[40] Ibid. a. 22: οὐδαμοῦ γὰρ συμβαίνει προεπίστασθαι τὸ καθ’ ἕκαστον, ἀλλ’ ἅμα τῇ ἐπαγωγῇ λαμβάνειν τὴν τῶν κατὰ μέρος ἐπιστήμην ὥσπερ ἀναγνωρίζοντας, &c. Cf. Anal. Post. I. ii. p. 71, b. 9, seq.; Plato, Menon, pp. 81-82.
We thus, by help of the universal, acquire a theoretical knowledge of particulars, but we do not know them by the special observation properly belonging to each particular case: so that we may err in respect to them without any positive contrariety between our cognition and our error; since what we know is the universal, while what we err in is the particular. We may even know that A is predicable of all B, and that B is predicable of all C; and yet we may believe that A is not predicable of C. We may know that every mule is barren, and that the animal before us is a mule, yet still we may believe her to be in foal; for perhaps we may never have combined in our minds the particular case along with the universal proposition.[41] A fortiori, therefore, we may make the like mistake, if we know the universal only, and do not know the particular. And this is perfectly possible. For take any one of the visible particular instances, even one which we have already inspected, so soon as it is out of sight we do not know it by actual and present cognition; we only know it, partly from the remembrance of past special inspection, partly from the universal under which it falls.[42] We may know in one, or other, or all, of these three distinct ways: either by the universal; or specially (as remembered): or by combination of both — actual and present cognition, that is, by the application of a foreknown generality to a case submitted to our senses. And as we may know in each of these three ways, so we may also err or be deceived in each of the same three ways.[43] It is therefore quite possible that we may know, and that we may err or be deceived about the same thing, and that, too, without any contrariety. This is what happens when we know both the two premisses of the syllogism, but have never reflected on them before, nor brought them into conjunction in our minds. When we believe that the mule before us is in foal, we are destitute of the actual knowledge; yet our erroneous belief is not for that reason contrary to knowledge; for an erroneous belief, contrary to the universal proposition, must be represented by a counter-syllogism.[44]
[41] Ibid. II. xxi. p. 67, a. 36: οὐ γὰρ ἐπίσταται ὅτι τὸ Α τῷ Γ, μὴ συνθεωρῶν τὸ καθ’ ἑκάτερον.
[42] Analyt. Prior. II. xxi. p. 67, a. 39: οὐδὲν γὰρ τῶν αἰσθητῶν ἔξω τῆς αἰσθήσεως γενόμενον ἴσμεν, οὔδ’ ἂν ᾐσθημένοι τυγχάνωμεν, εἰ μὴ ὡς τῷ καθόλου καὶ τῷ ἔχειν τὴν οἰκείαν ἐπιστήμην, ἀλλ’ οὐχ ὡς τῷ ἐνεργεῖν.
Complete cognition (τὸ ἐνεργεῖν, according to the view here set forth) consists of one mental act corresponding to the major premiss; another corresponding to the minor; and a third including both the two in conscious juxta-position. The third implies both the first and the second; but the first and the second do not necessarily imply the third, nor does either of them imply the other; though a person cognizant of the first is in a certain way, and to a certain extent, cognizant of all the particulars to which the second applies. Thus the person who knows Ontology (the most universal of all sciences, τοῦ ὄντος ᾗ ὄν), knows in a certain way all scibilia. Metaphys. A., p. 982, a. 21: τούτων δὲ τὸ μὲν πάντα ἐπίστασθαι τῷ μάλιστα ἔχοντι τὴν καθόλου ἐπιστήμην ἀναγκαῖον ὑπάρχειν· οὕτος γὰρ οἶδέ πως πάντα τὰ ὑποκείμενα. Ib. a. 8: ὑπολαμβάνομεν δὴ πρῶτον μὲν ἐπίστασθαι πάντα τὸν σοφὸν ὡς ἐνδέχεται, μὴ καθ’ ἕκαστον ἔχοντα ἐπιστήμην αὐτῶν. See the Scholia of Alexander on these passages, pp. 525, 526, Brandis; also Aristot. Analyt. Post. I. xxiv. p. 86, a. 25; Physica, VII. p. 247, a. 5. Bonitz observes justly (Comm. ad Metaphys. p. 41) as to the doctrine of Aristotle: “Scientia et ars versatur in notionibus universalibus, solutis ac liberis à conceptu singularum rerum; ideoque, etsi orta est à principio et experientiâ, tradi tamen etiam iis potest qui careant experientiâ.â€�
[43] Analyt. Prior. II. xxi. p. 67, b. 3: τὸ γὰρ ἐπίστασθαι λέγεται τριχῶς, ἢ ὡς τῇ καθόλου, ἢ ὡς τῇ οἰκείᾳ, ἢ ὡς τῷ ἐνεργεῖν· ὥστε καὶ τὸ ἠπατῆσθαι τοσαυταχῶς.
