Sometimes we may get premisses which look like those of a true syllogism, but are not so in reality; the major proposition ought to be an universal, but it may happen to be only indefinite, and the syllogism will not in all cases be valid; yet the distinction between the two often passes unnoticed.[74] Another source of fallacy is, that we may set out the terms incorrectly; by putting (in modern phrase) the abstract instead of the concrete, or abstract in one premiss and concrete in the other.[75] To guard against this, we ought to use the concrete term in preference to the abstract. For example, let the major proposition be, Health cannot belong to any disease; and the minor. Disease can belong to any man; Ergo, Health cannot belong to any man. This conclusion seems valid, but is not really so. We ought to substitute concrete terms to this effect:— It is impossible that the sick can be well; Any man may be sick; Ergo, It is impossible that any man can be well. To the syllogism, now, as stated in these concrete terms, we may object, that the major is not true. A person who is at the present moment sick may at a future time become well. There is therefore no valid syllogism.[76] When we take the concrete man, we may say with truth that the two contraries, health-sickness, knowledge-ignorance, may both alike belong to him; though not to the same individual at the same time.
[74] Ibid. I. xxxiii. p. 47, b. 16-40: αὕτη μὲν οὖν ἡ ἀπάτη γίνεται ἐν τῷ παρὰ μικρόν· ὠς γὰρ οὐδὲν διαφέρον εἰπεῖν τόδε τῷδε ὑπάρχειν, ἢ τόδε τῷδε παντὶ ὑπάρχειν, συγχωροῦμεν.
M. B. St. Hilaire observes in his note (p. 155): “L’erreur vient uniquement de ce qu’on confond l’universel et l’indeterminé séparés par une nuance très faible d’expression, qu’on ne doit pas cependant negliger.â€� Julius Pacius (p. 264) gives the same explanation at greater length; but the example chosen by Aristotle (ὁ Ἀριστομένης ἐστὶ διανοητὸς Ἀριστομένης) appears open to other objections besides.
[75] Analyt. Prior. I. xxxiv. p. 48, a. 1-28.
[76] Ibid. a. 2-23. See the Scholion of Alexander, p. 181, b. 16-27, Brandis.
Again, we must not suppose that we can always find one distinct and separate name belonging to each term. Sometimes one or all of the three terms can only be expressed by an entire phrase or proposition. In such cases it is very difficult to reduce the reasoning into regular syllogism. We may even be deceived into fancying that there are syllogisms without any middle term at all, because there is no single word to express it. For example, let A represent equal to two right angles; B, triangle; C, isosceles. Then we have a regular syllogism, with an explicit and single-worded middle term; A belongs first to B, and then to C through B as middle term (triangle). But how do we know that A belongs to B? We know it by demonstration; for it is a demonstrable truth that every triangle has its three angles equal to two right angles. Yet there is no other more general truth about triangles from which it is a deduction; it belongs to the triangle per se, and follows from the fundamental properties of the figure.[77] There is, however, a middle term in the demonstration, though it is not single-worded and explicit; it is a declaratory proposition or a fact. We must not suppose that there can be any demonstration without a middle term, either single-worded or many-worded.
[77] Ibid. I. xxxv. p. 48, a. 30-39: φανερὸν ὅτι τὸ μέσον οὐχ οὕτως ἀεὶ ληπτέον ὡς τόδε τι, ἀλλ’ ἐνίοτε λόγον, ὅπερ συμβαίνει κἀπὶ τοῦ λεχθέντος. A good Scholion of Philoponus is given, p. 181, b. 28-45, Brand.
When we are reducing any reasoning to a syllogistic form, and tracing out the three terms of which it is composed, we must expose or set out these terms in the nominative case; but when we actually construct the syllogism or put the terms into propositions, we shall find that one or other of the oblique cases, genitive, dative, &c., is required.[78] Moreover, when we say, ‘this belongs to that,’ or ‘this may be truly predicated of that,’ we must recollect that there are many distinct varieties in the relation of predicate to subject. Each of the Categories has its own distinct relation to the subject; predication secundum quid is distinguished from predication simpliciter, simple from combined or compound, &c. This applies to negatives as well as affirmatives.[79] There will be a material difference in setting out the terms of the syllogism, according as the predication is qualified (secundum quid) or absolute (simpliciter). If it be qualified, the qualification attaches to the predicate, not to the subject: when the major proposition is a qualified predication, we must consider the qualification as belonging, not to the middle term, but to the major term, and as destined to re-appear in the conclusion. If the qualification be attached to the middle term, it cannot appear in the conclusion, and any conclusion that embraces it will not be proved. Suppose the conclusion to be proved is. The wholesome is knowledge quatenus bonum or quod bonum est; the three terms of the syllogism must stand thus:—
Major — Bonum is knowable, quatenus bonum or quod bonum est.
Minor — The wholesome is bonum.
Ergo — The wholesome is knowable, quatenus bonum, &c.
For every syllogism in which the conclusion is qualified, the terms must be set out accordingly.[80]