, of all of which B is stated; while if A is said (without quantification) of that, of all of which B is
said, Bmay belong to C and yet A not belong to all C, or to anyC. 37. Thus if we take the three terms, it is clear that' A is said of that of which B is said, universally' means' A is said of all the things of which B is said'; and if B is said of all of C, so is A; if not, not. 33. We must not suppose that something paradoxical results from isolating the terms; for we do not use the assumption that each term stands for an individual thing; it is like the geometer's assumption that a line is a foot long when it is not-which he does not use as a premiss. Only two premisses related as whole and part can form the basis of proof. Our exhibition of terms is akin to the appeal to sense-perception; neither our examples nor the geometer's figures are necessary to the proof, as the premisses are. 49bI4-JZ. OUK EaTL . . . WQ.VTOS:. A.'s object here is to point out that the premiss which must be universal, in a first-figure syllogism, is the major. This will yield a universal or a particular conclusion according as the minor is universal or particular; a particular major will yield no conclusion, whether the minor be universal or particular. Maier points out (2 a. 265 n. 2) that this section forms the starting-point of Theophrastus' theory about syllogisms KaT"
7'po">',,!,,,w. ct.
AI. 378. 12-379.
II.
In b 26 AI. (371- 25--6) and P. 1351. 8-10) interpret as if there were a comma before KaTa 7TaV'ToS', taking these words with >'
not be thought to justify objection to the method, since the premisses are only illustrative and the validity of a form of syllogism does not depend on the truth of the premisses we choose to illustrate it. To this Maier objects that there has been no reference in the context to the use of examples, so that the remark would be irrelevant. This interpretation, however, comes nearer to doing justice to the words ou8iv ya.p 1rpOuxpwp.EfJa 'Tip T68E 7(, Elvat. since this might be interpreted to mean 'for we make no
use of the assumption that the particular fact is as stated in our example'. But that is evidently rather a loose interpretation of these words. There is one passage that seems to solve the difficulty-Soph.
on
Ka~ tern 'nS' -rptTOS' av8pw1roS' ,"ap' aUroll Kat 'TOUS' KaO' EKUcrrOV' TO yap av(JpW1TOS Kat a1TQV'TO Kowall OU 'T.op..9a S.1ga, ~n " ... ay8pW1TO~ 1(7'.\. point to the reading Ecrrat-. 38. KQ.Ta. TOUS dPTl ....£vous TP01rOUS TpElSJ i.e. Celarent (2Sh4O.6'.), Cesare (27'5-..oyl.O' ....os, d. I. 4- 26. 4-53'2. ET< S' . . . j>ESOSOV. ct. 1. 27-31. 53'2-3. ET< S' . . . a.PXus. ct. 1. 32-46. 3-b3. E1I'Ei. 8' . .. TOUTC.I.IV. In this passage A. considers the problem, what conclusions, besides the primary conclusion, a syllogism can be held to prove implicitly. He first (A) ('3-14) considers conclusions that follow by conversion of the primary conclusion. Such conclusions follow from A, E, or I conclusions, but not from an 0 conclusion, since this alone is not convertible either simply or per accidens. (B) He considers secondly ("5-b 3) conclusions
COMMENTARY derivable from the original syllogism, with regard to terms which can be subsumed either under the middle or under the minor term (the latter expressed by ~",l TQ O1J/L",<paCT/La, '17). A. considers first (I) syllogisms in which the conclusion is universal, (a) in the first figure. If we have the syllogism All C is A, All B is C, Therefore all B is A, then if all D is B, it is implicitly proved that all D is A ('21-2). And if all E is C, it follows that all E is A ('22-4). Similar reasoning applies to an original syllogism of the form No C is A, All B is C, Therefore no B is A ('24). (b) In the second figure. If we have the syllogism No B is A , All C is A, Therefore no C is B, then if all Dis C, it is implicitly proved that no Dis B ('25-8). If all E is A, it follows that no E is B, but this does not follow from the original syllogism. That syllogism proved that no C (and therefore implicitly that no D) is B; but it assumed (that no B is A, or in other words) that no A is B, and it is from this+ All E is A that it follows that no E is B ('29-34). A. next considers (2) syllogisms in which the conclusion is particular, and as before he takes first (a) syllogisms in the first figure. While in '19-24 B was the minor and C the middle term, he here takes B as middle term and C as minor. Here a term subsumable under C cannot be inferred to be A, or not to be A (undistributed middle). A term subsumable under B can be inferred to be (or not to be) A, but not as a result of the original syllogism (but as a result of the original major premiss All B is A (or No B is A)+the new premiss All D is B) ('34-40). The commentators make A.'s criticism in -29-34 tum on the fact that the major premiss of Cesare (No B is A) needs to be converted, in order to yield by the dictum de omni et nullo the conclusion that no E is B. But this consideration does not apply to the syllogisms dealt with in '34-40. Take a syllogism in DariiAll B is A, Some C is B, Therefore some C is A. Then if all D is B, it follows from the original major premiss+All D is B, without any conversion, that all D is A. And there was no explicit reference in the case of Cesare ('29-34) to the necessity of conversion. I conclude that A.'s point was not that, but that the conclusion No E is B followed not from the original syllogism, but from its major premiss. Finally (b), A. says ('4o-b3) that in the case of syllogisms with
particular conclusions in the second or third figure, subsumption of a new term under the minor term yields no conclusion (undistributed middle), but subsumption under the middle term yields a conclusion-one, however, that does not follow from the original syllogism (but from its major premiss), as in the case of
II. I. 53"7-12 427 syllogisms with a universal conclusion, so that we should either not reckon such secondary conclusions as following from the universal syllogisms, or reckon them (loosely) as following from the particular syllogisms as well (Wa-r' ~ ov8" EK~'i laTa, 7} leal E1T' TOVrwV). I take the point of these last words to be that A. has now realized that he was speaking loosely in treating (in " 2'-4) the conclusions reached by subsumption under the middle term of a syllogism in Barbara or Celarent as secondary conclusions from
that syllogism; they, like other conclusions by subsumption under the middle term, are conclusions not from the original syllogism, but from its major premiss, i.e. by parity of reasoning. A. omits to point out that from Camestres, Baroco, Disamis, and Bocardo. by subsumption of a new term under the middle term, no conclusion relating the new term to the major term can
be drawn. "TEP'lTlK.]. i.e. the particular negative. 7. >i 8-9Eiaa.c., i.e. the A mentioned in bu 14 (the whole datum from which inference proceeds), not the A mentioned in b2I -2 (the major term). , 27. TCUT11S 8' oUX OVOTEpaS ETUXEV. (J1TO'T€Pa.s (for 01TO'TtPa.) is rather an extraordinary example of attraction, but has parallels in A" e,g. An. Post. 79b 4" 80"4, 8"9. 2.8-30' EclV1TEP o)."v ... 01TOTEPa.crOUV. All B is A is 'wholly false' when no B is A, and No B is A 'wholly false' when all B is A (S4'4-{i). All B is A and No B is A are 'partly false' when some B is A and some is not. Cf. S6'S_b3 n. 54'7-15. (iv 8TJ ... r. The phrases ~ TO AB, ~ TO Br in '8, I2 are abbreviations of.q 'TrprYracTty; Jq,' ~£iTat TO AB (TO Br). Similar instances are to be found in An, Post. 94'3', Phys. 2ISb8, 9, etc. &-,. Ka.t 'lrQVTL • • • A, 'i.e. that all B is A 11-14. b .... o£w~ o· ... ECM'a.L. A. begins the sentence meaning to say 'similarly if A belongs to all B, etc., the conclusion cannot be tme' (c!. '9), but by inadvertence says 'the conclusion will be false', which makes the ov8' in all incorrect; but the anacoluthon is a very natural one. 13. Ka.t ..,,,OEVt ~ TO B, TO A, 'i.e. that no B is A'. 31-2. oTov oaa. .•. e,g, when B and C are species of A, neither included in the other. 38. olov Toi~ E~ u).).ou YEvOu~ ••• YEvo~, 'e.g. when A is a genus, and B and C are species of a different genus'. bS-6. olov TO YEVO~ .•. SLa.+Op~, <e.g. when A is a genus, B a species within it, and C a differentia of it' (confined to the genus but not to the species).
n
I.
Ii"",]"a.,
II. 2. 53b1O-55"5 11-13. OIOY TO Vivos •••
8la.4>Op~,
43'
'e.g. when A is a genus, B
a species of a different genus, and C a differentia of the second genus' (confined to that genus but not to the species). 5511:13-14. otov TO YEvOs .•• E'l8EUL, 'e.g. when A is a genus, B a species of another genus, and C an accident of the various species of A' (not confioed to A, and never predicable of B). IS. AEUK~ Sf: Tlv£. In order to correspond with ilI2 Tip 8£ r ny, f'~ inrapXEw and with 1117 TJ A TWL 'T~ r OVX inrdP~E'. this should read AEVKo/ 8£ 'TWL ou, and this shOl;lld perhaps be read; but it has no MS. support, and in 56"4, an exactly similar passage, '\.VK or that C is B because A is B and C is A. There is no other method of reciprocal proof; for if we take a middle term distinct from C and A there is no circle, and if we take as premisses both the old premisses we shall simply get the same syllogism. 32. Where the original premisses are inconvertible one of our new premisses will be unproved; for it cannot be proved from the original premisses. But if all three terms are convertible, we can prove all the propositions from one another. Suppose we have shown (I) that All B is A and All C is B entail All Cis A. (2) that All C is A and All B is C entail All B is A. (3) that All A is Band All C is A entail All C is B. Then we have still to prove that all B is C and that all A is B. which are the only unproved premisses we have used. We prove (4) that all A is B by assuming that all C is B and all A is C. and (s) that all B is C by assuming that all A is C and all B is A. 58a6. In both these syllogisms we have assumed one unproved premiss. that all A is C. If we can prove this. we shall have proved all six propositions from each otber. Now ii (6) we take the premisses All B is C and All A is B. both the premisses have been proved. and it follows that all A is C. I2. Thus it is only when the original premisses are convertible that we can effect reciprocal proof; in other cases we simply assume one of our new premisses without proof. And even when the terms are convertible we use to prove a proposition what was previously proved from the proposition. All B is C and All A is B are proved from All A is C. and it is proved from them. ::u.
26.
Syllogism No B is A. Aile is B. :. No e is A.
Reciprocal proof No C is A. All B ise. :. No B is A. All of that, none of which is A, is B. NoCis A. :. All e is. B.
II. 5. 57br8-58'32 SyUogism 36. All B is A. SameC is B. :. Some C is A.
"z. 6.
No B is A. Some C is B.
439
Reciprocal proof The universal premiss cannot be proved reciprocally, nor can anything be proved from
the other two propositions, since these are both particular. All A is B. Some C is A. :. Some C is B. The universal premiss cannot be proved.
:. Some C is not A. Some of that, some of which is not A, is B. Some C is not A. :. Some C is B. 57bI~20. To 8£ KUKA'!? .•. AO~-m1Y' The construction would be easier if we had >"a{1£tv in h20, or if the second 'TOV in hI9 were
omitted; but either emendation is open to the objection that it involves A. in identifying TO 3£lKvvaOat (passive) with 'TO (1V!-'7TEp&vaa9at (middle). The traditional text is possible: 'Circular and reciprocal proof means proof achieved by means of the ,original conclusion and by converting one of the premisses simply and inferring the other premiss: 24. Kat TO A TIi> B. The sense and the parallel passage b25- 7 show that these words should be omitted. 25-6. ft ei [on] ... u1Tapxov. on must be rejected as ungrammatical.
S8aI4-15. EV SE TOLS a.AAO~S ••• E'1rO~EV refers to 57b32-5. where A. pointed out that when the terms are not simply convertible, the circular proof can be effected only by assuming something that is unprovable, viz. the converse of one of the original premisses. He omits to point out that even when the tenns are coextensive, the converse of an A proposition cannot be
inferred from that proposition, though its truth may be known independently. 22. EO"TW TO ~EV B •. • UTra.PXE(.V, 'let it be the case that B belongs to all C'. Waitz is justified in reading ll1TapxnV, with all the best MSS. Cf. "30 (where it is read by all the MSS.) and L. and S. S.v. (:lp.t, A. VI. h. 25. E").").ous . . . Su.'v. As Heiberg (Abh. zu, Gesch. d. Math. Wissemchallen, xviii. 18-'9) remarks, the first conditional clause refers to the proposition which appears as Euc. i. .8 ('if a straight line falling on two straight lines makes the exterior angle equal to the interior and opposite angle on the same side of the straight line ... the straight lines will be parallel'). while the second refers to Euc. i. 27 ('if a straight line falling on two straight lines makes the alternate angles equal, the straight lines will be parallel'), since only in some pre-Euclidean proof of this proposition, not in the proof of i. 28, can the sum of the angles of a triangle have played a part. Cf. 65'4-7 n . IM4' '0 8. ",.u8" •... ",.u80.. Chapter 18 continues the treatment of the subject dealt with in the previous chapter, viz. the importance of finding the premiss that is really responsible for the falsity of a conclusion; if the premisses that immediately precede the conclusion have themselves been derived from prior premisses, at least one of the latter must be false. I«)-ZO. ~~ ]b27-8. ·OTllY S' ... "",tw. This applies only to syllogisms in Barbara (b28-32). A. says £11l. 'ToG fLTJ fnrapx£ul waarnw!> (b 32 ), but this means only that conversion is possible also with syllogisms in Celarent; only in one of the three cases discussed in b34-68 1 1 does the conversion assume the converse of the conclusion, as in the case of Barbara. 3z-68a3. Kal E'lrl TOU I-'TJ lnra.pxnv . . . ">"oy,al-'ou . If we start as A. does with a syllogism of the form No B is A, All C is B, Therefore no C is A, only three conversions are possible: (r) All C is B, No A is B, Therefore no A is C; (2) All B is C, No C is A, Therefore no A is B; (3) All B is C, No A is C, Therefore no A is B. b34-6 refers to the first of these conversions. b37 -8 is
479
difficult. The vulgate reading, KaL El -rijJ B 'TO r ciV'TtUTP€tP££, Kal -rtf> A all'tW'Tr"cp€L, gives the invalid inference All B is C, No B is A, Therefore no A is C. We must read either (a) Kat €l 'Tip B 'TO r ciV'n0'7PECPEL, KaL 'TO A aV'TLO"Tpicpn (or aV7"tcrrpiifi€£), or (b) Kat El TO B 7"0 r aJl7'tC1'TpEcpn, Kat np A aV'Tw-rpEcpEL (or o.v'TW'Tp''''n), either of which readings gives the valid inference (2) above. 338-68al is also difficult. The vulgate reading Kat £l 'T() r 7TPOS 'TO A aJl'ncrrp'rpn gives the invalid inference All C is B, No A is C, Therefore no A is B. In elucidating this conversion, A. explicitly assumes not All C is B, but its converse ( ydp T..ou dg,ovf'€V E7raYEtY. (In Soph. El. 174'34, cited under (.), it is possible that TO Ka86>.ov should be taken as governed by E7rayayov'Ta as well as by EPW7'T1T..oyov, a usage which plainly has affinities with usages (I), (.), (3). (5) There is a usage of 'mlyw8a< (middle) which has often been thought to be the origin of the technical meaning of ETTaywyrJ, viz. its usage in the sense of citing, adducing, with such words as fJ-ap'Tupas, fJ-apTVpta, €lKO"aS (L. and S. II. 3). A. has E7rf:l.y€oBaL 7rOU1~V (Met. 995as). and E7raYOf'EYOL Kat 'TO" "0f''''Ipov (Part. An. 673'15), but apparently never uses the word of the citation of individual examples to prove a general conclusion. There is, however, a trace of this usage in A.'s use of E1TaKnKos, E7raK'TLKws. In A n. Post. 77 b33 E7TaKnK~ 7rpO'TaOLS and in Phys. 210bS E1TaK'TLKWS OK07TOVCTL-V the reference is to the examination of individual instances rather than to the drawing of a universal conclusion. The same may be true of the famous reference to Socrates as having introduced E7raK'TtKOt >..OyOL (Met. I07Sb2S); for in fact Socrates adduced individual examples much more often to refute
