500 



NATURE 



{Sept. 19, 1889 



we have seen that the mathematical method is likely to be 

 serviceable (see above, p. 49S). 



It is not to be supposed, however, that the work of our 

 Section is wholly destructive ; that like the islanders of whom 

 it was said that they earned a precarious livelihood by washing 

 one another's clothes, so we are occupied only in mangling each 

 other's theories. Like imprudent sectaries, by our mutual re- 

 criminations we have obscured the virtues common to our pro- 

 fession. What Jevons said of Cairnes, that his own opinions 

 were much more valuable than his objections against other 

 jieople's opinions, is true of Jevons himself and other controver- 

 sial economists. Now, this possibility of mutual misunderstand- 

 ing by persons who are both in the right is connected with a 

 circumstance which it is not irrelevant here to notice. It is that 

 in our subject, unlike physics, it is often not clear what is the 

 prime factor, what elements may be omitted in a first approxima- 

 tion. One writer on rent may emphasize distance from the 

 centres of population as the main attribute, and introduce fertility 

 of soil as a perturbation of the abstract result given by the 

 first view. Another fixes attention on the powers of the soil, 

 and allows for other elements, as for friction. So in the theory 

 of money, the state of credit or the quantity of metal have each 

 been regarded as the prime variable.^ It need not be pointed 

 out how unfavourable to exact science is such a state of the 

 subject-matter. Imagine an astronomer hesitating whether in 

 the determination of Jupiter's movements the sun or the planet 

 Saturn played the most important part. That is the condition 

 of many of our speculations. 



It will not be expected that from such materials any very ela- 

 borate piece of reasoning can be constructed. Accordingly 

 another point of contrast with mathematical physics is the brevity 

 of our calculations. The whole difficulty is in the statement of 

 our problems. The purely computative part of the work is in- 

 considerable. Scarcely has the powerful engine of symbolic 

 language been applied when the train of reasoning comes to a 

 stop. The case is like that of the swell in Punch, who, about 

 to enter a hansom, inquires solicitously of the driver whether he 

 has got a good horse. "Yes, sir; very good 'oss." "Aw — • 

 then dwive to next door." However, our road, though short, is 

 so slippery as to require every precaution. 



It follows that in economics, unlike physics, the use of 

 symbols may perhaps be dispensed with by native intelligence. 

 It must be admitted that the correct theory of value has been 

 rediscovered by Menger, and restated by his follower, Bohm- 

 Bawerk, without the explicit use of mathematics. Without the 

 law, they have done by nature the things contained under the 

 law. Still, under a higher dispensation, they might have at- 

 tained greater perfection. Nor can equal accuracy be ascribed 

 to all the followers of Menger. Nor is the terseness which 

 comes of mathematical study a characteristic of this Austrian 

 school {m). 



Another point of contrast between the mathematical science of 

 the physicist and the economist is that the former appeals to a 

 larger public. Mathematics is as it were the universal language 

 of the physical sciences. It is for physicists what Latin used to 

 be for scholars ; but it is unfortunately Greek to many econo- 

 mists. Hence the writer who wishes to be widely read — who 

 does not say, with the French author, ^^ J'imprifne pour moi" — 

 will do well not to multiply mathematical technicalities beyond the 

 indispensable minimum, which we have seen reason to suppose 

 is not very large. The parsimony of symbols, which is often an 

 elegance in the physicist, is a necessity for the economist. 

 Indeed, it is tenable that our mathematical constructions should 

 be treated as a sort of scaffolding, to be removed when the 

 edifice of science is completed. As Prof. Marshall, one of the 

 highest authorities on this subject, says : " When a man has 

 cleared up his mind about a difficult economic question by mathe- 

 matical reasoning, he generally finds it best to throw aside his 

 mathematics and express what he has to say in language that is 

 understanded of the people " {Acadetny, June 1881). Upon this 

 view mathematical discipline might be compared to grammar or 

 to the study of classical literature, which it is profitable to 

 have learnt thoroughly, while it is pedantic to obtrude one's 

 learning. 



From these considerations it may appear that our little branch 

 of science is of quite a rudimentary form. The solid structure 

 and regular ramifications of the more developed mathematical 



_ ^ Compare Cournot : "Ce que I'un neglige dans une premiere appraxima- 

 tion comme un fait secondaire et accessjire, un autre le regardsra comme le 

 fait principal ct dominant " (" Principes," book iv. chap. vii.). 



ciences are wanting. A less unfavourable contrast would be 

 presented if we compare! our method, not with applied mathe- 

 matics generally, but with that particular branuh of it which 

 comes nearest to ours in its proximity to human interests — the 

 use of the calculus of probabilities in social statistics. 



