eBook of George Grote, Aristotle

51 Analyt. Post. II. xiii. p. 97, b. 35-39. — (διαλέγεσθαί φησι, τὸ διαλεκτικῶς ὁμιλεῖν. — Schol. p. 248, b. 23, Brand.). Aristotle considers it metaphorical when the term acute is applied both to a sound and to an angle.

The treatment of this portion of the Aristotelian doctrine by Prantl (Geschichte der Logik, vol. I. ch. iv. pp. 246, 247, 338), is instructive. He brings out, in peculiar but forcible terms, the idea of “notional causality” which underlies Aristotle’s Logic. “So also ist die Definition das Aussprechen des schöpferischen Wesensbegriffes.… Soweit der schöpferische Wesensbegriff erreicht werden kann, ist durch denselben die begriffliche Causalität erkannt; und die Einsicht in diese primitive Ursächlichkeit wird in dem Syllogismus vermittelst des Mittelbegriffes erreicht. Ueber den schöpferischen Wesensbegriff hinauszugehen, ist nicht möglich.… Sobald die Definition mehr als eine blosse Namenserklärung ist — und sie muss mehr seyn — erkennt sie den Mittelbegriff als schöpferische Causalität.… Die ontologische Bedeutung des Mittelbegriffes ist, dass er schöpferischer Wesensbegriff ist.” Rassow (pp. 51, 63, &c.) adopts a like metaphorical phrase:— “Definitionem est, explicare notionem; quæ quidem est creatrix rerum causa.”

To obtain and enunciate correctly the problems suitable for discussion in each branch of science, you must have before you tables of dissection and logical division, and take them as guides;52 beginning with the highest genus and proceeding downward through the successively descending scale of sub-genera and species. If you are studying animals, you first collect the predicates belonging to all animals; you then take the highest subdivision of the genus animal, such as bird, and you collect the predicates belonging to all birds; and so on to the next in the descending scale. You will be able to show cause why any of these predicates must belong to the man Sokrates, or to the horse Bukephalus; because it belongs to the genus animal, which includes man and horse. Animal will be the middle term in the demonstration.53 This example is taken from the class-terms current in vulgar speech. But you must not confine yourself to these; you must look out for new classes, bound together by the possession of some common attribute, yet not usually talked of as classes, and you must see whether other attributes can be found constantly conjoined therewith. Thus you find that all animals having horns, have also a structure of stomach fit for rumination, and teeth upon one jaw only. You know, therefore, what is the cause that oxen and sheep have a structure of stomach fit for rumination. It is because they have horns. Having-horns is the middle term of the demonstration.54 Cases may also be found in which several objects possess no common nature or attribute to bind them into a class, but are yet linked together, by analogy, in different ways, to one and the same common term.55 Some predicates will be found to accompany constantly this analogy, or to belong to all the objects quâ analogous, just as if they had one and the same class-nature. Demonstration may be applied to these, as to the former cases.

52 Analyt. Post. II. xiv. p. 98, a. 1. πρὸς δὲ τὸ ἔχειν τὰ προβλήματα, λέγειν δεῖ τάς τε ἀνατομὰς καὶ τὰς διαιρέσεις, οὕτω δὲ διαλέγειν, ὑποθέμενον τὸ γένος τὸ κοινὸν ἁπάντων. This is Waitz’s text, which differs from Julius Pacius and from Firmin Didot.

Themistius (pp. 94-95) explains τὰς ἀνατομὰς to be anatomical drawings or exercises prepared by Aristotle for teaching: καὶ τὰς ἀνατομὰς ἔχειν δεῖ προχείρως, ὅσαι πεποίηνται Ἀριστοτέλει.

The collection of Problems or questions for investigation was much prosecuted, not merely by Aristotle but by Theophrastus (Schol. p. 249, a. 12, Br.).

53 Analyt. Post. II. xiv. p. 98, a. 5-12.

54 Ibid. a. 13-19. Aristotle assumes that the material which ought to have served for the upper teeth, is appropriated by Nature for the formation of horns.

