Chapter VII: Analytica Posteriora I (2)

[Footnote 39: Ibid. I. xii. p. 77**, b. 34 seq. This passage is to me hardly intelligible. It is differently understood by commentators and translators. John Philoponus in the Scholia (p. 217, b. 17-32, Brandis), cites the explanation of it given by Ammonius, but rejects that explanation, and waits for others to supply him with a better. Zabarella (Comm. in Analyt. Post. pp. 426, 456, ed. Venet 1617) admits that as it stands, and where it stands, it is unintelligible, but transposes it to another part of the book (to the end of cap. xvii., immediately before the words [Greek: phanero\n de\ kai\ o(/ti], &c., of c. xviii.), and gives an explanation of it in this altered position. But I do not think he has succeeded in clearing it up.]

[Footnote 40: Ibid. I. xii. p. 77, b. 40-p. 78, a. 13.]

Knowledge of Fact and knowledge of the Cause must be distinguished, and even within the same Science.[41] In some syllogisms the conclusion only brings out [Greek: to\ o(/ti]--the reality of certain facts; in others, it ends in [Greek: to\ dio/ti]--the affirmation of a cause, or of the _Why_. The syllogism of the _Why_ is, where the middle term is not merely the cause, but the proximate cause, of the conclusion. Often, however, the effect is more notorious, so that we employ it as middle term, and conclude from it to its reciprocating cause; in which case our syllogism is only of the [Greek: o(/ti]; and so it is also when we employ as middle term a cause not proximate but remote, concluding from that to the effect.[42] Sometimes the syllogisms of the [Greek: o(/ti] may fall under one science, those of the [Greek: dio/ti] under another, namely, in the case where one science is subordinate to another, as optics to geometry, and harmonics to arithmetic; the facts of optics and harmonics belonging to sense and observation, the causes thereof to mathematical reasoning. It may happen, then, that a man knows [Greek: to\ dio/ti] well, but is comparatively ignorant [Greek: tou= o(/ti]: the geometer may have paid little attention to optical facts.[43] Cognition of the [Greek: dio/ti] is the maximum, the perfection, of all cognition; and this, comprising arithmetical and geometrical theorems, is almost always attained by syllogisms in the First figure. This figure is the most truly scientific of the three; the other two figures depend upon it for expansion and condensation. It is, besides, the only one in which universal affirmative conclusions can be obtained; for in the Second figure we get only negative conclusions; in the Third, only particular. Accordingly, propositions declaring Essence or Definition, obtained only through universal affirmative conclusions, are yielded in none but the First figure.[44]

[Footnote 41: Ibid. I. xiii. p. 77, a. 22 seq.]

[Footnote 42: Themistius, p. 45: [Greek: polla/kis sumbai/nei kai\ a)ntistre/phein a)llê/lois to\ ai)tion kai\ to\ sêmei=on kai\ a)/mphô dei/knusthai di' a)llê/lôn, dia\ tou= sêmei/ou me\n ô(s to\ o(/ti, dia\ thate/rou de\ ô(s to\ dio/ti.]

"Cum enim vera demonstratio, id est [Greek: tou= dio/ti], fiat per causam proximam, consequens est, ut demonstratio vel per effectum proximum, vel per causam remotam, sit demonstratio [Greek: tou= o(/ti]" (Julius Pacius, Comm. p. 422).

M. Barthélemy St. Hilaire observes (Note, p. 82):--"La cause éloignée non immédiate, donne un syllogisme dans la seconde figure.--Il est vrai qu'Aristote n'appelle cause que la cause immédiate; et que la cause éloignée n'est pas pour lui une véritable cause."

See in Schol. p. 188, a. 19, the explanation given by Alexander of the syllogism [Greek: tou= dio/ti].]

[Footnote 43: Analyt. Post. I. xiii. p. 79, a. 2, seq.: [Greek: e)ntau=tha ga\r to\ me\n o(/ti tô=n ai)sthêtikô=n ei)de/nai, to\ de\ dio/ti tô=n mathêmatikô=n], &c. Compare Analyt. Prior. II. xxi. p. 67, a. 11; and Metaphys. A. p. 981, a. 15.]

[Footnote 44: Analyt. Post. I. xiv. p. 79, a. 17-32.]

As there are some affirmative propositions that are indivisible, _i.e._, having affirmative predicates which belong to a subject at once, directly, immediately, indivisibly,--so there are also some indivisible negative propositions, _i.e._, with predicates that belong negatively to a subject at once, directly, &c. In all such there is no intermediate step to justify either the affirmation of the predicate, or the negation of the predicate, respecting the given subject. This will be the case where neither the predicate nor the subject is contained in any higher genus.[45]

[Footnote 45: Ibid. I. xv. p. 79, a. 33-b. 22. The point which Aristotle here especially insists upon is, that there may be and are immediate, undemonstrable, _negative_ (as well as affirmative) predicates: [Greek: phanero\n ou)=n o(/ti e)nde/chetai/ te a)/llo a)/llô| _mê\ u(pa/rchein_ a)to/môs]. (Themistius, Paraphr. p. 48, Spengel: [Greek: a)/mesoi de\ prota/seis ou) katapha/seis mo/non ei)si/n, a)lla\ kai\ a)popha/seis o(moi/ôs ai(\ mê\ du/nantai dia\ sullogismou= deichthê=nai, au(=tai d' ei)si\n e)ph' ô(=n ou)dete/rou tô=n o(/rôn a)/llos tis o(/lou katêgorei=tai.]) It had been already shown, in an earlier chapter of this treatise (p. 72, b. 19), that there were _affirmative_ predicates immediate and undemonstrable. This may be compared with that which Plato declares in the Sophistes (pp. 253-254, seq.) about the intercommunion [Greek: tô=n genô=n kai\ tô=n ei)dô=n] with each other. Some of them admit such intercommunion, others repudiate it.]

