Chapter 24

23Analyt. Post. II. x. p. 93, b. 29-37.

24Ibid. p. 93, b. 38, seq. οἷον ἀπόδειξις τοῦ τί ἐστιν, τῇ θέσει διαφέρων τῆς ἀποδείξεωςÂ· â€” συλλογισμὸς τοῦ τί ἐστι, πτώσει διαφέρων τῆς ἀποδείξεως â€” differing â€œsitu et positione terminorumâ€� (Julius Pacius, p. 493).

25Ibid. p. 94, a. 9: ὁ δὲ τῶν ἀμέσων ὁρισμός, θέσις ἐστὶ τοῦ τί ἐστιν ἀναπόδεικτος. Compare I. xxiv. p. 85, b. 24: ᾧ γὰρ καθâ€™ 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:â€”

1. The Essence or Quiddity (Form) â€” τὸ τί ἦν εἶναι.

2. The necessitating conditions (Matter) â€” τό τίνων ὄντων ἀνάγκη τοῦτâ€™ εἶναι.

3. The proximate mover or stimulator of change (Efficient) â€” ἡ τί πρῶτον ἐκίνησε.

4. That for the sake of which (Final Cause or End) â€” 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 â€” the demonstrationby 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.26The 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

26Analyt. Post. II. xi. p. 94, a. 21-36. Themistius, p. 83: μάλιστα μὲν γὰρ ἐπὶ πάσης ἀποδείξεως ὁ μέσος ἔστιν οἷον ἡ ὕλη τῷ συλλογισμῷÂ· οὕτος γὰρ ὁ ποιῶν τὰς δύο προτάσεις, ἐφâ€™ αἷς τὸ συμπέρασμα.

27Analyt. Post. II. xi. p. 94, a. 36-b. 21.

The Final Cause or End is prior in the order of nature, but posterior to the terms of the conclusion in the order of time or generation; while the Efficient is prior in the order of time or generation. The Formal and Material are simultaneous with the effect, neither prior nor posterior.28Sometimes the same fact may proceed both from a Final cause, and from a cause of Material Necessity; thus the light passes through our lantern for the purpose of guiding us in the dark, but also by reason that the particles of light are smaller than the pores in the glass. Nature produces effects of finality, or with a view to some given end; and also effects by necessity, the necessity being either inherent in the substance itself, or imposed by extraneous force. Thus a stonefallsto the ground by necessity of the first kind, butascendsby necessity of the second kind. Among products of human intelligence some spring wholly from design without necessity; but others arise by accident or chance and have no final cause.29

28Analyt. Post. II. xi. p. 94, a. 21-26. Themistius, p. 83: ἡ γένεσις οὖν τοῦ μέσου καὶ αἰτίου τὴν αὐτὴν οὐκ ἔχει τάξιν ἐφâ€™ ἁπάντων, ἀλλâ€™ οὗ μὲν πρώτην ὡς ἐπὶ τῶν κινητικῶν, οὗ δὲ τελευταίαν ὡς ἐπὶ τῶν τελῶν καὶ ὧν ἕνεκα, οὗ δâ€™ ἅμα ὡς ἐπὶ τῶν ὁρισμῶν καὶ τοῦ τί ἦν εἶναι.

29Analyt. Post. II. p. 94, b. 27-p. 95, a. 9.