55 Ibid. a. 20-23: ἔτι δ’ ἄλλος τρόπος ἐστὶ κατὰ τὸ ἀνάλογον ἐκλέγειν. He gives as examples, σήπιον, ἄκανθα, ὀστοῦν.

Problems must be considered to be the same, when the middle term of the demonstration is the same for each, or when the middle term in the one is a subordinate or corollary to that in the other. Thus, the cause of echo, the cause of images in a mirror, the cause of the rainbow, all come under the same general head or middle term (refraction), though with a specific difference in each case. Again, when we investigate the problem, Why does the Nile flow with a more powerful current in the last half of the (lunar) month? the reason is that the month is then more wintry. But why is the month then more wintry? Because the light of the moon is then diminishing. Here are two middle terms, the one of which depends upon the other. The problem for investigation is therefore the same in both.56

56 Analyt. Post. II. xv. p. 98, a. 24-34. Theophrastus is said to have made collections of “like problems,” problems of which the solution depended upon the same middle term (Schol. p. 249, a. 11, Brand.).

Respecting Causa and Causatum question may be made whether it is necessary that when the causatum exists, the causa must exist also? The answer must be in the affirmative, if you include the cause in the definition of causatum. Thus, if you include in the definition of a lunar eclipse, the cause thereof, viz., intervention of the earth between moon and sun — then, whenever an eclipse occurs, such intervention must occur also. But it must not be supposed that there is here a perfect reciprocation, and that as the causatum is in this case demonstrable from the cause, so there is the like demonstration of the cause from the causatum. Such a demonstration is never a demonstration of διότι; it is only a demonstration of ὅτι. The causatum is not included in the definition of the cause; if you demonstrate that because the moon is eclipsed, therefore the earth is interposed between the moon and the sun, you prove the fact of the interposition, but you learn nothing about the cause thereof. Again, in a syllogism the middle term is the cause of the conclusion (i.e., it is the reason why the major term is predicated of the minor, which predication is the conclusion); and in this sense the cause and causatum may sometimes reciprocate, so that either may be proved by means of the other. But the causatum here reciprocates with the causa only as premiss and conclusion (i.e., we may know either by means of the other), not as cause and effect; the causatum is not cause of the causa as a fact and reality, as the causa is cause of the causatum.57

57 Analyt. Post. II. xvi. p. 98, a. 35, seq. Themistius, pp. 96-97: οὐ γάρ ἐστιν αἴτιον τοῦ τὴν γῆν ἐν μέσῳ εἶναι τὸ τὴν σελήνην ἐκλείπειν, ἀλλὰ μέσον τοῦ συλλογισμοῦ· καὶ τοῦ συμπεράσματος ἴσως αἴτιον, τοῦ πράγματος δὲ οὐδαμῶς. Themistius here speaks with a precision which is not always present to the mind of Aristotle; for he discriminates the cause of the fact from the cause of the affirmed fact or conclusion. M. Barthélemy St. Hilaire says (Plan Général des Derniers Analytiques, p. cxl.):— “Ainsi, la démonstration de l’effet par la cause apprend pourquoi la chose est; la démonstration par l’effet apprend seulement que la chose est. On sait que la terre s’interpose, mais on ne sait pas pourquoi elle s’interpose: et ce qui le montre bien, c’est que l’idée de l’interposition de la terre est indispensable à la définition essentielle de l’éclipse tandis que l’idée de l’éclipse n’a que faire dans la définition de l’interposition. L’interposition de la terre fait donc comprendre l’éclipse; tandis que l’éclipse ne fait pas du tout comprendre l’interposition de la terre.”

The question then arises, Can there be more than one cause of the same causatum? Is it necessary that the same effect should be produced in all cases by the same cause? In other words, when the same predicate is demonstrated to be true of two distinct minors, may it not be demonstrated in one case by one middle term, and in the other case by a different middle term?58 Answer: In genuine and proper scientific problems the middle term is the rational account (definition, interpretation) of the major extreme; this middle term therefore, or the cause, must in all cases be one and the same. The demonstration in these cases is derived from the same essence; it is per se, not per accidens. But there are other problems, not strictly and properly scientific, in which cause and causatum are connected merely per accidens; the demonstration being operated by a middle term which is not of the essence of the major, but is only a sign or concomitant.59 According as the terms of the conclusion are related to each other, so also will the middle term be related to both. If the conclusion be equivocal, the middle term will be equivocal also; if the predicate in the conclusion be in generic relation to the subject, the major also will be in generic relation to the middle. Thus, if you are demonstrating that one triangle is similar to another, and that one colour is similar to another, the word similar in these two cases is not univocal, but equivocal; accordingly, the middle term in the demonstration will also be equivocal. Again, if you are demonstrating that four proportionals will also be proportionals alternately, there will be one cause or middle term, if the subject of the conclusion be lines; another, if the subject be numbers. Yet the middle term or cause in both is the same, in as far as both involve a certain fact of increment.60

58 Analyt. Post. II. xvi. p. 98, b. 25.

59 Ibid. xvii. p. 99, a. 4: ἔστι δὲ καὶ οὗ αἴτιον καὶ ᾧ σκοπεῖν κατὰ συμβεβηκός· οὐ μὴν δοκεῖ προβλήματα εἶναι.

“Veluti si probemus grammaticum esse aptum ad ridendum, quia homo est aptus ad ridendum.” (Julius Pacius, p. 514.)

