Grammar of Assent

In the first place, Inference, being conditional, is hampered with other propositions besides that which is especially its own, that is, with the premisses as well as the conclusion, and with the rules connecting the latter with the former. It views its own proper proposition in the medium of prior propositions, and measures it by them. It does not hold a proposition for its own sake, but as dependent upon others, and those others it entertains for the sake of the conclusion. Thus it is practically far more concerned with the comparison of propositions, than with the propositions themselves. It is obliged to regard all the propositions, with which it has to do, not so much for their own sake, as for the sake of each other, as regards the identity or likeness, independence or dissimilarity, which has to be mutually predicated of them. It follows from this, that the more simple and definite are the words of a proposition, and the narrower their meaning, and the more that meaning in each proposition is restricted to the relation which it has to the words of the other propositions compared with it,—in other words, the nearer the propositions concerned in the inference approach to being mental abstractions, and the less they have to do with the concrete reality, and the more closely they are made to express exact, intelligible, comprehensible, communicable notions, and the less they stand for objective things, that is, the more they are the subjects, not of real, but of notional apprehension,—so much the more suitable do they become for the purposes of Inference.

Hence it is that no process of argument is so perfect, as that which is conducted by means of symbols. In Arithmetic 1 is 1, and just 1, and never anything else but 1; it never is 2, it has no tendency to change its meaning, and to become 2; it has no portion, quality, admixture of 2 in its meaning. And 6 under all circumstances is 3 times 2, and the sum of 2 and 4; nor can the whole world supply anything to throw doubt upon these elementary positions. It is not so with language. Take, by contrast, the word "inference," which I have been using: it may stand for the act of inferring, as I have used it; or for the connecting principle, or inferentia, between premisses and conclusions; or for the conclusion itself. And sometimes it will be difficult, in a particular sentence, to say which it bears of these three senses. And so again in Algebra, a is never x, or anything but a, wherever it is found; and a and b are always standard quantities, to which x and y are always to be referred, and by which they are always to be measured. In Geometry again, the subjects of argument, points, lines, and surfaces, are precise creations of the mind, suggested indeed by external objects, but meaning nothing but what they are defined to mean: they have no colour, no motion, no heat, no qualities which address themselves to the ear or to the palate; so that, in whatever combinations or relations the words denoting them occur, and to whomsoever they come, those words never vary in their meaning, but are just of the same measure and weight at one time and at another.

What is true of Arithmetic, Algebra, and Geometry, is true also of Aristotelic argumentation in its typical modes and figures. It compares two given words separately with a third, and then determines how they stand towards each other, in a bonâ fide identity of sense. In consequence, its formal process is best conducted by means of symbols, A, B, and C. While it keeps to these, it is safe; it has the cogency of mathematical reasoning, and draws its conclusions by a rule as unerring as it is blind.

Symbolical notation, then, being the perfection of the syllogistic method, it follows that, when words are substituted for symbols, it will be its aim to circumscribe and stint their import as much as possible, lest perchance A should not always exactly mean A, and B mean B; and to make them, as much as possible, the calculi of notions, which are in our absolute power, as meaning just what we choose them to mean, and as little as possible the tokens of real things, which are outside of us, and which mean we do not know how much, but so much certainly as, (in proportion as we enter into them,) may run away with us beyond the range of scientific management. The concrete matter of propositions is a constant source of trouble to syllogistic reasoning, as marring the simplicity and perfection of its process. Words, which denote things, have innumerable implications; but in inferential exercises it is the very triumph of that clearness and hardness of head, which is the characteristic talent for the art, to have stripped them of all these connatural senses, to have drained them of that depth and breadth of associations which constitute their poetry, their rhetoric, and their historical life, to have starved each term down till it has become the ghost of itself, and everywhere one and the same ghost, "omnibus umbra locis," so that it may stand for just one unreal aspect of the concrete thing to which it properly belongs, for a relation, a generalization, or other abstraction, for a notion neatly turned out of the laboratory of the mind, and sufficiently tame and subdued, because existing only in a definition.

Thus it is that the logician for his own purposes, and most usefully as far as those purposes are concerned, turns rivers, full, winding, and beautiful, into navigable canals. To him dog or horse is not a thing which he sees, but a mere name suggesting ideas; and by dog or horse universal he means, not the aggregate of all individual dogs or horses brought together, but a common aspect, meagre but precise, of all existing or possible dogs or horses, which all the while does not really correspond to any one single dog or horse out of the whole aggregate. Such minute fidelity in the representation of individuals is neither necessary nor possible to his art; his business is not to ascertain facts in the concrete, but to find and dress up middle terms; and, provided they and the extremes which they go between are not equivocal, either in themselves or in their use, and he can enable his pupils to show well in a vivâ voce disputation, or in a popular harangue, or in a written dissertation, he has achieved the main purpose of his profession.

Such are the characteristics of reasoning, viewed as a science or scientific art, or inferential process, and we might anticipate that, narrow as by necessity is its field of view, for that reason its pretensions to be demonstrative were incontrovertible. In a certain sense they really are so; while we talk logic, we are unanswerable; but then, on the other hand, this universal living scene of things is after all as little a logical world as it is a poetical; and, as it cannot without violence be exalted into poetical perfection, neither can it be attenuated into a logical formula. Abstract can only conduct to abstract; but we have need to attain by our reasonings to what is concrete; and the margin between the abstract conclusions of the science, and the concrete facts which we wish to ascertain, will be found to reduce the force of the inferential method from demonstration to the mere determination of the probable. Thus, whereas (as I have already said) Inference starts with conditions, as starting with premisses, here are two reasons why, when employed upon questions of fact, it can only conclude probabilities: first, because its premisses are assumed, not proved; and secondly, because its conclusions are abstract, and not concrete. I will now consider these two points separately.

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