[43] Analyt. Post. I. xiii. p. 79, a. 2, seq.: ἐνταῦθα γὰρ τὸ μὲν ὅτι τῶν αἰσθητικῶν εἰδέναι, τὸ δὲ διότι τῶν μαθηματικῶν, &c. Compare Analyt. Prior. II. xxi. p. 67, a. 11; and Metaphys. A. p. 981, a. 15.
[44] Analyt. Post. I. xiv. p. 79, a. 17-32.
As there are some affirmative propositions that are indivisible, i.e., having affirmative predicates which belong to a subject at once, directly, immediately, indivisibly, — so there are also some indivisible negative propositions, i.e., with predicates that belong negatively to a subject at once, directly, &c. In all such there is no intermediate step to justify either the affirmation of the predicate, or the negation of the predicate, respecting the given subject. This will be the case where neither the predicate nor the subject is contained in any higher genus.[45]
[45] Ibid. I. xv. p. 79, a. 33-b. 22. The point which Aristotle here especially insists upon is, that there may be and are immediate, undemonstrable, negative (as well as affirmative) predicates: φανερὸν οὖν ὅτι ἐνδέχεταί τε ἄλλο ἄλλῳ μὴ ὑπάρχειν ἀτόμως. (Themistius, Paraphr. p. 48, Spengel: ἄμεσοι δὲ προτάσεις οὐ καταφάσεις μόνον εἰσίν, ἀλλὰ καὶ ἀποφάσεις ὁμοίως αἳ μὴ δύνανται διὰ συλλογισμοῦ δειχθῆναι, αὗται δ’ εἰσὶν ἐφ’ ὧν οὐδετέρου τῶν ὅρων ἄλλος τις ὅλου κατηγορεῖται.) It had been already shown, in an earlier chapter of this treatise (p. 72, b. 19), that there were affirmative predicates immediate and undemonstrable. This may be compared with that which Plato declares in the Sophistes (pp. 253-254, seq.) about the intercommunion τῶν γενῶν καὶ τῶν εἰδῶν with each other. Some of them admit such intercommunion, others repudiate it.
In regard both to these propositions immediate and indivisible, and to propositions mediate and deducible, there are two varieties of error.[46] You may err simply, from ignorance, not knowing better, and not supposing yourself to know at all; or your error may be a false conclusion, deduced by syllogism through a middle term, and accompanied by a belief on your part that you do know. This may happen in different ways. Suppose the negative proposition, No B is A, to be true immediately or indivisibly. Then, if you conclude the contrary of this[47] (All B is A) to be true, by syllogism through the middle term C, your syllogism must be in the First figure; it must have the minor premiss false (since B is brought under C, when it is not contained in any higher genus), and it may have both premisses false. Again, suppose the affirmative proposition, All B is A, to be true immediately or indivisibly. Then if you conclude the contrary of this (No B is A) to be true, by syllogism through the middle term C, your syllogism may be in the First figure, but it may also be in the Second figure, your false conclusion being negative. If it be in the First figure, both its premisses may be false, or one of them only may be false, either indifferently.[48] If it be in the Second figure, either premiss singly may be wholly false, or both may be partly false.[49]
[46] Analyt. Post. I. xvi. p. 79, b. 23: ἄγνοια κατ’ ἀπόφασιν — ἄγνοια κατὰ διάθεσιν. See Themistius, p. 49, Spengel. In regard to simple and uncombined ideas, ignorance is not possible as an erroneous combination, but only as a mental blank. You either have the idea and thus know so much truth, or you have not the idea and are thus ignorant to that extent; this is the only alternative. Cf. Aristot. Metaph. Θ. p. 1051, a. 34; De Animâ, III. vi. p. 430, a. 26.
[47] Analyt. Post. I. xvi. p. 79, b. 29. M. Barthélemy St. Hilaire remarks (p. 95, n.):— “Il faut remarquer qu’Aristote ne s’occupe que des modes universels dans la première et dans la seconde figure, parceque, la démonstration étant toujours universelle, les propositions qui expriment l’erreur opposée doivent l’être comme elle. Ainsi ce sont les propositions contraires, et non les contradictoires, dont il sera question ici.�
For the like reason the Third figure is not mentioned here, but only the First and Second: because in the Third figure no universal conclusion can be proved (Julius Pacius, p. 431).
[48] Analyt. Post. I. xvi. p. 80, a. 6-26.
[49] Ibid. a. 27-b. 14: ἐν δὲ τῷ μέσῳ σχήματι ὅλας μὲν εἶναι τὰς προτάσεις ἀμφοτέρας ψευδεῖς οὐκ ἐνδέχεται — ἐπί τι δ’ ἑκατέραν οὐδὲν κωλύει ψευδῆ εἶναι.