Logic, Inductive and Deductive

by William Minto

The Cambridge mathematician's boast about his new theorem—"The best of it all is that it can never by any possibility be made of the slightest use to anybody for anything"—might be made with truth about many of the later developments of Logic. We may say the same, indeed, about the later developments of any subject that has been a playground for generation after generation of acute intellects, happy in their own disinterested exercise. Educational subjects—subjects appropriated for the general schooling of young minds—are particularly apt to be developed out of the lines of their original intention. So many influences conspire to pervert the original aim. The convenience of the teacher, the convenience of the learner, the love of novelty, the love of symmetry, the love of subtlety; easy-going indolence on the one hand and intellectual restlessness on the other—all these motives act from within on traditional matter without regard to any external purpose whatever. Thus in Logic difficulties have been glossed over and simplified for the dull understanding, while acute minds have revelled in variations and new and ingenious manipulations of the old formulæ, and in multiplication and more exact and symmetrical definition of the old distinctions.

To trace the evolution of the forms and theories of Logic under these various influences during its periods of active development is a task more easily conceived than executed, and one far above the ambition of an introductory treatise. But it is well that even he who writes for beginners should recognise that the forms now commonly used have been evolved out of a simpler tradition. Without entering into the details of the process, it is possible to indicate its main stages, and thus furnish a clue out of the modern labyrinthine confusion of purposes.

How did the Aristotelian Logic originate? Its central feature is the syllogistic forms. In what circumstances did Aristotle invent these? For what purpose? What use did he contemplate for them? In rightly understanding this, we shall understand the original scope or province of Logic, and thus be in a position to understand more clearly how it has been modified, contracted, expanded, and supplemented.

Logic has always made high claims as the scientia scientiarum, the science of sciences. The builders of this Tower of Babel are threatened in these latter days with confusion of tongues. We may escape this danger if we can recover the designs of the founder, and of the master-builders who succeeded him.

Aristotle's Logic has been so long before the world in abstract isolation that we can hardly believe that its form was in any way determined by local accident. A horror as of sacrilege is excited by the bare suggestion that the author of this grand and venerable work, one of the most august monuments of transcendent intellect, was in his day and generation only a pre-eminent tutor or schoolmaster, and that his logical writings were designed for the accomplishment of his pupils in a special art in which every intellectually ambitious young Athenian of the period aspired to excel. Yet such is the plain fact, baldly stated. Aristotle's Logic in its primary aim was as practical as a treatise on Navigation, or "Cavendish on Whist". The latter is the more exact of the two comparisons. It was in effect in its various parts a series of handbooks for a temporarily fashionable intellectual game, a peculiar mode of disputation or dialectic,[¹] the game of Question and Answer, the game so fully illustrated in the Dialogues of Plato, the game identified with the name of Socrates.

We may lay stress, if we like, on the intellectuality of the game, and the high topics on which it was exercised. It was a game that could flourish only among a peculiarly intellectual people; a people less acute would find little sport in it. The Athenians still take a singular delight in disputation. You cannot visit Athens without being struck by it. You may still see groups formed round two protagonists in the cafés or the squares, or among the ruins of the Acropolis, in a way to remind you of Socrates and his friends. They do not argue as Gil Blas and his Hibernians did with heat and temper, ending in blows. They argue for the pure love of arguing, the audience sitting or standing by to see fair play with the keenest enjoyment of intellectual thrust and parry. No other people could argue like the Greeks without coming to blows. It is one of their characteristics now, and so it was in old times two thousand years ago. And about a century before Aristotle reached manhood, they had invented this peculiarly difficult and trying species of disputative pastime, in which we find the genesis of Aristotle's logical treatises.

To get a proper idea of this debate by Question and Answer, which we may call Socratic disputation after its most renowned master, one must read some of the dialogues of Plato. I will indicate merely the skeleton of the game, to show how happily it lent itself to Aristotle's analysis of arguments and propositions.

A thesis or proposition is put up for debate, e.g., that knowledge is nothing else than sensible perception,[²] that it is a greater evil to do wrong than to suffer wrong,[³] that the love of gain is not reprehensible.[⁴] There are two disputants, but they do not speak on the question by turns, so many minutes being allowed to each as in a modern encounter of wits. One of the two, who may be called the Questioner, is limited to asking questions, the other, the Respondent, is limited to answering. Further, the Respondent can answer only "Yes" or "No," with perhaps a little explanation: on his side the Questioner must ask only questions that admit of the simple answer "Yes" or "No". The Questioner's business is to extract from the Respondent admissions involving the opposite of what he has undertaken to maintain. The Questioner tries in short to make him contradict himself. Only a very stupid Respondent would do this at once: the Questioner plies him with general principles, analogies, plain cases; leads him on from admission to admission, and then putting the admissions together convicts him out of his own mouth of inconsistency.[⁵]

Now mark precisely where Aristotle struck in with his invention of the Syllogism, the invention on which he prided himself as specially his own, and the forms of which have clung to Logic ever since, even in the usage of those who deride Aristotle's Moods and Figures as antiquated superstitions. Suppose yourself the Questioner, where did he profess to help you with his mechanism? In effect, as the word Syllogism indicates, it was when you had obtained a number of admissions, and wished to reason them together, to demonstrate how they bore upon the thesis in dispute, how they hung together, how they necessarily involved what you were contending for. And the essence of his mechanism was the reduction of the admitted propositions to common terms, and to certain types or forms which are manifestly equivalent or inter-dependent. Aristotle advised his pupils also in the tactics of the game, but his grand invention was the form or type of admissions that you should strive to obtain, and the effective manipulation of them when you had got them.

An example will show the nature of this help, and what it was worth. To bring the thing nearer home, let us, instead of an example from Plato, whose topics often seem artificial to us now, take a thesis from last century, a paradox still arguable, Mandeville's famous—some would say infamous—paradox that Private Vices are Public Benefits. Undertake to maintain this, and you will have no difficulty in getting a respondent prepared to maintain the negative. The plain men, such as Socrates cross-questioned, would have declared at once that a vice is a vice, and can never do any good to anybody. Your Respondent denies your proposition simply: he upholds that private vices never are public benefits, and defies you to extract from him any admission inconsistent with this. Your task then is to lure him somehow into admitting that in some cases what is vicious in the individual may be of service to the State. This is enough: you are not concerned to establish that this holds of all private vices. A single instance to the contrary is enough to break down his universal negative. You cannot, of course, expect him to make the necessary admission in direct terms: you must go round about. You know, perhaps, that he has confidence in Bishop Butler as a moralist. You try him with the saying: "To aim at public and private good are so far from being inconsistent that they mutually promote each other". Does he admit this?