[9] Ibid. p. 17, a. 6: ὁ δὲ ἀποφαντικὸς τῆς νῦν θεωρίας. See the Scholion of Ammonius, pp. 95, 96, 108, a. 27. In the last passage, Ammonius refers to a passage in one of the lost works of Theophrastus, wherein that philosopher distinguished τὸν ἀποφαντικὸν λόγον from the other varieties of λόγος, by the difference of σχέσις: the ἀποφαντικὸς λόγος was πρὸς τὰ πράγματα, or objective; the others were πρὸς τοὺς ἀκροωμένους, i.e. varying with the different varieties of hearers, or subjective.
[10] Ibid. p. 17, a. 25.
[11] Ibid. p. 17, a. 25.
[12] Ibid. p. 17, a. 30: ἅπαν ἂν ἐνδέχοιτο καὶ ὃ κατέφησέ τις ἀποφῆσαι, καὶ ὃ ἀπέφησέ τις καταφῆσαι.
To every affirmative proposition there is thus opposed a contradictory negative proposition; to every negative a contradictory affirmative. This pair of contradictory opposites may be called an Antiphasis; always assuming that the predicate and subject of the two shall be really the same, without equivocation of terms — a proviso necessary to guard against troublesome puzzles started by Sophists.[13] And we must also distinguish these propositions opposite as Contradictories, from propositions opposite as Contraries. For this, it has to be observed that there is a distinction among things (πράγματα) as universal or singular, according as they are, in their nature, predicable of a number or not: homo is an example of the first, and Kallias is an example of the second. When, now, we affirm a predicate universally, we must attach the mark of universality to the subject and not to the predicate; we must say, Every man is white, No man is white. We cannot attach the mark of universality to the predicate, and say, Every man is every animal; this would be untrue.[14] An affirmation, then, is contradictorily opposed to a negation, when one indicates that the subject is universally taken, and the other, that the subject is taken not universally, e.g. Omnis homo est albus, Non omnis homo est albus; Nullus homo est albus, Est aliquis homo albus. The opposition is contrary, when the affirmation is universal, and the negation is also universal, i.e., when the subject is marked as universally taken in each: for example, Omnis homo est albus, Nullus homo est albus. Of these contrary opposites, both cannot be true, but both may be false. Contradictory opposites, on the other hand, while they cannot both be true, cannot both be false; one must be false and the other true. This holds also where the subject is a singular term, as Sokrates.[15] If, however, an universal term appear as subject in the proposition indefinitely, that is, without any mark of universality whatever, e.g., Est albus homo, Non est albus homo, then the affirmative and negative are not necessarily either contrary or contradictory, though they may be so sometimes: there is no opposition, properly speaking, between them; both may alike be true. This last observation (says Aristotle) will seem strange, because many persons suppose that Non est homo albus is equivalent to Nullus homo est albus; but the meaning of the two is not the same, nor does the truth of the latter follow from that of the former,[16] since homo in the former may be construed as not universally taken.
[13] Ibid. p. 17, a. 33: καὶ ἔστω ἀντίφασις τοῦτο, κατάφασις καὶ ἀπόφασις αἱ ἀντικείμεναι.
It seems (as Ammonius observes, Schol. p. 112, a. 33) that ἀντίφασις in this sense was a technical term, introduced by Aristotle.
[14] Aristot. De Interpr. p. 17, a. 37-b. 14: ἐπεὶ δ’ ἐστὶ τὰ μὲν καθόλου τῶν πραγμάτων, τὰ δὲ καθ’ ἕκαστον (λέγω δὲ καθόλου μὲν ὃ ἐπὶ πλειόνων πέφυκε κατηγορεῖσθαι, καθ’ ἕκαστον δὲ ὃ μὴ, οἷον ἄνθρωπος μὲν τῶν καθόλου, Καλλίας δὲ τῶν καθ’ ἕκαστον)· &c. Ammonius (in Schol. p. 113, a. 38) says that what is predicated, either of many subjects or of one, must be μία φύσις.
The warning against quantifying the predicate appears in this logical treatise of Aristotle, and is repeated in the Analytica Priora, I. xxvii. p. 43, b. 17. Here we have: οὐδεμία κατάφασις ἀληθὴς ἔσται, ἐν ᾗ τοῦ κατηγορουμένου καθόλου τὸ καθόλου κατηγορεῖται, οἷον ἔστι πᾶς ἄνθρωπος πᾶν ζῷον (b. 14).
[15] Ibid. b. 16-29.