ANALYTICA POSTERIORA II.
Aristotle begins the Second Book of the Analytica Posteriora by an enumeration and classification of Problems or Questions suitable for investigation. The matters knowable by us may be distributed into four classes:—
| Ὅτι. | Διότι. | Εἰ ἔστι. | Τί ἐστι. |
| 1. Quod. | 2. Cur. | 3. An sit. | 4. Quid sit. |
Under the first head come questions of Fact; under the second head, questions of Cause or Reason; under the third, questions of Existence; under the fourth, questions of Essence. Under the first head we enquire, Whether a fact or event is so or so? Whether a given subject possesses this or that attribute, or is in this or that condition? enumerating in the question the various supposable alternatives. Under the second head, we assume the first question to have been affirmatively answered, and we proceed to enquire, What is the cause or reason for such fact, or such conjunction of subject and attribute? Under the third head, we ask, Does a supposed subject exist? And if the answer be in the affirmative, we proceed to enquire, under the fourth head, What is the essence of the subject?1
1 Analyt. Post. II. i. p. 89, b. 23, seq. Themistius observes, p. 67, Speng.: ζητοῦμεν τίνυν ἢ περὶ ἁπλοῦ τινὸς καὶ ἀσυνθέτου, ἢ περὶ συνθέτου καὶ ἐν προτάσει. Themistius has here changed Aristotle’s order, and placed the third and fourth heads before the first and second. Compare Schol. p. 240, b. 30; p. 241, a. 18. The Scholiast complains of the enigmatical style of Aristotle: τῇ γριφώδει τοῦ ῥητοῦ ἐπαγγελία (p. 240, b. 25).
We have here two distinct pairs of Quæsita: Obviously the second head presupposes the first, and is consequent thereupon; while the fourth also presupposes the third. But it might seem a more suitable arrangement (as Themistius and other expositors have conceived) that the third and fourth heads should come first in the list, rather than the first and second; since the third and fourth are simpler, and come earlier in the order of philosophical exposition, while the first and second are more complicated, and cannot be expounded philosophically until after the philosophical exposition of the others. This is cleared up by adverting to the distinction, so often insisted on by Aristotle, between what is first in order of cognition relatively to us (nobis notiora), and what is first in order of cognition by nature (naturâ notiora). To us (that is to men taken individually and in the course of actual growth) the phenomena of nature2 present themselves as particulars confused and complicated in every way, with attributes essential and accidental implicated together: we gradually learn first to see and compare them as particulars, next to resolve them into generalities, bundles, classes, and partially to explain the Why of some by means of others. Here we start from facts embodied in propositions, that include subjects clothed with their attributes. But in the order of nature (that is, in the order followed by those who know the scibile as a whole, and can expound it scientifically) that which comes first is the Universal or the simple Subject abstracted from its predicates or accompaniments: we have to enquire, first, whether a given subject exists; next, if it does exist, what is its real constituent essence or definition. We thus see the reason for the order in which Aristotle has arranged the two co-ordinate pairs of Quæsita or Problems, conformable to the different processes pursued, on the one hand, by the common intellect, growing and untrained — on the other, by the mature or disciplined intellect, already competent for philosophical exposition and applying itself to new incognita.
2 Schol. Philopon. p. 241, a. 18-24: τούτων τὸ εἰ ἔστι καὶ τὸ τί ἐστιν εἰσὶν ἁπλᾶ, τὸ δὲ ὅτι καὶ τὸ διότι σύνθετα — πρότερα γὰρ ἡμῖν καὶ γνωριμώτερα τὰ σύνθετα, ὡς τῇ φύσει τὰ ἁπλᾶ.
Mr. Poste observes upon this quadruple classification by Aristotle (p. 96):— “The two last of these are problems of Inductive, but first principles of Deductive, Science; the one being the hypothesis, the other the definition. The attribute as well as the subject must be defined (I. x.), so that to a certain degree the second problem also is assumed among the principles of Demonstration.”
Comparing together these four Quæsita, it will appear that in the first and third (Quod and An), we seek to find out whether there is or is not any middle term. In the second and fourth (Cur and Quid), we already know or assume that there is a middle term; and we try to ascertain what that middle term is.3 The enquiry Cur, is in the main analogous to the enquiry Quid; in both cases, we aim at ascertaining what the cause or middle term is. But, in the enquiry Cur, what we discover is perhaps some independent fact or event, which is the cause of the event quæsitum; while, in the enquiry Quid, what we seek is the real essence or definition of the substance — the fundamental, generating, immanent cause of its concomitant attributes. Sometimes, however, the Quid and the Cur are only different ways of stating the same thing. E.g., Quid est eclipsis lunæ? Answer: The essence of an eclipse is a privation of light from the moon, through intervention of the earth between her and the sun. Cur locum habet eclipsis lunæ? Answer: Because the light of the sun is prevented from reaching the moon by intervention of the earth. Here it is manifest that the answers to the enquiries Quid and Cur are really and in substance the same fact, only stated in different phrases.4
3 Analyt. Post. II. i. p. 889, b. 37-p. 90, a. 7. συμβαίνει ἄρα ἐν ἁπάσαις ταῖς ζητήσεσι ζητεῖν ἢ εἰ ἔστι μέσον, ἢ τί ἐστι τὸ μέσον· τὸ μὲν γὰρ αἴτιον τὸ μέσον, ἐν ἅπασι δὲ τοῦτο ζητεῖται. Compare Schol. p. 241, b. 10, Br.
