第77章 Chapter V(53)

Augustin Cournot (18011877)appears to have been the first (72)who，with a competent knowledge of both subjects，endeavoured to apply mathematics to the treatment of economic questions.His treatise entitled Recherches sur les PrincipesMathématiques de La Théorie des Richesses was published in 1838.He mentions in it only one previous enterprise of thesame kind (though there had in fact been others)that，namely，of Nicolas Fran?ois Canard，whose book，published in 1802，was crowned by the Institute，though "its principles were radically false as well as erroneously applied."NotwithstandingCournot's just reputation as a writer on mathematics，the Recherches made little impression.The truth seems to be that hisresults are in some cases of little importance，in others of questionable correctness，and that，in the abstractions to which hehas recourse in order to facilitate his calculations，an essential part of the real conditions of the problem is sometimesomitted.His pages abound in symbols representing unknown functions，the form of the function being left to be ascertainedby observation of facts，which he does not regard as a part of his task，or only some known properties of the undeterminedfunction being used as bases for deduction.Jevons includes in his list of works in which a mathematical treatment ofeconomics is adopted a second treatise which Cournot published in 1863，with the title Principes de La Théorie desRichesses .But in reality，in the work so named，which is written with great ability，and contains much forcible reasoning inopposition to the exaggerations of the ordinary economists，the mathematical method is abandoned，and there is not analgebraical formula in the book.The author admits that the public has always shown a repugnance to the use ofmathematical symbols in economic discussion，and，though he thinks they might be of service in facilitating exposition，fixingthe ideas，and suggesting further developments，he acknowledges that a grave danger attends their use.The danger，according to him，consists in the probability that an undue value may be attached to the abstract hypotheses from which theinvestigator sets out，and which enable him to construct his formulae.And his practical conclusion is that mathematicalprocesses should be employed only with great precaution，or even not employed at all if the public judgment is against them，for "this judgment，"he says，"has its secret reasons，almost always more sure than those which determine the opinions ofindividuals."It is an obvious consideration that the acceptance of unsound or one-sided abstract principles as the premises ofargument does not depend on the use of mathematical forms，though it is possible that the employment of the latter may byassociation produce an illusion in favour of the certainty of those premises.But the great objection to the use of mathematicsin economic reasoning is that it is necessarily sterile.If we examine the attempts which have been made to employ it，weshall find that the fundamental conceptions on which the deductions are made to rest are vague，indeed metaphysical，in theircharacter.Units of animal or moral satisfaction，of utility，and the like，are as foreign to positive science as a unit ofnormative faculty would be；and a unit of value，unless we understand by value the quantity of one commodity exchangeableunder given conditions for another，is an equally indefinite idea.Mathematics can indeed formulate ratios of exchange whenthey have once been observed；but it cannot by any process of its own determine those ratios，for quantitative conclusionsimply quantitative premises，and these are wanting.There is then no future for this kind of study，and it is only waste ofintellectual power to pursue it.But the importance of mathematics as an educational introduction to all the higher orders ofresearch is not affected by this conclusion.The study of the physical medium，or environment，in which economicphenomena take place，and by which they are affected，requires mathematics as an instrument；and nothing can ever dispensewith the didactic efficacy of that science，as supplying the primordial type of rational investigation，giving the livelysentiment of decisive proof，and disinclining the mind to illusory conceptions and sophistical combinations.And a knowledgeof at least the fundamental principles of mathematics is necessary to economists to keep them right in their statements ofdoctrine，and prevent their enunciating propositions which have no definite meaning.Even distinguished writers sometimesbetray a serious deficiency in this respect；thus they assert that one quantity"varies inversely as "another，when what ismeant is that the sum (not the product)of the two is constant；and they treat as capable of numerical estimation the amountof an aggregate of elements which，differing in kind，cannot be reduced to a common standard.As an example of the lattererror，it may be mentioned that "quantity of labour，"so often spoken of by Ricardo，and in fact made the basis of his system，includes such various species of exertion as will not admit of summation or comparison.