in the theory of value and prices.
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shown either that mental feelings admit of being expressed in pre-cise quantitative forms, or, on the other hand, that economic phe-nomena do not depend upon mental feelings, I am unable to see howthis conclusion can be avoided.” [There are examples in Cournot ,Walras , Auspitz und Lieben, Marshall, etc., which I think are fairinstances of the “ production of an economic truth, not beforeknown.” It is admitted, however, that each of these truths couldhave been discovered without “ mathematical method ” by someremarkably clear headed reasoner. But the same is true in physics.The deduction used in every physical truth could be reasoned outwithout diagrams or formulae. A railway will best convey a manfrom New York to San Francisco though it is perfectly possible towalk. Cairnes certainly has an erroneous idea of the use of mathe-matical method in physical investigations. Mathematics afford thephysicist a complete and precise view of his subject, and this con-dition of mind permits and facilitates his discovery. The discoveryis only indirectly due to mathematics though it might never havebeen made without it. Cairnes apparently thinks that physical truthhas been discovered by the manipulation of equations. The historyof physics will not bear him out. So far as I know only one physi-cal discovery was made in that way—a discovery in light. See thequotation from Peirce at the beginning of this appendix.]
Wagner* [in reviewing Marshall’s Prin. of Econ.]: “I do notbelieve that this mode of treating the subject has an independentvalue of its own for solving our problems. Indeed Marshall himselfadmits as much [does he ? Cf. preceding statement of Marshall.]* * * He has used diagrams and formulae only for purposes ofillustration and for greater precision of statement.” [Diagrams andformulae are never used for any other purpose yet they surely havean independent value in (say) physics. Cf. § 1.]
Ingram :f “ There is not much encouragement to pursue suchresearches, which will in fact never be anything more than academicplaythings, and which involve the very real evil of restoring themetaphysical entities previously discarded.” Also,]; “ Units of animalor moral satisfaction, of utility and the like are as foreign to positivescience as a unit of dormative faculty would be.” [See Part I, Ch. I],Also:§ “ Mathematics can indeed formulate ratios of exchange when