4 Analyt. Post. II. ii. p. 90, a. 14-23, 31: τὸ τί ἐστιν εἰδέναι ταὐτό ἐστι καὶ διὰ τί ἐστιν.
That the quæsitum in all these researches is a middle term or medium, is plain from those cases wherein the medium is perceivable by sense; for then we neither require nor enter upon research. For example, if we were upon the moon, we should see the earth coming between us and the sun, now and in each particular case of eclipse. Accordingly, after many such observations, we should affirm the universal proposition, that such intervention of the earth was the cause of eclipses; the universal becoming known to us through induction of particular cases.5 The middle term, the Cause, the Quid, and the Cur, are thus all the same enquiry, in substance; though sometimes such quæsitum is the quiddity or essential nature of the thing itself (as the essence of a triangle is the cause or ground of its having its three angles equal to two right angles, as well as of its other properties), sometimes it is an extraneous fact.6
5 Ibid. a. 24-30. ἐκ γὰρ τοῦ αἰσθέσθαι καὶ τὸ καθόλου ἐγένετο ἂν ἡμῖν εἰδέναι· ἡ μὲν γὰρ αἴσθησις ὅτι νῦν ἀντιφράττει· καὶ γὰρ δῆλον ὅτι νῦν ἐκλείπει· ἐκ δὲ τούτου τὸ καθόλου ἂν ἐγένετο.
The purport and relation of this quadruple classification of problems is set forth still more clearly in the sixth book of the Metaphysica (Z. p. 1041) with the explanations of Bonitz, Comm. pp. 358, 359.
6 Analyt. Post. II. ii. p. 90, a. 31.
But how or by what process is this quæsitum obtained and made clear? Is it by Demonstration or by Definition? What is Definition, and what matters admit of Definition?7 Aristotle begins by treating the question dialectically; by setting out a series of doubts and difficulties. First, Is it possible that the same cognition, and in the same relation, can be obtained both by Definition and by Demonstration? No; it is not possible. It is plain that much that is known by Demonstration cannot be known by Definition; for we have seen that conclusions both particular and negative are established by Demonstration (in the Third and Second figures), while every Definition is universal and affirmative. But we may go farther and say, that even where a conclusion universal and affirmative is established (in the First figure) by Demonstration, that same conclusion can never be known by Definition; for if it could be known by Definition, it might have been known without Demonstration. Now we are assured, by an uncontradicted induction, that this is not the fact; for that which we know by Demonstration is either a proprium of the subject per se, or an accident or concomitant; but no Definition ever declares either the one or the other: it declares only the essence.8
7 Ibid. iii. p. 90, a. 37: τί ἐστιν ὁρισμός, καὶ τίνων, εἴπωμεν, διαπορήσαντες πρῶτον περὶ αὐτῶν.
8 Analyt. Post. II. iii. p. 90, b. 13: ἱκανὴ δὲ πίστις καὶ ἐκ τῆς ἐπαγωγῆς· οὐδὲν γὰρ πώποτε ὁρισάμενοι ἔγνωμεν, οὔτε τῶν καθ’ αὑτὸ ὑπαρχόντων οὔτε τῶν συμβεβηκότων. ἔτι εἰ ὁ ὁρισμὸς οὐσίας τις γνωρισμός, τὰ γε τοιαῦτα φανερὸν ὅτι οὐκ οὐσίαι.
Again, let us ask, vice versâ, Can everything that is declared by Definition, or indeed anything that is declared by Definition, be known also by Demonstration? Neither is this possible. One and the same cognitum can be known only by one process of cognition. Definitions are the principia from which Demonstration departs; and we have already shown that in going back upon demonstrations, we must stop somewhere, and must recognize some principia undemonstrable.9 The Definition can never be demonstrated, for it declares only the essence of the subject, and does not predicate anything concerning the subject; whereas Demonstration assumes the essence to be known, and deduces from such assumption an attribute distinct from the essence.10
9 Ibid. b. 18-27.
10 Ibid. b. 33, seq.: ἔτι πᾶσα ἀπόδειξις τὶ κατά τινος δείκνυσιν, οἷον ὅτι ἔστιν ἢ οὐκ ἔστιν· ἐν δὲ τῷ ὁρισμῷ οὐδὲν ἕτερον ἑτέρου κατηγορεῖται, οἷον οὔτε τὸ ζῷον κατὰ τοῦ δίποδος οὐδὲ τοῦτο κατὰ τοῦ ζῷου — ὁ μὲν οὖν ὁρισμὸς τί ἐστι δηλοῖ, ἡ δὲ ἀπόδειξις ὅτι ἢ ἔστι τόδε κατὰ τοῦδε ἢ οὐκ ἔστιν.
Themistius (p. 71, Speng.) distinguishes the ὁρισμός itself from ἡ πρότασις ἡ τὸν ὁρισμὸν κατηγορούμενον ἔχουσα.
Prosecuting still farther the dialectical and dubitative treatment,11 Aristotle now proceeds to suggest, that the Essence (that is, the entire Essence or Quiddity), which is declared by Definition, can never be known by Demonstration. To suppose that it could be so known, would be inconsistent with the conditions of the syllogistic proof used in demonstrating. You prove by syllogism, through a middle term, some predicate or attribute; e.g. because A is predicable of all B, and B is predicable of all C, therefore A is predicable of all C. But you cannot prove, through the middle term B, that A is the essence or quiddity of C, unless by assuming in the premisses that B is the essence of C, and that A is the essence of B; accordingly, that the three propositions, AB, BC, AC, are all co-extensive and reciprocate with each other. Here, then, you have assumed as your premisses two essential propositions, AB, BC, in order to prove as an essential proposition the conclusion AC. But this is inadmissible; for your premisses require demonstration as much as your conclusion. You have committed a Petitio Principii;12 you have assumed in your minor premiss the very point to be demonstrated.
11 Analyt. Post. II. iv. p. 91, a. 12: ταῦτα μὲν οὖν μέχρι τούτου διηπορήσθω. One would think, by these words, that τὸ διαπορεῖν (or the dubitative treatment) finished here. But the fact is not so: that treatment is continued for four chapters more, to the commencement of ch. viii. p. 93.
