Here Proposition (1) is an affirmative, of which (2) is the direct and appropriate negative: also Proposition (3) is an affirmative (Aristotle so considers it), of which (4) is the direct and appropriate negative. The great aim of Aristotle is to mark out clearly what is the appropriate negative or Ἀπόφασις to each Κατάφασις (μία ἀπόφασις μιᾶς καταφάσεως, p. 17, b. 38), making up together the pair which he calls Ἀντίφασις, standing in Contradictory Opposition; and to distinguish this appropriate negative from another proposition which comprises the particle of negation, but which is really a new affirmative.
The true negatives of homo est justus — Omnis homo est justus are, Homo non est justus — Non omnis homo est justus. If you say, Homo est non justus — Omnis homo est non justus, these are not negative propositions, but new affirmatives (ἐκ μεταθέσεως in the language of Theophrastus).
[CHAPTER V.]
ANALYTICA PRIORA I.
Reviewing the treatise De Interpretatione, we have followed Aristotle in his first attempt to define what a Proposition is, to point out its constituent elements, and to specify some of its leading varieties. The characteristic feature of the Proposition he stated to be — That it declares, in the first instance, the mental state of the speaker as to belief or disbelief, and, in its ulterior or final bearing, a state of facts to which such belief or disbelief corresponds. It is thus significant of truth or falsehood; and this is its logical character (belonging to Analytic and Dialectic), as distinguished from its rhetorical character, with other aspects besides. Aristotle farther indicated the two principal discriminative attributes of propositions as logically regarded, passing under the names of quantity and quality. He took great pains, in regard to the quality, to explain what was the special negative proposition in true contradictory antithesis to each affirmative. He stated and enforced the important separation of contradictory propositions from contrary; and he even parted off (which the Greek and Latin languages admit, though the French and English will hardly do so) the true negative from the indeterminate affirmative. He touched also upon equipollent propositions, though he did not go far into them. Thus commenced with Aristotle the systematic study of propositions, classified according to their meaning and their various interdependences with each other as to truth and falsehood — their mutual consistency or incompatibility. Men who had long been talking good Greek fluently and familiarly, were taught to reflect upon the conjunctions of words that they habitually employed, and to pay heed to the conditions of correct speech in reference to its primary purpose of affirmation and denial, for the interchange of beliefs and disbeliefs, the communication of truth, and the rectification of falsehood. To many of Aristotle’s contemporaries this first attempt to theorize upon the forms of locution familiar to every one would probably appear hardly less strange than the interrogative dialectic of Sokrates, when he declared himself not to know what was meant by justice, virtue, piety, temperance, government, &c.; when he astonished his hearers by asking them to rescue him from this state of ignorance, and to communicate to him some portion of their supposed plenitude of knowledge.
Aristotle tells us expressly that the theory of the Syllogism, both demonstrative and dialectic, on which we are now about to enter, was his own work altogether and from the beginning; that no one had ever attempted it before; that he therefore found no basis to work upon, but was obliged to elaborate his own theory, from the very rudiments, by long and laborious application. In this point of view, he contrasts Logic pointedly with Rhetoric, on which there had been a series of writers and teachers, each profiting by the labours of his predecessors.[1] There is no reason to contest the claim to originality here advanced by Aristotle. He was the first who endeavoured, by careful study and multiplied comparison of propositions, to elicit general truths respecting their ratiocinative interdependence, and to found thereupon precepts for regulating the conduct of demonstration and dialectic.[2]
[1] See the remarkable passage at the close of the Sophistici Elenchi, p. 183, b. 34-p. 184, b. 9: ταύτης δὲ τῆς πραγματείας οὐ τὸ μὲν ἦν τὸ δὲ οὐκ ἦν προεξειργασμένον, ἀλλ’ οὐδὲν παντελῶς ὑπῆρχε — καὶ περὶ μὲν τῶν ῥητορικῶν ὑπῆρχε πολλὰ καὶ παλαιὰ τὰ λεγόμενα, περὶ δὲ τοῦ συλλογίζεσθαι παντελῶς οὐδὲν εἴχομεν πρότερον ἄλλο λέγειν, ἀλλ’ ἢ τριβῇ ζητοῦντες πολὺν χρόνον ἐπονοῦμεν.
[2] Sir Wm. Hamilton, Lectures on Logic, Lect. v. pp. 87-91, vol. III.:— “The principles of Contradiction and Excluded Middle can both be traced back to Plato, by whom they were enounced and frequently applied; though it was not till long after, that either of them obtained a distinctive appellation. To take the principle of Contradiction first. This law Plato frequently employs, but the most remarkable passages are found in the Phædo (p. 103), in the Sophista (p. 252), and in the Republic (iv. 436, vii. 525). This law was however more distinctively and emphatically enounced by Aristotle.… Following Aristotle, the Peripatetics established this law as the highest principle of knowledge. From the Greek Aristotelians it obtained the name by which it has subsequently been denominated, the principle, or law, or axiom, of Contradiction (ἀξίωμα τῆς ἀντιφάσεως).… The law of Excluded Middle between two contradictories remounts, as I have said, also to Plato; though the Second Alcibiades, in which it is most clearly expressed (p. 139; also Sophista, p. 250), must be admitted to be spurious.… This law, though universally recognized as a principle in the Greek Peripatetic school, and in the schools of the middle ages, only received the distinctive appellation by which it is now known at a comparatively modern date.â€�
The passages of Plato, to which Sir W. Hamilton here refers, will not be found to bear out his assertion that Plato “enounced and frequently applied the principles of Contradiction and Excluded Middle.â€� These two principles are both of them enunciated, denominated, and distinctly explained by Aristotle, but by no one before him, as far as our knowledge extends. The conception of the two maxims, in their generality, depends upon the clear distinction between Contradictory Opposition and Contrary Opposition; which is fully brought out by Aristotle, but not adverted to, or at least never broadly and generally set forth, by Plato. Indeed it is remarkable that the word Ἀντίφασις, the technical term for Contradiction, never occurs in Plato; at least it is not recognized in the Lexicon Platonicum. Aristotle puts it in the foreground of his logical exposition; for, without it, he could not have explained what he meant by Contradictory Opposition. See Categoriæ, pp. 13-14, and elsewhere in the treatise De Interpretatione and in the Metaphysica. Respecting the idea of the Negative as put forth by Plato in the Sophistes (not coinciding either with Contradictory Opposition or with Contrary Opposition), see ‘Plato and the Other Companions of Sokrates,’ vol. II. [ch. xxvii. pp. 449-459]. I have remarked in that chapter, and the reader ought to recollect, that the philosophical views set out by Plato in the Sophistes differ on many points from what we read in other Platonic dialogues.