II. 23 a general proposition than he used them inductively, to establish such a proposition. Of the passages in which the word '"ayWI"1 Itself occurs, many give no definite clue to the precise shade of meaning intended; but many do give such a clue. In most passages '"ayWI"1 clearly means not the citation of individual instances but the advance from them to a universal; and this has affinities with senses (I), (.), (3), (4) of '''''y«", not with sense (S). E.g. Top. IOS'13 '"ayw0/ ~ awo 'TWV KaB' EKacrra E1TL 'TO Ko,(JO>"OV £4>o8o~, An. Post. SIbI ~ E7TaywyTJ lie 'TWV KQ.Ta. IL€POS, An. Pro 68hI5 E1TayWi'11 EUTt ... 'TO 4~hcl £'TEPOV Oanpov aKpov -rcji p.EUI.p uv)J.,oywo.aOa,. But occasionally E1TayW"Y"'l seems to mean 'adducing of instances' (corresponding to sense (5) of Emiynv)-Top. I08b IO Tfi KaO' €IC4UTQ. br'i 'TWV OILotwv braywyfj 'TO Ka06i\ov dgwvp.O' E7Taynv, Sopko El. 174-36 (iLa ".,ryv rijS' E7Taywyijs J.LvF:lav. Cat. _I3 h37 8-7]).,ov tjj KaO' EKacrrov E7Taywyfj. Met . 1048a35 8fjAOV 8' bTl. nov KaO' EKacrra 7fj E7raywyfj 8 {1ov>..ofL£(}a >"'YEtV. TOU
(The use of '"ayWl"1 in 67"3 corresponds exactly to that of ETrayoJLO'os in An. Post. 71-21. Here, as in Top. IIIb38. a deductive, not an inductive, process is referred to.) The first of these two usages of '"aywl"7 has its parallels in other authors (L. and S. sense S a), and has an affinity with the use of the word in the sense of 'allurement, enticement' (L. and S. sense 4 a). The second usage seems not to occur in other authors. Plato's usage of throws no great light on that of A. The most relevant passages are Polito 278 a E7TCiy~tV atiTovs- E1TL ", f'~1TW Y<J'VwC1Kof'£va (usage (I) of '''''Y''") , and Hipp. Maj . • &) b, Laws 8'3 a, Rep. 364 c, Proi. 347 e, Lys. "5 c (usage S). E1raywyrJ occurs in Plato only in the sense of 'incantation' (Rep. 364C, Laws 933d), which is akin to usage (I) of '''''y,," rather than to usage (S). It is by a confiation of these two ideas, that of an advance in thought (without any necessary implication that it is an advance from particular to universal) and that of an adducing of particular instances (without any necessary implication of the drawing of a positive conclusion), that the technical sense of '"ayWl"1 as used by A. was developed. A.'s choice of a word whose main meaning is just 'leading on', as his technical name for induction, is probably influenced by his view that induction is m8a.vtfn·£pov than deduction (TOP. 10S',6). A. refers rather loosely in the first paragraph to three kinds of argument--demonstrative and dialectical argument on the one hand, rhetorical on the other. His view of the relations between the three would, if he were writing more carefully, be stated as
'''''y,,"
COMMENTARY follows: The object of demonstration i~ to reach knowledge, or science; and to this end (a) its premisses must be known, and (b) its procedure must be strictly convincing; and this implies that . it must be in one of the three figures of syllogism-preferably in the first, which alone is for A. self-evidencing. The object of dialectic and of rhetoric alike is to produce conviction (1f'''''''); and therefore (a) their premisses need not be true; it is enough if they are [vBogo., likely to win acceptance; and (b) their method need not be the strict syllogistic one. Many of their arguments · are quite regular syllogistic ones, formally just like those used in demonstration. But many others are in forms that are likely to produce conviction, but can be logically justified only if they can be reduced to syllogistic form; and it is this that A. proposes to do in chs. 23-7. Thus these chapters form a natural appendix to the treatment of syllogism in I. I-II. 22. The distinction between dialectical and rhetorical arguments is logically unimportant. They are of the same logical type; but when used in ordinary conversation or the debates of the schools A. calls them dialectical, when used in set speeches he calls them rhetorical. Conviction, says A. ('>13-14), is always produced either by syllogism or by induction; and this statement is echoed in many other passages. But besides these there are processes akin to syllogism (.IK6. and OTJ''''ov, ch. 27) or to induction (1fapaB ..yp.a, ch. 24). And with them he discusses reduction (ch. 25) and objection (ch. 26), which are less directly connected with his theme ---&.cusses them because he wants to refer to all the kinds of argument known to him. Induction and 'the syllogism from induction' (i.e. the syllogism we get when we cast an inductive argument into syllogistic form) 'infer that the major term is predicable of the middie term, by means of the minor term' (b'S-17). The statement is paradoxical; it is to be explained by noticing that the terms are named with reference to the position they would occupy in a demonstrative syllogism (which is the ideal type of syllogism). A. bases his example of the inductive syllogism on a theory earlier held, that the absence of a gall-bladder is the cause of long life in animals (Part. An. 677&30 8c.d KaL xaprlrrro.'To. AtyOvaL 'TWV d.pxalwv ol tjxWKOYTf~ at'nov Elvct4 TOU 'TrAEk C~v XpOJIOV 'T'd p.,q lXEW XcM~V). A. had his doubts about the COmpleteness of this explanation; in An. Post. 99b4-7 he suggests that it may be true for quadrupeds but that the long life of birds is due to their dry constitution or to some third cause. The theory serves, however, to illustrate his
point. In the demonstrative syllogism. that which explains facts by their actual grounds or causes. the absence of a gallbladder is the middle term that connects long life with the animal species that possess long life. Thus the inductive syllogism which aims at showing not why certain animal species are longlived but tlua all gall-less animals are long-lived. is said to prove the major term true of the middle term {not. of course. its own middle but that of the demonstrattve syllogism} by means of the minor {not its own minor but that of the demonstrative syllogism}. Now if instead of reasoning demonstratively 'AIl B is A, All C is B. Therefore all C is A', we try to prove from All C is A, All C is B, that all B is A, we commit a fallacy, from which we can save ourselves only if in addition we know that all B is C (b23 €l ow aV7"LaTp€q,£' 'TO r Tq, B Ka~ JL~ VrrEpnlllEL TO ,.,.EUOV, i.e. if B, the plaov of the demonstrative syllogism, is not wider than C). 68~o. -' ~ 8. r ~o KQ8' 'ka.crroy I"'Kp611IOY. In b' 7-9 A. says that, to make the inference valid, r must consist of all the particulars. Critics have pointed out that in order to prove that all gall-less animals are long-lived it is not necessary to know that all long-lived animals fall within one or another of the species examined, but only that all ·gall-less animals do. Accordingly Grote (Arist.' 187 n. b) proposed to read a)(o>.ov for fL4KpOpwv, and M. Consbruch {Arch. j. Gesch. d. Phil. v {d19'}, 310} proposed to omit p.4Kp&P,OV, Grote's emendation is not probable. Consbruch's is more attractive, since JA41(~fJl.O" might easily be a gloss; and it derives some support from P.'s paraphrase, which says (473. 16-17) simply 'TO r olav Kopae KaL oaa To~iiTa . .\€,tn ow on 0 KOpae leaL 0 l'Aaq,or axoAa p.aKpOpuJ. EWW. But P.'s change of instances shows that he is paraphrasing very freely, and therefore that his words do not throw much light on the reading. The argument would be clearer if ILQltpo/1wv, which is the major tenn A, were not introduced into the statement of what r stands for. But the vulgate reading offers no real difficulty. In saying J¢/ cP BE r TO K0.8' IKacrrov p.aKpO{Jwv, A. does not say that r stands for all fL4KpOP.4, but only that it stands for the particular fLo.KpOPW. in question, those from whose being fL4KpOPW. it is inferred that all ttXOAa. are fWoKpO{1W.. :11-3. T9 8" r ... T9 r. The structure of the whole passage b2I --1 shows that in the present sentence A. must be stating the data AIl C is A, All C is B, and in the next sentence adding the further datum that' All C is B' is convertible, and drawing the conclusion All B is A. Clearly, then, he must not, in this sentence, state the first premiss in a form which already implies that all
COMMENTARY B is A, so that ']'TeLV yap 'TO O:XOAOV lLaKp6{J,ov cannot be right; we must read r for O:XOAOV. Finding p.aKp6{Jwv (which is what A stands for) substituted by A. for A in b 22 , an early copyist has rashly substituted axoAov for r; but r survives (though deleted) in n after axo.\ov, and Pacins has the correct reading. Instead of the colon before and the comma after 1T~p.a'Ta OIJl< EptO"TLKo. . . . ovaE y\-t,rt £CTTL I/JEvSoypd4rrJp.a 7T€P~ dArl)£~, otOIl 'TO •17T1rQKpo:rovs ~ 0: T€:TpaywvLap.os d 'OLd. 'TCdV JL71vt(JlCwv, ib. 172-2 orov 0" 'TE'rpaYWIILaILOS 0: p.EII ~ul 'TooV p.TJvlaKWV aUK £purrLKOS, and Phys. 185a14 a}La S' ovBE "'-VEW a.1rov-ra 7TPOcnJK€L, dAA' Tj aaa £1< TWV o.PXwv 'TLS l7Tt8ELKVV~ !f£v8naL, aaa 8E JL1}. ou, olov TOil -rerpaywvwp.oll 'TOil p.£v 'OU1 'TWV TjI':'f'Jj.U]:rwv YEwp.€-rpLKOV
'O,a.Avaat. There has been much discussion
as to the details of the attempt. The text of Soph. El. '71b15 implies that it was different from the attempt of Hippocrates of Chios: but there is enough evidence, in the commentators on the Physics, that it was Hippocrates that attempted a solution by means of lunes, and Diels is probably right in holding ~ .; T Therefore no S is P. He interprets Q.vaYK7] 'lTpOS 7'0 KaOO.\ov TW1I 7Tp07"£tJlOP.EVWV T7Jv o.V7upaaw td7TE'iV (b2 o- I ) as meaning 'he must take as his premiss the opposite of the universal proposition from which as a major premiss the opposed 1Tp6TauLs was derived'. If the article in TO Ka06>..ov is to be stressed. this interpretation must be accepted; for if A. is thinking of S as having only one superordinate, the opposed syllogisms must be related as shown above. It is, however, quite unnecessary to ascribe this further restriction to A. What the words in question mean is 'he must frame his contradiction with a view to the universal (Le. some universal) predicable of the things put forward by the opponent' (i.e. of the subject of his "poTaa«). For A. goes on to say 'e.g., if the opponent claims that no contraries are objects of a single science, he should reply that opposites (the genus which includes both contraries and contradictories) are'-without suggesting that the opponent has said 'No opposites are objects of a single science, and therefore no contraries are'. In fact an EvcrraaLs would he much more plausible if it did not start by a flat contradiction of the opponent's original premiss, but introduced a new middle tenn; and A. can hardly have failed to see this. This interpretation is confirmed by what A. says about the attempt to prove
II.
26. 6], 8.0 Kat •.• ian•. Cook Wilson argued (in Trans. of the Oxford Philol. Soc. 1883-4, 45-6) that this points to an earlier form of the doctrine of enthymeme than that which is usual in the Prior A nalytics and the Rhetoric; that A. recoguized at this early stage an analogy between lYA 8 " qJETO · Ot'>A nVTWl1El1Ec,ot Ka.t Ot . Ot.rTWS' Q1raw£ll'To(' 24 , n.Y'TUJ EV7Jr W>18w< (I024b32). The arguments for supposing Antisthenes to be referred to are stated by Maier (2 b. 'S n. 2); he follows Dfunmler too readily in scenting allusions to Antisthenes in Plato, but he is probably right in saying that A.'s allusions are to Antisthenes. Cf. my note on Met. IOOS b2-S. We cannot certainly identify the second school, referred to (in b&-7) as having held that knowledge is possible because there is no objection to circular proof. P. offers no conjecture on the subject. Cherniss (A.'s Criticism of Plato and the Academy, i. 68) argues that 'it is probable that the thesis which A. here criticizes was that of certain followers of Xenocrates who had abandoned the last vestiges of the theory of ideas and therewith the objects of direct knowledge that served as the principles of demonstrative reason' ; and he may well be right. 6. 1I'Q.VTWV pkv-rOl. a.1I'OSEl.€'t; EtVQ.L. a.1T68E~'S' is more idiomatic than d"oS,~6) and refers to those who hold that circular reasoning gives knowledge. That knowledge is not possible otherwise than by proof is common ground to both schools ('>IS-I6), so that o:.uw< wonld not serve to distinguish the first school from the second. P. read .lAWS (42.II, 4S. 17). 22. ttTTa.Ta~ 8E 'lTOTE TO. Uf1Eaa.. This is a rather careless account of the situation more ·a ccurately expressed in 9Sb22 by the words O"T?jO'E1'"al 1TOV Els aj.L£(1ol'. What A. means is that in the attempt to prove what we want to prove, we must sooner or later come to inunediate premisses, not admitting of proof.
5I 4
8e, {TfTELV a.1TOOE~W a1To8£l,fw Elva, (£15'
.uv
I('a~ -rlvwv
SIS 23-4. 1(00L ou J'ovov .. . yVWpltO~EV. A.'s fullest account of the faculty by which o.pXa.i come to be known is to be found in An. Post. ii. 19. 29. ()V1rEP TP011'OY •.• yvwP"J10V is rather loosely tacked on'a distinction of senses of "prior" with which induction familiarizes us', since in it what is prior in itself is established by means of
what is prior to us. 3~2. Et S' OllTWS •.• yVWP',",WTEpWV. If the establishment of what is prior in itself by what is prior to us be admitted, (a) knowledge in the strict sense will not have been correctly defined by us in ch. 2 as proof from what is prior in itself, since there is another kind of it, or rather (b) the other is not strictly proof (nor strictly knowledge). 3" YWOI'EvtJ y'. Neither Bekker's reading "l'wo('5) is that of attributes which while belonging to certain subjects cannot be defined without mentioning these subjects. In all the instances A. gives of this sort of situation ('3SJ>I, b'~1) these attributes occur in pairs such that every instance of the subject must have one or other of the attributes; but there is no reason why they should not occur in groups of three (e.g. equilateral, isosceles, scalene as attributes of the triangle) or of some larger number. For the sake of completeness A. mentions two other cases in which the expression Ko.8'o.w6 is used. (3) ("5-10) From propositions in which an attribute belonging Ko.8' o.w6 to a subject is asserted of it, he turns to propositions in which a thing is said to exist Ka.8' 0..n-6. It is only individual substances ("7) that exist KO,(}' atha. not in virtue of some implied substratwn. When on the other hand we refer to something by an adjectival or participial phrase such as TO AEVKOV or 'TO f3a8lC'!v, we do not mean that the quality or the activity referred to exists in its own right; it can exist only by belonging to something that has or does it; what is white must be a body (or a snrface), what.is walking an animal. Finally (4) (b c>-16) we use the phrase to describe a necessary '
COMMENTARY connexion not between an attribute and a subject, but between two events, viz. the causal relation, as when we say that a thing to which one event happened became Ka8' Oov.ro involved in another event, KaT&' standing for 8,a, which more definitely refers to the causal relation. This fourth type of Ka8' aVro is akin to the first two in that it points to a necessary relation between that which is Ka8' aVro and that to which it is Ka8' aVro, but the relation here involves temporal sequence, as distinguished from the timeless connexions between attribute and subject that are found in the first two types. 34. oaa. U1rCl.PXEL TE EV T~ Tt Ecrnv. - If the position of 'TIE be stressed, A. should be here giving the first characteristic of a certain kind of Ka(t aliTa, to be followed by another characteristic introduced by Kat; and this we can actually get if we terminate the parenthesis at lcrrl, a36. But then the second clause, J(a~ EV 'T~ .\Oycp TqJ >'..1yovn -rl Ecrnv EVVTTtl.PXn. would be practically a repetition of the first. It is better therefore to suppose that T< is, as often, slightly misplaced, and that what answers to the present clause is Kat oao,s ... B'7}AoiiV'n, a37-8. Zarabella (b. 'DU()s Ar;st. Libb. Post. Anal. Comm.' 23 R-V) points out that oaa inrapxn £V Tcp Tl £C1TtV does not mean, strictly. 'those that are present in the Tl £C1TW'. The construction of imapxnv is not with £v (as is that of &tnrapx£w) but with a simple dative, and the proper translation is 'those things which belong to a given subject, as elements in its essence'. The full construction, with both the dative and €V, is found in 74bg ToiS' 8' aUra £V 520
Tcp
'Tl £C1TW tnrapx€f. KC1T'f'}YOpOVP.EVOtS (lUrwv. tca.t oaOLS TWV U1ra.PXOVTWV .... SrtXOUVTl. tmapxnv, in
3?-8.
