668 TRANSACTIONS OF SECTION F. 



economists, and who have no leisure to keep themselves abreast of the newest 

 modes of professorial expression. Now it is of the highest importance that we 

 should do everything to encourage and nothing to deprive ourselves of this 

 criticism, which is essential in order to keep economic thought sane and sound 

 and in touch with realities. On all grounds it would be deplorable if through 

 the obscurity of its language economic science should relapse into the position of 

 an esoteric doctrine confined to a small circle of initiates, only the bare results 

 of which are capable of dogmatic statement to the outside world. Not only is 

 the doctrine unlikely to be accepted on these terms, but, being ex hypothesi a 

 doctrine elaborated in the closet by experts without contact with the fresh 

 breezes of everyday business experience, it is quite certain to suffer in balance 

 and proportion and reality, and in all that gives it value to the world. 



Of course the vast bulk of public criticisms and suggestions on technical 

 projects or scientific theories are shallow, irrelevant, and futile. But even though 

 there be 99 per cent, of chaff, the odd 1 per cent, of grain may well be priceless. 

 Now I would say very seriously that it is of the highest importance to our 

 science not to be cut off by any barrier of unintelligible phraseology from the 

 advantage of the co-operation, whether by criticism or suggestion, of that great 

 body of persons who, while not professional economists, are practical experts in 

 one or other of the branches of economic knowledge. 



What I have said with regard to the use of special technical phraseology in 

 economic reasonings intended for the eye of the general reader applies of course 

 with special force to the use of mathematical symbols and modes of expression. 

 I do not think that either by taste or training I am likely to underrate the value 

 of mathematical methods in elucidating economic problems. The essentially 

 mathematical conception of functions and mutually dependent variables offers 

 incomparably the most powerful and appropriate method of expressing the inter- 

 relations among such economic phenomena as rent, interest, price, wages, product, 

 and capital. Moreover, the apparatus of the infinitesimal calculus affords the 

 only satisfactory mode of representing and analysing continuous economic changes. 

 Ordinary verbal argument on complicated questions (say) of international values 

 or of the ultimate incidence of taxation, can hardly go beyond the analysis of 

 certain particular cases of discontinuous changes selected for purposes of 

 illustration. 



Nevertheless, I trust that those who recognise with me the value of 

 mathematical modes of expression will be extremely careful to restrict mathe- 

 matical language to the pages of technical economic journals or the footnotes 

 and appendices of more popular treatises, and to re-state all the conclusions 

 arrived at by this means, with at least an outline of the arguments which lead 

 to them, in ordinary language free from technical symbols. 



The last-mentioned condition is, I think, important, not merely for the reasons 

 vvhich I have already given, but for another which applies peculiarly to mathe- 

 matical arguments. Before starting our mathematical analysis we are bound, of 

 course, to define very precisely the meaning of the quantities which the symbols 

 express, and this in itself is very salutary, for it compels us to recognise frankly 

 the hypotheses on which our argument will depend. But when the mathematical 

 process has once begun we very quickly lose sight of the economic contents of the 

 symbols. As the school-girl in the examination said : ' Algebraical symbols are 

 what you use when you don't know what you are talking about.' Now from the 

 point when we lose sight of the economic significance of our symbols we lose the 

 means of applying the check of common-sense to the intermediate stages of our 

 analysis, and we do not recover this power of criticism until the final results 

 emerge and are interpreted in ordinary language. Between the points at which 

 our economic assumptions are translated into mathematical formula and our 

 ultimate results are re-translated into ordinary language, there is nothing to 

 enable us to take stock of the position and to warn us of the direction in which we 

 may be drifting. 



Another tendency which I see in economic research is to attach increasing 

 importance to quantitative measurement with the aid of the separate though 

 auxiliary science of statistics. 



This is a tendency which is wholly welcome and which is likely to become of 

 increasing importance in the immediate future. Like all salutary movements ifc 



