CORRESP ONDENCE. 



745 



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 observa- 

 tion ; 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, be- 

 longs 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 ad- 

 mit of simple statement ; but they must be 

 curiously transposed before they can be ap- 

 plied 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 mathemat- 

 ical 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 con- 

 struction, that it is of no practical value to 

 separate the mathematical portion and sub- 

 ject it to isolated discussion. 



" The branches of mathematics are as 

 various as the sciences to which they be- 

 long, 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 phys- 

 ical appearance, there is often a close re- 

 semblance 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 inter- 

 pretation. The words of common language 

 are usually unfit for this purpose, so that 

 other symbols must be adopted, and mathe- 

 matics treated by such symbols is called 

 algebra. Algebra is, then, formal mathe- 

 matics." I am, etc., C. S. P. 



We cheerfully give place to the fore- 

 going, 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 ob- 

 jects, on the strength of intimate acquaint- 

 ance 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, acquaint- 

 ed 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 impor T 

 tance of Spencer's philosophy, which he ac- 

 counts 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, gath- 

 ered 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 under- 

 stand, with a predisposition to underrate 

 him. He, therefore, could not have ap- 

 proached his works in an impartial or judi- 

 cial 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 pub- 

 lished a word of his philosophy, several of 

 the ablest men in England joined in an ap- 

 peal 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 philo- 

 sophical system is awaited with eagerness 

 by the leading minds of the foremost coun- 

 tries 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 