In regard both to these propositions immediate and indivisible, and to propositions mediate and deducible, there are two varieties of error.[46] You may err simply, from ignorance, not knowing better, and not supposing yourself to know at all; or your error may be a false conclusion, deduced by syllogism through a middle term, and accompanied by a belief on your part that you do know. This may happen in different ways. Suppose the negative proposition, No B is A, to be true immediately or indivisibly. Then, if you conclude the contrary of this[47] (All B is A) to be true, by syllogism through the middle term C, your syllogism must be in the First figure; it must have the minor premiss false (since B is brought under C, when it is not contained in any higher genus), and it may have both premisses false. Again, suppose the affirmative proposition, All B is A, to be true immediately or indivisibly. Then if you conclude the contrary of this (No B is A) to be true, by syllogism through the middle term C, your syllogism may be in the First figure, but it may also be in the Second figure, your false conclusion being negative. If it be in the First figure, both its premisses may be false, or one of them only may be false, either indifferently.[48] If it be in the Second figure, either premiss singly may be wholly false, or both may be partly false.[49]

[Footnote 46: Analyt. Post. I. xvi. p. 79, b. 23: [Greek: a)/gnoia kat' a)po/phasin--a)/gnoia kata\ dia/thesin]. See Themistius, p. 49, Spengel. In regard to simple and uncombined ideas, ignorance is not possible as an erroneous combination, but only as a mental blank. You either have the idea and thus know so much truth, or you have not the idea and are thus ignorant to that extent; this is the only alternative. Cf. Aristot. Metaph. [Greek: Th]. p. 1051, a. 34; De Animâ, III. vi. p. 430, a. 26.]

[Footnote 47: Analyt. Post. I. xvi. p. 79, b. 29. M. Barthélemy St. Hilaire remarks (p. 95, n.):--"Il faut remarquer qu'Aristote ne s'occupe que des modes universels dans la première et dans la seconde figure, parceque, la démonstration étant toujours universelle, les propositions qui expriment l'erreur opposée doivent l'être comme elle. Ainsi ce sont les propositions contraires, et non les contradictoires, dont il sera question ici."

For the like reason the Third figure is not mentioned here, but only the First and Second: because in the Third figure no universal conclusion can be proved (Julius Pacius, p. 431).]

[Footnote 48: Analyt. Post. I. xvi. p. 80, a. 6-26.]

[Footnote 49: Ibid. a. 27-b. 14: [Greek: e)n de\ tô=| me/sô| schê/mati o(/las me\n ei)=nai ta\s prota/seis a)mphote/ras pseudei=s ou)k e)nde/chetai--e)pi/ ti d' e(kate/ran ou)de\n kôlu/ei pseudê= ei)=nai.]]

Let us next assume the affirmative proposition, All B is A, to be true, but mediate and deducible through the middle term C. If you conclude the contrary of this (No B is A) through the same middle term C, in the First figure, your error cannot arise from falsity in the minor premiss, because your minor (by the laws of the figure) must be affirmative; your error must arise from a false major, because a negative major is not inconsistent with the laws of the First figure. On the other hand, if you conclude the contrary in the First figure through a different middle term, D, either both your premisses will be false, or your minor premiss will be false.[50] If you employ the Second figure to conclude your contrary, both your premisses cannot be false, though either one of them singly may be false.[51]

[Footnote 50: Analyt. Post. I. xvi. p. 80, b. 17-p. 81, a. 4.]

[Footnote 51: Ibid. p. 81, a. 5-14.]

Such will be the case when the deducible proposition assumed to be true is affirmative, and when therefore the contrary conclusion which you profess to have proved is negative. But if the deducible proposition assumed to be true is negative, and if consequently the contrary conclusion must be affirmative,--then, if you try to prove this contrary through the same middle term, your premisses cannot both be false, but your major premiss must always be false.[52] If, however, you try to prove the contrary through a different and inappropriate middle term, you cannot convert the minor premiss to its contrary (because the minor premiss must continue affirmative, in order that you may arrive at any conclusion at all), but the major can be so converted. Should the major premiss thus converted be true, the minor will be false; should the major premiss thus converted be false, the minor may be either true or false. Either one of the premisses, or both the premisses, may thus be false.[53]

[Footnote 52: Ibid. xvii. p. 81, a. 15-20.]

[Footnote 53: Ibid. a. 20-34. Mr. Poste's translation (pp. 65-70) is very perspicuous and instructive in regard to these two difficult chapters.]

Errors of simple ignorance (not concluded from false syllogism) may proceed from defect or failure of sensible perception, in one or other of its branches. For without sensation there can be no induction; and it is from induction only that the premisses for demonstration by syllogism are obtained. We cannot arrive at universal propositions, even in what are called abstract sciences, except through induction of particulars; nor can we demonstrate except from universals. Induction and Demonstration are the only two ways of learning; and the particulars composing our inductions can only be known through sense.[54]

[Footnote 54: Analyt. Post. I. xviii. p. 81, a. 38-b. 9. In this important chapter (the doctrines of which are more fully expanded in the last chapter of the Second Book of the Analyt. Post.), the text of Waitz does not fully agree with that of Julius Pacius. In Firmin Didot's edition the text is the same as in Waitz; but his Latin translation remains adapted to that of Julius Pacius. Waitz gives the substance of the chapter as follows (ad Organ. II. p. 347):-- "Universales propositiones omnes inductione comparantur, quum etiam in iis, quæ a sensibus maxime aliena videntur et quæ, ut mathematica ([Greek: ta\ e)x a)phaire/seôs]), cogitatione separantur à materia quacum conjuncta sunt, inductione probentur ea quæ de genero (e. g., de linea vel de corpore mathematico), ad quod demonstratio pertineat, prædicentur [Greek: kath' au(ta/] et cum ejus natura conjuncta sint. Inductio autem iis nititur quæ sensibus percipiuntur; nam res singulares sentiuntur, scientia vero rerum singularium non datur sine inductione, non datur inductio sine sensu."]