A.'s logic, has a rather general significance, including the 'belonging' of a predicate to its subject, as straight and curved belong to a line, and the 'belonging' to a thing of an element in its nature, as a line belongs to a triangle. £W7TclPXHV on the other hand is a technical word used to denote the presence of something as an element in the essence (and therefore in the definition) of another thing. In certain passages the distinction is very clearly marked: a38j)Z olov TO dOv iJ'Trapxu ypap.p.fj . . . KCl' 11'(ia, TOVrOtS' £VV7J'apXOvatv £v 1"0/ AOyC:P T~ Tl £errl. AEyOV'n lV(JC1 p.£v ypap.p.-IJ KT.\ ., 841i12 KaO' av.-rd. BE- 8t:nws' oaa 1"£ yap £V £KEiVOtS' £VV'1tapXE' £V Tcp Tl £C1T" Ka, ors aUrd. £V 1"4> Tl £C1TW (sc. £VV'1tapx£ 4) V1TupXOVatv (participle agreeing with ots) aliTois' otov Tip aptOp.ep 'TO '1T£ptTT(W, 0 (/7J'UPXU p.~ ap'Op.ep, EVV7rapxEt 8' Clv.rOS 0: ap,OfLos EV.,.ep .\Oylp aUTou, ib. 20 '1Tp6rrov 0: aptOp.os £vv7J'apeU V7rclPXOVa,v mh-o/. For other instances of £VV1Ta.PXnv d. 73~I7, 18, 84a25. Any-
I. 4. 73'34-b18
521
thing that EVtnTapXEt £,., something may be said inrapxnv to it, but not vice versa. In view of these passages I concluded that v1Tapx6vTwV should be read here, and afterwards found that I had been anticipated by Bonitz (Arist. Stud. iv. 21). The emendation derives some support from T. 10. 30 OCTWI! S11 CTvI-L{J€/l.,pco'TWV TW' 'TOY "oroI' ci1TO~,8oV'TES TO. fmOK€lJL£va alhoir UVV€.rPEAKop.€8a €v Tip A&Y~, -ruih-a Kaf), aUTO. inrapXEtv 'TOVTotS' "/rETa, 'TOLS' VrrOK€tf'EvotS. The MSS. are similarly confused in '38, 84"3, '9, zo, and in An. Pro 6S"S. 39-bI. Kni. TO 1TEptTTOV .•• E1'Ep6 ....TJKE~. Not only odd and even, but prime and composite, square and oblong (i.e. non-square composite), are leaO' aVro to number in the second sense of KaO'
av.ro.
b7 . teal TO AEUKav (AEUKOV). The editions have lea' A£VKOV. But this does not give a good sense, and n's Kat TO AEVKO" points the way to the true reading. 16-18. Tel apo. AryOf1EVa .. . a.Va.yKT)~. A. seems here to be picking out the first two senses of Ko.O' uv.ro as those most pertinent to his purpose (the other two having been mentioned in order to give an exhaustive account of the senses of the phrase). Similarly it is they alone that are mentioned in 84'II-28. They are specially pertinent to the subject of the Posterior Analytics (demonstrative science). Propositions predicating of their subject what is Kaff am-a to it in the first sense (viz. its definition or some element in its definition) occur among the premisses of demonstration. With regard to propositions predicating of their subject something that is KaO' aVTo to it in the second sense. A. seems not to have made up his mind whether their place is among the premisses or among the conclusions of scientific reasoning. In 74bS-IZ they are clearly placed among the premisses. In 7S'z8-3I propositions asserting of their subjects something that is KaO' aVro to them are said to occur both as pTemisses and as conclusions, but A. does not there distinguish between the two kinds of KaO' aVTO proposition. lit 76-32--6 TO EVO'; (a KaO' aUTO attribute of the second kind) appears to be treated, in contrast to p.ovas and J.l.EYE(JOS, as something whose existence has to be proved. not to be assumed; and 1rt:tPt'T'TOV and apnov are clearly so treated in J 76b6-u. In 75 1140-r and in 84an-I7 propositions involving teaO am-a attributes are said to bet objects of proof, and this must refer to those which involve KaO aVTo attributes of the second kind, since A ..says consistently that both the essence and the existence of KaO' mho attributes of the first kind are assumed, not proved. The truth is that A. has not distinguished between two types
COMMENTARY of proposition involving Ko.8? aUro attributes of the second kind. That every line is either straight, crooked, or curved, or that every number is either odd or even, must be assumed; that a particular line is straight (i.e. that three particular points are collinear), or that a number reached by a particular arithmetical operation is odd, must be proved. Thus to the two types of za.a. o.pxai recogoized by A. in 72"18- 24 he ought to have added a third type, disjunctive propositions such as 'every number must be either odd or even'.
52 2
17. OUTWS- ~s
€vU1Ta.PXEW
TOlS l(aT1"1yopou"EVO~S
'i1 EVUTra.PXEc:r9a.L,
'as inhering in (i.e. being included in the essence of) the subjects that are accused of possessing them' (mode (1) of the Ka8' aVr6 ("34- 7)), 'or being iulrered in by them (i.e. having the subjects included in their essence): (mode (2) of the Ka8' a~76 ("37-b3)). KarrrrOpOVf.LEVOV,
generally used of the predicate. is occasionally,
as here, used of the subject 'accused', i.e. predicated about (cl. An. Pro 47b,). For ws btnr&'PXEtV = ws btmapxoll'TD., cf. 75.25. 19. fJ cnrAws 'il TQ a.v·nKEl~a. a1TAwS' applies to the attributes that are K0.8' aUTO in the first sense, 'To. ciVnKEll-'EVa to those that are Ka.()' aUTO in the second sense. 2I-Z. EC1TL ycip . . . E1TETa." . Of two contrary tenns, i.e. two
terms both positive in form but essentially opposed, either one stands for a characteristic and the other stands for the complete absence of that characteristic, while intermediate terms standing for partial absences of it are possible (as there are colours between white and black), or one term is 'identical with the contradictory of the other, within the same genus'. In the latter case, while the one term is not the bare negation of the other (if it were, they would be contradictories, not contraries), yet within the only genus of which either is an appropriate predicate, every term must be characterized either by the one or by the other. Not every entity must be either odd or even; but the only entities that can be odd or even (i.e. numbers) must be one or the other. The not-odd in number is even, not in the sense that 'even' means nothing more than 'not odd', but inasmuch as every number that is not odd must in consequence be even E1TE7'a.,). 25-32. To . . Ev o~v •• • 'Laov. A. has in a28- b24 stated the first two conditions for a predicate's belonging Ka86>.ov to its subjectthat it must be true of every instance (Ka.'Ta. 'lTa.voros) and true in virtue of the subject's nature (Ka8' aVr6). He now adds a third condition, that it must be true of the subject fi aVr6, precisely as being itself, not as being a species of a certain genus. It is
(n
52 3 puzzling. then, to find A. saying TO Ka8' awo lea, QliTo -rQVTOV (b2 8). It must be remembered, however, that he is making his terminology as he goes. Having first used Ka8' Qv-ro and Uawo as standing for different conditions, he now intimates that KaO' aUTO in a stricter sense means the same as '9 QV'TO; that which belongs to a subject strictly KaO' av,.6 is precisely that which belongs to it qua itself, not in virtue of a generic nature which it shares with other things; d. 74'2 n. This strict sense of Ka06AOIJ is, perhaps, found nowhere else in A. ; usually the word is used in the sense of KQ'T(l1TQV'Tt:>S' simply; e.g. in 99'33-4. 32-74a3. TO ka.96Xou Sf: . . . 11')'1:0\1, Universality is present when (I) the given predicate is tme of every chance instance of the subject, and (2) the given subject is the first, i.e. widest, class, such that the predicate is true of every chance instance of it. As a subject of 'having angles equal to two right angles', figure violates the first condition, isosceles triangle the second; only triangle satisfies both. 34. oun T~ ax1\ . . a.T\ EaT" tca.80Aou is answered irregularly by 'TO 8' laoCTKEA£S' 1(1""\., b38. 74az. TWV 8' a).. Awv ... a.1ho, .i.e. not K0.8' aUTO in the stricter sense of KaO' av,.6 in which it is identified with a~T6 (73b28~).
n
n
CHAPTER 5 How we fall into, and hew we can avoid, the ,"or of thinking our conclusion, a true universal proposition when it is not 74'4. We may wrongly suppose a conclusion to be universal, when (I) it is impossible to find a class higher than the sub-9up-.TJv I'EV .•. oU'"!"''T'I}Uts Y' ) , Kat•'TO •• , o tov at p.a" " p.aTtKat. 'I} OE 1Taaa EOXa-rOV EV 1fj dVaAVUEt 'TrPW'TOV ElvaL €v Tjj Y£V€UEL, In deliberation we desire an end; we ask what means wonld produce that end, what means wonld produce those means, and so on, till we find that certain means we can take forthwith wonld produce the desired end. This is compared to the search, in mathematics, for simpler propositions which will enable us to prove what we desire to prove-which is in fact the method of mathematical discovery, as opposed to that of mathematical proof. This gives the clue to what A. is saying here, viz. If true conclusions could only follow from true premisses, the task of analysing a problem would be easy, since premisses and conclusion conld be seen to follow from each other (>6-8) . We shonld proceed as follows. We shonld suppose the truth of A, which we want to prove. We should reason 'if this is true, certain other propositions are true', and if we found among these a pair B, which we knew to be true, we could at once infer that A is true (as-io). But since in fact true conclusions can be derived from false premisses (An. Pr. ii. 2- 4), if A entails B and B is true it does not follow that A is true, and so the analysis of problems is not easy, except in mathematics, where it more often happens that a proposition which entails others is in turn entailed by them. This is because the typical propositions of mathematics are reciprocal,' the predicates being necessary to the subjects and
COMMENTARY 550 the subjects to the predicates (as in definitions) ('1-13). Thus, for instance, since it is because of attributes peculiar to the equilateral triangle that it is proved to be equiangulat, the equiangular triangle can equally well be proved to be equilateral. This constitutes a second characteristic in which mathematics differs from dialectical argument ('12; the first was mentioned in 77b27-33). The passage may usefully be compared with another dealing with the method of mathematical discovery, Met. 1°51'21-33, where A. emphasizes the importance of the figure in helping the discovery of the propositions which will serve to prove the demonstrandum.
For a cleat discussion of analysis in Greek geometry, see R. Robinson in Mind, xlv (1936), 464- 73. 14-21. AU~€Ta.~ S' .. . TOG E. The advancement of a science,
says A., is not achieved by interpolating new middle terms. This is because the existing body of scientific knowledge must already have based all its results on a knowledge of the immediate pre. misses from which they spring; otherwise it would not be science. Advancement takes place in two ways : (I) vertically, by extrapolating new terms, e.g. terms lower than the lowest minor term hitherto used ('14-16), and (2) laterally, by linking a major term, already known to be linked with one minor through one middle term, t o another minor through another middle ; e.g. if we already know that 'finite number' (or 'number finite or infinite') is predicable of a particular odd number, through the middle term 'finite odd number', we can extend our knowledge by making the corresponding inference about a particular even number, through the middle t erm 'finite even number'. What A. is speaking of here is the extension of a science by the taking up of new problems which have a common major tenn with a problem
already solved; when he speaks of science as coming into being (not as being extended) by interpolation of premisses, he is thinking of the solution of a single problein of the form 'why is B A l' (c!. 84bl 9-85'12).
CHAPTER 13 Knowledge of fact and knowledge of reasoned fact 78'ZZ. Knowledge of a fact and knowledge of the reason for it differ within a single science, (I ) if the syllogism does not proceed by immediate premisses (for then we do not grasp the proximate reason for the truth of the conclusion); (2) (a) if it proceeds by immediate premisses. but infers not the consequent
55I from the ground but the less familiar from the more familiar of two convertible terms. 28. For sometimes the term which is not the ground of the other is the more familiar, e.g. when we infer the nearness of the planets from their not twinkling (having grasped by perception or induction that that which does not twinkle is near). We have then proved that the planets are near, but have proved this not from its cause but from its effect. 39. (b) If the inference were reversed-if we inferred that the planets do not twinkle from their being near-we should have a syllogism of the reason. b 4 • So too we may either infer the spheriCal shape of the moon from its phases, or vice versa. I I . (3) Where the middle terms are not convertible and the non-causal term is the more familiar. the fact is proved but not the reason. 13. (4) (a) So too when the middle term taken is placed outside the other two. Why does a wall not breathe? 'Beca\1se it is not an animal.' If this were the cause, being an animal should be the cause of breathing. So too if the presence of a condition is the cause of an attribute, its absence is the cause of the absence of the attribute. 21. But the reason given is not the reason for the wall's not breathing; for not every animal breathes. Such a syllogism is in the second figure-Everything that breathes is an animal, No wall is an animal, Therefore no wall breathes. :a8. Such reasonings are like (b) far-fetched explanations, which consist in taking too remote a middle term-like Anacharsis' 'there are no female flute-players in Scythia because there are no vines'. 32. These are distinctions between knowledge of a fact and knowledge of the reason within one science, depending on the choice of middle term; the reason is marked off from the fact in another way when they are studied by different scienceswhen one science is subaltern to another, as optics to plane geometry, mechanics to solid geometry, harmonics to arithmetic, observational astronomy to mathematical. 39. Some such sciences are virtually 'synonymous', e.g. mathematical and nautical astronomy. mathematical harmonics and that which depends on listening to notes. Observers know the fact, mathematicians the reason, and often do not know the fact, as people who know universal laws often through lack of observation do not know the particular facts. 79"6. This is the case with things which manifest forms but
COMMENTARY have a distinct nature of their own. For mathematics is concerned with forms not characteristic of any particular subject-matter: or if geometrical attributes do characterize a particular subjectmatter, it is not as doing so that mathematics studies them. 10. There is a science related to optics as optics is to geometry, e.g. the theory of the rainbow; the fact is the business of the physicist, the reason that of the student of optics, or rather of the mathematical student of optics. Many even of the sciences that are not subaltern are so related, e.g. medicine to geometry ; the physician knows that round wounds heal more slowly, the geometer knows why they do so.