[44] Ibid. b. 5: οὐδὲν οὖν κωλύει καὶ εἰδέναι καὶ ἠπατῆσθαι περὶ αὐτό, πλὴν οὐκ ἐναντίως. ὅπερ συμβαίνει καὶ τῷ καθ’ ἑκατέραν εἰδότι τὴν πρότασιν καὶ μὴ ἐπεσκεμμένῳ πρότερον. ὑπολαμβάνων γὰρ κύειν τὴν ἡμίονον οὐκ ἔχει τὴν κατὰ τὸ ἐνεργεῖν ἐπιστήμην, οὐδ’ αὖ διὰ τὴν ὑπόληψιν ἐναντίαν ἀπάτην τῇ ἐπιστήμῃ· συλλογισμὸς γὰρ ἡ ἐναντία ἀπάτη τῇ καθόλου. About erroneous belief, where a man believes the contrary of a true conclusion, adopting a counter-syllogism, compare Analyt. Post. I. xvi. p. 79, b. 23: ἄγνοια κατὰ διάθεσιν.
It is impossible, however, for a man to believe that one contrary is predicable of its contrary, or that one contrary is identical with its contrary, essentially and as an universal proposition; though he may believe that it is so by accident (i.e. in some particular case, by reason of the peculiarities of that case). In various ways this last is possible; but this we reserve for fuller examination.[45]
[45] Analyt. Prior. II. xxi. p. 67, b. 23: ἀλλ’ ἴσως ἐκεῖνο ψεῦδος, τὸ ὑπολαβεῖν τινὰ κακῷ εἶναι τὸ ἀγαθῷ εἶναι, εἰ μὴ κατὰ συμβεβηκός· πολλαχῶς γὰρ ἐγχωρεῖ τοῦθ’ ὑπολαμβάνειν. ἐπισκεπτέον δὲ τοῦτο βέλτιον. This distinction is illustrated by what we read in Plato, Republic, v. pp. 478-479. The impossibility of believing that one contrary is identical with its contrary, is maintained by Sokrates in Plato, Theætetus, p. 190, B-D, as a part of the long discussion respecting ψευδὴς δόξα: either there is no such thing as ψευδὴς δόξα, or a man may know, and not know, the same thing, ibid. p. 196 C. Aristotle has here tried to show in what sense this last-mentioned case is possible.
Whenever (Aristotle next goes on to say) the extremes of a syllogism reciprocate or are co-extensive with each other (i.e. when the conclusion being affirmative is convertible simply), the middle term must reciprocate or be co-extensive with both.[46] If there be four terms (A, B, C, D), such that A reciprocates with B, and C with D, and if either A or C must necessarily be predicable of every subject; then it follows that either B or D must necessarily also be predicable of every subject. Again, if either A or B must necessarily be predicable of every subject, but never both predicable of the same at once; and if, either C or D must be predicable of every subject, but never both predicable of the same at once; then, if A and C reciprocate, B and D will also reciprocate.[47] When A is predicable of all B and all C, but of no other subject besides, and when B is predicable of all C, then A and B must reciprocate with each other, or be co-extensive with each other; that is, B may be predicated of every subject of which A can be predicated, though B cannot be predicated of A itself.[48] Again, when A and B are predicable of all C, and when C reciprocates with B, then A must also be predicable of all B.[49]