Aristotle next proceeds to show (what in previous passages he had assumed)[55] that, if Demonstration or the syllogistic process be possible--if there be any truths supposed demonstrable, this implies that there must be primary or ultimate truths. It has been explained that the constituent elements assumed in the Syllogism are three terms and two propositions or premisses; in the major premiss, A is affirmed (or denied) of all B; in the minor, B is affirmed of all C; in the conclusion, A is affirmed (or denied) of all C.[56] Now it is possible that there may be some one or more predicates higher than A, but it is impossible that there can be an infinite series of such higher predicates. So also there may be one or more subjects lower than C, and of which C will be the predicate; but it is impossible that there can be an infinite series of such lower subjects. In like manner there may perhaps be one or more middle terms between A and B, and between B and C; but it is impossible that there can be an infinite series of such intervening middle terms. There must be a limit to the series ascending, descending, or intervening.[57] These remarks have no application to reciprocating propositions, in which the predicate is co-extensive with the subject.[58] But they apply alike to demonstrations negative and affirmative, and alike to all the three figures of Syllogism.[59]

[Footnote 55: Analyt. Prior. I. xxvii. p. 43, a. 38; Analyt. Post. I. ii. p. 71, b. 21.]

[Footnote 56: Analyt. Post. I. xix. p. 81, b. 10-17.]

[Footnote 57: Ibid. p. 81, b. 30-p. 82, a. 14.]

[Footnote 58: Ibid. p. 82, a. 15-20. M. Barthélemy St. Hilaire, p. 117:--"Ceci ne saurait s'appliquer aux termes réciproques, parce que dans les termes qui peuvent être attribués réciproquement l'un à l'autre, on ne peut pas dire qu'il y ait ni premier ni dernier rélativement à l'attribution."]

[Footnote 59: Analyt. Post. I. xx., xxi. p. 82, a. 21-b. 36.]

In Dialectical Syllogism it is enough if the premisses be admitted or reputed as propositions immediately true, whether they are so in reality or not; but in Scientific or Demonstrative Syllogism they must be so in reality: the demonstration is not complete unless it can be traced up to premisses that are thus immediately or directly true (without any intervening middle term).[60] That there are and must be such primary or immediate premisses, Aristotle now undertakes to prove, by some dialectical reasons, and other analytical or scientific reasons.[61] He himself thus distinguishes them; but the distinction is faintly marked, and amounts, at most, to this, that the analytical reasons advert only to essential predication, and to the conditions of scientific demonstration, while the dialectical reasons dwell upon these, but include something else besides, viz., accidental predication. The proof consists mainly in the declaration that, unless we assume some propositions to be true immediately, indivisibly, undemonstrably,--Definition, Demonstration, and Science would be alike impossible. If the ascending series of predicates is endless, so that we never arrive at a highest generic predicate; if the descending series of subjects is endless, so that we never reach a lowest subject,--no definition can ever be attained. The essential properties included in the definition, must be finite in number; and the accidental predicates must also be finite in number, since they have no existence except as attached to some essential subject, and since they must come under one or other of the nine later Categories.[62] If, then, the two extremes are thus fixed and finite--the highest predicate and the lowest subject--it is impossible that there can be an infinite series of terms between the two. The intervening terms must be finite in number. The Aristotelian theory therefore is, that there are certain propositions directly and immediately true, and others derived from them by demonstration through middle terms.[63] It is alike an error to assert that every thing can be demonstrated, and that nothing can be demonstrated.

[Footnote 60: Ibid. xix. p. 81, b. 18-29.]

[Footnote 61: Ibid. xxi. p. 82, b. 35; xxii. p. 84, a. 7: [Greek: _logikô=s_ me\n ou)=n e)k tou/tôn a)/n tis pisteu/seie peri\ tou= lechthe/ntos, _a)nalutikô=s_ de\ dia\ tô=nde phanero\n suntomô/teron.] In Scholia, p. 227, a. 42, the same distinction is expressed by Philoponus in the terms [Greek: logikô/tera] and [Greek: pragmatôde/stera]. Compare Biese, Die Philosophie des Aristoteles, pp. 134, 261; Bassow, De Notionis Definitione, pp. 19, 20; Heyder, Aristot. u. Hegel. Dialektik, pp. 316, 317.

Aristotle, however, does not always adhere closely to the distinction. Thus, if we compare the _logical_ or _dialectical_ reasons given, p. 82, b. 37, seq., with the _analytical_, announced as beginning p. 84, a. 8, seq., we find the same main topic dwelt upon in both, namely, that to admit an infinite series excludes the possibility of Definition. Both Alexander and Ammonius agree in announcing this as the capital topic on which the proof turned; but Alexander inferred from hence that the argument was purely _dialectical_ ([Greek: logiko\n e)pichei/rêma]), while Ammonius regarded it as a reason thoroughly convincing and evident: [Greek: o( me/ntoi philo/sophos] (Ammonius) [Greek: e)/lege mê\ dia\ tou=to le/gein _logika\_ ta\ e)picheirê/mata; e)narge\s ga\r o(/ti ei)si\n o(rismoi/, ei) mê\ a)katalêpsi/an ei)saga/gômen] (Schol. p. 227, a. 40, seq., Brand.).]