60 Analyt. Post. II. xvii. p. 99, a. 8-16.

The major term of the syllogism will in point of extension be larger than any particular minor, but equal or co-extensive with the sum total of the particulars. Thus the predicate deciduous, affirmable of all plants with broad leaves, is greater in extension than the subject vines, also than the subject fig-trees; but it is equal in extension to the sum total of vines and fig-trees (the other particular broad-leaved plant). The middle also, in an universal demonstration, reciprocates with the major, being its definition. Here the true middle or cause of the effect that vines and fig-trees shed their leaves, is not that they are broad-leaved plants, but rather a coagulation of sap or some such fact.61

The last chapter of the present treatise is announced by Aristotle as the appendix and completion of his entire theory of Demonstrative Science, contained in the Analytica Priora, which treats of Syllogism, and the Analytica Posteriora, which treats of Demonstration. After formally winding up the whole enquiry, he proceeds to ask regarding the principia of Demonstrative Science: What are they? How do they become known? What is the mental habit or condition that is cognizant of them?62

62 Analyt. Post. II. xix. p. 99, b. 15-19: περὶ μὲν οὖν συλλογισμοῦ καὶ ἀποδείξεως, τί τε ἑκάτερόν ἐστι καὶ πῶς γίνεται, φανερόν, ἅμα δὲ καὶ περὶ ἐπιστήμης ἀποδεικτικῆς· ταὐτὸν γάρ ἐστιν. περὶ δὲ τῶν ἀρχῶν, πῶς τε γίνονται γνώριμοι, καὶ τίς ἡ γνωρίζουσα ἕξις, ἐντεῦθέν ἐστι δῆλον προαπορήσασι πρῶτον.

Bekker and Waitz, in their editions, include all these words in ch. xix.: the older editions placed the words preceding περὶ δὲ in ch. xviii. Zabarella observes the transition to a new subject (Comm. ad Analyt. Post. II. ch. xv. p. 640):— “Postremum hoc caput (beginning at περὶ δὲ) extra primariam tractationem positum esse manifestum est: quum præcesserit epilogus respondens proœmio quod legitur in initio primi libri Priorum Analyticorum.”

Aristotle has already laid down that there can be no Demonstration without certain præcognita to start from; and that these præcognita must, in the last resort, be principia undemonstrable, immediately known, and known even more accurately than the conclusions deduced from them. Are they then cognitions, or cognizant habits and possessions, born along with us, and complete from the first? This is impossible (Aristotle declares); we cannot have such valuable and accurate cognitions from the first moments of childhood, and yet not be at all aware of them. They must therefore be acquired; yet how is it possible for us to acquire them?63 The fact is, that, though we do not from the first possess any such complete and accurate cognitions as these, we have from the first an inborn capacity or potentiality of arriving at them. And something of the same kind belongs to all animals.64 All of them possess an apprehending and discriminating power born with them, called Sensible Perception; but, though all possess such power, there is this difference, that with some the act of perception dwells for a longer or shorter time in the mind; with others it does not. In animals with whom it does not dwell, there can be no knowledge beyond perception, at least as to all those matters wherein perception is evanescent; but with those that both perceive and retain perceptions in their minds, ulterior knowledge grows up.65 There are many such retentive animals, and they differ among themselves: with some of them reason or rational notions arise out of the perceptions retained; with others, it is not so. First, out of perception arises memory; next, out of memory of the same often repeated, arises experience, since many remembrances numerically distinct are summed up into one experience. Lastly, out of experience, or out of the universal notion, the unum et idem which pervades and characterizes a multitude of particulars, when it has taken rest and root in the mind, there arises the principium of art and science: of science, in respect to objects existent; of art, in respect to things generable.66 And thus these mental habits or acquirements neither exist in our minds determined from the beginning, nor do they spring from other acquirements of greater cognitive efficacy. They spring from sensible perception; and we may illustrate their growth by what happens in the panic of a terrified host, where first one runaway stops in his flight, then a second, then a third, until at last a number docile to command is collected. One characteristic feature of the mind is to be capable of this process.67

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.