I 



TRANSACTIONS OF SUCTION F. 681 



emphatically all sympathy with the flagrant abuses to which the injudicious use of 

 abstract reasouing is undoubtedly liable. 



To continue the comparison which I was institutinj' between the mathematical 

 theory of Economics and the Calculus of Probabilities, they have one very un- 

 pleasant property in common — a liability to slips. As De Morgan says,' ' Every- 

 body makes errors in Probabilities at times, and big ones.' He goes on to mention 

 a mistake committed by both Laplace and Poisson, the ineptitude of which he 

 can only parallel by the reasoning of a little girl whom he had called a ' daughter of 

 Eve ' ; to which she retorted, ' Then you must be a daughter of Adam.' It is not 

 to be concealed that economic reasoning, even in its severest form, is sometimes 

 equally inconsequent. I should have hesitated to assert that Cournot has made 

 some serious mistakes in mathematics applied to Political Economy, but that 

 the authority of the eminent mathematician Bertrand'^ may be cited in support 

 of that assertion. 



Again, the more abstract theories of Value and of Probabilities seem to re- 

 semble each other in their distance from the beaten curriculum. Each forms, as 

 it were, a little isolated field on the rarely crossed frontier and almost inaccessible 

 watershed between the moral and the physical sciences. 



The same character of remoteness belongs perhaps to another province, which 

 is also comparable with ours — the mathematical side of Formal Logic, the symbolic 

 Laws of Thought which Boole formulated. There was a certain congruity between 

 Jevons's interest in his logical machine and in what he called the * Mechanics of 

 Industry.' But I venture to regard the latter pursuit as much more liberal and 

 useful than any species of syllogism-grinding. 



If you accept these parallels, you will perhaps come to the conclusion that the 

 mathematical theory of Political Economy is a study much more important than 

 many of the curious refinements which have occupied the ingenuity of scientific 

 men ; that as compared with a great part of Logic and Metaphysics it has an intimate 

 relation to life and practice ; that, as a means of discovering truth and an educa- 

 tional discipline, it is on a level with the more theoretical part of Statistics ; while 

 it falls far short of Mixed Mathematics in general in respect of that sort of pre- 

 established harmony between the subject-matter and the reasoning which makes 

 Mathematical Physics the most perfect type of applied science. 



But we must remember — and the mention of the Theory of Probabilities may 

 remind us — that any such judgment is liable to considerable error. We cannot 

 hope to measure the utility of a study with precision, but rather to indicate the 

 estimate on either side of which competent judges -n-ould diverge— a central 

 point, which will be found, if I mistake not, equally removed from the position of 

 Goasen, who compares the new science to astronomy, and the attitude of Dr. Ingram 

 towards the researches which he regards as nothing more than ' academic play- 

 things, and which involve the very real evil of restoring the metaphysical entities 

 previously discarded.' ■' 



One more general caution is suggested by another of the technical terms which 

 we have employed. What we are concerned to discover is not so much whether 

 mathematical reasoning is useful, but what is its ' final utility ' as compared with 

 other means of research. It is likely that a certain amount of mathematical 

 discipline — say as much as Mr. Wicksteed imparts in his excellent ' Alphabet of 

 Economic Science' — is a more valuable acquisition to a mind already stored with 

 facts than the addition of a little more historical knowledge. 



But, in reverting to the subject of final utility, I am reminded that Presidential 

 Addresses, like other things, are subject to this law ; and that a discourse on 

 method prolonged beyond the patience of the hearers is apt to become what Jevona 

 called a discommodity. 



' Writing to Sir W. R. Hamilton {Life of Hamilton, by R. Grave.s, vol. iii.) 



- Journal de» SavanU, 1883. I hope to show on some future occiusion that M. 



Bertrand's censures of Cournot and Professor Walras are far too .severe. 



' See the passage relating to Jevoui in the article on Political Economy in the 



Encyclopcedia Britannica, 9th edition. 



