not so, the system could not be in equilibrium; and since the removal of any single force will destroy this balance of all the forces, it is obvious that any single force suffices to balance the forces which otherwise would have a resultant. Do we therefore affirm that, because in this one relation a single force is equivalent to a multitude of various forces, in other relations the same equivalence exists? By no means. We have specified the relation in which the equivalence obtains. In this relation many forces are condensed into one - mathematically they are one- having one resultant. To balance this resultant, an equivalent force in the same line and in the opposite direction is requisite; and any force which, acting in this line and this direction, suffices to balance the resultant, is an equivalent.

26. The mathematician condenses many and various. forces into one resultant, without prejudice to their several values, or to the operation of such values in other relations; so the logician condenses many Predicates into one Subject, without prejudice to their several values in other relations; and any one of these Predicates is the equivalent of all the rest when detached from the group; and the group minus this one element then stands for the Subject. To the Taste, the group of sensible qualities named Orange is acid-sweet, and it is nothing else. To the Sight, the group is yellow and spherical, but not acidsweet, nor rough and firm. To the Touch, it is rough and firm, not yellow nor acid-sweet. Thus the Subject is either each of these Predicates by turns, or it is the incorporation of all of them. The equilibrium of a system is either that of two forces, or the incorporation of all the forces.

27. A Predicate is a Subject specified: it is what is said or thought in particular of a group of particulars. Both are groups of neural units, which, by the process of

inclusion, form one group. When a single sensation is felt, and there is at the same time no larger group present to Consciousness which we can assign as the Subject, when the cause of the sensation is therefore unknown, we still follow the law of predication, and assign this sensation to a vague "Something." The sensible quality is then the Predicate, which specifies the otherwise unknown Subject, being all we know of the Subject. Now, why must this law of predication operate? Why can we not prevent thought from passing to an antecedent? Why must we in every case regard a sensible quality as forming an integral portion of some group of qualities? It is because Grouping is the process of Thought; and because Change, being the fundamental condition of Consciousness, necessarily involves at least two terms, a point of departure and a point of arrival.

CHAPTER III.

REASONING: THE SYLLOGISM.

28. THE one process which constitutes mental life is that of Grouping. We have just considered it under the aspect of Judgment. As the process of measuring is always the same whether the unit of measure chosen be an inch, a yard, a mile, or a semidiameter of the earth, so the process of Grouping is the same whether the unit. chosen be a neural tremor, a sensation or group of tremors, a perception or group of sensations present and revived, a conception or group of perceptions transformed into a symbol, a judgment, or a proposition which groups judgments. Reasoning-ratiocination is not a different process from Judging, but the operation in the two cases is performed on different groups. A proposition expresses the identification of two terms subject and predicate in three terms, subject, predicate, and copula. A ratiocination is a judgment, the terms of which are two propositions; and the syllogism expresses this in three members, the major and minor premises, and the conclusion, employing three terms, major, minor, and middle.

29. We made a distinction between a judgment and a statement, or enunciation of the proposition; that is to say, between a judging operation, and the product of that operation stated in words. We must make a similar distinction between a ratiocination and its verbal expression. The question may then be discussed whether the syllo

gism is the type of all ratiocination; and this again will raise the question, whether it is the true form of expression. The old logicians and psychologists regarded the syllogistic process as the process of reasoning. That opinion, although rudely shaken by moderns, still holds its ground, and has eminent supporters. We shall see presently that it is not the type of ratiocination, — is no representation of the logical process; and that, however it may require three terms for its expression, a logical conclusion involves but two; for the conclusion is simply an inclusion, a judgment of which the terms are judgments. Reasoning is the same process as judging: it is a process of inference, inclusion. The process of judging has two terms only; the process of reasoning only two. As the copula identifies the subject and predicate, the conclusion identifies the major and minor premise: it resumes what they have assumed and subsumed.*

30. Mr. Spencer has argued that the syllogism requires four terms, not three; and it is certain that he thereby gives a more explicit form to the verbal process. His four terms, however, are condensed into two judgments in the logical process. A little consideration makes this evident. We do not think in this form, All men are mortal; Mr. B― is a man, therefore Mr. B—— is mortal." No one ever thought that. The process is: "Mr. B is what man is, and man is mortal." Each of these terms may require interpretation, but that is another process; the inclusion of the one group in the other is all that constitutes the act of reasoning.

31. To see how far the syllogistic process exhibits

* Sir W. Hamilton names the premises respectively sumption and subsumption. The general term, or major premise, sums together all experiences; the particular term, or minor premise, is subsumed under it. Hence the conclusion (inclusion of the two in one) may be called the resumption, since it reasserts in one expression what has already been asserted in two.

what takes place in the logical process, let us glance at a familiar illustration.

Two boys on entering a fruiterer's shop are told that all the pears and apples there exposed for sale cost a Charles selects one pear and one apple, and penny each. puts down twopence. Harry selects a peach and puts down a penny. Remonstrance of the fruiterer! Charles reasoned correctly; but did his mind pass through a syllogistic process of three terms? He did not say to himself, "All the pears and apples are a penny each; this is a pear, and this is an apple ... each costs a penny." This is what he might have said to the fruiterer, or to Harry, in case of any dispute; this is how he might have justified his reasoning; but this was not the process of his reasoning. That process was the seeing of ratios, ratiocination. The ratios were given in the "all" and "each." No doubt having arisen respecting the import. of the terms, the pear and the apple selected by him being admitted among the objects denoted by the all,the statements that all cost a penny each, and that each of the all costs a penny, are equivalent. Of precisely the same kind is the statement respecting Mr. Bman, as one of the "all" of mortal men.

the

32. But Harry, who has laid hands on a peach, reasoned incorrectly. His paralogism consisted in the substitution of terms; but the mental operation on these terms was the same as that in Charles's mind. To him, as to Charles, the "all" included "each." His intuition of ratios was subjectively correct, though objectively false. He included in the "all" what the fruiterer's terms excluded. And the use of the syllogistic form which enabled Charles to justify his intuition by rendering the terms and their ratio conspicuous, enables the fruiterer to point out to Harry the objective incorrectness of his intuition. But this process of justification is not the pro