pothesis; but it is the judge over both, and it is the arbiter to which either must refer its claims; and neither law can rule, nor theory explain, without the sanction of mathematics. It deduces from a law all its consequences, and develops them into the suitable form for comparison with observation; and thereby measures the strength of the argument from observation in favor of a proposed law, or of a proposed form of application of a law.
"Mathematics, under this definition, belongs to every inquiry, moral as well as physical. Even the rules of logic, by which it is rigidly bound, could not be deduced without its aid. The laws of argument admit of simple statement; but they must be curiously transposed before they can be applied to the living speech and verified by observation. In its pure and simple form, the syllogism cannot be directly compared with all experience, or it would not have required an Aristotle to discover it. It must be transmuted into all the possible shapes in which reasoning loves to clothe itself. The transmutation is the mathematical process in the establishment of the law. Of some sciences it is so large a portion that they have been quite abandoned to the mathematician, perhaps not altogether to the advantage of philosophy. Such is the case with geometry and analytic mechanics. But in many other sciences, as in all those of mental philosophy and most of the branches of natural history, the deductions are so immediate, and of such simple construction, that it is of no practical value to separate the mathematical portion and subject it to isolated discussion.
"The branches of mathematics are as various as the sciences to which they belong, and each subject of physical inquiry has its appropriate mathematics. In every form of material manifestation there is a corresponding form of human thought, so that the human mind is as wide in its range of thought as the physical universe in which it thinks. The two are wonderfully matched. But where there is a great diversity of physical appearance, there is often a close resemblance in the processes of deduction. It is important, therefore, to separate the intellectual work from the external form. Symbols must be adopted which may serve for the embodiment of forms of argument, without being trammeled by the conditions of external representation or special interpretation. The words of common language are usually unfit for this purpose, so that other symbols must be adopted, and mathematics treated by such symbols is called algebra. Algebra is, then, formal mathematics." I am, etc.,C. S. P.
We cheerfully give place to the foregoing, prompted as it is by the generous desire of the writer to speak for one who can no longer speak for himself. Yet it hardly appears how our correspondent has much improved his friend's case. He objects, on the strength of intimate acquaintance with Mr. Wright and the spirit of his work, to our remark that he "was hunting through Spencer's various books in search of flaws." We certainly are not entitled to speak of Mr. Wright's motives, any further than they can be fairly gathered from his writings. No fair-minded person, acquainted with Herbert Spencer's labors, can deny that Mr. Wright's criticism upon him, in the North American Review of 1865, was a very prejudiced piece of work. C. S. P. admits that he greatly under-estimated the importance of Spencer's philosophy, which he accounts for by the natural bias of one who entertains rival views in the same field. Yet the article was far less a judgment of the philosophy, of which but a single volume had then appeared, than an estimate, gathered from an examination of Spencer's various productions, of his competency to produce a philosophy. He undertook to measure the man, and, as we now understand, with a predisposition to underrate him. He, therefore, could not have approached his works in an impartial or judicial temper, but rather in a state of feeling which interested him in their defects. At any rate, if he was not in quest of flaws, it is difficult to see how it was that he found nothing else. Six years before Mr. Wright wrote, and before Mr. Spencer had published a word of his philosophy, several of the ablest men in England joined in an appeal to the Government to secure for him a position of trust, on the ground that he was eminently the man to do a great and special work for the advancement and organization of knowledge that should be a national honor; and now, a dozen years after Mr. Wright wrote, the sixth volume of his philosophical system is awaited with eagerness by the leading minds of the foremost countries in the world. That is to say, he is doing the work that English philosophers predicted long ago (on the basis of what he had already published) that he would do. His works must, therefore, have had some excellences, some elements of strength, which it was the duty of candid criticism to recognize. But Mr. Wright seems to have
