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ON THE USE OF THE DIFFERENTIAL CALCULUS IN ECONOMICS
TO DETERMINE CONDITIONS OF MAXIMUM ADVANTAGE
Description and Division.
The extension to Social Science of principles approved in Mathematical Physics is a theme worthy of «Scientia». For this journal, as announced at its inception, is «born of the desire to co-ordinate the work carried on in different fields of knowledge». Alone in a world of specialists it seems to realize that part of Plato’s scheme of education which consisted in bringing the sciences together and contemplating them in their mutual relations.
There is indeed a certain resemblance between the ancient philosophy and the modern study of Mathematical Psychics in so far as both attain large general views rather than particulars adapted to art and practice. But we are not committed to the contempt of fact which seems to characterise the Platonic precept that «in astronomy, as in geometry, we should employ problems, and let the heavens alone, if we would approach the subject in the right way»1 The Newtonian astronomy is rather the model of our Science; but we can only follow it at a great distance owing to the multiplicity of variables in Social Science and the want of a unit for measuring advantage in a subjective sense. Often we must be content with knowing that knowledge is unattainable without more data than we possess — the Socratic lesson of modesty which was taught by Cournot and Jevons2.
- Republic VII., 529, Jowett’s translation; a precept which Macaulay contrasts unfavourably with Bacon’s method.
- The use of Mathematics to make clear the nature and extent of the assumptions implied in dealing with economic problems has been noticed by Professor J. S. Nicholson in a recent lecture (Transactions of the Faculty of Actuaries. No, 35, Vol. I, Part IV.).