[Footnote 62: Analyt. Post. I. xxii. p. 83, a. 20, b. 14. Only eight of the ten Categories are here enumerated.]

[Footnote 63: Ibid. I. xxii. p. 84, a. 30-35. The paraphrase of Themistius (pp. 55-58, Spengel) states the Aristotelian reasoning in clearer language than Aristotle himself. Zabarella (Comm. in Analyt. Post. I. xviii.; context. 148, 150, 154) repeats that Aristotle's proof is founded upon the undeniable fact that there _are_ definitions, and that without them there could be no demonstration and no science. This excludes the supposition of an infinite series of predicates and of middle terms:--"Sumit rationem à definitione; si in _predicatis in quid_ procederetur ad infinitum, sequeretur auferri definitionem et omnino essentiæ cognitionem; sed hoc dicendum non est, quum omnium consensioni adversetur" (p. 466, Ven. 1617).]

It is plain from Aristotle's own words[64] that he intended these four chapters (xix.-xxii.) as a confirmation of what he had already asserted in chapter iii. of the present treatise, and as farther refutation of the two distinct classes of opponents there indicated: (1) those who said that everything was demonstrable, demonstration in a circle being admissible; (2) those who said that nothing was demonstrable, inasmuch as the train of predication upwards, downwards, and intermediate, was infinite. Both these two classes of opponents agreed in saying, that there were no truths immediate and indemonstrable; and it is upon this point that Aristotle here takes issue with them, seeking to prove that there are and must be such truths. But I cannot think the proof satisfactory; nor has it appeared so to able commentators either of ancient or modern times--from Alexander of Aphrodisias down to Mr. Poste.[65] The elaborate amplification added in these last chapters adds no force to the statement already given at the earlier stage; and it is in one respect a change for the worse, inasmuch as it does not advert to the important distinction announced in chapter iii., between universal truths known by Induction (from sense and particulars), and universal truths known by Deduction from these. The truths immediate and indemonstrable (not known through a middle term) are the inductive truths, as Aristotle declares in many places, and most emphatically at the close of the Analytica Posteriora. But in these chapters, he hardly alludes to Induction. Moreover, while trying to prove that there must be immediate universal truths, he neither gives any complete list of them, nor assigns any positive characteristic whereby to identify them. Opponents might ask him whether these immediate universal truths were not ready-made inspirations of the mind; and if so, what better authority they had than the Platonic Ideas, which are contemptuously dismissed.

[Footnote 64: Analyt. Post. I. xxii. p. 84, a. 32: [Greek: o(/per e)/phame/n tinas le/gein kat' a)rcha/s], &c.]

[Footnote 65: See Mr. Poste's note, p. 77, of his translation of this treatise. After saying that the first of Aristotle's _dialectical_ proofs is faulty, and that the second is a _petitio principii_, Mr. Poste adds, respecting the so-called _analytical_ proof given by Aristotle:--"It is not so much a proof, as a more accurate determination of the principle to be postulated. This postulate, the existence of first principles, as concerning the constitution of the world, appears to belong properly to Metaphysics, and is merely borrowed by Logic. See Metaph. ii. 2, and Introduction." In the passage of the Metaphysica ([Greek: a]. p. 994) here cited the main argument of Aristotle is open to the same objection of _petitio principii_ which Mr. Poste urges against Aristotle's second _dialectical_ argument in this place.

Mr. John Stuart Mill, in his System of Logic, takes for granted that there _must_ be immediate, indemonstrable truths, to serve as a basis for deduction; "that there cannot be a chain of proof suspended from nothing;" that there must be ultimate laws of nature, though we cannot be sure that the laws now known to us are ultimate.

On the other hand, we read in the recent work of an acute contemporary philosopher, Professor Delboeuf (Essai de Logique Scientifique, Liège, 1865, Pref. pp. v, vii, viii, pp. 46, 47:)--"Il est des points sur lesquels je crains de ne m'être pas expliqué assez nettement, entre autres la question du fondement de la certitude. Je suis de ceux qui repoussent de toutes leurs forces l'axiome si spécieux qu'on ne peut tout démontrer; cette proposition aurait, à mes yeux, plus besoin que toute autre d'une démonstration. Cette démonstration ne sera en partie donnée que quand on aura une bonne fois énuméré toutes les propositions indémontrables; et quand on aura bien défini le caractère auquel on les reconnait. Nulle part on ne trouve ni une semblable énumération, ni une semblable définition. On reste à cet égard dans une position vague, et par cela même facile à défendre."

It would seem, by these words, that M. Delboeuf stands in the most direct opposition to Aristotle, who teaches us that the [Greek: a)rchai\] or _principia_ from which demonstration starts cannot be themselves demonstrated. But when we compare other passages of M. Delboeuf's work, we find that, in rejecting all undemonstrable propositions, what he really means is to reject all _self-evident universal truths_, "C'est donc une véritable illusion d'admettre des vérités évidentes par elles-mêmes. Il n'y a pas de proposition fausse que nous ne soyons disposés d'admettre comme axiome, quand rien ne nous a encore autorisés à la repousser" (p. ix.). This is quite true in my opinion; but the immediate indemonstrable truths for which Aristotle contends as [Greek: a)rchai\] of demonstration, are not announced by him as _self-evident_, they are declared to be results of sense and induction, to be raised from observation of particulars multiplied, compared, and permanently formularized under the intellectual _habitus_ called Noûs. By Demonstration Aristotle means deduction in its most perfect form, beginning from these [Greek: a)rchai\] which are inductively known but not demonstrable (_i. e._ not knowable deductively). And in this view the very able and instructive treatise of M. Delboeuf mainly coincides, assigning even greater preponderance to the inductive process, and approximating in this respect to the important improvements in logical theory advanced by Mr. John Stuart Mill.

