[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.â€�
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.