That the middle term is the Cause, is equally true in respect toEntia,Fientia,PrÃ¦terita, andFutura; only that in respect toEntia, the middle term or Cause must be anEns; in respect toFientiait must be aFiens; in respect toPrÃ¦terita, aPrÃ¦teritum; and in respect toFutura, aFuturum; that is, in each case, it must be generated at the corresponding timewith the major and minor terms in the conclusion.30What is the cause of an eclipse of the moon? The cause is, that the earth intervenes between moon and sun; and this is true alike of eclipses past, present, and future. Such an intervention is the essence or definition of a lunar eclipse: the cause is therefore Formal, and cause and effect are simultaneous, occurring at the same moment of time. But in the other three Causes â€” Material, Efficient, Final â€” where phenomena are successive and not simultaneous, can we say that the antecedent is cause and the consequent effect, time being, as seems to us, acontinuum? In cases like this, we can syllogize from the consequent backward to the antecedent; but not from the antecedent forward to the consequent. If the house has been built, we can infer that the foundations have been laid; but, if the foundations have been laid, we cannot infer that the house has been built.31There must always be an interval of time during which inference from the antecedent will be untrue; perhaps, indeed, it may never become true. Cause andcausatumin these three last varieties of Cause, do not universally and necessarily reciprocate with each other, as in the case of the Formal cause. Though time is continuous, events or generations are distinct points marked in a continuous line, and are not continuous with each other.32The number of these points that may be taken is indeed infinite; yet we must assume some of them as ultimate and immediateprincipia, in order to construct our syllogism, and provide our middle term.33Where the middle term reciprocates and is co-extensive with the major and the minor, in such cases we have generation of phenomena in a cycle;e.g., after the earth has been made wet, vapour rises of necessity: hence comes a cloud, hence water; which again falls, and the earth again becomes wet.34Finally, wherever our conclusion is not universally and necessarily true, but true only in most cases, our immediateprincipiamust also be of the same character, true in most cases, but in most cases only.35

30Analyt. Post. II. xii. p. 95, a. 10, 36: τὸ γὰρ μέσον ὁμόγονον δεῖ εἶναι, &c.

31Ibid. a. 24 seq., b. 32; Julius Pacius, ad loc.; Biese, Die Philosophie des Aristot. pp. 302-303.

32Analyt. Post. II. xii. p. 95, a. 39-b. 8; Themistius, p. 86.

33Analyt. Post. II. xii. p. 95, b. 14-31: ἀρχὴ δὲ καὶ ἐν τούτοις ἄμεσος ληπτέα.

34Ibid. b. 38-p. 96, a.7.

35Ibid. p. 96, a. 8-19.

How are we to proceed in hunting out those attributes that are predicatedin Quid,36as belonging to the Essence of the subject? The subject being a lowest species, we must look out for such attributes as belong to all individuals thereof, but which belongalso to individuals of other species under the same genus. We shall thus find one, two, three, or more, attributes, each of which, separately taken, belongs to various individuals lying out of the species; but the assemblage of which, collectively taken, does not belong to any individual lying out of the species. The Assemblage thus found is the Essence; and the enunciation thereof is the Definition of the species. Thus, the triad is included in the genus number; in searching for its definition, therefore, we must not go beyond that genus, nor include any attributes (such asens, &c.) predicable of other subjects as well as numbers. Keeping within the limits of the genus, we find that every triad agrees in being an odd number. But this oddness belongs to other numbers also (pentad, heptad, &c.). We therefore look out for other attributes, and we find that every triad agrees in being a prime number, in two distinct senses; first, that it is not measured by any other number; secondly, that it is not compounded of any other numbers. This last attribute belongs to no other odd number except the triad. We have now an assemblage of attributes, which belong each of them to every triad, universally and necessarily, and which, taken all together, belongexclusivelyto the triad, and therefore constitute its essence or definition. The triad is a number, odd, and prime in the two senses.37Thedefinitumand the definition are here exactly co-extensive.

36Ibid. xiii. p. 96, a. 22: πῶς δεῖθηρεύειντὰ ἐν τῷ τί ἐστι κατηγορούμενα;

37Analyt. Post. II. xiii. p. 96, a. 24-b. 14. εἰ τοίνυν μηδενὶ ὑπάρχει ἄλλῳ ἢ ταῖς ἀτόμοις τριάσι, τοῦτâ€™ ἂν εἴη τὸ τριάδι εἶναι. ὑποκείσθω γὰρ καὶ τοῦτο, ἡ οὐσία ἡ ἑκάστου εἶναι ἡ ἐπὶ ταῖς ἀτόμοις ἔσχατος τοιαύτη κατηγορία. ὥστε ὁμοίως καὶ ἄλλῳ ὁτῳοῦν τῶν οὕτω δειχθέντων τὸαὐτῷ εἶναιἔσται.