Among the universal propositions which are not derived from Induction, but which serve as [Greek: a)rchai\] for Deduction and Demonstration, we may reckon the religious, ethical, æsthetical, social, political, &c., beliefs received in each different community, and impressed upon all newcomers born into it by the force of precept, example, authority. Here the major premiss is felt by each individual as carrying an authority of its own, stamped and enforced by the sanction of society, and by the disgrace or other penalties in store for those who disobey it. It is ready to be interpreted and diversified by suitable minor premisses in all inferential applications. But these [Greek: a)rchai\] for deduction, differing widely at different times and places, though generated in the same manner and enforced by the same sanction, would belong more properly to the class which Aristotle terms [Greek: ta\ e)/ndoxa].]

We have thus recognized that there exist immediate (ultimate or primary) propositions, wherein the conjunction between predicate and subject is such that no intermediate term can be assigned between them. When A is predicated both of B and C, this may perhaps be in consequence of some common property possessed by B and C, and such common property will form a middle term. For example, equality of angles to two right angles belongs both to an isosceles and to a scalene triangle, and it belongs to them by reason of their common property--triangular figure; which last is thus the middle term. But this need not be always the case.[66] It is possible that the two propositions--A predicated of B, A predicated of C--may both of them be immediate propositions; and that there may be no community of nature between B and C. Whenever a middle term can be found, demonstration is possible; but where no middle term can be found, demonstration is impossible. The proposition, whether affirmative or negative, is then an immediate or indivisible one. Such propositions, and the terms of which they are composed, are the ultimate elements or _principia_ of Demonstration. Predicate and subject are brought constantly into closer and closer conjunction, until at last they become one and indivisible.[67] Here we reach the unit or element of the syllogizing process. In all scientific calculations there is assumed an unit to start from, though in each branch of science it is a different unit; _e.g._ in barology, the pound-weight; in harmonics, the quarter-tone; in other branches of science, other units.[68] Analytical research teaches us that the corresponding unit in Syllogism is the affirmative or negative proposition which is primary, immediate, indivisible. In Demonstration and Science it is the Noûs or Intellect.[69]

[Footnote 66: Analyt. Post. I. xxiii. p. 84, b. 3-18. [Greek: tou=to d' ou)k a)ei\ ou(/tôs e)/chei.]]

[Footnote 67: Ibid. b. 25-37. [Greek: a)ei\ to\ me/son puknou=tai, e(/ôs a)diai/reta ge/nêtai kai\ e(/n. e)/sti d' e(/n, o(/tan a)/meson ge/nêtai kai\ mi/a pro/tasis a(plô=s ê( a)/mesos.]]

[Footnote 68: Analyt. Post. I. xxiii. p. 84, b. 37: [Greek: kai\ ô(/sper e)n toi=s a)/llois ê( a)rchê\ a(plou=n, tou=to d' ou) tau)to\ pantachou=, a)ll' e)n barei= me\n mna=, e)n de\ me/lei di/esis, a)/llo d' e)n a)/llô|, ou(/tôs e)n sullogismô=| to\ e(\n pro/tasis a)/mesos, e)n d' a)podei/xei kai\ e)pistê/mê| o( nou=s.]]

[Footnote 69: Ibid. b. 35-p. 85, a. 1.]

Having thus, in the long preceding reasoning, sought to prove that all demonstration must take its departure from primary undemonstrable _principia_--from some premisses, affirmative and negative, which are directly true in themselves, and not demonstrable through any middle term or intervening propositions, Aristotle now passes to a different enquiry. We have some demonstrations in which the conclusion is Particular, others in which it is Universal: again, some Affirmative, some Negative, Which of the two, in each of these alternatives, is the best? We have also demonstrations Direct or Ostensive, and demonstrations Indirect or by way of _Reductio ad Absurdum_. Which of these two is the best? Both questions appear to have been subjected to debate by contemporary philosophers.[70]

[Footnote 70: Ibid. xxiv. p. 85, a. 13-18. [Greek: a)mphisbêtei=tai pote/ra belti/ôn; ô(s d' au(/tôs kai\ peri\ tê=s a)podeiknu/nai legome/nês kai\ tê=s ei)s to\ a)du/naton a)gou/sês a)podei/xeôs.]]

Aristotle discusses these points dialectically (as indeed he points out in the Topica that the comparison of two things generally, as to better and worse, falls under the varieties of **dialectical enquiry[71]), first stating and next refuting the arguments on the weaker side. Some persons may think (he says) that demonstration of the Particular is better than demonstration of the Universal: first, because it conducts to fuller cognition of that which the thing is in itself, and not merely that which it is _quatenus_ member of a class; secondly, because demonstrations of the Universal are apt to generate an illusory belief, that the Universal is a distinct reality apart from and independent of all its particulars (_i.e._, that figure in general has a real existence apart from all particular figures, and number in general apart from all particular numbers, &c.), while demonstrations of the Particular do not lead to any such illusion.[72]

[Footnote 71: Aristot. Topic. III. i. p. 116, a. 1, seq.]

[Footnote 72: Analyt. Post. I. xxiv. p. 85, a. 20-b. 3. Themistius, pp. 58-59, Spengel: [Greek: ou) ga\r o(mô/numon to\ katho/lou e)sti/n, ou)de\ phônê\ mo/non, a)ll' u(po/stasis, ou) chôristê\ me\n ô(/sper ou)de\ ta\ sumbebêko/ta, e)nargô=s d' ou)=n emphainome/nê toi=s pra/gmasin.] The Scholastic doctrine of _Universalia in re_ is here expressed very clearly by Themistius.]

