Again, I need hardly dwell upon the question whether logic treats of language, notions, or things. As reasonably might we debate whether a mathematician treats of symbols, quantities, or things. A mathematician certainly does treat of symbols, but only as the instruments whereby to facilitate his reasoning concerning quantities; and as the axioms and rules of mathematical science must be verified in concrete objects in order that the calculations founded upon them may have any validity or utility, it follows that the ultimate objects of mathematical science are the things themselves. In like manner I conceive that the logician treats of language so far as it is essential for the embodiment and exhibition of thought. Even if reasoning can take place in the inner consciousness of man without the use of any signs, which is doubtful, at any rate it cannot become the subject of discussion until by some system of material signs it is manifested to other persons. The logician then uses words and symbols as instruments of reasoning, and leaves the nature and peculiarities of language to the grammarian. But signs again must correspond to the thoughts and things expressed, in order that they shall serve their intended purpose. We may therefore say that logic treats ultimately of thoughts and things, and immediately of the signs which stand for them. Signs, thoughts, and exterior objects may be regarded as parallel and analogous series of phenomena, and to treat any one of the three series is equivalent to treating either of the other series.
The Process of Inference.
The fundamental action of our reasoning faculties consists in inferring or carrying to a new instance of a phenomenon whatever we have previously known of its like, analogue, equivalent or equal. Sameness or identity presents itself in all degrees, and is known under various names; but the great rule of inference embraces all degrees, and affirms that so far as there exists sameness, identity or likeness, what is true of one thing will be true of the other. The great difficulty doubtless consists in ascertaining that there does exist a sufficient degree of likeness or sameness to warrant an intended inference; and it will be our main task to investigate the conditions under which reasoning is valid. In this place I wish to point out that there is something common to all acts of inference, however different their apparent forms. The one same rule lends itself to the most diverse applications.
The simplest possible case of inference, perhaps, occurs in the use of a pattern, example, or, as it is commonly called, a sample. To prove the exact similarity of two portions of commodity, we need not bring one portion beside the other. It is sufficient that we take a sample which exactly represents the texture, appearance, and general nature of one portion, and according as this sample agrees or not with the other, so will the two portions of commodity agree or differ. Whatever is true as regards the colour, texture, density, material of the sample will be true of the goods themselves. In such cases likeness of quality is the condition of inference.
Exactly the same mode of reasoning holds true of magnitude and figure. To compare the sizes of two objects, we need not lay them beside each other. A staff, string, or other kind of measure may be employed to represent the length of one object, and according as it agrees or not with the other, so must the two objects agree or differ. In this case the proxy or sample represents length; but the fact that lengths can be added and multiplied renders it unnecessary that the proxy should always be as large as the object. Any standard of convenient size, such as a common foot-rule, may be made the medium of comparison. The height of a church in one town may be carried to that in another, and objects existing immovably at opposite sides of the earth may be vicariously measured against each other. We obviously employ the axiom that whatever is true of a thing as regards its length, is true of its equal.