12 Analyt. Post. II. iv. p. 91, a. 12-32: ταῦτα δ’ ἀνάγκη ἀντιστρέφειν· εἰ γὰρ τὸ Α τοῦ Γ ἴδιον, δῆλον ὅτι καὶ τοῦ Β καὶ τοῦτο τοῦ Γ, ὥστε πάντα ἀλλήλων. — λαμβάνει οὖν ὃ δεῖ δεῖξαι· καὶ γὰρ τὸ Β ἔστι τί ἐστιν ἄνθρωπος. Themistius, pp. 72, 73: τὸν ἀποδεικνύντα τὸ τί ἦν εἶναι τοῦ ἀνθρώπου, ἄλλο τι δεῖ προλαβεῖν τοῦ αὐτοῦ τὸ τί ἦν εἶναι. — οὗ γὰρ βούλεται τὸν ὁρισμὸν ἀποδεῖξαι, τούτου προλαμβάνει τινὰ ὁρισμὸν εἶναι χωτὶς ἀποδείξεως.
M. Barthélemy St. Hilaire, notes, p. 205:— “Il faut donc, pour conclure par syllogisme que A est la définition essentielle de C, que A soit la définition essentielle de B, et que B soit lui-même la définition essentielle de C. Mais alors la définition de la chose sera dans le moyen terme lui-même, avant d’être dans la conclusion; en effet, la mineure: B est la définition essentielle de C, donne la définition essentielle de C, sans qu’il soit besoin d’aller jusqu’à la conclusion. Donc la démonstration de l’essence ainsi entendue est absurde.”
If you cannot obtain Definition as the conclusion of syllogistic Demonstration, still less can you obtain it through the method of generic and specific Division; which last method (as has been already shown in the Analytica Priora) is not equal even to the Syllogism in respect of usefulness and efficacy.13 You cannot in this method distinguish between propositions both true and essential, and propositions true but not essential; you never obtain, by asking questions according to the method of generic subdivision, any premisses from which the conclusion follows by necessity. Yet this is what you ought to obtain for the purpose of Demonstration; for you are not allowed to enunciate the full actual conclusion among the premisses, and require assent to it. Division of a genus into its species will often give useful information, as Induction also will;14 but neither the one nor the other will be equivalent to a demonstration. A definition obtained only from subdivisions of a genus, may always be challenged, like a syllogism without its middle term.
13 Analyt. Post. II. v. p. 91, b. 12, seq.; Analyt. Prior. I. xxxi. p. 46, a. 31. Aristotle here alludes to the method pursued by Plato in the Sophistes and Politicus, though he does not name Plato: ἡ διὰ τῶν διαιρέσεων ὁδός, &c.
14 Analyt. Post. II. v. p. 91, b. 15-33: οὐδὲ γὰρ ὁ ἐπάγων ἴσως ἀποδείκνυσιν, ἀλλ’ ὅμως δηλοῖ τι. Compare Themistius, p. 74.
Again, neither can you arrive at the definition of a given subject, by assuming in general terms what a definition ought to be, and then declaring a given form of words to be conformable to such assumption; because your minor premiss must involve Petitio Principii. The same logical fault will be committed, if you take your departure from an hypothesis in which you postulate the definition of a certain subject, and then declare inferentially what the definition of its contrary must be. The definition which you here assume requires proof as much as that which you infer from it.15 Moreover, neither by this process, nor by that of generic subdivision, can you show any reason why the parts of the definition should coalesce into one essential whole. If they do not thus coalesce — if they be nothing better than distinct attributes conjoined in the same subject, like musicus and grammaticus — the real essence is not declared, and the definition is not a good one.16
15 Analyt. Post. II. vi. p. 92, a. 6-28. Themist. p. 76.
Rassow renders ἐξ ὑποθέσεως — “assumptâ generali definitionis notione;” and also says: “τὸ τί ἦν εἶναι — generalem definitionis notionem; τὸ τί ἐστιν — certam quandam definitionem, significare perspicuum est.” (Aristotelis de Notionis Definitione Doctrina, p. 65).
16 Analyt. Post. II. vi. p. 92, a. 32. That the parts of the definition must coalesce into one unity is laid down again in the Metaphysica, Z. pp. 1037, 1038, where Aristotle makes reference to the Analytica as haying already treated the same subject, and professes an intention to complete what has been begun in the Analytica; ἐφ’ ὅσον ἐν τοῖς Ἀναλυτικοῖς περὶ ὁρισμοῦ μὴ εἴρηται.
After stating some other additional difficulties which seem to leave the work of Definition inexplicable, Aristotle relinquishes the dubitative treatment, and looks out for some solution of the puzzle: How may it be possible that the Definition shall become known?17 He has already told us that to know the essence of a thing is the same as to know the cause or reason of its existence; but we must first begin by knowing that the definiendum exists; for there can be no definition of a non-entity, except a mere definition of the word, a nominal or verbal definition. Now sometimes we know the existence of the subject by one or other of its accidental attributes; but this gives us no help towards finding the definition.18 Sometimes, however, we obtain a partial knowledge of its essence along with the knowledge of its existence; when we know it along with some constant antecedent, or through some constant, though derivative, consequent. Knowing thus much, we can often discover the cause or fundamental condition thereof, which is the essence or definition of the subject.19 Indeed, it may happen that the constant derivative, and the fundamental essence on which it depends, become known both together; or, again, the cause or fundamental condition may perhaps not be the essence of the subject alone, but some fact including other subjects also; and this fact may then be stated as a middle term. Thus, in regard to eclipse of the moon, we know the constant phenomenal fact about it, that, on a certain recurrence of the time of full moon, the moon casts no light and makes no shadow. Hence we proceed to search out the cause. Is it interposition of the earth, or conversion of the moon’s body, or extinction of her light, &c.? The new fact when shown, must appear as a middle term, throwing into syllogistic form (in the First figure) the cause or rational explanation of a lunar eclipse; showing not merely that there is an eclipse, but what an eclipse is, or what is its definition.20
17 Analyt. Post. II. vii. p. 92, a. 34, seq. The ἀπόριαι continue to the end of ch. vii. He goes on, ch. viii. p. 93, a. 1-2: πάλιν δὲ σκεπτέον τί τούτων λέγεται καλῶς, καὶ τί οὐ καλῶς, &c. “Tout ce qui précède ne représente pas la théorie proprement dite; ce n’est qu’une discussion préliminaire” (Barth. St. Hilaire, not. p. 222). These difficult chapters are well illustrated by Hermann Rassow, ch. i. pp. 9-14.