To these arguments Aristotle replies:--1. It is not correct to say that cognition of the Particular is more complete, or bears more upon real existence, than cognition of the Universal. The reverse would be nearer to the truth. To know that the isosceles, _quatenus_ triangle, has its three angles equal to two right angles, is more complete cognition than knowing simply that the isosceles has its three angles equal to two right angles. 2. If the Universal be not an equivocal term--if it represents one property and one definition common to many particulars, it then has a real existence as much or more than any one or any number of the particulars. For all these particulars are perishable, but the class is imperishable. 3. He who believes that the universal term has one meaning in all the particulars, need not necessarily believe that it has any meaning _apart_ from all particulars; he need not believe this about Quiddity, any more than he believes it about Quality or Quantity. Or if he does believe so, it is his own individual mistake, not imputable to the demonstration. 4. We have shown that a complete demonstration is one in which the middle term is the cause or reason of the conclusion. Now the Universal is most of the nature of Cause; for it represents the First Essence or the _Per Se_, and is therefore its own cause, or has no other cause behind it. The demonstration of the Universal has thus more of the Cause or the _Why_, and is therefore better than the demonstration of the Particular. 5. In the Final Cause or End of action, there is always some ultimate end for the sake of which the intermediate ends are pursued, and which, as it is better than they, yields, when it is known, the only complete explanation of the action. So it is also with the Formal Cause: there is one highest form which contains the _Why_ of the subordinate forms, and the knowledge of which is therefore better; as when, for example, the exterior angles of a given isosceles triangle are seen to be equal to four right angles, not because it is isosceles or triangle, but because it is a rectilineal figure. 6. Particulars, as such, fall into infinity of number, and are thus unknowable; the Universal tends towards oneness and simplicity, and is thus essentially knowable, more fully demonstrable than the infinity of particulars. The demonstration thereof is therefore better. 7. It is also better, on another ground; for he that knows the Universal does in a certain sense know also the Particular;[73] but he that knows the Particular cannot be said in any sense to know the Universal. 8. The _principium_ or perfection of cognition is to be found in the immediate proposition, true _per se_. When we demonstrate, and thus employ a middle term, the nearer the middle term approaches to that _principium_, the better the demonstration is. The demonstration of the Universal is thus better and more accurate than that of the Particular.[74]

[Footnote 73: Compare Analyt. Post. I. i. p. 71, a. 25; also Metaphys. A. p. 981, a. 12.]

[Footnote 74: Analyt. Post. I. xxiv. p. 85, b. 4-p. 86, a. 21. Schol. p. 233, b. 6: [Greek: o(moi/ôs de\ o)/ntôn gnôri/môn, ê( di' e)latto/nôn me/sôn ai(retôte/ra; ma=llon ga\r e)ggute/rô tê=s tou= nou= e)nergei/as.]]

Such are the several reasons enumerated by Aristotle in refutation of the previous opinion stated in favour of the Particular. Evidently he does not account them all of equal value: he intimates that some are purely dialectical ([Greek: logika/]); and he insists most upon the two following:--1. He that knows the Universal knows in a certain sense the Particular; if he knows that every triangle has its three angles equal to two right angles, he knows potentially that the isosceles has its three angles equal to the same, though he may not know as yet that the isosceles _is_ a triangle. But he that knows the Particular does not in any way know the Universal, either actually or potentially.[75] 2. The Universal is apprehended by Intellect or Noûs, the highest of all cognitive powers; the Particular terminates in sensation. Here, I presume, he means, that, in demonstration of the Particular, the conclusion teaches you nothing more than you might have learnt from a direct observation of sense; whereas in that of the Universal the conclusion teaches you more than you could have learnt from direct sensation, and comes into correlation with the highest form of our intellectual nature.[76]

[Footnote 75: Analyt. Post. I. xxiv. p. 86**, a. 22: [Greek: a)lla\ tô=n me\n ei)rême/nôn e)/nia logika/ e)sti; _ma/lista_ de\ dê=lon o(/ti ê( katho/lou kuriôte/ra, o(/ti--o( de\ tau/tên e)/chôn tê\n pro/tasin] (the Particular) [Greek: _to\ katho/lou ou)damô=s oi)=den, ou)/te duna/mei ou)/t' e)nergei/a|_.]]

[Footnote 76: Ibid. a. 29: [Greek: kai\ ê( me\n katho/lou noêtê/, ê( de\ kata\ me/ros ei)s ai)/sthêsin teleuta=|.] Compare xxiii. p. 84, b. 39, where we noticed the doctrine that [Greek: Nou=s] is the _unit_ of scientific demonstration.]

Next, Aristotle compares the Affirmative with the Negative demonstration, and shows that the Affirmative is the better. Of two demonstrations (he lays it down) that one which proceeds upon a smaller number of postulates, assumptions, or propositions, is better than the other; for, to say nothing of other reasons, it conducts you more speedily to knowledge than the other, and that is an advantage. Now, both in the affirmative and in the negative syllogism, you must have three terms and two propositions; but in the affirmative you assume only that something _is_; while in the negative you assume both that something _is_, and that something _is not_. Here is a double assumption instead of a single; therefore the negative is the worse or inferior of the two.[77] Moreover, for the demonstration of a negative conclusion, you require one affirmative premiss (since from two negative premisses nothing whatever can be concluded); while for the demonstration of an affirmative conclusion, you must have two affirmative premisses, and you cannot admit a negative. This, again, shows that the affirmative is logically prior, more trustworthy, and better than the negative.[78] The negative is only intelligible and knowable through the affirmative, just as _Non-Ens_ is knowable only through _Ens_. The affirmative demonstration therefore, as involving better principles, is, on this ground also, better than the negative.[79] _A fortiori_, it is also better than the demonstration by way of _Reductio ad Absurdum_, which was the last case to be considered. This, as concluding only indirectly and from impossibility of the contradictory, is worse even than the negative; much more therefore is it worse than the direct affirmative.[80]

[Footnote 77: Analyt. Post. I. xxv. p. 86, a. 31-b. 9.]

