Some things usually considered essential to logical forms, as the modality of propositions and syllogisms, and the conversion of the other figures of the syllogism into the first, I have not included in the above outline, for the reason that the former does not properly fall within the province of logic, which has to do only with the form and not with the matter of a proposition or an argument, while, as to the latter, it is only an accidental, and not an essential circumstance, what may be the figure of a syllogism, and it is, therefore, of no importance to reduce the second and third figures to the first.
VII. Use and Value of the Syllogism.
Having considered the various forms which the syllogism may assume, as also the laws or canons which govern it, we proceed to inquire, finally, as to its use and value in reasoning.
All mediate reasoning syllogistic.—It must be conceded, I think, that all mediate reasoning, all inference, which is not immediate and direct, but which, in order to reach its conclusion, compares one thing with another, is essentially syllogistic. The greater part of our reasoning processes are of this sort. When fully and explicitly stated, such reasoning resolves itself into some form of syllogism. It is not, as sometimes stated, a mode of reasoning, but the mode which all reasoning, except such as is direct and immediate, tends to assume. Not always, indeed, is this reasoning fully drawn out and explicitly stated, but all valid reasoning admits of being thus stated; nay, it is not, as to form at least, complete until it is so expressed.
Not always syllogistically expressed.—In ordinary conversation, and even in public address, we omit many intermediate steps in the trains and processes of our arguments, for the reason that their statement is not essential to our being understood, the hearer's mind supplying, for itself, the connecting links as we proceed; just as in speaking or writing, we make many abbreviations, drop out some letters and syllables here and there, in our hasty utterance, and yet all such short-hand processes imply and are based upon the full form; and it would be as correct and as reasonable to say that the fully written or fully spoken word is merely a mode of speaking and writing, which, when the grammarian and rhetorician come into contact with common people, they lay aside for the ordinary forms of speech, as to say that syllogism is merely a mode of reasoning, which the logician lays aside when he comes out of his study, and reasons with other men.
Chief Value of the Syllogism.—The chief use of the syllogism, I apprehend, however, to be, not in presenting a train of argument for the purpose of convincing and persuading others; for the laws of thought do not require us in such a case to state every thing that is even essential to the argument, but only so much as shall clearly indicate our meaning, and enable the hearer or reader to follow us; but rather in testing the soundness or detecting the unsoundness of an argument, whether our own, or that of an opponent. For this purpose, an acquaintance with the forms and laws of syllogism may be of great service to the writer and to the orator.
Objection to the Syllogism.—But it is objected to the syllogism that it is of no value in the discovery and establishment of truth, inasmuch as, by the very laws of the syllogism, there can be nothing more in the conclusion than was assumed in the premises. There is, and can be, in this way, no progress from the known to the unknown. The very construction of the syllogism, it is said, involves a petitio principii. When I say, All men are mortal; Socrates is a man; therefore, Socrates is mortal; the major premiss, it is said, affirms the very thing to be proved; that Socrates is mortal is virtually affirmed in the proposition that all men are so. Either, then, the syllogism proves nothing which was not known before, or else the general proposition, with which it sets out, is unwarranted, as asserting more than we know to be true, and, in that case, the conclusion is equally unreliable; in either case nothing is gained by the process; the syllogism is worthless.
Lies equally against all reasoning.—This objection, if valid against the syllogism, is valid against and overthrows not the syllogism merely, but all reasoning of whatever kind, and in whatever form. It is an objection which really applies, not to the form which an argument may happen to assume, but to the essential nature of reasoning itself. As was shown in discussing the nature of the reasoning process, all reasoning is, in its nature, essentially analytic. It is the evolution of a truth that lies involved in some already admitted truth. It simply develops, draws out, what was therein contained. Its starting-point must always be some admitted position, its conclusions must always be some inevitable necessary consequence of that admission. The mortality of Socrates is, indeed, involved and contained in the general proposition which affirms the mortality of all men, and so, also, is every inferred truth contained in that from which it is inferred.
Conclusion not affirmed in the Premiss.—But while contained, it is not affirmed, in the premiss. To say that all men are mortal, is not to say that Socrates is so, but only to say what implies that. The conclusion which draws out and affirms what was involved, but not affirmed, in the premiss, is an advance in the order of thought, a step of progress, and not merely an idle repetition, and the syllogism, as a whole, moves the mind onward from the starting-point to a position not otherwise explicitly and positively reached. It is a movement onward, and not merely a rotation of the wheel about its own axis.
The Form accidental.—In so far as the objection of petitio principii relates, not to the nature of reasoning, but only to its form, this is entirely a matter of accident, and does not pertain to the syllogism as such. As was shown in treating of the different forms of syllogism, the order of the propositions is not essential. We may, if we like, state the conclusion first, and then the reasons, as, All A is C, for all A is B, and all B is C; or we may state the same thing in a different form, as, A and B are equal; B and C are equal; therefore, A and C are equal. Both are syllogisms, the former analytic, the latter unfigured, but to neither does the objection of petitio principii apply so far as regards the mere form of statement. Nor does it apply to that form of syllogism in which the major premiss is a singular proposition, as, e. g., Cæsar was fortunate; Cæsar was a tyrant; therefore, a tyrant may be fortunate. Here the subject of the conclusion is not formally contained in that of the major premiss, as Socrates is contained in the expression, all men, a part of the whole.