There is really only one theorem in the higher part of the 

 calculus, but it is a very difficult one, the theory of errors, or 

 deviation from averages. The direct applications of this theory 

 to human affairs are not very considerable. Perhaps the most 

 conspicuous example is afforded by an investigation to which, if 

 I had undertaken to review the woi'k done in our subject s during 

 the past year, I ought to have directed particular attention — Mr. 

 Galton's rigid proof of the fact and amount of regressitn, 

 or reversion, in children compared with parents, and other 

 relationships. 



But, beyond the isolated instances in vvrhich the theory ot 

 deviations is applied in social statistics with the same strictness 

 and cogency as in physics, there is a wide zone of cases in which 

 the abstract theory is of use as giving us some idea of the value 

 to be attached to statistical results. Mr. Galton justly complains 

 of the statisticians who "limit their inquiries to averages, and do 

 not revel in the more comprehensive views " of the deviations 

 from averages. " Their souls seem as dull to the charm of 

 variety as that of the native of one of our flat English counties, 

 whose retrospect of Switzerland was that, if its mountains could 

 be thrown into its lakes, two nuisances would be got rid of at 

 once." But great caution is required in transferring the theory 

 of errors to human affairs ; and the calculus of probabilities 

 may easily be made, in Mill's phrase, the "opprobrium of 

 mathematics." 



Now, in all these respects there is a considerable resemblance 

 between the higher parts of the two branches of science which 

 are cultivated in this Section. It may be said that in pure 

 economics there is only one fundamental theorem, but that is a 

 very difficult one : the theory of bargain in a wide sense. The 

 direct application of mathematical reasoning is, as we have seen, 

 limited — more limited, I think, than the corresponding function 

 of the higher statistics. But, on the other hand, the regulative 

 effect, the educational influence, of studies like those of Cournot 

 and Jevons are probably very extensive. 



How extensive, it would be difficult to decide without defining 

 the limits of a province within which our special subject is in- 

 cluded — the use of abstract reasoning in political economy. 

 Now, on this vexed question, and with reference to the heated 

 controversy between the historical and the deductive schools, 

 the mathematical economist as such is not committed to any 

 side. It may be dangerous to take wide general views ; it may 

 be better to creep from one particular to another rather than 

 ascend to speculative heights. Our only question here is 

 whether, if that ascent is to be made, it is better to proceed by 

 the steep but solid steps of mathematical reasoning, or to beguile 

 the severity of the ascent by the zigzag windings of the flowery 

 path of "literature. It is tenable that the former course is safest, 

 as not allowing us to forget at what a dangerous height of ab- 

 straction we proceed. As Prof. Foxwell has well said,^ with 

 reference to the mathematical methods in the hands of Jevons 

 and Prof. Marshall, "It has made it impossible for the educated 

 economist to mistake the limits of theory and practice, or to 

 i-epeat the confusions which brought the study into discredit and 

 almost arrested its growth." 



I trust that I have succeeded in distinguishing the question 

 what is the worth of abstract reasoning in political economy 

 from the much more easily answered question whether, if it is 

 worth doing, it is worth doing well.''' The mathematical econo- 

 mist is concerned to separate his method from that mathematical 

 and metaphysical reasoning which Burke repudiates as inapplic- 

 able to human affairs ; from that abstract method which he has 

 in view when he says : — "Nothing can be more hard than the 

 heart of a thoroughbred metaphysician. It comes nearer to the 

 cold malignity of a wicked spirit than to the frailty and passion 

 of a man " (" Letters on a Regicide Peace "). Burke is referring 

 to the Jacobin philosophers ; but our witliers are unwrung, if 

 similar words should be applied to some of the "sophisters and 

 economists " of a later generation. Just as a political party, if 



' In his imporfant letter on " The Economic Movement in England" in 

 the Quarterly Journal of Economics for October 1888. 



^ Cf. Prof. FoxwmH. loc. cit.\ — 'What the n iw school protest against is first 

 the unscientific and meagre way in which deduction was used. In their view, 

 though it IS wvrth while to study, and therefore worth while to study 

 accurately, the workings of private interest under a system of competition, 

 yet human nature is not all self-interest. ..." 