[Footnote 78: Ibid. b. 10-30.]

[Footnote 79: Ibid. b. 30-39.]

[Footnote 80: Ibid. I. xxvi. p. 87, a. 2-30. Waitz (II. p. 370), says: "deductio (ad absurdum), quippe quæ per ambages cogat, post ponenda, est demonstrationi rectæ."

Philoponus says (Schol. pp. 234-235**, Brand.) that the Commentators all censured Aristotle for the manner in which he here laid out the Syllogism [Greek: di' a)duna/tou]. I do not, however, find any such censure in Themistius. Philoponus defends Aristotle from the censure.]

If we next compare one Science with another, the prior and more accurate of the two is, (1) That which combines at once the [Greek: o(/ti] and the [Greek: dio/ti]; (2) That which is abstracted from material conditions, as compared with that which is immersed therein--for example, arithmetic is more accurate than harmonics; (3) The more simple as compared with the more complex: thus, arithmetic is more accurate than geometry, a monad or unit is a substance without position, whereas a point (more concrete) is a substance with position.[81] One and the same science is that which belongs to one and the same generic subject-matter. The premisses of a demonstration must be included in the same genus with the conclusion; and where the ultimate premisses are heterogeneous, the cognition derived from them must be considered as not one but a compound of several.[82] You may find two or more distinct middle terms for demonstrating the same conclusion; sometimes out of the same logical series or table, sometimes out of different tables.[83]

[Footnote 81: Analyt. Post. I. xxvii. p. 87, a. 31-37. Themistius, Paraphras. p. 60, ed. Speng.: [Greek: kat' a)/llon de\ (tro/pon), e)a\n ê( me\n peri\ u(pokei/mena/ tina kai\ ai)sthêta\ pragmateu/êtai, ê( de\ peri\ noêta\ kai\ katho/lou.]

Philoponus illustrates this (Schol. p. 235, b. 41, Br.): [Greek: oi(=on ta\ Theodosi/ou sphairika\ a)kribe/stera/ e)stin e)pistê/mê| tê=s tô=n Au)tolu/kou peri\ kinoume/nês sphai/ras.] &c.]

[Footnote 82: Analyt. Post. I. xxviii. p. 87, a. 38-b. 5. Themistius, p. 61: [Greek: dê=lon de\ tou=to gi/netai proi+ou=sin e)pi\ ta\s a)napodei/ktous a)rcha/s; au(=tai ga\r ei) mêdemi/an e)/choien sugge/neian, e(/terai ai( e)pistê=mai.]]

[Footnote 83: Analyt. Post. I. xxix. p. 87, b. 5-18. Aristotle gives an example to illustrate this general doctrine: [Greek: ê(/desthai, to\ kinei=sthai, to\ ê)remi/zesthai, to\ metaba/llein]. As he includes these terms und this subject among the topics for demonstration, it is difficult to see where he would draw a distinct line between topics for Demonstration and topics for Dialectic.]

There cannot be demonstrative cognition of fortuitous events,[84] for all demonstration is either of the necessary or of the customary. Nor can there be demonstrative cognition through sensible perception. For though by sense we perceive a thing as such and such (through its sensible qualities), yet we perceive it inevitably as _hoc aliquid_, _hic_, _et nunc_. But the Universal cannot be perceived by sense; for it is neither _hic_ nor _nunc_, but _semper et ubique_.[85] Now demonstrations are all accomplished by means of the Universal, and demonstrative cognition cannot therefore be had through sensible perception. If the equality of the three angles of a triangle to two right angles were a fact directly perceivable by sense, we should still have looked out for a demonstration thereof: we should have no proper scientific cognition of it (though some persons contend for this): for sensible perception gives us only particular cases, and Cognition or Science proper comes only through knowing the Universal.[86] If, being on the surface of the moon, we had on any one occasion seen the earth between us and the sun, we could not have known from that single observation that such interposition is the cause universally of eclipses. We cannot directly by sense perceive the Universal, though sense is the _principium_ of the Universal. By multiplied observation of sensible particulars, we can hunt out and elicit the Universal, enunciate it clearly and separately, and make it serve for demonstration.[87] The Universal is precious, because it reveals the Cause or [Greek: dio/ti], and is therefore more precious, not merely than sensible observation, but also than intellectual conception of the [Greek: o(/ti] only, where the Cause or [Greek: dio/ti] lies apart, and is derived from a higher genus. Respecting First Principles or _Summa Genera_, we must speak elsewhere.[88] It is clear, therefore, that no demonstrable matter can be known, properly speaking, from direct perception of sense; though there are cases in which nothing but the impossibility of direct observation drives us upon seeking for demonstration. Whenever we can get an adequate number of sensible observations, we can generalize the fact; and in some instances we may perhaps not seek for any demonstrative knowledge (_i.e._ to explain it by any higher principle). If we could see the pores in glass and the light passing through them, we should learn through many such observations why combustion arises on the farther side of the glass; each of our observations would have been separate and individual, but we should by intellect generalize the result that all the cases fall under the same law.[89]

[Footnote 84: Analyt. Post. I. xxx. p. 87, b. 19-27.]

[Footnote 85: Ibid. xxxi. p. 87, b. 28: [Greek: ei) ga\r kai\ e)/stin ê( ai)/sthêsis tou= toiou=de kai\ mê\ tou=de/ tinos, a)ll' ai)stha/nesthai/ ge a)nagkai=on to/de ti kai\ pou= kai\ nu=n.]]

