in the theory of value and prices.
10 1
roents admit of simple statement, but they must be curiously trans-posed before they can be applied to the living speech and verifiedby 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 shapesin which reasoning loves to clothe itself. The transmutation is themathematical process in the establishment of the law.”*
I make this quotation for .1 believe many persons, especially 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 economistshave hoped for a similar mysterious use of mathematics in their ownscience.
§2-
We must distinguish carefully between what maybe designatedas mathematics and mathematical method. The former belongs, asProf. Peirce says, to every science. In this sense economics hasalways been mathematical. The latter has reference to the use ofsymbols and their operations. It is this which is to be discussedhere. A symbol may be a letter, a diagram, or a model. All threeare used in geometry and physics.f
By an operation on symbols is meant a rule the formulation ofwhich depends on the mention of those symbols (as the operation ofdifferentiation). To employ mathematical method is to pass fromwhat is given to what is required by the aid of such a rule. Toavoid mathematical method is to do it without the rule. Symbolsand their operations are aids to the human memory and imagina-tion.
§3.
The utility of mathematical method is purely relative, as is allutility. It helps greatly some persons, slightly others, is even ahindrance to some.
Before a schoolboy studies “ mechanics ” he is usually given inhis arithmetic problems of uniform motion. It would sorely puzzlehim if he were compelled to use the formula s = ut. The employ-ment of symbols has for him only disutility. But when in