in ethics we have "real knowledge." He gives two examples of sciences in which we have this "real knowledge," (i) mathematics, (ii) ethics. Both these sciences consist of perfectly demonstrable propositions. Both are concerned, not with simple ideas, which always imply as their archetypes external things, but with complex ideas, which are their own archetypes. Both deal with those abstract ideas which Locke calls "mixed modes and relations." The mathematician considers the properties of the triangle as abstract ideas. The idea of a triangle is so framed as to make it possible that a 'real' concrete triangle should conform to it. But whether such a 'real' triangle exists is irrelevant to the mathematician. Similarly, in ethics we deal only with abstract ideas. Ethics is a purely abstract science. To the moral philosopher it is of no moment whether a concrete just act anywhere exists.[1] Mathematics and ethics are both demonstrated on the basis of certain definitions and axioms. Between moral ideas there are the same necessary relations as hold between mathematical ideas. "I doubt not but from self-evident propositions by necessary consequences as incontestable as those in mathematics the measures of right and wrong might be made out."[2]
Locke never altogether abandoned his belief in a mathematically demonstrated science of ethics,[3] though he came to feel less and less able to demonstrate it himself. This is clear both from the changes which he introduced in the fourth edition of the Essay,[4] and from his correspondence with Molyneux. Molyneux repeatedly requested him "to oblige the world with a treatise of morals ... according to the mathematical method." Locke replied (September 20, 1692) expressing distrust in his own ability for the task; but promising to consider it. Nearly four years later he finally declined to undertake it.
It is thus not strange that Berkeley, already keenly interested in mathematics, should have felt that the mathematical demon-