552
,8a:z:z-b31. To 8' ()TI. • • • a.~'D',>"o,. The distinction between knowledge of a fact and knowledge of the reason for it, where both fall within the same science, is illustrated by A. with reference to the following cases: (1) ('23--6) 'if the syllogism is not conducted by way of immediate premisses'. I.e. if D is A because B is A, C is B, and D is C, and one says' D is A because B is A and D is B' or 'because C is A and D is C', one is stating premisses which entail the conclusion but do not fully explain it because one of them (' D is B', or 'C is A ') itself needs explanation. (2) Where 'B is A' stands for an immediate connexion and is convertible and being A is in fact the cause of being B, then (a) ('26-39) if you reason 'C is A because B is A and Cis B' (e.g. 'the planets are near because stars that do not twinkle are near· and the planets do not twinkle'), you are grasping the fact that C is A but not the reason for it, since in fact C is B because it is A. not A because it is B. But (b) ('311- 13) The case is plainly not improved if, of two nonconvertible terms which might be chosen alternatively as middle term, we choose that which is not the cause but the effect of the other. Here not only does our proof merely prove a fact without giving the ground of it, but we cannot by rearranging our terms get a proof that does this. Pacius illustrates the case by the syllogism What is capable of laughing is an animal, Man is
553 capable of laughing, Therefore man is an animal. Such terms will not lend themselves to a syllogism
'Toil
8t6'TL, i.e. one in which
the cause appears as middle term; for we cannot truly say All animals are capable of laughing, Man is an animal, Therefore man is capable of laughing. (4) (a) (b I3- 28) 'When the middle term is placed outside.' In An. Pro26b39, 28'14 A. says that in the second and third fignres riBE'Tat. 'TO p-'crov ~gw 'TWV alCpwv, and this means that it does not occur as subject of one premiss and predicate of the other, but as predicate of both or subject of both. But the third fignre is not here in question, since the Posterior A nalytics is concerned only with universal conclusions; what A. has in mind is the second
figure (b23 - 4). And the detail of the passage (b I5- I6, 24-8) ('Things that breathe are animals, Walls are not animals, Therefore walls do not breathe') shows that the case A. has in mind is that in which the middle term is asserted of the major and denied of the minor (Camestres)-the middle, further, not being coextensive with the major but wider in extension than it. Then the fact that the middle term is untrue of the minor entails that the major term is untrue of the minor, but is not the precise ground of its being so. For if C's non-possession of attribute A were the cause of its non-possession of attribute B, "its possession of A would entail its possession of B; but obviously the possession of a wider attribute does not entail the possession of a narrower one. (b) (b28- 3I) A. says that another situation is akin to this, viz. that in which people, speaking Ka8' 'm25-8) cor-
rects himself by dividing it into wrong opinion so reached and that formed without reasoning. Wrong opinion of the former kind admits of different varieties; that of the latter kind is 2-5. TlJV s. Ar . , . ~".. PX... 'but the premiss All C is A may be true, i.e. if A is an atomic predicate both of C and of B
1'""
(for when the same tenn is an atomic predicate of more than one
term, neither of these will be included in the other). But it makes no difference if A is not an atomic predicate of both C and B.' The case in question is that in which in fact All C is A, no B is C, and no B is A; therefore V-ml.pXEf. in a3 and 5 and Ka'T7}'Yopfj'Tat in '3 must be taken to include the case of deniability as well as that of assertibility; and this usage of the words is not uncommon in the A nalytics ; d. 82'r4 n. And in fact, whether A is immediately assertible of both C and B, immediately deniable of both, or immediately assertible of one and deniable of the other, C cannot be included in B, or B in C; in the first case they will be coordinate classes immediately under A, in the second case genera outside it and one another; in the third case one will be a class under A and one a class outside A. In '2-4 A. assumes that A is directly assertible of C and directly deniable of B . But, he adds in '4-5, it makes no difference if it is not directly related to both. That it is directly deniable of B is the assumption throughout 79b29- 8o'5; what A. must mean is that it makes no difference if it is not directly assertible of C (i.e. if C is a species of a genus under A, instead of a genus directly under A). And in fact it does not; the facts will still be that all C is A, no B is C, and no B is A. In '4 vc>YK'l yap • , ,dv,". A. must mean that A is included in C; for (1) A cannot fall outside C, since ex hypothesi B is included in both, and (2) A cannot include C, since if all C were A, tben, all B being C, All B is A would be a mediable and not (as it is throughout as_b r6 assumed to be) an immediate proposition. A. ignores the possibility that A and C should be overlapping classes, with B included in the overlap. 2']-33. 0).0.$ ....0, Elva.. ",as 1rpoTa.aE~S ci .... +OTl:pa.S ~E.U8Eis ••• €1T~ Tl S' (KQ.TEpa.V ouBEY KW).,UEI. ",(UBil EtvaL. •All B is A' is wholly false when in fact no B is A; 'No B is A' wholly false when in fact all B is A ; 'All B is A' and 'No B is A' are partly false when in fact some B is A and some is not (c!. An.Pr. 53b,8-30 n.). JZ-3 .•t O~y • • • ci8uVQTov, 'if, then, taken thus (i.e. being supposed to be All A is C, No B is C, or No A is C, All B is C), the premisses were both wholly false, the truth would be tbat no A is C and all B is C, or that all A is C and no B is C; but this is impossible, because in fact all B is A ('28) . b~. ~ "'" r A "-pOTClU.,, r A must be read, as in b , and 14; for A. always puts the predicate first, r A standing for on Tn r 'T el!O. a1TeLpov £pxoV'Ta, might refer to any of the three; but el €UTtJJ a.1T68E(.gL!> a1TavTo!> refers to the third. for the absence of an ultimate subject or of an ultimate predicate would not imply that all propositions are provable ; there might still be immediate connexions between pairs of terms within the series. 1TPO!> aAA'1Aa 'TTepalJJual. means that some terms are bounded at each other, 'touch' each other; in other words that there are terms with no tenn between them. Finally, it Is the third qnestion that is carried on into the next paragraph. 9-14. ~OJlo(ws 8E ... iUTo.TCU. Take the proposition No B is A. Either this is unmediable, or there is a term H such that no His A, and all B is H. Again either No H is A is unmediable, or there is a term e such that no e is A, and all 'H is €J. The question is whether an indefinite number of terms can always be interpolated between B and A. or there are immediate negative propositions. 14. Tj livELpa. ots U1rclpX'1. 1TPOTf:POtS. The question is whether there is an infioite number of terms higher than B to which A cannot belong. We must therefore either read ot!> ovX tnr&'Pxet with n, or more probably take tnrapxel. to be used in the sense in
569 which it means 'occurs as predicate' whether in an affirmative or a negative statement; d. 80-2- 5 n. 15-20. 'E1Tl Sf: TWY Q,VTtaTPE+OVTWV • • • Ka.T'I')yopla.v. A. now
recurs to the first two questions, and points out that the situation with regard to these is different if we consider not terms related in linear fashion so that one is properly predicated of the other but not vice versa, but terms which are properly predicated of each other. Here there is no first or last subject. Such terms fonn a shuttle service, if there are but two, or a circle if there are more, of endless predication. whether you say that each tenn is subject to an infinite chain of attributes, or is that and also attribute to an infinite chain of subjects (EiT' ap.-I) that his 'genuine predications' are the kind that occur in the sciences. The only examples he gives here of genuine subjects are 'the log' and 'the man', which are substances. The sciences make, indeed, statements about things that are not substances, such as the number seven Of the right-angled triangle, but they at least think of these as being related to their attributes as a substance is related to its attributes (ct. 87a36), and not as 'TO AEVKOV is related to eVAoV. or 'TO P.OVUtKOV to AWKOy. He concludes (83a21-3) that the predications we have to consider are those in which there is predicated of something either an element in its essence or that it has a certain quality or is of a certain quantity or in a certain relation, or doing or. suffering something. or at a certain place, or occurs at a certain time. He next (83'24-35) distingnishes, among genuine predications, those which 'indicate essence' (i.e. definitions, which indicate what the subject is, and partial definitions, which indicate what it is a particulari2ation of, i.e. which state its genus) from those which merely indicate a quality, relation, etc., of the subject, and groups the latter under the term crvp.{3.{37J"oTa. But it must be rewed that these include not ouly accidents but also properties, which, while not included in the essence of their subjects, are necessary consequences of that essence. The predication of crvp.{3.{37JKOTa is of course .to be distinguished from the predication "aTa avp.{3.{37J"OS dealt with in the previous paragraph. A. repeats here ('3-2) what he has already pointed out, that crvp.{3.{37JKOTa depend for their existence on a subject in which they inherethat their esse (as we might say) is inesse-and takes occasion 4985
P
P
COMMENTARY to denounce the Platonic doctrine of Forms as sinning against this principle. Now follows a passage ('36-b 12) whose connexion with the general argument is particularly hard to seize; any interpretation must be regarded as only conjectural. 'If B cannot be a quality of A and A a quality of B-a quality of its own quality-two terms cannot be predicated of each other as if each were a genuine subject to the other (d. '31). though if A has the quality B, we can truly say "that thing which has the quality B is A" (as has been pointed out in '1- 23). There are two possibilities to be considered. (I) ('39-b1O) Can A be predicated as an element in the essence of its own predicate (Le. as its genus or differentia) ? This is impossible, because (as we have seen in 82b37-83'1) the series which starts with "man" and moves upwards through the differentia "biped" to the genus "animal" must have a limit, since definition of essence is possible and the enumeration of an infinity of elements in the essence is impossible; jU$t as the series which starts with "animal" and moves downwards through "man" must have a limit in an individual man. Thus a term cannot be predicated as the genus of its own genus, since that would make man a species of himself. (2) (b , 0-17 ) The second possibility to be examined is that a term should be predicated of its own quality or of some attribute it has in another category other than substance. Such an assertion can only be (as we have seen in -1-23) an assertion Karel UVP.fJ4J71Kor. All attributes in categories other than substance are accidents and are genuinely predicable only of substances, and thus limited in the downward direction. And they are also limited in the upward direction, since any predicate must be in one or other of the categories, and both the attributes a thing can have in any category and the number of the categories are limited.' A.'s main purpose is to maintain the limitation of the chain of predication at both ends, beginning with an individual substance and ending with the name of a category. But with this is curiously intermingled a polemic against the possibility of counter-predication. We can connect the two themes, it seems, only by supposing that he is anxious to exclude not one but two kinds of infinite chain; not only a chain leading ever to wider and wider predicates, but also one which is infinite in the sense that it returns upon itself, as a ring does (Phys. 207'2). Such a chain would be of the form 'A is B, B is C . . . Y is Z, Z is A', and would therefore involve that A is predicable of B as well as B of A; and that is what he tries in this section
I. 22 579 to prove to be impossible, if 'predication' be limited to genuine predication. . There follows a passage (b I7 - 3I ) in which A. sums up his theory of predication. The main propositions he lays down are the following: (I) A term and its definition are the only things that can strictly be predicated of each other (bI8- I9). (2) The ultimate predicate in all strict predication is a substance (b2 0-2 ). (3) Upwards from a substance there stretches a limited chain of predications in which successively wider elements in its essence are predicated (b27 -1!). (4) Of these elements in the definition of a substance can be predicated properties which they entail, and of these also the series is limited (b2 6-8). (5) There are thus subjects (i.e. individual substances) from which stretches up a limited chain of predication, and attributes (i.e. categories) from which stretches down a limited chain of predication, such attributes being neither predicates nor subjects to anything prior to them, sc. because there is no genus prior to them (i.e. wider than they are) (b28-3I). Thus A. contemplates several finite chains of predication reaching upwards from an individual subject like Callias. There is a main chain of which the successive terms are Callias, infima species to which Callias belongs, differentia of that species, proximate genus, differentia of that genus, next higher genus ... category (i.e. substance). But also each of these elements in the essence of the individual subject entails one or more properties and is capable of having one or more accidental attributes, and each of these generates a similar train of differentiae and genera, terminating in the category of which the property or accident in question is a specification-quality. quantity, relation, etc. The second dialectical proof (b32 -1!4'6) runs as follows: Wherever there are propositions more fundamental than a given proposition, that proposition admits of proof; and where a proposition admits of proof, there is no state of mind towards it that is better than knowledge, and no possibility of knowing it except by proof. But if there were an infinite series of propositions more fundamental than it, we could not prove it, and therefore could not know it. The finitude of the chain is a necessary precondition of knowledge; nothing can be known by proof, unless something can be known without proof. The analytical proof (84'7- 28) runs as follows: Demonstration is concerned with propositions ascribing predicates to subjects to which they belong per se. Such attributes fall into two classesthe two which were described in 73'34- b3, viz. (I) attributes
580
COMMENTARY involved in the definition of the subject (illustrated by plurality or divisibility as belonging per se to number), (2) attributes whose definition includes mention of the subjects to which they belong. The latter are illustrated by 'odd' as belonging per se to number; but since such Ka.rl" am.a attributes are said to be convertible with their subjects (84'22-5), 'add' must be taken to stand for 'odd or even', which we found in 73'39-40. The original premisses of demonstration (if we leave out of account d,twp,a:ra and V'TrOfN.UElS) are definitions (72814- 24), which ascribe to subjects predicates of the first kind. From these original premisses (with the help of the dgui>f£aTa and V1TOfJEUt::tS-) are deduced propositions predicating of their subjects attributes KaO' a&.6 of the second kind; and by using propositions of both kinds further propositions of the second kind are deduced. Ka8' ath6 attributes of the second kind are dealt with in 148 1825, those of the first in '25- 8. There cannot be an infinite chain of propositions asserting KaO" aUTO attributes of the second kind, e.g. 'number is either odd or even, what is either odd or even is either a or b, etc.'; for thus, number being included in the definition of 'odd' and of 'even', and 'odd or even' being included in that of 'a or b', number would be included in the definition of ' a or b', and of any subsequent term in the series, and· the definition of the term at infinity would include an infinity of preceding terms. Since this is impossible (definition being assumed to be always possible, and the traversing of an infinite series impossible; d. 82b37 --838r), no subject can have an infinite series of Ka8' aUro attributes of the second kind ascending from it (84'18-22) . It must be noted, however (822-5), that, since in such predications the predicate belongs to the subject precisely in virtue of the subject's nature, and to nothing else, in a series of such terms all the terms after the first must b~ predicable of the first, and the first predicable of all the others, so that it will be a series of convertible terms, not of terms of which each is wider than the previous one, i.e. not an ascending but what may be called a neutral series; thus it will be infinite as the circumference of a cirCle is infinite, in the sense that it returns on itself, but not an infinite series of the kind whose existence we are denying. Again ('25- 8) KaO' a&.6 terms of the first kind are all involved in the essence of their subject, and these for the same reason cannot be infinite in number. We have already seen (in eh. 20) that if the series is finite in both directions, there cannot be an infinity of terms between any .. two terms within the series. We have now shown, therefore, that
581 there must be pairs of terms which are immediately connected. the connexion neither needing nor admitting of proof (!4"29-b2). 83 1, . 01TEP AEUKOV TL J 'identical with a species of white'. x3. 01TEP teaL EYEvETO, 'which is what we made it in our assettion'. 24-5. wETL TO. ....EV ... 1CQ.T1')yopeiTal., 'further, predicates that
indicate just what their subject is. or just what it is a species of'. is to be explained differently from 071t:p AEVKOV n
01T£P EKEivo TL
in '7 and the other phrases of the form 01TEP . .. on which occur in the chapter. It plainly means not 'just what a species of that
subject is'. but 'j ust what that subject is a species of'.
n
not with EKEivo but with O'TT'EP, 30. OTrEP ya.p t~OY EO'TLY 0 Qv8pw1T"os. More strictly 07T£P
going
''Pav
'identical with a species of animal'. But A.'s object here is not to distinguish genus from species. but both from non-essential attributes. 3:&-5. TO. yap dS" ... Elatv. npE'Tlup.a'Ta is applied literally to buzzing, twanging. chirruping. twittering; metaphorically to speech without sense. This is the harshest thing A. ever says about the Platonic Forms. and must represent a mood of violent reaction against his earlier belief. The remark just made ("32). that there is nothing white without there being a subject in which whiteness inheres, leads him to express his disapproval of the Platonic doctrine, which in his view assigned such a separate existence to abstractions. Even if there were Platonic Forms, he says. the sciences (whose method is the subject of the Posterior Attalytics) are concerned only with forms incorporated in individuals. I conjecture that after these words we should insert E"tS7} /LEV o15v ... op,wvvJLov (77-5-9), which is out of place in its present position. It seems impossible to say what accident in the history of the text has led to the misplacement. 36-8. "En E"L ••• OUTW'). 1TOWT7}S' is here used to signify an attribute in any category. 1TO~TES' are then subdivided into essential attributes ('39-bro) and non-essential attributes (bro-r7 ). as in Met. I020bI3- 18). 39-bI. 11 ya.p ... Ka.T11yoPOUIlEvou. These words are answered irregularly by ouSE" JLTJv 'TOV 1TOtOV ~ nov aAAWv ouS/", hIO . bI2-J7' a.AAa. 81) ... .,..oTE, 'but now to prove that . .. ; the proof is contained in the fact that ... .' For this elliptical use of on d. An. Pro 62-32, 40,bI4 . n may be right in reading ci,uu. S~'>'ov OT< (the reading I»i being due to abbreviation of Sij.>.ov). but the leetio difficilior is preferable. 17. 'Y'TI'ClkELTC1t • • • btos KClTTIYOPEio9Clt is to be interpreted in n.
582
COMMENTARY
the light of the remainder of the sentence, 'we assume that one thing is predicated of one other thing'. The only exception is that in a defmitory statement a thing is predicated of itself (5a11-13). He cures the passage by reading E17TEP, which gives the sense 'if there are to be' (as there must be) 'immediate
intervals'. For the construction d. bI 6, 801130--2, 81818- 19; El . .. £07'0.' in 77afJ ; el JLl),,),,€, £ueuOo,t in 80h35 ; d7TEP 8Ei ... Elva,- in 72b3. 26. 14-17. EV ~VTOL T~ a.UT~ yEvU ... 8ElkVUJl€Va.. The point of this addition is to state that while the middle terms used to prove the possession of the same Ka8' av.ro attribute by different subjects need not be identical, all the middle terms so used must fall within the same genus (e.g. be arithmetical, or geometrical), and all the premisses must be derived from the same set of ultimate premisses, since, as we sawin ch. 7. propositions appropriate to one genus cannot be used to prove conclusions about another genus.
585
Km O'Tol.XEia ••• Ka.8&,,"ou.
The sentence is improved by reading Ta.n-.£ in b 2I , but remains difficult; to bring out A.'s meaning, his language must be expanded. 'And there are elements of the proof the same as, or more strictly as many as, the middle terms; for the immediate premisses are elements-either all of them (and these are of course one more numerous than the middle terms) or those that are major premisses (and these are exactly as many as the middle terms).' The suggestion is that in a chain of premisses such as All B is A, All Cis B , All D is Conly the first two are elements of the proof, since in a syllogism the major premiss already contains implicitly the conclusion (d. 86 122-9. and 86b30 €l &.pxT! O'VAAOYLO'ILOV ~ Ka8oAov 1Tpo.TaatS ap.Euor) . For Kat (b2I ) = 'or more strictly' cf. Denniston, Greek Particles, 20-2.
29 2
(7).