18 Analyt. Post. II. viii. p. 93, a. 3: ἐπεὶ δ’ ἐστίν, ὡς ἔφαμεν, ταὐτὸν τὸ εἰδέναι τί ἐστι καὶ τὸ εἰδέναι τὸ αἴτιον τοῦ εἰ ἔστι· Ibid. a. 24: ὅσα μὲν οὖν κατὰ συμβεβηκὸς οἴδαμεν ὅτι ἔστιν, ἀναγκαῖον μηδαμῶς ἔχειν πρὸς τὸ τί ἐστιν· οὐδὲ γὰρ ὅτι ἔστιν ἴσμεν· τὸ δὲ ζητεῖν τί ἐστι μὴ ἔχοντας ὅτι ἔστι, μηδὲν ζητεῖν ἐστίν. καθ’ ὅσων δ’ ἔχομέν τι, ῥᾷον· ὥστε ὡς ἔχομεν ὅτι ἔστιν, οὕτως ἔχομεν καὶ πρὸς τὸ τί ἐστιν. Compare Brentano, Ueber die Bedeutung des Seienden nach Aristoteles, p. 17.
19 Analyt. Post. II. viii. p. 93, a. 21. Themistius, p. 79, Speng.: ὅσα δὲ ἀπὸ τῶν οἰκείων τε καὶ ἐξ αὐτοῦ τοῦ πράγματος, ἀπὸ τούτων ἤδη ῥᾷον εἰς τὸ τί ἐστι μεταβαίνομεν.
20 Ibid. p. 93, a. 30-b. 14.
Aristotle has thus shown how the Essence or Quiddity (τί ἐστι) may become known in this class of cases. There is neither syllogism nor demonstration thereof, yet it is declared through syllogism and demonstration: though no demonstration thereof is possible, yet you cannot know it without demonstration, wherever there is an extraneous cause.21
21 Ibid. b. 15-20: ὥστε συλλογισμὸς μὲν τοῦ τί ἐστιν οὐ γίνεται οὐδ’ ἀπόδειξις, δῆλον μέντοι διὰ συλλογισμοῦ καὶ δι’ ἀποδείξεως.
Mr. Poste translates an earlier passage (p. 93, a. 5) in this very difficult chapter as follows (p. 107): “If one cause is demonstrable, another indemonstrable cause must be the intermediate; and the proof is in the first figure, and the conclusion affirmative and universal. In this mode of demonstrating the essence, we prove one definition by another, for the intermediate that proves an essence or a peculiar predicate must itself be an essence or a peculiar predicate. Of two definitions, then, one is proved and the other assumed; and, as we said before, this is not a demonstration but a dialectical proof of the essence.” Mr. Poste here translates λογικὸς συλλογισμός “dialectical proof.” I understand it rather as meaning a syllogism, τοῦ ὑπάρχειν simply (Top. I. v. p. 102, b. 5), in which all that you really know is that the predicate belongs to the subject, but in which you assume besides that it belongs to the subject essentially. It is not a demonstration because, in order to obtain Essence in the conclusion, you are obliged to postulate Essence in your premiss. (See Alexander ad Topic. I. p. 263, Br.). You have therefore postulated a premiss which required proof as much as the conclusion.
But the above doctrine will hold only in cases where there is a distinct or extraneous cause; it will not hold in cases where there is none. It is only in the former (as has been said) that a middle term can be shown; rendering it possible that Quiddity or Essence should be declared by a valid formal syllogism, though it cannot be demonstrated by syllogism. In the latter, where there is no distinct cause, no such middle term can be enunciated: the Quiddity or Essence must be assumed as an immediate or undemonstrable principium, and must be exposed or set out in the best manner practicable as an existent reality, on Induction or on some other authority. The arithmetician makes his first steps by assuming both what a monad is and that there exists such a monad.22
22 Analyt. Post. II. ix. p. 93, b. 21. ἔστι δὲ τῶν μὲν ἕτερόν τι αἴτιον, τῶν δ’ οὐκ ἔστιν. ὥστε δῆλον ὅτι καὶ τῶν τί ἐστι τὰ μὲν ἄμεσα καὶ ἀρχαί εἰσιν, ἃ καὶ εἶναι καὶ τί ἐστιν ὑποθέσθαι δεῖ ἢ ἄλλον τρόπον φανερὰ ποιῆσαι. ὅπερ ὁ ἀριθμητικὸς ποιεῖ· καὶ γὰρ τί ἐστι τὴν μονάδα ὑποτίθεται, καὶ ὅτι ἔστιν.
Themistius, p. 80: ἃ καὶ εἶναι καὶ τί ἐστιν ὑποθέσθαι δεῖ, ἢ ἄλλον τρόπον φανερὰ ποιῆσαι ἐξ ἐπαγωγῆς ἢ πίστεως ἢ ἐμπειρίας. Rassow, De Notionis Definitione, pp. 18-22.
We may distinguish three varieties of Definition. 1. Sometimes it is the mere explanation what a word signifies; in this sense, it has nothing to do with essence or existence; it is a nominal definition and nothing more.23 2. Sometimes it enunciates the Essence, cause, or reason of the definitum; this will happen where the cause is distinct or extraneous, and where there is accordingly an intervening middle term: the definition will then differ from a demonstration only by condensing into one enunciation the two premisses and the conclusion which together constitute the demonstration.24 3. Sometimes it is an immediate proposition, an indemonstrable hypothesis, assuming Essence or Quiddity; the essence itself being cause, and no extraneous cause — no intervening middle term — being obtainable.25
23 Analyt. Post. II. x. p. 93, b. 29-37.
24 Ibid. p. 93, b. 38, seq. οἷον ἀπόδειξις τοῦ τί ἐστιν, τῇ θέσει διαφέρων τῆς ἀποδείξεως· — συλλογισμὸς τοῦ τί ἐστι, πτώσει διαφέρων τῆς ἀποδείξεως — differing “situ et positione terminorum” (Julius Pacius, p. 493).