Where the matter that we study is the entire genus, we must begin by distributing it into its lowest species;e.g.number into dyad, triad, &c.; in like manner, taking straight line, circle, right angle, &c.38We must first search out the definitions of each of these lowest species; and these having been ascertained, we must next look above the genus, to the Category in which it is itself comprised, whetherQuantum,Quale, &c. Having done thus much we must study the derivative attributes or propria of the lowest species through the common generalities true respecting the larger. We must recollect that these derivative attributes are derived from the essence and definition of the lowest species, the complex flowing from the simple as itsprincipium: they belongper seonly to the lowest species thusdefined; they belong to the higher genera only through those species.39It is in this way, and not in any other, that the logical Division of genera, according to specific differences, can be made serviceable for investigation of essential attributes; that is, it can only be made to demonstrate what is derivative from the essence. We have shown already that it cannot help in demonstrating essence or Definition itself. We learn to marshal in proper order the two constituent elements of our definition, and to attach each specific difference to the genus to which it properly belongs. Thus we must not attempt to distribute the genus animal according to the difference of having the wing divided or undivided: many animals will fall under neither of the two heads; the difference in question belongs to the lower genus winged animal, and distributes the same into two species. The characteristic or specific difference must be enunciated and postulated by itself, and must be attached to its appropriate genus in order to form the definition. It is only by careful attention to the steps of legitimate logical Division that we can make sure of including all the particulars and leaving out none.40

38Ibid. b. 18. The straight line is the first or lowest of all lines: no other line can be understood, unless we first understand what is meant by a straight line. In like manner the right angle is the first of all angles, the circle the first of all curvilinear figures (Julius Pacius, ad loc. p. 504).

39Analyt. Post. II. xiii. p. 96, b. 19-25: μετὰ δὲ τοῦτο, λάβόντα τί τὸ γένος, οἷον πότερον τῶν ποσῶν ἢ τῶν ποιῶν, τὰ ἴδια πάθη θεωρεῖν διὰ τῶν κοινῶν πρώτων. τοῖς γὰρ συντιθεμένοις ἐκ τῶν ἀτόμων (speciebus infimis) τὰ συμβαίνοντα ἐκ τῶν ὁρισμῶν ἔσται δῆλα, διὰ τὸ ἀρχὴν εἶναι πάντων τὸν ὁρισμόν καὶ τὸ ἁπλοῦν, καὶ τοῖς ἁπλοῖς καθâ€™ αὑτὰ ὑπάρχειν τὰ συμβαίνοντα μόνοις, τοῖς δâ€™ ἄλλοις κατâ€™ ἐκεῖνα.Themistius illustrates this obscure passage, p. 89. The definitions of εὐθεῖα γραμμή, κεκλασμένη γραμμή, περιφερὴς γραμμή, must each of them contain the definition of γραμμή (= μῆκος ἀπλατές), since it is in the Category Ποσόν (ποσὸν μῆκος ἀπλατές). But the derivative properties of the circle (περιφερὴς γραμμή) are deduced from the definition of a circle, and belong to it in the first instancequÃ¢περιφερὴς γραμμή, in a secondary wayquÃ¢γραμμή.

Themistius illustrates this obscure passage, p. 89. The definitions of εὐθεῖα γραμμή, κεκλασμένη γραμμή, περιφερὴς γραμμή, must each of them contain the definition of γραμμή (= μῆκος ἀπλατές), since it is in the Category Ποσόν (ποσὸν μῆκος ἀπλατές). But the derivative properties of the circle (περιφερὴς γραμμή) are deduced from the definition of a circle, and belong to it in the first instancequÃ¢περιφερὴς γραμμή, in a secondary wayquÃ¢γραμμή.