~'n'1 TGS cipXas ... ECM'lV. Cf. E.N. 1095832 EU ya.p 0 ID&:rwv 1j1Topn 'ToVro Kal E{'ljTEt, 'TTonpov ano 'TWV apxwv ;; E1Ti Tar a.PXas Ecrnv .ry &865'. As the imperfect tenses .imply. the reference is to Plato's oral teaching rather than to Rep. 510 b-
23-4' a.).)." ,;
Ka~
c. 25. El J1Ev ••• U1Ta.pX'" 7j wpou.pov cp OVX {J7Ta.pX€' is a correction. POEUDV suggests something that links two extremes, and something intermediate in extent between them; and in a syllogism in Barbara the middle term must at least be not wider than the major and not narrower than the minor. But in a negative syllogism the middle term serves not to link but to separate the extremes, and in a syllogism in Celarent nothing is implied about the comparative width of the major and middle terms; they are merely known to exclude each other. But the middle term at least more directly excludes the major than the minor does. 31-8513. "OTQ.V BE . . . "£1M'Et.. A. here considers affinnative syllogisms, and takes account ouly of proof in the first figure, ignoring the second, which cannot prove an affinnative, and the third, which cannot prove a universal. If we want to prove that all B is A, we can ouly do so by premisses of the form All C is A, All B is C. If we want to prove either of these premisses, we can only do so by a syllogism of similar form. Clearly, then, we never take a middle wider than and inclusive of A, nor (though A. does not mention this) one narrower than and included in B ; all the middle terms will fall within the 'interval' that extends from B to A, and will break this up into shorter, and ultimately into unitary, intervals. 31-3 . "OTQ.V 8E . .. A. The editions have oJ.Lofws 'TO A. But if we start with the proposition All B is A, there is no guarantee that 511
COMMENTARY 586 we can find a term 'directly predicable of B, and having A directly predicable of it'; and in the next sentence A. contemplates a further packing of the interval between B and A. n must be right in reading op.ou"s TO .:!; the further packing will then be of the interval between.:! and A. 35-6. Ecrn. 8" ... 0. ....£..>..ov TO. 'lTpOS 1", 'for correlatives increase concomitantly' . 10. "'En Et aLpE1'wTEpa. K1'>"., d. 85h23 n. 22.-9 .•A>">"o. TWV }lEv E'PTJtU.VWV ... EvEPYE'~. This is not a new argument; it is the argument of '1-13 expanded, with explicit introduction of the distinction of SOllal.uS' and JvJfYY~,a. Thus A.
is in fact saying that while some of the previous arguments are dialectical, one of them is genuinely scientific. Zabarella tries to distinguish this argument from that of '1-13 by saying that whereas the present argument rests on the fact that knowledge that all B is A involves potential knowledge that particular B's are A, the earlier argument rests on the fact that knowledge that all B is A presupposes actual knowledge that some particular B's are A. But this is not a natural reading of -10-1 3.
A. does not mean by n]v 7TPOTlpo.v, r1jv vu·rJpav the major and minor premiss of a syllogism; for (a) what he is comparing in general throughout the chapter is not two premisses but two demonstrations, or the conclusions of two demonstrations; (b) it is not true that knowledge of a major premiss implies potential knowledge of the minor, though it is true to say that in a sense it implies potential knowledge of the conclusion; (c) in the example ('25-9) it is with knowledge of the conclusion that A. contrasts knowledge of the major premiss. .fJ 7Tpo'rEpa is the premiss of a more general demonstration, .fJ vcrrlpa the premiss of a less general demonstration. A. is comparing the first premiss in a proof of the form All B is A, AllC is B, All D is C, Therefore All D is A, with the first premiss in a proof ofthe form All C is A, All D is C, Therefore all D is A. It follows that TaVTT]v n}v 7TpoTauLv in a27-8 means TO lUOUI(~)'ES' 0-,.& SUO oplJaiS'. not TO laoal(~)'ES' 0-,., Tplywvov. 39-30. TJ Sf: Ka.TO l-'f:pOS .•• T«>"EUT~. If we imagine a series of demonstrations of gradually lessening generality, the last member
COMMENTARY of such a series would be a syllogism with an individual thing as its minor term, and in that case the conclusion of the syllogism is a fact which might possibly be apprehended by sense-per-
592
ception, as well as reached by inference.
CHAPTER 25 Affirmative demonstration is superior to negative
86'3" That an affirmative proof is better than a negative is clear from the following considerations. (,) Let it be granted that ceteris paribus, i.e. if the premisses are equally well known, a proof from fewer premisses is better than one from more premisses, because it produces knowledge more rapidly. 36. This assumption may be proved generally as follows: Let there be one proof that E is A by means of the middle terms B, r, .1 , and another by means of the middle terms Z, H. Then the knowledge that .1 is A is on the same level as the knowledge, by the second proof, that E is A . But that .1 is A is known better than it is known, by the first proof, that E is A; for the latter is known by means of the former. b7 . Now an affirmative and a negative proof both use thIee terms and two premisses; but the former assumes only that something is, and the latter both that something is and that something is not, and therefore uses more premisses, and is therefore inferior. 10. (2) We have shown that two negative premisses cannot yield a conclusion; that to get a negative conclusion we must have a negative and an affirmative premiss. We now point out that if we expand a proof, we must take in several affirmative premisses but only one negative. Let no B be A, and all r be B. To prove that no B is A, we take the premisses No .1 is A, All B is .1 ; to prove that all r is B, we take the premisses All E is B, All r is E. So we take in only one negative premiss. 22. The same thing.is true of the other syllogisms; an affirmative premiss needs two previous affirmative premisses; a negative premiss needs an affirmative and a negative previous premiss. Thus if a negative premiss needs a previous affinnative premiss, and not vice versa, an affirmative proof is better than a negative. 30. (3) The starting-point of a syllogism is the universal immediate premiss, and this is in an affirmative proof affirmative, in a negative proof negative; and an affixmative premiss is prior
to and more intelligible than a negative (for negation is knOwn on the ground of affirmation, and affirmation is prior, as being
593 is to not-being). Therefore the starting-point of an affirmative proof is better than that of a negative; and the proof that has the better starting-point is the better. Further, the affirmative proof is more primary, because a negative proof cannot proceed without an affinnative one. 86a33-b9' EO"TW ya.p . .. XElpwv. This argument is purely dia- ,
lectical, as we see from two facts. (I) What A. proves in '33-b7 is that an argument which uses fewer premisses is superior to one
that uses more, if the premisses are equally well known. But what he points out in b7-9 is that a negative proof uses more kinds of premiss than an affirmative, since it needs both an affirmative and a negative premiss. (2) The whole conception that there could be two demonstrations of the same fact using different numbers of equally well-known premisses (i.e. immediate premisses, or premisses approaching equally near to immediacy) is inconsistent with his view of demonstration, namely that of a single fact there is only one demonstration. viz. that which deduces it from the unmediable facts which are in reality the grounds of the fact's being a fact. 34. a.1TTU·l.Q.Twv i\ u1To9ioEWV. imOOED"S' and at'T'1)p.a are defined in contradistinction to each other in 76bz7-34 ; there is no allusion here to the special sense given to tmoOEa~S' in 72a18-20. hI D-I2. E1rEtSi} SES"KTo., ... u1TapXEt. The proof is contained in the treatment of the three figures in An. Pro i. 4-6, and summed up ib. 24. 4Ib6-]. 15. EV a.1ra.VTl OUAAOY'~~~, not only in each syllogism but in each sorites, as A. goes on to show. 22-3. b S' a..."JTO~ Tp01TO~ . . . OUAAOY'O'~wv. This may refer either (a) to further expansions of an argument by the interpolation of further middle terms, or (b) to arguments in the second or third figure. But in b 30-3 A. contemplates only first-figure syllogisms; for in the second figure a negative conclusion does not require a negative major premiss; so that (a) is probably the true interpretation here. . 3D-I. En Et . , . a.}lEao~. El is to be explained as in 8S h23J 8611 10. The major premiss is called the starting-point of the syllogism because knowledge of it implies potential knowledge of the conclusion (·22--<j). 38. QVEU ya.p Ti)~ S€'KVUOUI71lS • , • OT€P'1T'K~, because, as we have seen in h1 O-30 , a negative proof requires an affirmative premiss, which (if it requires proof) requires proof from affirmative premisses .
....,
Qq
594
COMMENTARY CHAPTER 26
Ostensive demonstration is superior to reductio ad impossibile 87aI . Since affirmative proof is better than negative. it is better than reductio ad impossibile. The difference between negative proof and reductio is this: Let no B be A, and all C be B. Then no C is A. That is a negative ostensive proof. But if we want to prove that B is not A. we assume that it is, and that C is B, which entails that C is A. Let this be known to be impossible; then if C is admittedly B, B cannot be A. I2. The terms are similarly arranged; the difference depends on whether it is better known that B is not A or that C is not A. When the falsity of the conclusion ('C is A') is the better known, that is reductio; when the major premiss (' B is not A ') is the better known, ostensive proof. Now' B is not A' is prior by nature to 'C is not A'. For premisses are prior to the conclusion from them, and 'C is not A' is a conclusion, 'B is not A' a premiss. For if we get the result that a certain proposition is disproved, that does not imply that the negation of it is a conclusion and the propositions from which this followed premisses; the premisses of a syllogism are propositions related as whole and part, but 'C is not A' and 'C is B' are not so related. 25. If, then, inference from what is prior is better, and the conclusions of both kinds of argument are reached from a negative proposition, but one from a prior proposition, one from a later one, negative demonstration is better than reductio, and a fortiori affirmative demonstration is so. 8,-10. OUK «po. ... U1l'a.PXE~V. Maier (SyU. d. Arist. 2 a. 231 n.) conjectures r for the MS. reading B, on the ground that otherwise this sentence would anticipate the result reached in the next sentence. But with his emendation the present sentence becomes a mere repetition of the previous one, so that nothing is gained. The next sentence simply sums up the three that precede it. I:Z-:Z5. o~ .... ev o~v opo~ ... u>">",,>"a.s. The two arguments, as stated in '3- 12, are (I) (Ostensive) No B is A, All C is B, ThereforenoC is A. (2) (Reductio) (a) If B is A, then-sinceC is B-C is A . But (b) in fact C is not A ; the conclusion of a syllogism cannot be false and both its premisses true; 'C is B' is true; therefore' B is A' is false. A. deliberately (it would seem) chooses a reductio the effect of which is to establish not the conclusion to which the ostensive syllogism led, but the major premiss of that
I. 26. 8]"10-28 595 syllogism. At the same time, to avoid complications about the quantity of the propositions, he introduces them in an unquanti-
tied form . The situation he contemplates is this: (1) There may be a pair of known propositions of the form' B is not A', 'C is B', which enable us to infer that C is not A . But (2). on the other hand, we may, while knowing that C is B and that C is not A, not know that B is not A, and be able to establish this only by considering what follows from supposing it to be false; then we use reductio. The arrangement of the terms is as before (au); i.e. in fact in both cases B is not A, C is B, and C is not A; the difference is that we use' B is not A' to prove 'e is not A' (as in (I)) when' B is not A' is to us the better known proposition, and 'c is not A' to prove 'B is not A' (as in (2 b)) when 'c is not A' is the better known. But the two processes are not equally natural ('17- 18); 'B is not A' is in itself the prior proposition, since it, with the other premiss 'C is B'. constitutes a pair of premisses related to one another as whole to part (a22- 3. d. An. Post. 4za8- 13. 47arD-I4. 49b37- 5oar). the one stating a general fule, the other bringing a particular case under it; while 'C is not A', with 'C is B', does not constitute such a pair (and in fact does not prove that B is not A, but only that some B is not A) . The second part of the reductio process is, as A. points out in An. Pro 4Ia23-30, soa29- 38, not a syllogism at all, but an argument E~ inro8'aEw~, involving besides the data that are explicitly mentioned ('C is not A' and 'C is B') the axiom that premisses (e.g. 'B is A' and 'C is E') from which an impossible conclusion (e.g. 'c is A ') follows cannot both be true. lt seems impossible to make anything of the MS. reading Ar Ka, A1J in &24. For what A. says is 'the only thing that can be a premiss of a syllogism is a proposition which is to another' (i.e. to the other premiss) 'either as whole to part or as part to whole' and it would be pointless to continue 'but the propositions AT (HC is not A ") and AB (" B is not A ") are not so related' ; for in the reductio there is no attempt to treat these propositions as joint premisses; 'C is not A' is datum, . B is not A' conclusion. Accordingly we must read Ar Ka< Br, which do appear as joint data in (2 b). The corruption was very likely to occur, in view of the association of the propositions 'e is not A' and' B is not A' in '14, 17- 18, 19- 20. 28. i) Ta.UT'llC; ~EAT'WY T] KQ.TTJyOpuct}. That affirmative proof is superior to negative was proved in ch. 25. J
COMMENTARY CHAPTER 27
The more abstract science is superior to the less abstract 87'31 . One science is x.nore precise than and prior to another, (1) if the first studies both the fact and the reason, the second only the fact; (2) if the first studies what is not, and the second what is, embodied in a subject-matter (thus arithmetic is prior to hannonics) ; (3) if the first studies simpler and the second more complex entities (thus arithmetic is prior to geometry, the unit being substance without position, the point substance with position).
8"31-3. 'A}G« ib. 5, Go.pia ib. 7·
I. 33. 89"33- b 9
609
CHAPTER 34 Quick wit 89blO. Quick wit is a power of hitting the middle term in an imperceptible time; e.g., if one sees that the moon always has
its bright side towards the sun, and quickly grasps the reason, viz. that it gets its light from the sun; or recognizes that someone is talking to a rich man because he is borrowing from him; or why two men are friends, viz. because they have a common enemy. On seeing the extremes tenus.
