in the theory of value and prices. 107 



ments admit of simple statement, but they must be curiously trans- 

 posed before they can be applied to the living speech and verified 

 by observation. 



In its pure and simple form the syllogism cannot be directly com- 

 pared 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."* 



I make this quotation for I believe many persons, especiall}^ econo- 

 mists, do not understand the character of mathematics in general. 

 They imagine that a physicist can sit in his study and with the cal- 

 culus as a talisman spin out some law of physics. Some economists 

 have hoped for a similar mysterious use of mathematics in their own 

 science. 



We must distinguish carefully between what may be designated 

 as mathematics and mathematical method. The former belongs, as 

 Prof. Peirce says, to every science. In this sense economics has 

 always been mathematical. The latter has reference to the use of 

 symbols and their operations. It is this which is to be discussed 

 here. A symbol may be a letter, a diagram, or a model. All three 

 are used in geometry and physics. f 



By an operation on symbols is meant a rule the formulation of 

 which depends on the mention of those symbols (as the operation of 

 differentiation). To employ mathematical method is to pass from 

 what is given to what is required by the aid of such a rule. To 

 avoid mathematical method is to do it without the rule. Symbols 

 and their operations are aids to the human memory and imagina- 

 tion. 



§3- 



The utility of mathematical method is purely relative, as is all 

 utility. It helps greatly some persons, slightly others, is even a 

 hindrance to some. 



Before a schoolboy studies "mechanics" he is usuallj^ given in 

 his arithmetic problems of uniform motion. It would sorely puzzle 

 him if he were compelled to use the f ormula s = t/^. The emplo}'- 

 ment of symbols has for him only disutility. But when in 



* Cf. Grassmann, Ausdehnungslehre, Introduction. 



f Few are aware how important models sometimes are in the treatment of 

 these sciences. Maxwell's model to rei)resent the relations of volume, entropy 

 and energy in thermodynamics is an excellent example. 