25 Ibid. p. 94, a. 9: ὁ δὲ τῶν ἀμέσων ὁρισμός, θέσις ἐστὶ τοῦ τί ἐστιν ἀναπόδεικτος. Compare I. xxiv. p. 85, b. 24: ᾧ γὰρ καθ’ αὑτὸ ὑπάρχει τι, τοῦτο αὐτὸ αὑτῷ αἴτιον. See Kampe, Die Erkenntniss-theorie des Aristoteles, p. 212, seq.
To know or cognize is, to know the Cause; when we know the Cause, we are satisfied with our cognition. Now there are four Causes, or varieties of Cause:—
1. The Essence or Quiddity (Form) — τὸ τί ἦν εἶναι.
2. The necessitating conditions (Matter) — τό τίνων ὄντων ἀνάγκη τοῦτ’ εἶναι.
3. The proximate mover or stimulator of change (Efficient) — ἡ τί πρῶτον ἐκίνησε.
4. That for the sake of which (Final Cause or End) — τὸ τίνος ἕνεκα.
All these four Causes (Formal, Material, Efficient, Final) appear as middle terms in demonstrating. We can proceed through the medium either of Form, or of Matter, or of Efficient, or of End. The first of the four has already been exemplified — the demonstration by Form. The second appears in demonstrating that the angle in a semi-circle is always a right angle; where the middle term (or matter of the syllogism, (τὸ ἐξ οὗ) is, that such angle is always the half of two right angles.26 The Efficient is the middle term, when to the question, Why did the Persians invade Athens? it is answered that the Athenians had previously invaded Persia along with the Eretrians. (All are disposed to attack those who have attacked them first; the Athenians attacked the Persians first; ergo, the Persians were disposed to attack the Athenians.) Lastly, the Final Cause serves as middle term, when to the question, Why does a man walk after dinner? the response is, For the purpose of keeping up his health. In another way, the middle term here is digestion: walking after dinner promotes digestion; digestion is the efficient cause of health.27
63 Analyt. Post. II. xix. p. 99, b. 25-30: πότερον οὐκ ἐνοῦσαι αἱ ἕξεις ἐγγίνονται, ἢ ἐνοῦσαι λελήθασιν. εἰ μὲν δὴ ἔχομεν αὐτάς, ἄτοπον· συμβαίνει γὰρ ἀκριβεστέρας ἔχοντας γνώσεις ἀποδείξεως λανθάνειν· εἰ δὲ λαμβάνομεν μὴ ἔχοντες πρότερον, πῶς ἂν γνωρίζοιμεν καὶ μανθάνοιμεν ἐκ μὴ προϋπαρχούσης γνώσεως; Compare, supra, Analyt. Post. I. iii. p. 72, b. 20-30; Metaphys. A. ix. p. 993, a. 1, with the Comment. of Alexander, p. 96, Bonitz.
64 Analyt. Post. II. xix. p. 99, b. 30: φανερὸν τοίνυν οὔτ’ ἔχειν οἷόν τε, οὔτ’ ἀγνοοῦσι καὶ μηδεμίαν ἔχουσιν ἕξιν ἐγγίνεσθαι· ἀνάγκη ἄρα ἔχειν μέν τινα δύναμιν, μὴ τοιαύτην δ’ ἔχειν ἢ ἔσται τούτων τιμιωτέρα κατ’ ἀκρίβειαν. φαίνεται δὲ τοῦτό γε πᾶσιν ὑπάρχον τοῖς ζῴοις.
65 Analyt. Post. II. xix. p. 99, b. 37: ὅσοις μὲν οὖν μὴ ἐγγίνεται, ἢ ὅλως ἢ περὶ ἃ μὴ ἐγγίνεται, οὐκ ἔστι τούτοις γνῶσις ἔξω τοῦ αἰσθάνεσθαι· ἐν οἷς δ’ ἔνεστιν αἰσθανομένοις ἔχειν ἔτι ἐν τῇ ψυχῇ. πολλῶν δὲ τοιούτων γινομένων ἤδη διαφορά τις γίνεται, ὥστε τοῖς μὲν γίνεσθαι λόγον ἐκ τῆς τῶν τοιούτων μονῆς, τοῖς δὲ μή. Compare Analyt. Poster. I. p. 81, a. 38, seq., where the dependence of Induction on the perceptions of sense is also affirmed. See Themistius, pp. 50-51, ed. Spengel. The first chapter of the Metaphysica (p. 981), contains a striking account of this generation of universal notions from memory and comparison of sensible particulars: γίνεται δὲ τέχνη, ὅταν ἐκ πολλῶν τῆς ἐμπειρίας ἐννοημάτων μία καθόλου γένηται περὶ τῶν ὁμοίων ὑπόληψις (“intellecta similitudo”). Also in the Physica VII. p. 247, b. 20 (in the Paraphrase of Themistius, as printed in the Berlin edition, at bottom of page): ἐκ γὰρ τῆς κατὰ μέρος ἐμπειρίας τὴν καθόλου λαμβάνομεν ἐπιστήμην.