40Analyt. Post. II. xiii. p. 96, b. 25-p. 97, a. 6.

Some contemporaries of Aristotle, and among them Speusippus, maintained that it was impossible either to define, or to divide logically, unless you knew all particulars without exception. You cannot (they said) know any one thing, except by knowing its differences from all other things; which would imply that you knew also all these other things.41To these reasoners Aristotle replies: It is not necessary to knowallthe differences of every thing; you know a thing as soon as you know its essence, with the propertiesper sewhich are derivative therefrom. There are many differences not belonging to the essence, but distinguishing from each other two things having the same essence: you may know the thing, without knowing these accidentaldifferences.42When you divide a genus into two species, distinguished by one proximate specific difference, such that there cannot be any thing that does not fall under one or other of thesemembra condividentia, and when you have traced the subject investigated under one or other of these members, you can always follow this road until no lower specific difference can be found, and you have then the final essence and definition of the subject; even though you may not know how manyothersubjects each of the two members may include.43Thus does Aristotle reply to Speusippus, showing that it is not necessary, for the definition of one thing, that you should knowallother things. His reply, as in many other cases, is founded on the distinction between the Essential and the Accidental.

41Ibid. p. 97, a. 6-10; Themistius, p. 92. Aristotle does not here expressly name Speusippus, but simply says φασί τινες. It is Themistius who names Speusippus; and one of the Scholiasts refers to Eudemus as having expressly indicated Speusippus (Schol. p. 248, a. 24, Br.).

42Analyt. Post. II. xiii. p. 97, a. 12: πολλαὶ γὰρ διαφοραὶ ὑπάρχουσι τοῖς αὐτοῖς τῷ εἴδει, ἀλλâ€™ οὐ κατâ€™ οὐσίαν οὐδὲ καθâ€™ αὑτά.

43Ibid. a. 18-22: φανερὸν γὰρ ὅτι ἂν οὕτω βαδίζων ἔλθῃ εἰς ταῦτα ὧν μηκέτι ἐστὶ διαφορά, ἕξει τὸν λόγον τῆς οὐσίας.

To obtain or put together a definition through logical Division, three points are to be attended to.44Collect the predicatesin Quid; range them in the proper order; make sure that there are no more, or that you have collected all. The essential predicates are genera, to be obtained not otherwise than by the method (dialectical) used in concluding accidents. As regards order, you begin with the highest genus, that which is predicable of all the others, while none of these is predicable of it, determining in like fashion the succession of the rest respectively. The collection will be complete, if you divide the highest genus by an exhaustive specific difference, such that every thing must be included in one or other of the two proximate and opposed portions; and then taking the species thus found as yourdividendum, subdivide it until no lower specific difference can be found, or you obtain from the elements an exact equivalent to the subject.45

44Ibid. a. 23: εἰς δὲ τὸ κατασκευάζειν ὅρον διὰ διαιρέσεων. The Scholiast, p. 248, a. 41, explains κατασκευάζειν by εὑρεῖν, συνθεῖναι, ἀποδοῦναι. He distinguishes it from ἀποδεικνύναι; demonstration of the definition being impracticable.

45Analyt. Post. II. xiii. p. 97, a. 23 seq. See Waitz, Comm. p. 418.

