[7] Ibid. b. 26: τὸ δ’ ἐν ὅλῳ εἰναι ἕτερον ἑτέρῳ, καὶ τὸ κατὰ παντὸς κατηγορεῖσθαι θατέρου θάτερον, ταὐτόν ἐστι — ταὐτὸν, i.e. ἀντεστραμμένως, as Waitz remarks in note. Julius Pacius says:— “Idem re, sed ratione differunt ut ascensus et descensus; nam subjectum dicitur esse vel non esse in toto attributo, quia attributum dicitur de omni vel de nullo subjectoâ€� (p. 128).
The definition given of a Syllogism is very clear and remarkable:— “It is a speech in which, some positions having been laid down, something different from these positions follows as a necessary consequence from their being laid down.� In a perfect Syllogism nothing additional is required to make the necessity of the consequence obvious as well as complete. But there are also imperfect Syllogisms, in which such necessity, though equally complete, is not so obviously conveyed in the premisses, but requires some change to be effected in the position of the terms in order to render it conspicuous.[8]
[8] Aristot. Anal. Prior. I. i. p. 24, b. 18-26. The same, with a little difference of wording, at the commencement of Topica, p. 100, a. 25. Compare also Analyt. Poster. I. x. p. 76, b. 38: ὅσων ὄντων τῷ ἐκεῖνα εἶναι γίνεται τὸ συμπέρασμα.
The term Syllogism has acquired, through the influence of Aristotle, a meaning so definite and technical, that we do not easily conceive it in any other meaning. But in Plato and other contemporaries it bears a much wider sense, being equivalent to reasoning generally, to the process of comparison, abstraction, generalization.[9] It was Aristotle who consecrated the word, so as to mean exclusively the reasoning embodied in propositions of definite form and number. Having already analysed propositions separately taken, and discriminated them into various classes according to their constituent elements, he now proceeds to consider propositions in combination. Two propositions, if properly framed, will conduct to a third, different from themselves, but which will be necessarily true if they are true. Aristotle calls the three together a Syllogism.[10] He undertakes to shew how it must be framed in order that its conclusion shall be necessarily true, if the premisses are true. He furnishes schemes whereby the cast and arrangement of premisses, proper for attaining truth, may be recognized; together with the nature of the conclusion, warrantable under each arrangement.
[9] See especially Plato, Theætêt. p. 186, B-D., where ὁ συλλογισμὸς and τὰ ἀναλογίσματα are equivalents.
[10] Julius Pacius (ad Analyt. Prior. I. i.) says that it is a mistake on the part of most logicians to treat the Syllogism as including three propositions (ut vulgus logicorum putat). He considers the premisses alone as constituting the Syllogism; the conclusion is not a part thereof, but something distinct and superadded. It appears to me that the vulgus logicorum are here in the right.
In the Analytica Priora, we find ourselves involved, from and after the second chapter, in the distinction of Modal propositions, the necessary and the possible. The rules respecting the simple Assertory propositions are thus, even from the beginning, given in conjunction and contrast with those respecting the Modals. This is one among many causes of the difficulty and obscurity with which the treatise is beset. Theophrastus and Eudemus seem also to have followed their master by giving prominence to the Modals:[11] recent expositors avoid the difficulty, some by omitting them altogether, others by deferring them until the simple assertory propositions have been first made clear. I shall follow the example of these last; but it deserves to be kept in mind, as illustrating Aristotle’s point of view, that he regards the Modals as principal varieties of the proposition, co-ordinate in logical position with the simple assertory.
[11] Eudemi Fragmenta, cii.-ciii. p. 145, ed. Spengel.
Before entering on combinations of propositions, Aristotle begins by shewing what can be done with single propositions, in view to the investigation or proving of truth. A single proposition may be converted; that is, its subject and predicate may be made to change places. If a proposition be true, will it be true when thus converted, or (in other words) will its converse be true? If false, will its converse be false? If this be not always the case, what are the conditions and limits under which (assuming the proposition to be true) the process of conversion leads to assured truth, in each variety of propositions, affirmative or negative, universal or particular? As far as we know, Aristotle was the first person that ever put to himself this question; though the answer to it is indispensable to any theory of the process of proving or disproving. He answers it before he enters upon the Syllogism.
The rules which he lays down on the subject have passed into all logical treatises. They are now familiar; and readers are apt to fancy that there never was any novelty in them — that every one knows them without being told. Such fancy would be illusory. These rules are very far from being self-evident, any more than the maxims of Contradiction and of the Excluded Middle. Not one of the rules could have been laid down with its proper limits, until the discrimination of propositions, both as to quality (affirmative or negative), and as to quantity (universal or particular), had been put prominently forward and appreciated in all its bearings. The rule for trustworthy conversion is different for each variety of propositions. The Universal Negative may be converted simply; that is, the predicate may become subject, and the subject may become predicate — the proposition being true after conversion, if it was true before. But the Universal Affirmative cannot be thus converted simply. It admits of conversion only in the manner called by logicians per accidens: if the predicate change places with the subject, we cannot be sure that the proposition thus changed will be true, unless the new subject be lowered in quantity from universal to particular; e.g. the proposition, All men are animals, has for its legitimate converse not, All animals are men, but only, Some animals are men. The Particular Affirmative may be converted simply: if it be true that Some animals are men, it will also be true that Some men are animals. But, lastly, if the true proposition to be converted be a Particular Negative, it cannot be converted at all, so as to make sure that the converse will be true also.[12]