66 Analyt. Post. II. xix. p. 100, a. 3-10: ἐκ μὲν οὖν αἰσθήσεως γίνεται μνήμη, ὥσπερ λέγομεν, ἐκ δὲ μνήμης πολλάκις τοῦ αὐτοῦ γινομένης ἐμπειρία· αἱ γὰρ πολλαὶ μνῆμαι τῷ ἀριθμῷ ἐμπειρία μία ἐστίν. ἐκ δ’ ἐμπειρίας, ἢ ἐκ παντὸς ἠρεμήσαντος τοῦ καθόλου ἐν τῇ ψυχῇ, τοῦ ἑνὸς παρὰ τὰ πολλά, ὃ ἂν ἐν ἅπασιν ἓν ἐνῇ ἐκείνοις τὸ αὐτό, τέχνης ἀρχὴ καὶ ἐπιστήμης· ἐὰν μὲν περὶ γένεσιν, τέχνης, ἐὰν δὲ περὶ τὸ ὄν, ἐπιστήμης.
A theory very analogous to this (respecting the gradual generation of scientific universal notions in the mind out of the particulars of sense) is stated in the Phædon of Plato, ch. xlv. p. 96, B., where Sokrates reckons up the unsuccessful tentatives which he had made in philosophy: καὶ πότερον τὸ αἷμά ἐστιν ᾧ φρονοῦμεν, ἢ ὁ ἀὴρ, ἢ τὸ πῦρ, ἢ τούτων μὲν οὐδέν, ὁ δὲ ἐγκέφαλός ἐστιν ὁ τὰς αἰσθήσεις παρέχων τοῦ ἀκούειν καὶ ὁπᾶν καὶ ὀσφραίνεσθαι, ἐκ τούτων δὲ γίγνοιτο μνήμη καὶ δόξα, ἐκ δὲ μνήμης καὶ δόξης, λαβούσης τὸ ἠρεμεῖν, κατὰ ταῦτα γίγνεσθαι ἐπιστήμην.
Boethius says, Comm. in Ciceronis Topica, p. 805:— “Plato ideas quasdam esse ponebat, id est, species incorporeas, substantiasque constantes et per se ab aliis naturæ ratione separatas, ut hoc ipsum homo, quibus participantes cæteræ res homines vel animalia fierent. At vero Aristoteles nullas putat extra esse substantias; sed intellectam similitudinem plurimorum inter se differentium substantialem, genus putat esse vel speciem. Nam cum homo et equus differunt rationabilitate et irrationabilitate, horum intellecta similitudo efficit genus. Ergo communitas quædam et plurimorum inter se differentium similitudo notio est; cujus notionis aliud genus est, aliud forma. Sed quoniam similium intelligentia est omnis notio, in rebus vero similibus necessaria est differentiarum discretio, idcirco indiget notio quadam enodatione ac divisione; velut ipse intellectus animalis sibi ipsi non sufficit,” &c.
The phrase intellecta similitudo plurimorum embodies both Induction and Intellection in one. A like doctrine appears in the obscure passages of Aristotle, De Animâ, III. viii. p. 429, b. 10; also p. 432, a. 3: ὁ νοῦς, εἶδος εἰδῶν, καὶ ἡ αἴσθησις, εἶδος αἰσθητῶν. ἐπεὶ δὲ οὐδὲ πρᾶγμα οὐθέν ἐστι παρὰ τὰ μεγέθη, ὡς δοκεῖ, τὰ αἰσθητὰ κεχωρισμένον, ἐν τοῖς εἴδεσι τοῖς αἰσθητοῖς τὰ νοητά ἐστιν.
67 Analyt. Post. II. xix. p. 100, a. 10-14: οὔτε δὴ ἐνυπάρχουσιν ἀφωρισμέναι αἱ ἕξεις, οὔτ’ ἀπ’ ἄλλων ἕξεων γίνονται γνωριμωτέρων, ἀλλ’ ἀπὸ αἰσθήσεως, — ἡ δὲ ψυχὴ ὑπάρχει τοιαύτη οὖσα οἵα δύνασθαι πάσχειν τοῦτο.
The varieties of intellectual ἕξεις enumerated by Aristotle in the sixth book of the Nikomachean Ethica, are elucidated by Alexander in his Comment. on the Metaphysica, (A. p. 981) pp. 7, 8, Bonitz. The difference of ἕξις and διάθεσις, the durable condition as contrasted with the transient, is noted in Categoriæ, pp. 8, 9. See also Eth. Nikom. II. i. ii. pp 1103, 4.
Aristotle proceeds to repeat the illustration in clearer terms — at least in terms which he thinks clearer.68 We perceive the particular individual; yet sensible perception is of the universal in the particular (as, for example, when Kallias is before us, we perceive man, not the man Kallias). Now, when one of a set of particulars dwells some time in the mind, first an universal notion arises; next, more particulars are perceived and detained, and universal notions arise upon them more and more comprehensive, until at last we reach the highest stage — the most universal and simple. From Kallias we rise to man; from such and such an animal, to animal in genere; from animal in genere, still higher, until we reach the highest or indivisible genus.69 Hence it is plain that the first and highest principia can become known to us only by Induction; for it is by this process that sensible perception builds up in us the Universal.70 Now among those intellective habits or acquirements, whereby we come to apprehend truth, there are some (Science and Noûs) that are uniformly and unerringly true, while others (Opinion and Ratiocination) admit an alternative of falsehood.71 Comparing Science with Noûs, the latter, and the latter only, is more accurate and unerring than Science. But all Science implies demonstration, and all that we know by Science is conclusions deduced by demonstration. We have already said that the principia of these demonstrations cannot be themselves demonstrated, and therefore cannot be known by Science; we have also said that they must be known more accurately than the conclusions. How then can these principia themselves be known? They can be known only by Noûs, and from particulars. It is from the principia known by Noûs, with the maximum of accuracy, that Science demonstrates her conclusions. Noûs is the great principium of Science.72
68 Analyt. Post. II. xix. p. 100, a. 14: ὃ δ’ ἐλέχθη μὲν πάλαι, οὐ σαφῶς δὲ ἐλέχθη, πάλιν εἴπωμεν.
Waitz supposes that Aristotle here refers to a passage in the first book of the Analytica Posteriora, c. xxxi. p. 87, b. 30. M. Barthélemy St. Hilaire thinks (p. 290) that reference is intended to an earlier sentence of this same chapter. Neither of these suppositions seems to suit (least of all the last) with the meaning of πάλαι. But whichever he meant, Aristotle has not done much to clear up what was obscure in the antecedent statements.
