MONISM IN ARITHMETIC. 



TN HIS Primer of Philosophy, Dr. Paul Carus defines monism 

 -*- as a " unitary conception of the world." Similarly, we shall 

 understand by monism in a science the unitary conception of that 

 science. The more a science advances the more does monism domi- 

 nate it. An example of this is furnished by physics. Whereas 

 formerly physics was made up of wholly isolated branches, like 

 Mechanics, Heat, Optics, Electricity, and so forth, each of which 

 received independent explanations, physics has now donned an al- 

 most absolute monistic form, by the reduction of all phenomena to 

 the motions of molecules. For example, optical and electrical phe- 

 nomena, we now know, are caused by the undulatory movements 

 of the ether, and the length of the ether-waves constitutes the sole 

 difference between light and electricity. 



Still more distinctly than in physics is the monistic element 

 .displayed in pure arithmetic, by which we understand the theory of 

 the combination of two numbers into a third by addition and the 

 direct and indirect operations springing out of addition. Pure arith- 

 metic is a science which has completely attained its goal, and which 

 can prove that it has, exclusively by internal evidence. For it may 

 be shown on the one hand that besides the seven familiar operations 

 of addition, subtraction, multiplication, division, involution, evolu- 

 tion, and the finding of logarithms, no other operations are defin- 

 able which present anything essentially new; and on the other hand 

 that fresh extensions of the domain of numbers beyond irrational, 

 imaginary, and complex numbers are arithmetically impossible. 

 Arithmetic may be compared to a tree that has completed its growth, 



