[28] Analyt. Post. II. xi. p. 94, a. 21-26. Themistius, p. 83: ἡ γένεσις οὖν τοῦ μέσου καὶ αἰτίου τὴν αὐτὴν οὐκ ἔχει τάξιν ἐφ’ ἁπάντων, ἀλλ’ οὗ μὲν πρώτην ὡς ἐπὶ τῶν κινητικῶν, οὗ δὲ τελευταίαν ὡς ἐπὶ τῶν τελῶν καὶ ὧν ἕνεκα, οὗ δ’ ἅμα ὡς ἐπὶ τῶν ὁρισμῶν καὶ τοῦ τί ἦν εἶναι.
[29] Analyt. Post. II. p. 94, b. 27-p. 95, a. 9.
That the middle term is the Cause, is equally true in respect to Entia, Fientia, Præterita, and Futura; only that in respect to Entia, the middle term or Cause must be an Ens; in respect to Fientia it must be a Fiens; in respect to Præterita, a Præteritum; and in respect to Futura, a Futurum; that is, in each case, it must be generated at the corresponding time with the major and minor terms in the conclusion.[30] What 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 — Material, Efficient, Final — 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, a continuum? 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.[31] There must always be an interval of time during which inference from the antecedent will be untrue; perhaps, indeed, it may never become true. Cause and causatum in 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.[32] The number of these points that may be taken is indeed infinite; yet we must assume some of them as ultimate and immediate principia, in order to construct our syllogism, and provide our middle term.[33] Where 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.[34] Finally, wherever our conclusion is not universally and necessarily true, but true only in most cases, our immediate principia must also be of the same character, true in most cases, but in most cases only.[35]
[30] Analyt. Post. II. xii. p. 95, a. 10, 36: τὸ γὰρ μέσον ὁμόγονον δεῖ εἶναι, &c.
[31] Ibid. a. 24 seq., b. 32; Julius Pacius, ad loc.; Biese, Die Philosophie des Aristot. pp. 302-303.
[32] Analyt. Post. II. xii. p. 95, a. 39-b. 8; Themistius, p. 86.
[33] Analyt. Post. II. xii. p. 95, b. 14-31: ἀρχὴ δὲ καὶ ἐν τούτοις ἄμεσος ληπτέα.
[34] Ibid. b. 38-p. 96, a. 7.
[35] Ibid. p. 96, a. 8-19.
How are we to proceed in hunting out those attributes that are predicated in Quid,[36] as 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 belong also 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 as ens, &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, belong exclusively to the triad, and therefore constitute its essence or definition. The triad is a number, odd, and prime in the two senses.[37] The definitum and the definition are here exactly co-extensive.