Page:The Economic Journal Volume 1.djvu/444

 THE ECONOMIC JOURNAL Keynes has shown some partiality to the deductive school. He not only, after Mill, Cairnes, Professors Sidgwick, Dunbar, Wagner, and the majority of considerable writ'ers on the subject., extols deductive reasoning, but also, going beyond those writers, ranks high that species of deduction which is effected through the channels of mathematical conceptions. We submit, however, that this course is less prejudicial t'an may appear at first sight to the claims of the 'practicaIs,' as Hill calls the party opposed to the a priorists. The generalizations of mathematical theory, are so manifestly abstract and in so high a degree iiealized as to run no risk of having their hypothetical character mistaken. Unlike the middle axioms which are expressed in familiar terms, the higher theory, to which symbolic and diagrammatic state- ment is appropriate, cannot be suspected of being immediately applic- able to practice. The former statement might be compared to a district map which affords, indeed, some guidance to the wayfarer, but may easily lead him out of the path if not supplemented by local inquiry. Whereas the mathematical method is like the map of a kingdom or the world; the pedestrian who attempted to guide his steps by such a chart would be not only a wayfaring man, but a fool. These reflections have been suggested to us by some remarks made by Professor Foxwell, to which Mr. Keynes refers with approbation. That Mr. Keynes has no partial bias in fayour of mathematical reasoning may be inferred from the discussion of statistics in relation to political economy, which occupies his concluding pages. For he has not even alluded, so far as we have observed, to what may be called the mathematical method of statistics, the use of the theory of errors in eliminating chance. The omission may be justified partly by the fact that statistics are treated only incidentally in Mr. Keynes' work; partly on the tenable supposition that the higher mathematics play a more important part in what may be called the analytical, than the statistical, side of social science. It is true that, as Mr. Keynes points out, the '6/e of mathematical science in political economy is to afford only regulative ideas, rather than numerical results such as the physicist has a right to expect. But then, in political economy, that indirect use extends over a wide sphere, whereas the points in social statistics, where the mathematical method is applicable, are compara- tively few. For it is generally better to attain certainty by augmenting observations, rather than by a nice use of the theory of errors to extract the utmost degree of probable evidence which may be afforded by a limited number of observations. The statistician is generally in the position of the American farmer, whom it pays better to extend his farm rather than to cultivate very highly a comparatively few acres. Mr. Keynes seems, therefore, justified in directing his attention to the logical, rather than the mathematical side of statistics. He gives useful instances of the fallacies to which induction, based upon figures, is liable. what the late Mr. Sargant emphatically called ' the lies of statistics.' This part of the work should be read in connection with the rcmarks