69 Analyt. Post. II. xix. p. 100, a. 15: στάντος γὰρ τῶν ἀδιαφόρων ἑνός, πρῶτον μὲν ἐν τῇ ψυχῇ καθόλου (καὶ γὰρ αἰσθησις τοῦ καθόλου ἐστίν, οἷον ἀνθρώπου, ἀλλ’ οὐ Καλλίου ἀνθρώπου) πάλιν δ’ ἐν τούτοις ἵσταται, ἕως ἂν τὰ ἀμερῆ στῇ καὶ τὰ καθόλου, οἷον τοιονδὶ ζῷον, ἕως ζῷον· καὶ ἐν τούτῳ ὡσαύτως.
These words are obscure: τὰ ἀμερῆ must mean the highest genera; indivisible, i.e. being a minimum in respect of comprehension. Instead of τὰ καθόλου, we might have expected τὰ μάλιστα καθόλου, or, perhaps, that καὶ should be omitted. Trendelenburg comments at length on this passage, Arist. De Animâ Comment. pp. 170-174.
70 Analyt. Post. II. xix. p. 100, b. 3: δῆλον δὴ ὅτι ἡμῖν τὰ πρῶτα ἐπαγωγῇ γνωρίζειν ἀναγκαῖον· καὶ γὰρ καὶ αἴσθησις οὕτω τὸ καθόλου ἐμποιεῖ. Compare, supra, Analyt. Post. I. xviii. p. 81, b. 1. Some commentators contended that Aristotle did not mean to ascribe an inductive origin to the common Axioms properly so called, but only to the special principia belonging to each science. Zabarella refutes this doctrine, and maintains that the Axioms (Dignitates) are derived from Induction (Comm. in Analyt. Post. II. xix. p. 649, ed. Venet., 1617):— “Quum igitur inductio non sit proprie discursus, nec ratio, jure dicit Aristoteles principiorum notitiam non esse cum ratione, quia non ex aliis innotescunt, sed ex seipsis dum per inductionem innotescunt. Propterea in illa propositione, quæ in initio primi libri legitur, sub doctrina discursiva cognitio principiorum non comprehenditur, quia non est dianoëtica. Hoc, quod modo diximus, si nonnulli advertissent, fortasse non negassent principia communia, quæ dicuntur Dignitates, inductione cognosci. Dixerunt enim Aristotelem hic de principiis loquentem sola principia propria considerasse, quæ cum non proprio lumine cognoscantur, inductione innotescunt; at Dignitates (inquiunt) proprio lumine ab intellectu nostro cognoscuntur per solam terminorum intelligentiam, ut quod omne totum majus est suâ parte; hoc enim non magis est evidens sensui in particulari, quam intellectui in universali, proinde inductione non eget. Sed hanc sententiam hic Averroes refutat, dicens hæc quoque inductione cognosci, sed non animadverti nobis tempus hujus inductionis; id enim omnino confitendum est, omnem intellectualem doctrinam à sensu originem ducere, et nihil esse in intellectu quod prius in sensu non fuerit, ut ubique asserit Aristoteles.”
To the same purpose Zabarella expresses himself in an earlier portion of his Commentary on the Analyt. Post., where he lays it down that the truth of the proposition, Every whole is greater than its part, is known from antecedent knowledge of particulars by way of Induction. Compare the Scholion of Philoponus, ad Analyt. Post. p. 225, a. 32, Brand., where the same is said about the Axiom, Things equal to the same are equal to each other.
71 Analyt. Post. II. xix. p. 100, b. 5: ἐπεὶ δὲ τῶν περὶ τὴν διάνοιαν ἕξεων, αἷς ἀληθεύομεν, αἱ μὲν ἀεὶ ἀληθεῖς εἰσίν, αἱ δὲ ἐπιδέχονται τὸ ψεῦδος, &c.
72 Ibid. fin. p. 100.
The manner in which Aristotle here describes how the principia of Syllogism become known to the mind deserves particular attention. The march up to principia is not only different from, but the reverse of, the march down from principia; like the athlete who runs first to the end of the stadium, and then back.73 Generalizing or universalizing is an acquired intellectual habit or permanent endowment; growing out of numerous particular acts or judgments of sense, remembered, compared, and coalescing into one mental group through associating resemblance. As the ethical, moral, practical habits, are acquirements growing out of a repetition of particular acts, so also the intellectual, theorizing habits are mental results generated by a multitude of particular judgments of sense, retained and compared, so as to imprint upon the mind a lasting stamp of some identity common to all. The Universal (notius naturâ) is thus generated in the mind by a process of Induction out of particulars which are notiora nobis; the potentiality of this process, together with sense and memory, is all that is innate or connatural.
73 Aristot. Eth. Nikom. I. iv. p. 1095, b. 1.
The principia, from which the conclusions of Syllogism are deduced, being thus obtained by Induction, are, in Aristotle's view, appreciated by, or correlated with, the infallible and unerring Noûs or Intellect.74 He conceives repeated and uncontradicted Induction as carrying with it the maximum of certainty and necessity: the syllogistic deductions constituting Science he regards as also certain; but their certainty is only derivative, and the principia from which they flow he ranks still higher, as being still more certain.75 Both the one and the other he pointedly contrasts with Opinion and Calculation, which he declares to be liable to error.