ODe
has recognized all the middle
BOOK II CHAPTER 1
There are four types of inquiry 89b23 . The objects of inquiry are just as many as the objects of knowledge; they are (I) the that, (2) the why, (3) whether the thing exists, (4) what it is. The question whether a thing is this or that (e.g. whether the sun does or does not suffer eclipse) comes under (I), as is shown by the facts that we cease from inquiring when we find that the sun does suffer eclipse, and do not begin to inquire if we already know that it does. When we know (I) the that, we seek (2) the why. 3I. Sometimes, on the other hand, we ask (3) whether the thing (e.g. a centaur, or a god) is, simply, not is thus or thus qualified, and when we know that it is, inquire (4) what it is. In the first Book A. has considered demonstration both as proving the existence of certain facts and as giving the reason for them. In the second Book he is·to consider demonstration as leading up to definition. By way of connecting the subjects of the two Books, he now starts with an enumeration of all possible subjects of inquiry, naming first the two that have been considered in the first Book-the question 'why' and the preliminary question of the 'that'-and going on to the two to be considered in the second Book, the question what a certain thing is, with the preliminary question whether the thing exists. It is probable that A. meant primarily by the four phrases TO OTt, TO 8'OTt, El Ecrn, ,rl £(rn the following four questions: (I) whether a certain subject has a certain attribute, (2) why it has t985
Rr
610 COMMENTARY it, (3) whether a certain subject exists, (4) what it is: and the examples given in this chapter conform to these distinctions. The typical example of (x) is 'whether the sun suffers eclipse', of (.) 'why it does', of (3) 'whether a god exists', of (4) 'what a god is'. But the phrases O'Tt [un and El Eu'n do not in themselves suggest the distinction between the possession of an attribute by a subject and the existence of a subject, and the phrase Tl lan does not suggest that only the definition of a subject is in question. Naturally enough, then, the distinctions become blurred in the next chapter. In 89b38--..lOOL, OlKla £aTlv; cpavEpov -rolvvv on 'T]TE'i 70 at7Lov' 7oiho 8~ £O'"T' 'TO 7l -ryv ElvaL, ws El17EI:v >"OYLKWS, 0 E'Tr' bUov}La, £(TTL 'Tlvos lVEKa, olov taws E17" olKlas 7) K>..lV7JS, E17' £vlwv BE 7l £KlVTjaE 'TrPW70V' atTLOv ya.p Kat 70th-O' (cf. I04Ib4--9, 1043aI4-21). But it
cannot be said that A. remains faithful to this view; the definitions . he offers of substances far more often proceed per genus et differentiam without any mention of a cause. The general upshot is that the questions El EarL and 7l £an, which in ch. I referred to substances, have in ch . .2 come to refer so much more to attributes and events that the former reference has almost receded from A.'s mind, though traces of it still remain. 89b39' 11 TO on ... G."""ws. 'TO b,;' ,upovs further characterizes TO 0.,.., making it plain that this refers to the question whether a certain subject has a certain particular attribute (e.g. whether the moon suffers eclipse, 9oa3). 'TO a,17'AwS" further characterizes TO El EG'TUI, indicating that this refers to the question whether
II. 2. 89b39-90'33 a certain subject (e.g. the moon, '5) or a certain attribute (e.g. the deprivation of light wbich we call night, ib.) exists at all. 90'3-4' OTJ..a{JWII Ka.~ 1j VA7] TWV UKEV«O'TWV Kat TO 7TVP Kai. 1'0. TO(.(tiiTa. Trull uwp.a:rwv Ka, ·n~. p..EfY11 'TOV OAOU KaL al inro8€uns TOU uvp.1T€pO.ap.O:TO~), SC. as being a quasi-material which is reshaped in the conclusion: cf. Met. IO'3b'7-21. Both T. and P. take A. to be referring in the present passage to the material cause, and to select the relation of premisses to conclusion simply as an tfxample of the relation of material cause to effect. But even if the premisses may by a metaphor be said (as in Phys. 195&16-19) to be an example of the material cause, it is inconceivable that if A. had here meant the material cause in general, he should not have illustrated it by some literal example of the material cause. Besides, the material cause could not be described as 'TO 'Ttl/WV OIl'TWV avdyKT} TO{h' £["0.1,, It does not necessitate that whose cause it is; it is only required to make this possible. Although in Phys. I95&,6-'9 A. includes the premisses of a syllogism as examples of the material cause, he corrects this in 200"5- 30 by pointing out that their · relation to the conclusion is the converse of the relation of a material cause to that whose cause it is. The premisses necessitate and are not necessitated by the conclusion; the material cause is necessitated by and does not necessitate that whose ainov it is. Nor could the material cause be described as identical with the formal cause (94'34- 5). It may be added that both the word v).7] and the notion for which it stands are entirely absent from the Organon. It could hardly be otherwise; v>.'1 is ayvwUTos Ka8' a'"'iv (Met. 1036'9); it does not occur as a term in any of our ordinary judgements (as apart from metaphysical judgements), and it is with judgements and the inferences that include them that logic is concerned. The term v".OKELjL£VOV, indeed, occurs in the Organon, but then it is used not as equivalent to v>.'1, but as standing either for an individual thing or for a whole class of individual things; the analysis of the individual thing into matter and form belongs not to logic but to physics (as A. understands physics) and to metaphysics, and it is in the Metaphysics and the physical works that the word v>.'1 is at home. A., then, is not putting forward his usual four causes. It may be that this chapter belongs to an early stage at which he had not reached the doctrine of the four causes. Or it may be that, realizing that he could not work the material cause into his thesis that the cause is the middle term, he deliberately substitutes for it a type of aiTtOV which will suit his thesis, namely, the ground of a conclusion as the atnov of the conclusion. Unlike efficient and final causation, in both of which there is temporal
COMMENTARY difference between cause and effect (h23-Q), in this kind of necessitation there is no temporal succession; ground and consequent are eternal and simultaneous. And since mathematics is the region in which such necessitation is most clearly evident, A. naturally takes his example from that sphere ('28-34). The four causes here named, then, are formal cause, ground (rtvwv OVTWV avciylOJ 'ToiYr' Elva,), efficient cause, final cause. But A.'s discussion does not treat these as all mutually exclusive. He definitely says that the ground is the same as the formal cause ('34-5). Further, he has already told us (in chs. 8, 10) that the middle term in a syllogism wl:ich at the same time proves and explains the existence of a consequence is an element in the definition of the consequence, i.e. in its formal cause (the general form of the definition of a consequential attribute being 'A is a B caused in C by the presence of D'). It is not that the middle term in a demonstration is sometimes the fonnal cause of the major term, sometimes its ground, sometimes its efficient cause, sometimes its final cause. It is always its formal cause (or definition), or rather an element in its formal cause; but this element is in some cases an eternal ground of the consequent (viz. when the consequence is itself an eternal fact), in some cases an efficient or a final cause (when the consequence is an event) ; the doctrine is identical with that which is briefly stated in Met.
on
I04Iaz7-30, rpavfpCJI,' 'Tolvvv '."TEl 'TO at'TLOv' TOVrO S" EO"Tt 'TO 'Tt 1]11' flvaL , WS fl1TftV AOYLKWS'. (; ('Tr" " (vtwv 1-'£11' EO"TL 'TtvoS' EVfKa, otov iuwS' hr" OlKlaS 7j KA[V11S, iTT' JvLwV at 'Tl EKtVT)UE 1Tpiinov' ainov yap Cf'b ~ • .1 • xaL, 'TOVTO, . 1 . [044 •36 n I 00;:." WS' 'TO• HOOS; TO•'Tt -'IV f IvaL, 'TL' 0't:'. wr O~ (VEXa; 'TO '''£AOS', WWS' at 'TaVra ap.tfow 'TO aUTO. In chs. 8 and 10
(e.g. 93b3- I2, 3~'7) the doctrine was illustrated by cases in which the element-in-the-definition which serves as middle term of the corresponding demonstration was in fact an efficient cause. Lunar eclipse is defined as 'loss of light by the moon owing to the interposition of the earth', thunder as 'noise in clouds due to the quenching of fire in them'. In this chapter A. attempts to show that in other cases the element-in-the-definition which serves as middle term of the corresponding demonstration is an eternal ground, and that in yet others it is a final c,ause. The case of the eternal ground is illustrated by the proof of the proposition that the angle in a semicircle is a right angle ('28-34). The proof A. has in mind is qnite different from Euclid's proof (EI. iii. 3I). It is only hinted at here, but is made clearer by Met. [05IaZ7 Ell' T,I'LKVKMo/ ope-;, Ka80>..ov 8ui 'Tt; EO-V tuaL 'T'PflS, 1j 'Tf {Jwns 8vo Ka~ -Ij EK JI.EUOV £1TLO"TafiE'Wa op07j, lSonL 8fjAOV 'TCY EXfLVO (i.e.
II. I I 0.,., SVO opOa: 'TO Tplywvov (10511'4). that the angles of a triangle equal two right angles) .18&7•. From 0, the centre .of the circle, Q
N·"---~-----::.I
OQ perpendicular to the diameter NP is drawn to meet the circumference, and NQ, PQ are joined. Then, NOQ and POQ being isosceles triangles; LOQN = ONQ, and LOQP = OPQ. Therefore OQN+OQP ~= NQP) = ONQ+OPQ, and therefore = half of the sum of the angles of NQP, i.e. of two right angles, and therefore = one right angle. (Then, using the theorem that angles in the same segment of a circle are equal (Euc. iii. 21), A. must have inferred that any angle in a semicircle is a right angle.) In this argument, NQP's being the half of two right angles is the ground of its being one right angle, or rather the causa cognoscendi of this. (This is equally true of the proof interpolated in the part of Euclid after iii. 31, and quoted in Heath, Mathematics it! Aristotle, 72; but A. probably had in inind in the present passage the proof which he clearly uses in the Metaphysics.) But A.'s comment 'this, the ground, is the same as the essence of the attribute demonstrated, because this is what its definition points to' ('34-5) is a puzzling statement. Reasoning by analogy (it would appear) from the fact that, e.g., thunder may fairly be defined as 'noise in clouds due to the quenching of fire in them', A. seems to cont~mplate some such definition of the rightness of the angle in a semicircle as 'its being right in consequence of being the half of two right angles'; and for this little can be said. The analogy between the efficient cause of an event and the causa cognoscendi of an eternal consequent breaks down; the one can fairly be included in the definition of the event, the other cannot be included in the definition of the consequent. Two comments may be made on A.'s identification of the ground of a mathematical consequent with the definition of the consequent. (I) The definition of 'right angle' in Euclid (and probably in the earlier Elements known to A.) is: o.rav Ev8Eia l.".' Ev8E'iav crra8E'iaa 'Tar Eq,E~ijS' ywvlas was d.M1j'\a.tS' 1TOtii, dplH] JKaTIpa TWV tawv ywvuUv Ian (El. i, Def. IO). Thus the right angle is defined as half of the sum of a certain pair of angles, and it is not unnatural that A. should have treated this as eqnivalent to 4C111s
T
t
COMMENTARY defining it as the half of two right angles. (2) While it is not defensible to define the rightness of the angle in a semicircle as its being right by being the half of two right angles, there is more to be said for a similar doctrine applied to a geometrical problem, instead of a geometrical theorem. The squaring of a rectangle can with some reason be defined as 'the squaring of it by finding a mean proportional between the sides' (De An. 4 13'13- 20).
A. offers no separate proof that the fOTmal cause of definition functions as middle term. He merely remarks ('3S-8) A. makes no attempt to identify it with the formal cause, or part of it. He merely points out that where efficient causation is involved, the event, in consequence of whose happening to a subject another event happens to that subject, functions as middle term between that subject and the later event. The syllogism, in the instance he gives, would be: Those who have invaded the country of another people are made war on in return, The Athenians have invaded the country of the Medes, Therefore the Athenians are made war on by the Medes. With regard to the final cause (h8-23) A. similarly argues that it too can function as the middle term of a syllogism explaining the event whose final cause it is. He begins by pointing out (h8-12) that where a final cause is involved, the proper answer to the question 'why?' takes the form 'in order that .. .'. He implies that such an explanation can be put into syllogistic form, with the final cause as middle term; but this is in fact impossible. If we are to keep the major and minor terms he seems to envisage in the example he takes, i.e. 'given to walking after dinner' and 'this man', the best argument we can make out of this is: Those who wish to be healthy walk after dinner, This man wishes to be healthy, Therefore this man walks after dinner. And here it is not 'health' but 'desirous of being healthy' that is the middle term. If, on the other hand, we say 'Walking after dinner produces health, This man desires health, Therefore this man walks after dinner', we abandon all attempt at syllogistic form. A. is in fact mistaken in his use of the notion of final cause. It is never the so-called final cause that is really operative, but the desire
II.
II
of an object; and this desire operates as an efficient cause, being what corresponds, in the case of purposive action, to a mechanical or chemical cause in physical action. Up to this point A. has tried to show how an efficient cause may function as middle term ('36-b8) and how a final cause may do so (b8-I2). He now (b12- 20) sets himself to show that an efficient cause and a final cause may as it were play into each other's hands, by pointing out that between a purposive action (such as walking after dinner) and the ultimate result aimed at (e.g. health) there may intervene an event which as efficient cause serves to explain the occurrence of the ultimate result, and may in turn be teleologically explained by the result which is its final cause. He offers first the following quasi-syllogism: Health (A) attaches to the descent of food into the stomach (B), Descent of food into the stomach attaches to walking after dinner (C), Therefore health attaches to walking after dinner. A. can hardly be acquitted of failing to notice the ambiguity in the word inrapx€w. In his ordinary formulation of syllogism it stands for the relation of predicate to subject, but here for that of effect to cause; and 'A is caused by B, B is caused by C, Therefore A is caused by C', while it is a sound argument. is not a syllogism. A. adds (b'9-20) that here B is 'as it were' a definition of A , i.e. that just as lunar eclipse may be defined by means of its efficient cause as 'failure of light in the moon owing to the interposition of the earth' (ch. 8), so health may be defined as 'good condition of the body due to the descent of food into the stomach'. This is only 'as it were' a definition of health, since it states not the whole set of conditions on which health depends, but only the condition relating to the behaviour of food. 'But instead of asking why A attaches to C' (A. continues in b2 0-3) 'we may ask why B attaches to C; and the answer is "because that is what being in health is-being in a condition in which food descends into the stomach." But we must transpose the definitions, and so everything will become plainer.' It may seem surprising that A. should attempt to explain by reference to the health produced by food's descent into the stomach (sc. and the digestion of it there) the sequence of the descent of food upon a walk after dinner-a sequence which seems to be sufficiently explained on the lines of efficient causation. And in particular, it is by no means easy to see what syllogism or quasi-syllogism he has in mind; the commentators are much puzzled by the passage and have not been very successful in dealing with it. We shall be helped towards understanding the passage if we take
COMMENTARY note of the very strong teleological element in A.'s biology (especially in the De Partibus Animalium). and consider in particular the following passages: Phys. 200aIS £CTTI. 8E 1'0 dvayltaiov €v TE TOtS I'aihjl-'a.or. Kat EV TOLS' KClTG. tfoVaw y"yvoplvol.S' Tpemov ·flVa. '11'apa1T)l'rwlwS" VrE"~ yap TO tiVOv To8l EUTW, avaylC7J TO Tplywvwv 8Jo 6p9a'ir LactS lxEU" ill' aUK ETrEi TOfiTO, EKEtPO' ill' yE' TOVrO p.,q Errrw, oV8E TO dJOv EaTO'. Ell BE 'TotS' ytYVOjUVOLS' iVEKd. TOV d.v&rraAw, liZ 'TO ..,.I.AOS' laTat ?j laTt, KCll 'TO lJl-'1Tpoa8Ev EaTa, 1j lcrrw' El 8£ JL't}. WCT1TEP EKE' p..q OVTOS' TOU UVj.J/TTEp&.up.aTor ~ apx:Tl 0;"( lena". Kal EIITClVOa TO 'flAoS' KaL TO o~ lVEKCl. Part. An. 639bz6 aVeiYK'} 8E '1'0"£)18£ TTJV iJ>..7]V iJ'1rap,a" ElluTCll. olKla 1j &:'\'\0 'n 'rEAoS"
E'
KaL yolaOa, TE KaL K'V7]81jvQ.' SEL 70SE 7TPWTOV, EtTa T08E, Kat TOi'iTOV 8~
'TOV Tpo."OJl J
on 7C.
where the reason for the difference is thus stated: a.t-rtov Sf VA1J ~ apxovaQ, rijr YEVEClEWS' EV Tip 1TOtEiv xat yfYVEa8al
nov }LEV ~
nUll
ano,
'TIXV71S' . Ell
n {nrupx£l.
'TL
P.EpOS TOV 1Tpd.YJLQTO~ /LEV
EaTtV oia KtllEia8at ixP' aVrfjr ~ S' ov, lea, -raVrr,S' -q f'EIJ d,lH 1} 8£ ci.8vva'Tos. 'Chance production is identical in kind with
TOtQtJ.r1}
oia 'TE the second half of the process of artistic production. The first half, the v6~u.. , is here entirely absent. The process starts with the unintended production of the first stage in the making, which in artistic production is intended. This may be produced by external agency, as when an unskilled person happens to rub a patient just in the way in which a doctor would have rubbed him ex arte. and thus originates the curative process. Or again, it may depend on the initiative resident in living tissue; the sick body may itself originate the healing process' (Aristotle's Metaphysics, ed. Ross, i, p. cxxi). Zabarella makes 9S'3-{) the basis of a distinction between what he calls the non-conjectural arts, like architecture and sculpture, which produce results that nothing else can produce, and produce them with fair certainty, and conjectural arts, like medicine or rhetoric, which merely contribute to the production of their results (nature, in the case of medicine, or the state of mind of one's hearers, in that of rhetoric, being the other contributing cause)-so that, on the one hand, these arts may easily fail to produce the results they aim at, and on the other the causes which commonly are merely contributory may produce the results without the operation of art.
Finally ('6-;1), A. points out that teleology is to be found, properly speaking, in these circumstances: (x) €JI oO'o,s Jv8lXl;TCtt Kat £L8£ Ka~ a.\.\WS', i.e. when physical circumstances alone do not
determine which of two or more events shall follow, when (2) the result produced is a good one, and (3) the result produced is not the result of chance. He adds that the teleology may be either the (unconscious) teleology of nature or the (conscious) teleology of art. Thus, as in Met. 1032a12- 13, A. is working on the assumption that events are produced by nature, by art (or, more generally, by action following on thought), or by chance. The production of good results by nature, and their production by art, are coupled together as being teleological. With the present rather crude account should be compared the more elaborate theory of chance and of necessity which A. develops in the Physics (d. my edition, 38-44). It is only by exercising a measure of goodwill that we can consider as syllogisms some of the 'syllogisms' put forward by A. in this chapter. But after all he does not use the word 'syllogism' here. What he says is that any of the four causes named can serve as
,.,.'0'011 between the subject and the attribute,
whose connexion
is to be explained. He had the conception, as his account of the practical syllogism shows (E.N. II44'3I-3 ol yap O1hUoytO'f'ot TWP '"paKTwv apx.TJv EXOV7'£S' "law .E7TEl&r] Towv8£ TO -rEAoS' Kat TO aptU'Tov'), of quasi-syllogisms in which the relations between terms,
from which the conclusion follows, are other than those of subject and predicate; i.e. of something akin to the 'relational inference' recognized by modern logic, in distinction from the syllogism. 94b8. "Oawv 8' ai'noY TO EVEICQ. T£VOC;. The editors write EVEKa. 'TWOS'. but the sense requires EVEKCt 'TtJloS' as in b u (ct. 'TO 'T[voS' EVEKCt, • 23).
