226 THE POPULAR SCIENCE MONTHLY. 



The truth that all our knowledge of objective reality depends upon 

 the establishment or recognition of relations, has been proclaimed by 

 innumerable thinkers, but, nevertheless, is constantly lost sight of, or 

 ignored. There is nothing more interesting and instructive, than a 

 review of the errors and perplexities that have been entailed by the 

 rejection or disregard of this truth both upon metaphysical specula- 

 tion, and upon physical science. The ontological vagaries spun from 

 the proposition that all reality is in its last elements absolute, do not, 

 of course, concern us here ; there is, however, one form of this propo- 

 sition which is so intimately connected with the main subject under 

 discussion, that it is, perhaps, well to indulge in a passing allusion to it. 



Leibnitz places at the head of his " Monadology " the principle that 

 there must be simple substances, because there are compound sub- 

 stances. " Necesse est" he says, " dari substantias simplices quia 

 dantur composite" This enthymeme, though it has been long since 

 exploded in metaphysics, is still regarded by many physicists as proof 

 of the real existence of absolutely simple constituents of matter. Nev- 

 ertheless, it is obvious that it is nothing but a vicious paralogism — a 

 fallacy of the class known in logic as fallacies of suppressed relative. 

 The existence of a compound substance certainly proves the existence 

 of component parts which, relatively to this substance, are simple. But 

 it proves nothing whatever as to the simplicity of these parts in them- 

 selves. 



Among the most notable intellectual hobbles resulting from the 

 attempt to deal with quantity as an absolute, self-determining entity 

 are the various theories of infinitesimals in mathematics, and of the 

 real basis of the differential and integral calculus. The consideration 

 of these theories is beyond the limits of my task, which restricts me to 

 the discussion of questions relating to physical science. But within 

 these limits, it is by no means difficult to find conspicuous proof of the 

 fact that the supposed physical constant of weight and volume, the 

 " atom," is by no means the only absolute real term — the only finite 

 infinitude — which is postulated by physical science in its most recent 

 forms. How completely the minds of modern physicists are under the 

 control of the conceit that physical entities, for purposes of their real 

 apprehension, can be disentangled from the net-work of relations as a 

 part of which they present themselves both to thought and to sense, is 

 at once seen upon the most cursory examination of the remarkable 

 speculative writings which have been published of late by eminent 

 scientific men. I select from the many lectures and essays of this 

 class which have fallen under my notice, a lecture delivered November 

 3, 1869, in the Aula of the University of Liepsic, by Dr. C. Neumann 

 (Professor of Mathematics at the university, and well known as the 

 author of several important contributions to the theory of Abel's In- 

 tegrals), " On the Principles of the Galileo-Newtonian Theory." 1 The 

 1 "Ueber die Principien der Galilei-Newton'schen Theorie. Akademische An- 



