Nor is it any disparagement of the proper value of formal reasonings thus to speak of them. That they cannot proceed beyond probabilities is most readily allowed by those who use them most. Philosophers, experimentalists, lawyers, in their several ways, have commonly the reputation of being, at least on moral and religious subjects, hard of belief; because, proceeding in the necessary investigation by the analytical method of verbal inference, they find within its limits no sufficient resources for attaining a conclusion. Nay, they do not always find it possible in their own special province severally; for, even when in their hearts they have no doubt about a conclusion, still often, from the habit of their minds, they are reluctant to own it, and dwell upon the deficiencies of the evidence, or the possibility of error, because they speak by rule and by book, though they judge and determine by common-sense. Every exercise of nature or of art is good in its place; and the uses of this logical inference are manifold. It is the great principle of order in our thinking; it reduces a chaos into harmony; it catalogues the accumulations of knowledge; it maps out for us the relations of its separate departments; it puts us in the way to correct its own mistakes. It enables the independent intellects of many, acting and re-acting on each other, to bring their collective force to bear upon one and the same subject-matter, or the same question. If language is an inestimable gift to man, the logical faculty prepares it for our use. Though it does not go so far as to ascertain truth, still it teaches us the direction in which truth lies, and how propositions lie towards each other. Nor is it a slight benefit to know what is probable, and what is not so, what is needed for the proof of a point, what is wanting in a theory, how a theory hangs together, and what will follow, if it be admitted. Though it does not itself discover the unknown, it is one principal way by which discoveries are made. Moreover, a course of argument, which is simply conditional, will point out when and where experiment and observation should be applied, or testimony sought for, as often happens both in physical and legal questions. A logical hypothesis is the means of holding facts together, explaining difficulties, and reconciling the imagination to what is strange. And, again, processes of logic are useful as enabling us to get over particular stages of an investigation speedily and surely, as on a journey we now and then gain time by travelling by night, make short cuts when the high-road winds, or adopt water-carriage to avoid fatigue.