112 Irving Fishei—Mathematical investigations

Mathematical method is making a new set of classifications basedon mathematical properties. Thus the classification by Auspitz undLieben of all commodities into three groups* * * § is, I believe, a newone, and one suggested by, and readily discussed by the use of theirdiagrams. The classification of capital into free and sunk is onewhich is emphasized by the mathematical writers, as Marshall, andis bearing fruit.f

I believe therefore that mathematical method has made severalreal contributions to economics, and that it is destined to make more.To verify this statement I would refer the reader to the books men-tioned in the bibliography among recent writers, especially Walras, Auspitz & Lieben, Marshall, Pidgeworth, Wicksteed and Cunyng-hame ; also, if it is proper to include those writers, who whileavoiding mathematical language are interpreting and extendingthe same ideas, Menger, Wieser, Bohm-Bawerk, Clark and Hobson.

It may not be amiss.to present a list of quotations from those whohave pursued or admired the mathematical path :

Whewell\ says : [Mathematical method in mechanics saves scien-tists three errors, viz :] “ They might have assumed their principleswrongly, they might have reasoned falsely from them in conse-quence of the complexity of the problem, or they might haveneglected the disturbing causes which interfered with the effect ofthe principal forces. * * * It appears, I think, that the sciences ofmechanics and political economy are so far analogous that some-thing of the same advantage may be looked for from the applicationof mathematics in the case of political economy.” Again :§ “Thismode of treatment might be expected to show more clearly thanany other within what limits and under what conditions propositionsin political economy are true.”

Cournot :|| L’emploi des signes math6matiques, est chose naturelletoutes les fois qu’il s’agit de discuter des relations entre des gran-deurs ; et lors m§me qu’ils ne seraient pas rigoureusement necess-aires, s’ils peuvent faciliter l’exposition, la rendre plus concise, mettresur la voie de ddveloppements plus etendus, prevenir les ecarts

* Page 46.

f See Cunynghame, Geom. Meth. of treating exchange value, monopoly, andrent. Econ. Jour., March, ’92, p. 35.

I Cambridge Philosophical Transactions, 1830, p. 194.

§ Cambridge Philosophical Transagtions, 1856, p. 1.

U Principes math, de la theorie des ricliesses, 1838. Preface,- p. viii.