When the investigation must proceed by getting together a group of similar particulars, you compare them, and note what is the same in all; then turn to another group which are the samein genereyet differin speciefrom the first group, and have a different point of community among themselves. You next compare the point of community among the members of the first group, and that among the members of the second group. If the two points of community can be brought under onerational formula, that will be the definition of the subject; but if at the end of the process, the distinct points of community are not found resolvable into any final one, this proves that the supposeddefiniendumis not one but two or more.46For example, suppose you are investigating, What is the essence or definition of magnanimity? You must study various magnanimous individuals, and note what they have in commonquÃ¢magnanimous.47Thus, Achilles, Ajax, Alkibiades were all magnanimous. Now, that which the three had in common was, that they could not endure to be insulted; on that account Alkibiades went to war with his countrymen, Achilles was angry and stood aloof from the Greeks, Ajax slew himself. But, again, you find two other magnanimous men, Sokrates and Lysander. These two had in common the quality, that they maintained an equal and unshaken temper both in prosperity and adversity. Now when you have got thus far, the question to be examined is, What is the point of identity between the temper that will not endure insult, and the temper that remains undisturbed under all diversities of fortune? If an identity can be found, this will be the essence or definition of magnanimity; to which will belong equanimity as one variety, and intolerance of insult as another. If, on the contrary, no identity can be found, you will then have two distinct mental dispositions, without any common definition.48

46Analyt. Post. II. xiii. p. 97, b. 7-15. πάλιν σκοπεῖν εἰ ταὐτὸν ἕως ἂν εἰς ἕνα ἔλθῃ λόγονÂ· οὗτος γὰρ ἔσται τοῦ πράγματος ὁρισμός. ἐὰν δὲ μὴ βαδίζῃ εἰς ἕνα ἀλλâ€™ εἰς δύο ἢ πλείω, δῆλον ὅτι οὐκ ἂν εἴη ἕν τι εἶναι τὸ ζητούμενον, ἀλλὰ πλείω.

47Ibid. b. 16: σκεπτέον ἐπί τινων μεγαλοψύχων, οὓς ἴσμεν, τί ἔχουσιν ἓν πάντες ᾗτοιοῦτοι.

48Ibid. b. 17-25. ταῦτα δύο λαβὼν σκοπῶ τί τὸ αὐτὸ ἔχουσιν ἥ τε ἀπάθεια ἡ περὶ τὰς τύχας καὶ ἡ μὴ ὑπομονὴ ἀτιμαζομένων. εἰ δὲ μηδέν, δύο εἴδη ἂν εἴη τῆς μεγαλοψυχίας.Ã†quam memento rebus in arduisServare mentem: non secus in bonisAb insolenti temperatamLÃ¦titiÃ¢. â€”HORACE.Ode, ii. 3.Aristotle says that there will be two species of magnanimity. But surely if the two so-called species connote nothing in common they are not rightly called species, nor is magnanimity rightly called a genus. Equanimity would be distinct from magnanimity; Sokrates and Lysander would not properly be magnanimous but equanimous.

48Ibid. b. 17-25. ταῦτα δύο λαβὼν σκοπῶ τί τὸ αὐτὸ ἔχουσιν ἥ τε ἀπάθεια ἡ περὶ τὰς τύχας καὶ ἡ μὴ ὑπομονὴ ἀτιμαζομένων. εἰ δὲ μηδέν, δύο εἴδη ἂν εἴη τῆς μεγαλοψυχίας.

Ã†quam memento rebus in arduisServare mentem: non secus in bonisAb insolenti temperatamLÃ¦titiÃ¢. â€”HORACE.Ode, ii. 3.

Aristotle says that there will be two species of magnanimity. But surely if the two so-called species connote nothing in common they are not rightly called species, nor is magnanimity rightly called a genus. Equanimity would be distinct from magnanimity; Sokrates and Lysander would not properly be magnanimous but equanimous.

