in the theory of value and prices. 117 



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 how 

 this conclusion can be avoided." [There are examples in Cournot, 

 Walras, Auspitz und Lieben, Marshall, etc., which T think are fair 

 instances of the "production of an economic truth, not before 

 known." It is admitted, however, that each of these truths could 

 have been discovered without " mathematical method " by some 

 remarkably clear headed reasoner. B^it the same is true in physics. 

 The deduction used in every physical truth could be reasoned out 

 without diagrams or formulae. A railway will best convey a man 

 from New York to San Francisco though it is perfectly possible to 

 walk. Cairnes certainly has an erroneous idea of the use of mathe- 

 matical method in physical investigations. Mathematics afford the 

 physicist a complete and precise view of his subject, and this con- 

 dition of mind permits and facilitates his discovery. The discovery 

 is only indirectly due to mathematics though it might never have 

 been made without it. Cairnes apparently thinks that physical truth 

 has been discovered by the manipulation of equations. The history 

 of 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 the 

 quotation from Peirce at the beginning of this appendix.] 



W(cgne7'* [in reviewing Marshall's Prin. of Econ.]: "I do not 

 believe that this mode of treating the subject has an independent 

 value of its own for solving our problems. Indeed Marshall himself 

 admits as much [does he ? Cf. preceding statement of Marsliall.] 

 * * * He has used diagrams and formulae only for purposes of 

 illustr9.tion and for greater precision of statement." [Diagrams and 

 formulae are never used for any other purpose yet they surely have 

 an independent value in (say) physics. Cf. § 1.] 



Ingram :\ " There is not much encouragement to pursue such 

 researches, which will in fact never be anything more than academic 

 playtlungs, and which involve the very real evil of restoring the 

 metaphysical entities previously discarded." Also,! " Units of animal 

 or moral satisfaction, of utility and the like are as foreign to positive 

 science as a unit of dormative faculty would be." [See Part I, Cli. 1 1. 

 Also:§ " Mathematics can indeed formulate ratios of exchange when 



^- Quart. Jour. Ec, April. '91, p. 837. 

 I Ency. Brit., 9th eel. Vol. xix, p. 899. 

 tEncy. Brit., 9th cd. Vol. xix, p. 8S(;. 

 SHiHt. Pol. Econ., New )m-k, 1888, p. 182. 



