Early Work in Moral Philosophy

Edgeworth's first book, New and Old Methods of Ethics, published in 1877, was strongly influenced by the great Cambridge philosopher Henry Sidgwick. It examined in detail the implications of utilitarianism for optimal distribu­tion.

On considering the major fierce debates in the second half of the nine­teenth century between egoism, evolutionism, idealism and intuitionism, Edgeworth's brand of utilitarianism became extremely eclectic. It embraced the majority of other principles, except for those of the Hegelian idealists, while regarding utilitarianism as the “sovereign principle”. Writing of this book, Keynes (1933 [1972]: 257) commented that:

Edgeworth’s peculiarities of style, his brilliance of phrasing, his obscurity of con­nection, his inconclusiveness of aim, his restlessness of direction, his courtesy, his caution, his shrewdness, his wit, his subtlety, his learning, his reserve—all are there full-grown. Quotations from the Greek tread on the heels of the differen­tial calculus.

Edgeworth generally distinguished between “impure” and “pure” utilitari­anism. In the latter case, individuals are assumed to be concerned with the welfare of society as a whole. The former case in fact corresponds more closely with a short-term version of egoism. Economic exchange can usefully be ana­lysed in terms of “jostling egoists”, but he believed that ultimately individuals would evolve to become pure utilitarians. A reason for believing that indi­viduals would make such a transition was later to be developed by Edgeworth in the form of his contractarian justification of utilitarianism as the appropri­ate principle of distributive justice.

Edgeworth’s early utilitarianism was influenced by his wide knowledge of work in experimental psychology. In his books of 1877 and 1881, there are many references to the work of Joseph Delboeuf, Gustav Fechner, Hermann von Helmholtz, Ernst Weber and Wilhelm Wundt. These references occur in the context of the nature of utility functions and, although Edgeworth at this time was not aware of the earlier work of Stanley Jevons, the same range of work was also cited by Jevons. In 1877, Edgeworth explicitly suggested, in connection with Fechner, that an additive form would not be appropriate.

A further aspect of Edgeworth’s utilitarianism is his attitude towards author­ity. An important issue for early utilitarians involved the nature of inductive evidence about the consequences of acts. Most people cannot know the full consequences of their acts, so that rules of moral conduct must be followed (in contrast with intuitionism where individuals are assumed to have immedi­ate consciousness of moral rules). In arriving at such rules, the opinions of highly regarded individuals are taken to be credible even though it may not be possible to show conclusively that they are “correct”. Edgeworth argued, for example, that ‘we ought to defer even to the undemonstrated dicta and opin­ions of the wise, who have a power of mental vision acquired by experience’ (Edgeworth 1925, ii: 149).

Edgeworth defined the problem of determining the optimal utilitarian dis­tribution as follows: ‘[G]iven a certain quantity of stimulus to be distributed among a given set of sentients...to find the law of distribution productive of the greatest quantity of pleasure' (Edgeworth 1877: 43). In treating this prob­lem mathematically, he used Lagrange multipliers, without any explanation, and concluded that ‘unto him that hath greater capacity for pleasure shall be added more of the means of pleasure' (ibid.). In using Lagrange multipliers, Edgeworth was also careful to discuss possible complications, referring to the possibility of multiple solutions and explicitly discussing corner solutions and inequality constraints.

Further complexities were then examined, where Edgeworth emphasised that utilitarianism implies equality of the ‘means of pleasure' only under a special set of assumptions, and in the general case the prescribed solution will be some form of inequality. In a more general treatment of the problem, Edgeworth used the calculus of variations, but again provided the reader with virtually no help in following his mathematical argument. His analysis of the utilitarian optimal distribution was continued in his paper on “The Hedonical Calculus” (Edgeworth 1879), which was later reprinted as the third part of Mathematical Psychics (Edgeworth 1881).

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