3Z-4. W(M'I'EP Et .•. +OI3WVTQL, 'as for instance if it thunders
both because when the fire is quenched there must be a hissing noise, and (if things are as the Pythagoreans say) to intimidate the inhabitants of Tartarus·. It seems necessary to insert on, and this derives support from T. 52. 26 Kat ~ ppovrrJ, 8,6'T(' 'TE aTToCTp~vvvP.EVOV K'TJ..., and E . 153. II 8td. 'T' ppOV'Tfj.; on TTVP aTTo· ap£vvVjJ.£vov K'TJ... 95·~. }lelA-U7TQ BE ... TE.XVn. The received punctuation (o'Tav I"'~ d:rro 'TvX']!> ~ YEV£U'!> V, werrE 'TO 'TEJ..O!> aya90v El1EKa TOV ylVE'Ta(' Ka, oj ",,Ja« oj Tlxvn) is wrong ; the comma after II must be omitted, and one must be introduced after aya86v. Further, 'TEJ..OS must be
understood in the sense of result, not of end.
COMMENTARY CHAPTER 12 The inference of past and future events
9SaIO. Similar effects, whether present, past, or future, have similar causes, correspondingly present, past, or future. This is obviously true in the case of the formal cause or definition (e.g. of eclipse, or of ice), which is always compresent with that whose cause it is. 2:1. But experience seems to show that there are also causes
distinct in time from their effects. Is this really so? 27. Though here the earlier event is the cause, we must reason from the later. Whether we specify the interval between the events or not, we cannot say 'since this has happened, this later
event must have happened'; for during the interval this would be untrue. 35. And we cannot say 'since this has happened, this other will happen'. For the middle term must be coeval with the major; and here again the statement would be untrue during the interval. hI. We must inquire what the bond is that secures that event succeeds event. So much is clear, that an event cannot be
con~
tiguous with the completion of another event. For the completion of one cannot be contiguous with the completion of another. since completions of events are indivisible limits, and therefore, like points, cannot be contiguous; and similarly an event cannot be contiguous with the completion of an event, any more than a line can with a point; for an event is divisible (containing an infinity of completed events), and the completion of an event is indivisible. 13. Here, as in other inferences, the middle and the major term must be immediately related. The manner of inference is: Since C has happened. A must have happened previously; If D has happened, C must have happened previously; Therefore since D has happened, A must have happened previously. But in thus taking middle terms shall we ever reach an immediate premiss, or will there (owing to the infinite divisibility of time) always be further middle terms. one completed event not being contiguous with another? At all events, we must start from an immediate connexion, that which is nearest to the present. 25. So too with the future. The manner of inference is: If D is to be, C must first be; If C is to be, A must first be; Therefore i! D is to be, A must first be. Here again, subdivision is possible ad infinitum; yet we must get an immediate proposition as starting-point.
II.
12
31. Inference from past to earlier past illustrated. 35. Inference from future to earlier future illustrated. 3S, We sometimes see a cycle of events taking place; and this
arises from the principle that when both premisses are convertible the conclusion is convertible.
¢'S. Probable conclusions must have probable premisses; for if the premisses were both universal, so would be the conclusion. 17. Therefore there must be immediate probable premisses, as well as immediate universal premisses.
A. starts this chapter by pointing out that if some existing thing A is the cause (i.e. the adequate and commensurate cause) of some existing thing B, A is also the cause of B's coming to be when it is coming to be, was the cause of its having come to be if it has come to be, and will be the cause of its coming to be if it comes to be in the future. He considers first ('14--I); the last step being justified by the remark that the attributes of the genus composed of certain infimae species follow from the definitions of the species, and uu
COMMENTARY belong to the genus because they belong directly to the species (b,,- S). There are great difficulties in this interpretation. (I) The interpretation put upon 'To. t3,a, 7TU'oTJ 8£wp€'iv S,d. 'TWV KOtVWV 7TPWTWV (h,o-I) is clearly impossible. The words suggest much rather the deducing of the peculiar consequential attributes of different species (mi./J-q suggests these rather than differentiae) from certain attributes common to all the species. (,) The interpretation of 'ToL'S' CTVV7',O£JLEVOtS' J.K 'Tall.l aTOp-WI! (b2I ) as meaning the genera, and of TOi'S a1TAois (b23) as meaning the species, while not impossible, is very unlikely; A. would be much more likely to call the genus simple and the species complex (el. lOO b, n.). O'VJL{3alvoVTa,like 11'0.81]. suggests properties rather than differentiae. and the contrast A. expresses is one between avp.{Jalvov-ra. and opt-up-ol, not between the Optup.bs of a genus and the optap.ol of its species. It might be objected that a reference to the deduction of properties would be out of place in a chapter that is concerned ouly with the problem of definition; the answer is that while the chapter as a whole is concerned with definition, this particular section concerns itself with the question what method of approach to the problem of definition is the best prelude to the scientific study of a subject-genus (b'S)-which study will of course aim (on A.'s principles) at deducing the properties of the genus from its definition. (3) the immediately following section on the utility of division (b'S-97"6) is relevant to the defining of infimae species (C!.V8pW7TOo.fJp.aTa (with which chs. 15-18 are concerned). but as to their proper formulation; his reason being
that if you say ("9- II) 'C is B because A js Band C is an A', you are not giving a scientific demonstration because in your minor premiss and your conclusion the predicate is wider than the
subject. You have not solved the real problem, viz. why B belongs to A, but have only reduced the improper question why C is B to the proper form 'why is A B?' This interpretation might seem to be an ultra-refinement; but it is justified by A.'s words, '"POt; 'TO ;xn~ 'Tel. ,"po{JATJ/.J.aTa.. The object in view is not that of solving the problems, but that of
having them in their truly scientific fonn. What he is doing in this chapter is to advise the scientific inquirer to have in his mind a 'Porphyry's tree' of the genera and species included in his subject-matter, and to discover the widest class, of the whole of which a certain attribute can be predicated-this widest class then serving to mediate the attribution of the attribute to classes included in the widest class. He further points out that sometimes ('1- 12) ordinary language furnishes us with a common name for the subject to which the attribute strictly belongs, sometimes ('13- 19) it has only a phrase like 'having horns', and sometimes (&20--3) where several subjects have an attribute in common, we cannot descry and name the common nature on which this depends but can only divine its presence. The chapter expresses, though in very few words, a just sense of the extent to which language helps us, and of the point at which it fails us, in oUI search for the universals on which the possession of common properties depends. I. Diiring points out in Aristotle's De Partibus Animalium: Critical and Literary Commentaries, '09-'4, that Aristotle's four main discussions of the problem of classification-Top. vi. 6, An. Post. ii. '4, Met. Z. 12, and De Part. An. i. 2- 4-show a gradual advance from the Platonic method of a priori dichotomy to one based on empirical study of the facts. 98a 'l-2. npo~ BE 1'0 €XE1.Y ••• EIC).€yE1.Y. In al .;\ly€w, and in &2 g15 he explains the fact that horned animals have a third stomach ('xivo.) by the principle of compensation. Because they have horns they have not front teeth in both jaws; and because of this, nature gives them an alternative aid to digestion.
CHAPTER 15
am middle term 7lIiU often explain severaJ properties 9B'24-
(1) Problems are identical in virtue of having the same middle tenn. In some cases the causes are the same only in genus, viz. those that operate in different subjects or in different ways, and then the problems are the same in genus but different in species. 29. (2) Other problems differ ouly in that the middle term of one falls below that of the other in the causal chain; e.g. why does the Nile rise in the second half of the month? Because this half is the stormier. But why is it the stormier? Because the moon is waning, The stormy weather falls below the waning of the moon in the causal chain.
In the previous chapter A. has shown that problems of the form 'why is C RI', 'why is D RI', 'why is E RI' may be reduced to one by finding a genus A of which C, D, and E are species, and the whole of which has the attribute B. Here various problems have a common predicate. In the present chapter he points out that problems with different predicates (and sometimes with different subjects) may meet through being soluble (1) by means of the same middle term, or (2) by means of middle terms of which one is 'under' the other. (1) ('24-9) avm,.pmw,," (defined
II. 14.98'12-15.98'32 665 thus by Simp!. Phys. 1350. 31-«"",,,.pu,.,.aO'o. 8. UAAOPPO", This passage is reduced to order by treating Wa7rEP (;i . . . aVTwv as parenthetical, and the rest of the sentence as asking two questions, Does effect
II. r6. 98'35-b38 en tail cause? and Does cause en tail effect? If both these things are true, it follows that the existence of each can be proved from the existence of the other (1)4-5). bl 6-ZI .•, 0•... oG . Bonitz (AT. Stud. ii, iii, 79) is right in pointing out that this is one sentence, with a colon or dash (not, as in the editions, a full stop) before .1 in b 19. The parenthesis ends with lKAei7r£tV (b'9), not with a,nov (b17). 17. TO yelp ai'nov . . . a.inoY, 7Tp6'TEPOV means 'prior in nature', not 'prior in time'; for A. holds that there are causes that are simultaneous with their effects; d. 95·I4~4. 22-3. EV ynp T~ AOY"! ... tU:a~, d. 93b3--'7. 25-31. "H EVSEXETQl ... ou I-lEVTOt ""av. A. raises here the pro-
blem whether there can be plurality of causes, and tentatively answers it in the affirmative. Ka, yap d (b 2S ) does not mean 'for even if'; it means 'yes, and if'. as in examples from dialogue quoted in Denniston, The Greek Particles, log-l0. The content of b2S- 3I , summarized, is 'Can there be more than one cause of one effect? Yes, and if the same predicate can be affirmed im-
mediately of more than one subject, this must be so.' 32-8. T) Et nEt ... 4»UAAOppOEiv. This is A.'s real answer to the question whether there can be plurality of causes. A 'problem', i.e. a proposition such as science seeks to establish, is always universal, in the sense explained in i. 4. viz. that the predicate is true of the subject Ka-rct 1Tarnos. KaO' aUTO, and aUTO (in virtue of the subject's being precisely what it is). It follows that the premisses must be universal; the cause, which is the subject of the major premiss. must be OAOV n, the whole and sole cause of the effect, which must in turn attach to it Ka86Aov (b32 - 3). E.g. if we ask what is the cause of deciduousness, we imply tbat there is a class of things the whole of which, and nothing but which, suffers this effect. and therefore that there is a cause which explains the suffering of this effect by this whole class and by nothing else, and must therefore be coextensive with the effect (b35~). Thus a system of propositions such as is suggested in a26--g cannot form a scientific demonstration. A cannot be a commensurately universal predicate of Band r, but ouly of something that includes them both, say Z; and this will not be a commensurately universal predicate of Ll and E, but only of that which includes them both, say H; the demonstration will be 'All Z and nothing else is A, All H and nothing else is Z, Therefore all H and nothing else is A'; and we shall have proved not only that but also precisely why all H and nothing else is A.
n
668
COMMENTARY CHAPTERS 17, 18
Different causes may produce the same effect, but not in things specifically the same 9')'1. Can there be more than one cause of the occurrence of an attribute in all the subjects in which it occurs? If there is scientific proof, there cannot; if the proof is from a sign or per accidens, there can. We may connect the attribute with the subject by means of a concomitant of either; but that is not regarded as scientific. If we argne otherwise than from a concomitant, the middle term will correspond to the major: (a) If the major is ambiguous, so is the middle term. (b) If the major is a generic property asserted of one of the species to which it belongs, so is the middle term. 8. Example of (b). II. Example of (a). IS. (c) If the major term is one by analogy, so is the middle term. 16. The effect is wider than each of the things of which it can be asserted, but coextensive with all together; and so is ' the middle term. The middle term is the definition of the major (which is why the sciences depend on definition). "5, The middle term next to the major is its definition. For there will be a middle term next to the particular subj ects, assigning a certain characteristic to them, and a middle connecting this with the major. 30. Schematic account. Suppose A to belong to B. and B to belong to all the species of D but extend beyond each of them. Then B will be universal in relation to the several species of D (for an attribute with which a subject is not convertible may be universal to it. though only one with which the subject as a whole is convertible is a primary universal to it), and the' cause of their being A. So A must be wider than B; else A might as well be the cause of the species of D being B. 37. If now all the species of E have the attribute A, there will be a term C which connects them with it. Thus there may be more than one term explaining th~ occurrence of the same attribute, but not its occurrence in subjects specifically the same. b7. If we do not Come forthwith to inunediate propositionsif there are consecutive middle terms-there will be consecutive causes. Which o( these is the cause of the particular subject's having the major as an attribute? Clearly the cause nearest to
II. 17, 18 669 the subject. If you have fOUl terms D, C, B, A (reading from minor to major), C is the cause of D's having B, and therefore of its having A; B is the cause of Cs having A and of its own having A. The question raised and answered in this chapter is the same that has been raised and answered in .lynv 5012 clA'18fUf09al To8f Ka-ru Toii3f 49a6 &.A7J8~~. 'fI'av 'TO iatm-;' of'OAayou· I«"ov 47ag coni. TO Elva, 52'32. b 67 zo if &.AT/Bwv ou" ;
gEWS
72 3 7
a.1To8€{·
(1v,uoyurrtl(~
EV iKaO'T'!J yivn 76a31 aUra~
a.1TclVTWV
88 3 18
aI, ap.EClOt 99b2I apxof"S(C1T€poS 86 b
J8
ib. I4 OVX
at
at
1TPW'J"aJ.