Every definition must be an universal proposition, applicable, not exclusively to one particular object, but to a class of greater or less extent. The lowest species is easier to define than the higher genus; this is one reason why we must begin with particulars, and ascend to universals. It is in the higher genera that equivocal terms most frequently escape detection.49When you are demonstrating, what you have first to attend to is, the completeness of the form of syllogizing: when you are defining,the main requisite is to be perspicuous and intelligible;i.e.to avoid equivocal or metaphorical terms.50You will best succeed in avoiding them, if you begin with the individuals, or with examples of the lowest species, and then proceed to consider not their resemblances generally, but their resemblances in certain definite ways, as in colour or figure. These more definite resemblances you will note first; upon each you will found a formula of separate definition; after which you will ascend to the more general formula of less definite resemblance common to both. Thus, in regard to the acute or sharp, you will consider the acute in sound, and in other matters (tastes, pains, weapons, angles, &c.), and you will investigate what is the common point of identity characterizing all. Perhaps there may be no such identity; the transfer of the term from one to the other may be only a metaphor: you will thus learn that no common definition is attainable. This is an important lesson; for as we are forbidden to carry on a dialectical debate in metaphorical terms, much more are we forbidden to introduce metaphorical terms in a definition.51

49Analyt. Post. II. xiii. p. 97, b. 29: καὶ γὰρ αἱ ὁμωνυμίαιλανθάνουσιμᾶλλον ἐν τοῖς καθόλου ἢ ἐν τοῖς ἀδιαφόροις.

50Analyt. Post. II. xiii. p. 97, b. 31: ὥσπερ δε ἐν ταῖς ἀποδείξεσι δεῖ τό γε συλλελογίσθαι ὑπάρχειν, οὕτω καὶ ἐν τοῖς ὅροιςτὸ σαφές.By τὸ σαφές, he evidently means the avoidance of equivocal or metaphorical terms, and the adherence to true genera and species. Compare Biese, Die Philosophie des Aristot. pp. 308-310.

50Analyt. Post. II. xiii. p. 97, b. 31: ὥσπερ δε ἐν ταῖς ἀποδείξεσι δεῖ τό γε συλλελογίσθαι ὑπάρχειν, οὕτω καὶ ἐν τοῖς ὅροιςτὸ σαφές.

By τὸ σαφές, he evidently means the avoidance of equivocal or metaphorical terms, and the adherence to true genera and species. Compare Biese, Die Philosophie des Aristot. pp. 308-310.

51Analyt. Post. II. xiii. p. 97, b. 35-39. â€” (διαλέγεσθαί φησι, τὸ διαλεκτικῶς ὁμιλεῖν. â€” Schol. p. 248, b. 23, Brand.). Aristotle considers it metaphorical when the termacuteis 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 â€œnotional causalityâ€� which underlies Aristotleâ€™s Logic. â€œSo also ist die Definition das Aussprechendes schÃ¶pferischen Wesensbegriffes.â€¦ Soweit der schÃ¶pferische Wesensbegriff erreicht werden kann, ist durch denselben die begriffliche CausalitÃ¤t erkannt; und die Einsicht in dieseprimitive UrsÃ¤chlichkeitwird in dem Syllogismus vermittelst des Mittelbegriffes erreicht. Ueber den schÃ¶pferischen Wesensbegriff hinauszugehen, ist nicht mÃ¶glich.â€¦ Sobald die Definition mehr als eine blosse NamenserklÃ¤rung ist â€” und sie muss mehr seyn â€” erkennt sie den Mittelbegriff als schÃ¶pferische CausalitÃ¤t.â€¦ Die ontologische Bedeutung des Mittelbegriffes ist, dass er schÃ¶pferischer Wesensbegriff ist.â€� Rassow (pp. 51, 63, &c.) adopts a like metaphorical phrase:â€” â€œDefinitionem est, explicare notionem; quÃ¦ quidem estcreatrix rerum causa.â€�

