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 may run away with us, in proportion as we enter into them, 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.