[Footnote 86: Ibid. b. 35: [Greek: dê=lon o(/ti kai\ ei) ê)=n ai)stha/nesthai to\ tri/gônon o(/ti dusi\n o)rthai=s i)/sas e)/chei ta\s gôni/as, e)zêtou=men a)\n a)po/deixin, kai\ ou)ch (_ô(/sper phasi/ tines_) ê)pista/metha; ai)stha/nesthai me\n ga\r a)na/gkê kath' e(/kaston, ê( d' e)pistê/mê tô=| to\ katho/lou gnôri/zein e)sti/n.]

Euclid, in the 20th Proposition of his first Book, demonstrates that any two sides of a triangle are together greater than the third side. According to Proklus, the Epikureans derided the demonstration of such a point as absurd; and it seems that some contemporaries of Aristotle argued in a similar way, judging by the phrase [Greek: ô(/sper phasi/ tines].]

[Footnote 87: Analyt. Post. I. xxxi. p. 88, a. 2: [Greek: ou) mê\n a)ll' e)k tou= theôrei=n tou=to polla/kis sumbai=non, to\ katho/lou a)\n thêreu/santes a)po/deixin ei)/chomen; e)k ga\r tô=n kath' e(/kasta pleio/nôn to\ katho/lou dê=lon.] Themistius, p. 62, Sp.: [Greek: a)rchê\ me\n ga\r a)podei/xeôs ai)/sthêsis, kai\ to\ katho/lou e)nnoou=men dia\ to\ polla/kis ai)sthe/sthai.]]

[Footnote 88: Analyt. Post. I. xxxi. p. 88, a. 6: [Greek: to\ de\ katho/lou ti/mion, o(/ti dêloi= to\ ai)/tion; ô(/ste peri\ tô=n toiou/tôn ê( katho/lou timiôte/ra tô=n ai)sthê/seôn kai\ tê=s noê/seôs, o(/sôn e(/teron to\ ai)/tion; peri\ de\ tô=n prô/tôn a)/llos lo/gos.]

By [Greek: ta\ prô=ta], he means the [Greek: a)rchai\] of Demonstration, which are treated especially in II. xix. See Biese, Die Philos. des Aristoteles, p. 277.]

[Footnote 89: Analyt. Post. I. xxxi. p. 88, a. 9-17. [Greek: e)/sti me/ntoi e)/nia a)nago/mena ei)s ai)sthê/seôs e)/kleipsin e)n toi=s problê/masin; e)/nia ga\r ei) e(ô/rômen, ou)k a)\n e)zêtou=men, ou)ch ô(s ei)do/tes tô=| o(ra=|n, a)ll' ô(s e)/chontes to\ katho/lou e)k tou= o(ra=|n.]

The text of this and the succeeding words seems open to doubt, as well as that of Themistius (p. 63). Waitz in his note (p. 374) explains the meaning clearly:--"non ita quidem ut ipsa sensuum perceptio scientiam afferat; sed ita ut quod in singulis accidere videamus, idem etiam in omnibus accidere coniicientes universe intelligamus."]

Aristotle next proceeds to refute, at some length, the supposition, that the _principia_ of all syllogisms are the same. We see at once that this cannot be so, because some syllogisms are true, others false. But, besides, though there are indeed a few Axioms essential to the process of demonstration, and the same in all syllogisms, yet these are not sufficient of themselves for demonstration. There must farther be other premisses or matters of evidence--propositions immediately true (or established by prior demonstrations) belonging to each branch of Science specially, as distinguished from the others. Our demonstration relates _to_ these special matters or premisses, though it is accomplished _out of_ or by means of the common Axioms.[90]

[Footnote 90: Analyt. Post. I. xxxii. p. 88, a. 18-b. 29. [Greek: ai( ga\r a)rchai\ dittai/, e)x ô(=n te kai\ peri\ o(\; ai( me\n ou)=n e)x ô(=n koinai/, ai( de\ peri\ o(/ i)/diai, oi(=on a)rithmo/s, me/gethos.] Compare xi. p. 77, a. 27. See Barthélemy St. Hilaire, Plan Général des Derniers Analytiques, p. lxxxi.]

Science or scientific Cognition differs from true Opinion, and the _cognitum_ from the _opinatum_, herein, that Science is of the Universal, and through necessary premisses which cannot be otherwise; while Opinion relates to matters true, yet which at the same time may possibly be false. The belief in a proposition which is immediate (_i. e._, undemonstrable) yet not necessary, is Opinion; it is not Science, nor is it Noûs or Intellect--the _principium_ of Science or scientific Cognition. Such beliefs are fluctuating, as we see every day; we all distinguish them from other beliefs, which we cannot conceive not to be true and which we call cognitions.[91] But may there not be Opinion and Cognition respecting the same matters? There may be (says Aristotle) in different men, or in the same man at different times; but not in the same man at the same time. There may also be, respecting the same matter, true opinion in one man's mind, and false opinion in the mind of another.[92]

[Footnote 91: Analyt. Post. I. xxxiii. p. 88, b. 30-p. 89, a. 10.]

[Footnote 92: Ibid. p. 89, a. 11-b. 6. That eclipse of the sun is caused by the interposition of the moon was to the astronomer Hipparchos scientific Cognition; for he saw that it _could not_ be otherwise. To the philosopher Epikurus it was Opinion; for he thought that it _might_ be otherwise (Themistius, p. 66, Spengel).]

With some remarks upon Sagacity, or the power of divining a middle term in a time too short for reflection (as when the friendship of two men is on the instant referred to the fact of their having a common enemy), the present book is brought to a close.[93]

[Footnote 93: Ibid. xxxiv. p. 89, b. 10-20.]