aUKetTTOS. Ell a. XP0Yfp 89 bro atrrpoAoyla 76bII ij Tt: 1La.61jlLaTt~ K(1i. ~ lIaV1't.on1 7Sb40 atrrpOAoyUO} EJL1Tt:!pla 46a19 aO'vAAoyttrroS 91b23 aO'vAAoyltrrws 77b40 aO'vlI(11TTOt ot uVAAoytO'ILO{ 42a21 a7"aK7"OV 7"0 J,A-EO'OV 32b19 aT£A£is 0' EV 7"0/ St:V1'EN O'X~}l(1Tt O'VAAOYLO'fLot 2S a4, ot EV 7"0/ 7"PITtfl 29a15 ot a. O'v'\'\oytO'fLO~ Tt:At:!oilvTat SU1 7"oil 1TPWTOV O'X11J-La7"OS 29a30 aTOfLOS 91 b.J2 47"0,uWS }l~ V1To.PXt:LV 79a33~b22 aueavt:! ~ O'(A~1IlJ 7Sb6 aUro, KaO' 73 a34, b28, &t aI2 a,po.lpf':O'ts. Ee a,po.tpfot:! Af':yolLf':Vo. 81 b3 ~Xt'\'\£I)S 97b18 aXPf':tOt oKlifJns 44b 26 fJpOV7"av 94 b32 fJpoJl'T1j 930i22, bS, 94 a3- 7 BpvO'wv 75b40
31, 45a26
le IJ1TOOEO'f':WS 40bz5 St'
StaypaILj.ta7"a 41 bI4
Sto.ypa,pnll Ka7"' Statpt:," 47 alI
aA~6nav
46as
8tatpf':i:08at
46a3S,
b7,20
8t(1lpwtS ~ at/i 7"00" yf':IIWV 46a31-b37, 91b29, ¢b25-97b6 ~ aui 7"WV O'vAAoyt,nat 9rb12, 36 KaTaoKt:va{£tv 0eov Sta TWV a. 97;123 ato.tp(7"tKoi OPOt 9r 39 StaMy£0'6at 1TPOS Tt 50;11Z opovs 92h32 StaAt:KTU(T] 1Tp07"acJts 24a22, 25 S. OIJAAoytaj.toi 46~, 65 a37 1} 3. 77;129, 31- 4 1Tpayp.o.7"£la 1} n£pi TT]V 8. 46a30 StaA£KTtKWS O'vAAoyitwOat SlbI9, 22 Sto.,\oyO( )( ,ua8~j.taTa 7sa12
a. 6aos ou
Sta.ILf':7"POS - 41a26, 46b29, 50;137, 65brS Stav01jT'~ j.to.O'f]OtS
71ax
7"0. ano Stavolas 95-3
StaVOLa &)b7
Sta1Top£iv 9O a37 SLa1TOp~j.taTa 93bzo
Statrr1jj...a 35ar2, 31, 3S14, 42b9, Szb 7, &t a35, bJ4 Sta,popa 46bn, S3bl, ¢b25-97b6 Sl£ats &t b39 St07"t )( OTt 53 b9. 7sa22, b33, 87a32, 89116,
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682
INDEX VERBORUM
50fa 43'39, 46'10. Sg'2- 4
7foMaxwr
""'~~ 88b3~"6 b
Sofa'nv 67 22 )( f."lOTo.uBcu SgIII 8ofaOT'Kws )( KaT' a.\~8nav 43b8 50faaTOV )( E"lIrnpOv B8b30 SuvaTos, SUllaTOv )( f.VSfXOP.fVOV 25'39 syn. fl,SfX0I"VOV 3IbS 5. ou.\.\oYlal-'0S 27'2, 28 1 16, 41 b33 SUOf1F'XnP"1TrYrfPOV 42b31
.ypfyopa,s 31b28, 41-,32'4 ErxwfHi, s~n. lvlllXfTaL ,32b30, 37 b7 ,lIOT'" B9 33 flSivaL 67116, 74b27-39. 76 128, 93'20--6 fJIAT(OV lxnv ToD fEt 83 b34, 36, 84 14. d. 72133
d8'7
(Platonica) TfpfTlap.o.Ta
faTL
83'33 Ta p.a87jp.aTa 1FfEpi .t lOTlv 79'7 • l"os )( OTJp.fEi:oll 7°13 ,tll41, p.~ .. Iva, Tolil )( ..tva, p.~ TOUTO 51 b5-52138 lOT'" f.1nOTaf'fEVOS, syn. EnlOTaTa, 5Ibl3 T6 OV 92bl4 Ta p.~ ol'Ta ib. 30 .rs. (VOS TLVOS ~I'TOS OVSllo' lOTW d.V&Y"'1S 34'17, cf. 40b3S, 73 8 7, 94124 AOYOS ,ts SLXWS 93 h 35 ;,,8~aLS (I) (v. 28123 n.) 28bl4
J,
(2) 48'25, 49% (KI(fEi:oBru TOUS 0povs 4818
(ICAo,l'Pallnll TrpoTaans 43 b l, 6, 47 1 10 ("A,tTr"V Bg b:z6. 90'3, 30. gBb I8 11C').t:~LS 7S b34, B8 aI. goal7, 93a23, 30, 37
(r) (v. 2S 123 n.) 28-1123, 30'9, II, 12. 49 b33 (2) 30b31, 48al, 29 lAo,ffOIl ClKloV 26'22, b3S, 28a14 ;A,yXos 66 4-17 lA"'1 Trt:pUPfEpij 79al5 (l-'pill~a8o" B4'36, 86 b I8, SSbS ip.Tropia. 46'18, looa5'"'9 (p."l"uw f.ls -n1" S,a.ipt:ow 97120 (l'"lTrTO"V oPO' B4b I2 tllaMclf 74'IS, 99IS tvo,VTlos. JvaVTlov )( 0."LIC,lI'0I0lo' 6I b I7, 24, 621II, 17, 28, 63b2S, 41, 6411S, 31 E. 1tpOTaaOs 63b28. 64-31 i"o,VTlwf )( rlVT'ICUP./VWS al'TLOTpltP."" 59h6 lvacXffC18al. JvafEX0IJ-OIOV 321I6-40h16 (1('T'8fEa8a~
)./'1I:T(U
2Sa37b cf. b I4 ,
32a20,33b28,30.34b27,35 33,J6b33. 59"It )( 3VI'QTOV 25"39 Tqi (CIT"" &Jlolw~ T4TTn'CU 2S b 2I, 32b2
syn. 311VtlTOV 3IbS 'JI"t:pl TOG Jv· 3ixt:u8a, C7v.\Aoy,O",.u5r 321r6--33b24, 36b26--J,bI8, 39 14- b6 lav " "'~v
a'
inr&.PXnv " ivMXf:f18«l i\a",paV'1}TU' TWV 1rpoTaat:wv 33b25-3Sb22, ,36b 29,
&orUS' -rj S' v,81xt:a8cu C1TJJlall7J 3Sh2s-J6h2$, 36b3I, ,38113-39&3, 40&4-bI6 )(
37bI9-3saI2,.39"7, b7- 40' 3 "
Jl~V
it
avaYInlS' {ma.PXOJ1
aV«YKatov 32"18, 28, 33 b9, 16, 22, 38135 def. 32&18, cf. 33b23. 28, 30, 34b27. 37.27 rTVJlPo1J1fa ,"claas 70S Ka:rd. TO ivS'Xt:u8ru. fTpOTaOns a:VT~C1Tp'rpn" 32129
KQTa.
auo
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YfT(U, TpOTfOlJr b4 O~K dVnUTpErpn 70 €v Tq; J,,8cxt:a8a.t Cl'TftPTITU(OV 36h35• 3783J TO p..~ i. 1-''180'1. S,xwS' Ai'ytTCU 37'15, 24
lV(Ka.
TO
TWOS'
T{VOS lVf:Ko.
)(
i,
&'v&YlOJr 94 b27
94123, bg
JllfP'Yf'iV 67 b3-9 ivOvJLTJp.a 701 10, 7I a IO
;pcrraa~s 6g'37-70'2, 73'33, 74bI8-2I, b 77 34"""9 iVlrlTapx~~p )( EJIV'm:l.p~aB(U 73hl7 if &'u~AWIo' SdKIo'uo8a~ 57 18, 28 E1raynp. "(1Faywp 9IbIS, 35, 92'37 f.7TaX8fjlo'fll 71 '24, 81 b5 (1Fayo~£JIOS 71'21 (1Faywy~ 42'23, 67'23, 68bI3-37, 72b29, 78"34, SI'38-b9, gob I4 , loob4 )( aIJ.\).oYLO~OS 42'3, 68bI4, 32-7, b 71"6, 10 I.f a"al'Twv 68 28, 69 8 16. )( 1Fap&Snyp.a 69'16 f.1FalC7'v(~ 1FpOTaO(S 77 b35 f.1Ta..U&TT'''' 79 b7 l.1FapaSnrAOVI"IIOP 49'u-:z6 J1F~IC7',lvnv g6'24 ;'"~a(J(U. TO. E"op.~Io'a 43 b7, II (1Ft n )( 0>.'7 .5411, b3 , J9, 35, 5511, 19, b 5, 7""'9. 23, 28, 31, .J6. ,38, 5613 )( a."Aws 66b39, 67 1 5 E, TWOS .\I-YEoBrn 48 b lo E1F,fjff3(UoDo8o.~ 47~
J"lfjA,tjJIS 44b40, 4S'17, b l9, 23 t:IUMLIG'VIo'(U 5°124, 8S 1 27 E"'KaTT/yopovp.&a 49125 E"'KO,pwllt"ip 77 1 26
INDEX VERBORUM T.&.o8o.~ 76b9 KtV1jOLS 48b31 KUwv 43126 KA.qons 'TWV OVOfUt'TWV
48b4 1 KOLvd 76a37-b22, 77126-31 88136-b3 Koplal(os
85 1 24
)( 1T'TWOHS' 1(. apxat
INDEX VERBORUM
TO, E"
o.pxU
I-'.qvlal(ol 6g-33 JL."xavll(os 76~4, 78b3'b Mll(KMOS I-'0VUII(OS 47 30 ~1ITj~." 10013-6 p.ovci.s 72~2
Karel
7"IIIOS
N(i:.\os gal31 VW(.., 76b9
KpVaTM).OS 95116
KVK.\(p 3t"IICV\IOOat 57br8-S914I, 7zbzS Yfllf:UtS' 9S b 38-¢ 1 7
>.ap./1&.V£(1I 24bro, 73124 9 1bU
>'al'1rr1/p 94bz8 ).("1(:(180.&
a1l"o
'TIllOS
)(
l>4II4
lIO(i:V 88-16
86 1 :22
.\oYUtoS'
V&."als 8817
.\0),"'005' 8fWPfjJl 8zb35, 88119 QVa.\VTU'WS' &t l ,. b z ).oyt0l-'0l 88 bI2 ).oyot ors l('(i1'111 ovof'a 48130
)(
viiv. Ta II.
ov
0: lew )( & iv -rfi IjIvxfj, 0: law 76b24 OIlOIL(l'Tw8'1S' 93b30 ds a,xwS' ib. 35 &."a .\. 85138 AvuIlv8pos 97hz1 >"vUtf'OS O'vA.\oYIO'Il0S 70131, 34 TG p.. 77bz7- 33. 78 a ] I,
p.a8'1f'(J. 4614
79 1 7- 10 lUlo"p.a'TIKOs 7113
1la.8'1C11S' 67121, 7I ar p.o.v8allOp.o ~
f1raywyfi -;
&.1I'o8Elfn
81140 p.€i'MO¢flJX1o.
97 b1 5- 2 5
I'(i'oll 4KPOV 26 121, b37 • 28113
Mivwv. & i .. 'To/ M. >.0')'05' 67121 i" Tip M. o:rrofJ71p.a 71129 Ell p. 241 17. 25110, Sf'S p.lpos 251120, 53 li4, 81 I O"KEvatOl'T1 Mw 7(i lv p.. 43ag
,...'pos.
TO
K(lTa-
al
4113. 44b40, 47 a,38-b I4 • 74 b2675117, 7Sbu. 76"9, 7S bS. SIII7. B9b3~30' 93 17. 95-36, 99-4 def. 25 b35, 26 bJ6, 28 al2 uxfj~l1 42b34, 35. 39. 4418, 47 b3. 48115. sobs Q'VEU~. uv.v.OY'O'~os- ou ylvt:T'al 66-28 oll(i:oll 8o b 17-22
I'.£aoll
JL(T'apatv((v 75138 ~£TMa~prlVEIv 39 1 27.
41 -39 TOS If'POTrlU((S 37blS ci TO aVTO SVlla· b T'aL 49 3 TOUS- '\oYOVS 94bn p.ET'OJ..."y"s-. KaTo j.'(T'&.>t."Y,IV a(l'\'\o,),IO"
~os 45bl7 ~ETo.t$oP4l97b37 I.") 1'111' UTTrlPXE.., 24119, 26b32. 3213S. d.S9 blO 1I'OA(~OS
94-J6
apx?
apX"I
JTTI~j.''''S
a..\.,,8~s a(l loobS TOU xpOJ.'Ov 9SblS
OSOs (11" TaS apxas 84b24 OiI(E'iOS- 71b23, 72&6. 74b26, d. 7s bJ8. 76&6 oi. Jlf'lf1T.ql-'''' )( Ka8oAov 67 127 O.\O'If'TEPOS- g6b39 o).os. (II O. Etva! 24b26, 25 b33, 3012, 53121 o).ov)( ~/pos 42a10, 16, 49 b37. 64117, bu. 6ga14 o~ovos 9S-37 0l-'0IOaxvfWV(S TTpoTo.aoS 27 bn , 34, 32b37, 33 137, 3617 o~wvv~la 8s b n, 16, 97 bJ6 o~wvvp.o s 99 1 7 ollOJLaTwBfJs Myos 93b31 01l'EP 49118, b7, 83 17, 14, 24- 30, Bg 135, b4
K'aY71'T£S
26
ou rnOtpouon' 7S130
">,(lT~V.uOS'
gab,
n'AaTwv, ref. to Meno 67'"21, 71az9, Thea el. 76bz5 'ITOtOT'fIS'.
av.u.0yu1POS KaTu
1tOU.lT7jTa
45 hY 7
1I'0~loua8(u 32%. 17
Prrr0PIKOS'
1I'0~v. cdr J.oyl't:a(l(U. 66135 1I'pouv>J.oytufl.or 42b5 lI'po1"aa,S' 24bl6, 43bl-46''30,
68 b u, 71ag
94 hI 0'':'\,,'''1 78b4 O"JJlt:WII 7oa3-b,3B. 7S a33. 99 a3 ' 1tpOTaa'S' an08nlCTuc, avaYKtu'o. 17 iv&tos 70·7 '\ap./Jcivt:To.I TPlXWS' ib. II )(OV>J.OYIO~S' ib. 24 a mjnloll 98 2I at'nv 94 b33 OKaA']vOS B4 b7 1:1o'ripar 17 T'ljll iT'pav tip.olav ""&'YK17 yillEu(lo.I To/ uup.rrt:paup.an 41b28 iK 800 ." . ."aoo. "n08nttS' 42132, d. 4ob36. 44"6, 53b2o, 66 117 Ta.S' .". fKAafl./Jailoil 43 b l, 47"10 0.1'1"1Kt:tP.(I'o.I n. 63b22 8Is Tav.,.ov ill Ta'S'.". 66127 QJlt:uoS' 72a7 ill8otos 74b23 i'lto.ICTII(~ 77 b 34 rrpontll':w 1"1]11 Ka80'\ou 47115 npOT(pOil Tfj tj,von )( "POS' ~p.6s 71 b33- 7zaS npoiinapxovaa yvw(ns 71al rrpoiirro'\ap./J&'IInil 62b36, 71 a l2 rrpwTov 71 b 21 Tw1 rrpWT'P tmapxnll 66 b20, 81b31, 35, g8b 27 11'. 1(0.1 QPX~ To.v.,.OV 7216 )( UUTo.TOil 82 b Z .". aJlrfxnlpws 96a36 "'PWTWS Tlll1 -vnapxnv 79a38, b 25 , 38 rrTW(J'ts 42b30 nu8ayopt:lol 94 h 33 'lTUI(I'OUTo.I TO p.laoll B4 b35
OTt:P'lTII(OS 37b20, 381J4, 39b22
686
INDEX VERBORUM
(1'T'''IL~
)( povas 87836
trrVt{Jnv 78a30 aTtH.X.iov 84 b 21 UTOpa. l(o~luS' 94 hIS ov.v.oyl'~a8Iu )( a1l'08UI(vVvfJl 24'
27. d. 8IbI8-z3 OVA>.OYlO'JlOS' def. 24 bIB .,lAuoS' )( Qn).~s ib. 22, 2Sb35. 26b29, 27116,
28-15, :l3 a zo, 3482 2SbZ7.7IbZ3
4Ib33
ot
)( Qno8nl,S'
8vvaTOS 2782, 28'16,
aT.)..', TE).nOVJlTa., 8&.« TOU 29130
ava-
ffT''''' yaYEiv nuVTos ds TOVs- '" TW '1I'prJJT'qJ OnJlfJ." 1(0.86>'0\1 29 b t. d. 4obI8, 41 h3
TfPWTOV OX71paTOS
3WCTucol)( at ,~ 1JnoO/oEwS 40b27 SUI TP'WV Jpwv ~J.'Ov 41 b36-42 131, BiblO .zs TO d3vvaTOV 41122, r1 ,
45823, b9• 8,a TOU d,8vvaTov 61'18 1'I'ch' loTCU u . 4Ih&--4zb26 BE' Karrryopucov 'nV(l TWV opwv dvu, 41b(;, d. 8l b Io-I4 SEt '1"0 Ka86>.ov thrcf.PXEW 41 b7 ll( SVo Trpo.,.&O'£WII 42832-40 fTWS nmopTfavMO')'lop.Wv 43 120-45'22 p...,·a}"fjl/Jtv i1 I(fJTa 1I'(N.~Ta 4Sh17 1I'wS' av&top.n- 'roth· u. 46b40 "O,UriIt'IS' 'o)'ov 66'32, 77 bS. 5 v,,66f(TIS 72'20-4, 76 bzS-77 '4 If U. 41'24. 72bIS. 8S b39. 92a6-33 It V. )( 811lt'Ttlt'wS 8nlO'vvcu 40b2S. 4SbI6 (Tu>.>.oy~aJUJl it 50'16 V1TOIt't:(pfVOV 79 a9, 8S'6, 13. b22, 91aU ylvos V. 75'42. 76'12 v".o>'TJ1T·n:)v 49b6 inrO>.."t/JIS 64'9, 66bI9, 79 b28
v.
t1XfiJlu 29·I9-b:z8. 39'S
rf,atvop.€Va.
TO.
78b39 rpavcu
rP.
lnr'
dCM'po>'oy,lt'~v
)( dfJ'o,;avcu 71'14. 73b23.
71'10, 22, 30
'"
I
INDEX VERBORUM aOlS
)(
aTTa¢auls 32 -28,
51 b 20,
33. 62al4 r$8afYTov 7Sl?24 .p8tVUII, 1jJ8lvoYTOS TOV JlTJVOS /)B"3! "r/>pOV1'}OlS 89h g tPvta9f1A.. TTt¢VKEVCll., coni. Ev3€Xf:08ru. 2ShI4 ,32b 7• 16
¢u)o.).oPPO(~V f>VULKOS
7rE1JV.ICOS
1rPw-rov
98"37, 38
70bg
.pV("oyvwjJ.OVf:rV
IfIWK£is
V1TI1PXUV (EtVa.!.)
T/J£v3~s E'Ttl TL
69"2
7ob7- 38
)(
OA1} 54"1,
hI9
';£680