74 The passages respecting ἀρχαὶ or principia, in the Nikomachean Ethica (especially Books I. and VI.), are instructive as to Aristotle’s views. The principia are universal notions and propositions, not starting up ready-made nor as original promptings of the intellect, but gradually built up out of the particulars of sense and Induction, and repeated particular acts. They are judged and sanctioned by Νοῦς or Intellect, but it requires much care to define them well. They belong to the ὅτι, while demonstration belongs to the διότι. Eth. Nik. I. vii. p. 1098, a. 33: οὐκ ἀπαιτητέον δ’ οὐδὲ τὴν αἰτίαν ἐν ἅπασιν ὁμοίως, ἀλλ’ ἱκανὸν ἔν τισι τὸ ὅτι δειχθῆναι καλῶς, οἷον καὶ περὶ τὰς ἀρχάς· τὸ δ’ ὅτι πρῶτον καὶ ἀρχή. τῶν ἀρχῶν δ’ αἱ μὲν ἐπαγωγῇ θεωροῦνται, αἱ δ’ αἰσθήσει, αἱ δ’ ἐθισμῷ τινι, καὶ ἄλλαι δ’ ἀλλῶς. μετιέναι δὲ πειρατέον ἑκάστας ᾗ πεφύκασιν, καὶ σπουδαστέον ὅπως ὁρισθῶσι καλῶς· μεγάλην γὰρ ἔχουσι ῥοπὴν πρὸς τὰ ἑπόμενα.
Compare Eth. Nik. VI. iii. p. 1139, b. 25, where the Analytica is cited by name — ἡ μὲν δὴ ἐπαγωγὴ ἀρχή ἐστι καὶ τοῦ καθόλου, ὁ δὲ συλλογισμὸς ἐκ τῶν καθόλου· εἰσὶν ἄρα ἀρχαὶ ἐξ ὧν ὁ συλλογισμός, ὧν οὔκ ἐστι συλλογισμός· ἐπαγωγὴ ἄρα. — ib. p. 1141, a. 7: λείπεται νοῦν εἶναι τῶν ἀρχῶν. — p. 1142, a. 25: ὁ μὲν γὰρ νοῦς τῶν ὅρων, ὧν οὔκ ἐστι λόγος. — p. 1143, b. 1.
75 Analyt. Post. I. ii. p. 72, a. 37: τὸν δὲ μέλλοντα ἕξειν τὴν ἐπιστήμην τὴν δι’ ἀποδείξεως οὐ μόνον δεῖ τὰς ἀρχὰς γνωρίζειν καὶ μᾶλλον αὐταῖς πιστεύειν ἢ τῷ δεικνυμένῳ, ἀλλὰ μηδ’ ἄλλο αὐτῷ πιστότερον εἶναι μηδὲ γνωριμώτερον τῶν ἀντικειμένων ταῖς ἀρχαῖς, ἐξ ὧν ἔσται συλλογισμὸς ὁ τῆς ἐναντίας ἀπάτης, εἴπερ δεῖ τὸν ἐπιστάμενον ἁπλῶς ἀμετάπειστον εἶναι.
Aristotle had inherited from Plato this doctrine of an infallible Noûs or Intellect, enjoying complete immunity from error. But, instead of connecting it (as Plato had done) with reminiscences of an anterior life among the Ideas, he assigned to it a position as terminus and correlate to the process of Induction.76 The like postulate and pretension passed afterwards to the Stoics, and various other philosophical sects: they could not be satisfied without finding infallibility somewhere. It was against this pretension that the Academics and Sceptics entered their protest; contending, on grounds sometimes sophistical but often very forcible, that it was impossible to escape from the region of fallibility, and that no criterion of truth, at once universal and imperative, could be set up.
76 Ibid. iii. p. 72, b. 20-30. καὶ οὐ μόνον ἐπιστήμην ἀλλὰ καὶ ἀρχὴν ἐπιστήμης εἶναι τινά φαμεν, ᾗ τοὺς ὅρους γνωρίζομεν.
Themistius, p. 14: ὧν δὴ ἄρχει πάλιν ὁ νοῦς ᾧ τοὺς ὅρους θηρεύομεν, ἐξ ὧν συγκεὶται τὰ ἀξιώματα.
The Paraphrase of Themistius (pp. 100-104) is clear and instructive, where he amplifies the last chapter, and explains Νοῦς as the generalizing or universalizing aptitude of the soul, growing up gradually out of the particulars furnished by Sense and Induction.
It is to be regretted that Aristotle should have contented himself with proclaiming this Inductive process as an ideal, culminating in the infallible Noûs; and that he should only have superficially noticed those conditions under which it must be conducted in reality, in order to avoid erroneous or uncertified results. This is a deficiency however which has remained unsupplied until the present century.77
77 Sir W. Hamilton, Lectures on Logic, Vol. III. Lect. xix. p. 380, says:— “In regard to simple syllogisms, it was an original dogma of the Platonic School, and an early dogma of the Peripatetic, that philosophy (science strictly so-called) was only conversant with, and was exclusively contained in, universals; and the doctrine of Aristotle, which taught that all our general knowledge is only an induction from an observation of particulars, was too easily forgotten or perverted by his followers. It thus obtained almost the force of an acknowledged principle, that everything to be known must be known under some general form or notion. Hence the exaggerated importance attributed to definition and deductions, it not being considered that we only take out of a general notion what we had previously placed therein, and that the amplification of our knowledge is not to be sought for from above but from below, — not from speculation about abstract generalities, but from the observation of concrete particulars. But however erroneous and irrational, the persuasion had its day and influence, and it perhaps determined, as one of its effects, the total neglect of one half, and that not the least important half, of the reasoning process. For while men thought only of looking upward to the more extensive notions, as the only objects and the only media of science, they took little heed of the more comprehensive notions, and absolutely contemned individuals, as objects which could neither be scientifically known in themselves nor supply the conditions of scientifically knowing aught besides. The Logic of Comprehension and of Induction was therefore neglected or ignored, — the Logic of Extension and Deduction exclusively cultivated, as alone affording the rules by which we might evolve higher notions into their subordinate concepts.”
(Hamilton, in this passage, considers the Logic of Induction to be the same as the Logic of Comprehension.)