J 18 Inriny jF'isher—Mathematical investiyations

they have once been observed; but it cannot by any process of itsown determine those ratios; for quantitative conclusions imply quan-titative premises and these are wanting. There is then no futurefor this kind of study, and it is only waste of intellectual power topursue it.” [What a “therefore”! Why require mathematics topredict prices in order to be admitted into good society with the his-torical school ? No mathematical economist has ever tried to dothis. Dr. Ingram does not discuss what mathematics has done orattempted, but complains loudly that it cannot do everything andtherefore has no future.]

Rabberio* in speaking of Prof. Pantaleoni’s Principi di EconomiaPura says: “As a monument of abstract logic, it bears fresh witnessto the unusual qualities of the author’s genius; but it is based on amethod which, frankly speaking, I consider dangerous. In the faceof pressing practical problems of every kind, both in production andin distribution, economic thought is drawn off into the field of bar-ren abstractions. Under an attractive semblance of mathematicalaccuracy these abstractions conceal much that is really false; forthey do not correspond in the least to the complexity of concretefacts. While they distract the student with an imaginary logicalconstruction, they lessen his interest in that positive study whichtells us what is, whereas logic by itself gives us only what isthought. Thus in last result they deprive*economic science of thatgreat practical importance which it should have in society.” [I amnot acquainted with Prof. Pantaleoni’s book nor with any Italianwriter. As to the criticism on mathematical method, however, Imay say that experience in other sciences shows that “ in face ofmany practical problems” it is wisest to “drawoff thought” for atime to pure theory. Before solving the problems of cannon pro-jectiles it is best to solve the problem of projectiles in general.Before an engineer is fit to build the Brooklyn bridge or to pro-nounce on it after it is built it is necessary to study mathematics,mechanics, the theory of stress and of the natural curve of a hang-ing rope, etc., etc. So also before applying political economy torailway rates, to the problems of trusts, to the explanation of somecurrent crisis, it is best to develop the theory of pol. econ. in general.When these special “practical problems” are examined the mathe-matical instrument will, I believe, often be the one to get the bestresults.

I am far from denying, however, that some mathematical econo-mists have exhibited a “false accuracy.” It has been due to

* Economics in Italy , Prof. Ugo. Eubberio, Pol. Sei. Quart., Sept. 1891, p. 462.