680 BEPORT— 1889. 



amount of regression, or reversion, in children compared with parents, and other 

 relationships. 



But, beyond the isolated instances in which the theory of 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. Gallon 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 mathe- 

 matics.' 



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 witliin which our special subject is included — 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 parti- 

 cular 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 hut 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 abstraction 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 

 repeat 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 

 economist is concerned to separate his method from that mathematical and meta- 

 physical reasoning which Burke repudiates as inapplicable to human affairs ; from 

 that abstract method which he has in view when he says : — ' The geometricians 

 . . . bring from the dry bones of their diagrams . . . dispositions that make them 

 worse than indifferent about those feelings and habitudes which are the supports 

 of the moral world.' ^ Burke is referring to the Jacobin philosophers ; but our 

 withers 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 popularly sus- 

 pected of complicity with crime, would do well to take every opportunity of clearing 

 themselves from that imputation, so the mathematical economist is called on to disown 



' In his important letter on 'The Economic Movement in England' in the Qxiarterly 

 Journal of Economics for October 1888. 



- Cf. Prof. Foxwell, loc. cit. ' What the new school protest against is first the un- 

 scientific and meagre way in which deduction was used. In their view, though it is 

 worth 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 . . .' 



^ Letter to a noble Lord. 



