stration of ethics was a task ready-laid to his hand. Locke had given one hint of the precise way in which the mathematical method might be applied. For Locke, "Certainty is but the agreement or disagreement of our ideas, and demonstration nothing but the perception of such agreement by the intervention of other ideas or mediums."[1] Now in mathematics algebra had been of use in supplying these intermediate ideas, and Locke thinks that by applying a kind of algebra in ethics a demonstrably certain system will be produced. Berkeley was not slow to fasten on this hint. "N. B." he says in the Commonplace Book, "to consider well what Locke saith concerning Algebra—that it supplies intermediate ideas. Also to think of a method affording the same use in morals, etc., that this doth in mathematics."[2] Berkeley was keenly interested in algebra (cf. the many references in the Commonplace Book, and the article "De Ludo Algebraico" (1707) in Miscellanea Mathematical). Algebra is itself a department of pure mathematics, for algebra deals with signs abstracted from the things signified. But the algebra of ethics would be a branch of applied mathematics. Thus "Morality may be demonstrated as mixt Mathematics."[3]
Berkeley never worked out his algebra of ethics.[4] But he
- ↑ Essay, IV, iv, 7.
- ↑ Commonplace Book, I, p. 40.
- ↑ Ibid., I, p. 46.
- ↑ It is noteworthy that nearly every philosopher of the seventeenth century believed in a mathematical treatment of ethics. There is, of course, Spinoza's Ethica Ordine Geometrico Demonstrata. In the Ethica of Geulinex there are many suggestions of the applicability of mathematics to morals. And Leibniz also holds that it may be convenient to treat ethics by the geometrical method. (Nouveaux Essais, III, xi, 17 and IV, xii, 8). In England, as Professor Gibson has pointed out (Mind, 1896), Cumberland, in addition to Locke, held this view. It is also present in Hobbes. There are probably two main reasons for the prevalence of the view at the time:—(i) So long as Scholasticism held the field, the validity of ethical criteria rested ultimately on the authority of the Church. But with the coming of the Renaissance and the Reformation, the problem of the authority of the moral standard became a very real one. How was moral heterodoxy to be met? To this question there were two answers. Ethics must again become theological. Or ethics must become mathematical. These were the only alternatives. Therefore those who, for any reason, disliked the idea of a theological ethics, or considered it philosophically inadequate, were driven to attempt to demonstrate ethics mathematically. For the philosophers of the seventeenth century as a whole, science means nothing but mathematics and mathematical physics. When the seventeenth"
