known. Two mountains not admitting of a side by side. comparison, can have their relative heights determined only by reference to some common datum line; as the level of the sea. The connexion between a certain sound and the blowing of a distant horn, can arise in the mind only by the help of a before-perceived connexion between such a sound and such an action. Observe, however, that in neither case can any progress be made so long as the relations are separately contemplated. Knowledge of the altitude of each mountain above the sea, gives no knowledge of their relative altitudes, until the two relations of their tops to the sea are thought of together, as having a certain relation. The remembrance that a special kind of sound is simultaneous with the blowing of a horn, leads to nothing unless this general relation is thought of in connexion with the particular relation to be inferred. Hence, every ratiocinative act is the indirect establishment of a definite relation between two things, by the process of establishing a definite relation between two definite relations.

These truths-That Reasoning, whether exhibited in a simple inference or in a chain of such inferences, is the indirect establishment of a definite relation between two things; and that the achievement of this is by one or many steps, each of which consists in the establishment of a definite relation between two definite relations; embody, under the most general form, the various results arrived at in previous chapters.*

A brief statement of the theory of Reasoning here elaborated in detail, will be found in an essay on "The Genesis of Science," published in the British Quarterly Review, for July, 1854 (since republished, with other essays in a permanent form). In that essay I have sought to show that scientific progress conforms to the laws of thought here set forth. It contains accumulated illustrations of the fact that the discoveries of exact science, from the earliest to the latest, severally consist in the establishment of the equalities of relations. That the progress of human reason, as viewed in its concrete results, should throughout exemplify this generalization, as it does in the clearest manner, affords further confirmation of the foregoing analysis.

CHAPTER IX.

CLASSIFICATION, NAMING, AND RECOGNITION.

§ 310. I need scarcely recall the closing section of the last chapter for the purpose of showing that there is a close alliance between Reasoning and Classification; for every student of Reasoning had this truth thrust upon him at the outset of his studies. The alliance is much closer than is supposed, however. Their dependence is reciprocal--Reasoning presupposes Classification, and Classification presupposes Reasoning. This statement seems to involve a contradiction; and would do so, were Reasoning and Classification wholly distinct things. But the solution of the apparent paradox lies in the fact that they are different sides of the same thing-are the necessary complements of each other. Already in describing reasoning as the classification of relations, its near approach to the classification of entities has been implied. And if we remember that on the one hand, classification of relations involves classification of the things or attributes between which they subsist, while, on the other hand, classification of entities involves classification of the relations among their constituent attributes; the kinship of the two will appear still closer. Let us compare them in detail.

The idea underlying all classification is that of similarity. When we group an object with certain others, we do so because in some or all of its characters it resembles them,

Whether it be in putting together as of one kind, the extremely-like individuals constituting a species; whether it be in uniting under the general division, Vertebrata, such diverse creatures as a fish and a man, a snake and a bird; or whether it be in regarding both animate and inanimate objects as members of the great class, solid bodies; there is always some community of attributes-always some similarity in virtue of which they are colligated. But, as was lately pointed out, similarity in its strictest sense equality of relations, and in its less strict sense means likeness of relations. When it is said that the two triangles ABC, DEF, are similar, the specific assertion involved is, that AB is to BC, as DE to EF; or, generally, that the quantitative relation between any two sides of the one, is equal to that between the homologous sides of the other.

B

means

D

E

And when the two annexed shells are classed as of the same species, the implied perception of similarity is a perception that the relations among the several parts of the one are equal to, or like, those among the homologous parts of the other not only the space-relations, but to a great extent the relations among colours, textures, and so on. What,

:

then, is the difference between these acts of thought? From the perception of similarity in the triangles, there is evolved an inference respecting the value of some side; and from the perception of similarity in the shells, there is evolved the idea of identity of class. How is this? An answer is easily found. Similarity has several implications. After the perception of similarity any one of these may present itself to consciousness; and according as one or other of the two leading kinds of implication is thought of, we have reasoning or we have classification. It is impossible to perceive anything to be similar to another, or others, without, to some extent, thinking of that other, or those others. At the same time it is impossible to perceive similarity between things, without being more or less conscious of that likeness of relations among their elements which constitutes their similarity. Either of these two latent implications may become the subject of distinct contemplation. If we consciously recall the things to which this particular one is similar, we classify; if, consciously dwelling on the likeness of relations, we think of certain implied attributes, we

reason.

"But how," it may be asked, " does this prove that classification presupposes reasoning; as well as that reasoning presupposes classification? It may be true that the intuition of similarity is their common root. It may be true. that our conscious inferences involve acts of classing. But it does not, therefore, follow that our conscious acts of classing involve inferences." The reply is, that in all ordinary cases the majority of the like relations in virtue of which any object is classed with certain before-known objects, are not presented in perception but represented in an act of reason. The structural, tangible, gustable, ponderable, and other sensible characters ascribed to an orange, are not included in the visual impression received from the orange; but, as all admit, are inferred from that impression. Yet these various inferred characters are included in the

concept-an orange. When I reach out my hand towards this reddish-yellow something, under the belief that it is juicy, and will slake thirst, I have already, in judging it to be an orange, conceived it as having various attributes besides the observed attributes; every one of which I know to exist, only by the same process that I know the juiciness to exist. The act of classing, then, involves a whole group of inferences; of which the particular inference avowedly drawn is only one. And had some other been drawn, as that the taste was sweet, what is now distinguished as the inference would have been one of the data; that is, one of the attributes involved in the judgment—this is an Should it be said that these various unspecified attributes are not inferred in the act of classing, but that the entire thought implied is-All reddishyellow, spherical, polished, pitted bodies of a certain size are juicy; the untruth of the position will be seen on remembering what takes place if a mock-orange made of painted stone is laid hold of. The unexpected weight and hardness, instantly lead to a change of classification: it is at once perceived that the body is not an orange. And this fact proves that something else than juiciness had been inferred; had been wrongly inferred; and had involved a wrong classification.

orange.

And here we see another vice of the theory which identifies syllogizing with reasoning. That theory proceeds upon the supposition that the act of referring any individual object to a class, is not an act of inference. The constant assumption is that the minor premiss, "This is a," is immediately known; whereas it is always known mediately. Reasoning is already involved in the cognition of the very data out of which reasoning is said to be evolved. On the hypothesis that the syllogism represents the entire ratiocinative process, it is contended that its conclusion is necessary. Meanwhile, the all-essential fact which it posits as the foundation of that conclusion, is