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 â€œnotional causalityâ€� which underlies Aristotleâ€™s Logic. â€œSo also ist die Definition das Aussprechendes schÃ¶pferischen Wesensbegriffes.â€¦ Soweit der schÃ¶pferische Wesensbegriff erreicht werden kann, ist durch denselben die begriffliche CausalitÃ¤t erkannt; und die Einsicht in dieseprimitive UrsÃ¤chlichkeitwird in dem Syllogismus vermittelst des Mittelbegriffes erreicht. Ueber den schÃ¶pferischen Wesensbegriff hinauszugehen, ist nicht mÃ¶glich.â€¦ Sobald die Definition mehr als eine blosse NamenserklÃ¤rung ist â€” und sie muss mehr seyn â€” erkennt sie den Mittelbegriff als schÃ¶pferische CausalitÃ¤t.â€¦ Die ontologische Bedeutung des Mittelbegriffes ist, dass er schÃ¶pferischer Wesensbegriff ist.â€� Rassow (pp. 51, 63, &c.) adopts a like metaphorical phrase:â€” â€œDefinitionem est, explicare notionem; quÃ¦ quidem estcreatrix rerum causa.â€�

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;52beginning with the highest genus and proceeding downwardthrough 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.53This 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.54Cases 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.55Some predicates will be found to accompany constantly this analogy, or to belong to all the objectsquÃ¢analogous, just as if they had one and the same class-nature. Demonstration may be applied to these, as to the former cases.

52Analyt. Post. II. xiv. p. 98,a. 1. πρὸς δὲ τὸ ἔχειν τὰ προβλήματα, λέγειν δεῖ τάς τεἀνατομὰςκαὶ τὰς διαιρέσεις, οὕτω δὲ διαλέγειν, ὑποθέμενον τὸ γένος τὸ κοινὸν ἁπάντων. This is Waitzâ€™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.).

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.).

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

54Ibid. 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.

55Ibid. a. 20-23: ἔτι δâ€™ ἄλλος τρόπος ἐστὶκατὰ τὸ ἀνάλογονἐκλέγειν. 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 whyisthe month then more wintry? Because the light of the moon is then diminishing. Here aretwo middle terms, the one of which depends upon the other. The problem for investigation is therefore the same in both.56

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

RespectingCausaandCausatumquestion may be made whether it is necessary that when thecausatumexists, thecausamust exist also? The answer must be in the affirmative, if you include the cause in the definition ofcausatum. Thus, if you include in the definition of a lunar eclipse, the cause thereof, viz., intervention of the earth between moon and sun â€” 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 thecausatumis in this case demonstrable from the cause, so there is the like demonstration of the cause from thecausatum. Such a demonstration is never a demonstration of διότι; it is only a demonstration of ὅτι. Thecausatumis 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 andcausatummay sometimes reciprocate, so that either may be proved by means of the other. But thecausatumhere reciprocates with thecausaonly as premiss and conclusion (i.e., we may know either by means of the other), not as cause and effect; thecausatumis not cause of thecausaas a fact and reality, as thecausais cause of thecausatum.57

57Analyt. 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 συλλογισμοῦÂ· 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 ofthe factfrom the cause of theaffirmed factorconclusion. M. BarthÃ©lemy St. Hilaire says (Plan GÃ©nÃ©ral des Derniers Analytiques, p. cxl.):â€” â€œAinsi, la dÃ©monstration de lâ€™effet par la cause apprend pourquoi la chose est; la dÃ©monstration par lâ€™effet apprend seulement que la chose est. On sait que la terre sâ€™interpose, mais on ne sait pas pourquoi elle sâ€™interpose: et ce qui le montre bien, câ€™est que lâ€™idÃ©e de lâ€™interposition de la terre est indispensable Ã la dÃ©finition essentielle de lâ€™Ã©clipse tandis que lâ€™idÃ©e de lâ€™Ã©clipse nâ€™a que faire dans la dÃ©finition de lâ€™interposition. Lâ€™interposition de la terre fait donc comprendre lâ€™Ã©clipse; tandis que lâ€™Ã©clipse ne fait pas du tout comprendre lâ€™interposition de la terre.â€�

The question then arises, Can there be more than one cause of the samecausatum? 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?58Answer: 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 isper se, notper accidens. But there are other problems, not strictly and properly scientific, in which cause andcausatumare connected merelyper 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.59According 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

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