of y; then we find the value of y in terms of x; and so on we may continue forever without coming nearer to a solution." (Principles of Psychology, § 272.)
Carrying a little further this simile, will, I think, show where lies the insuperable difficulty felt by Mr. Sidgwick. Taking x and y as the subjective and objective activities, unknown in their natures and known only as phenomenally manifested, and recognizing the fact that every state of consciousness implies, immediately or remotely, the action of object on subject, or subject on object, or both, we may say that every state of consciousness will be symbolized by some modification of x y—the phenomenally-known product of the two unknown factors. In other words, xy' x'y, x'y', x"y', x'y", etc., etc., will represent all perceptions and thoughts. Suppose, now, that these are thoughts about the object; composing some hypothesis respecting its character as analyzed by physicists. Clearly, all such thoughts, be they about shapes, resistances, momenta, molecules, molecular motions, or what not, will contain some form of the subjective activity x. Now, let the thoughts be concerning mental processes. It must similarly happen that some mode of the unknown objective activity, y, will be in every case a component. Now, suppose that the problem is the genesis of mental phenomena, and that, in the course of the inquiry, bodily organization and the functions of the nervous system are brought into the explanation. It will happen, as before, that these, considered as objective, have to be described and thought about in modes of x y. And when by the actions of such a nervous system, conceived objectively in modes of x y, and acted upon by physical forces which are conceived in other modes of x y, we endeavor to explain the genesis of sensations, perceptions, and ideas, which we can think of only in other modes of x y, we find that all our factors, and therefore all our interpretations, contain the two unknown terms, and that no interpretation is imaginable that will not contain the two unknown terms.
What is the defense for this apparently circular process? Simply that it is a process of establishing congruity among our symbols. It is the finding a mode of so symbolizing the unknown activities subjective and objective, and so operating with our symbols, that all our acts may be rightly guided—guided, that is, in such ways that we can anticipate when, where, and in what quantity, one of our symbols will be found. Mr. Sidgwick's difficulty arises, I think, from having insufficiently borne in mind the statements made at the outset, in "The Data of Philosophy," that such conceptions as "are vital, or cannot be separated from the rest without mental dissolution, must be assumed true provisionally;" that "there is no mode of establishing the validity of any belief except that of showing its entire congruity with all other beliefs," and that "Philosophy, compelled to make those fundamental assumptions without which thought is impossible,