338 EOBEET LATTA : tion of an uncreated thing the rules are (1) that it should exclude all cause, i.e., that the object should need for its explanation no other thing besides its own being ; (2) given the definition there should remain no room for doubt whether the thing exists or not ; (3) it should contain no substantives which can be used as adjectives, i.e., the object denned should not be explained by abstractions and (4) we should be able to deduce all the properties of the thing from its definition. Now these rules are practically the same as those for the definition of a created thing. The first and second rules amount to saying that the proximate cause of the uncreated thing must be the thing itself, that it must be produced by no other thing. The fourth rule requires, as in the case of the created thing, that the idea be tested by its consequences, in other words, that the thing is real through its necessary relation to the whole system of things. The third rule is a caution against abstractions, which is equally applicable to the definition of a created thing, but is especially in point here, because in the definition of an uncreated thing proxi- mate cause becomes causa sui. If it had been possible, as in the case of the created thing, to refer the uncreated thing to something else necessarily presupposed in it, there would have been less danger of abstraction. As it is, it seems to me impossible to escape abstraction in the definition of an uncreated thing. The definition of a thing can only mean a statement of the relations of that thing within some system of which it is a member or element, and this is virtually acknowledged by Spinoza in his rules for the definition of a created thing. But if this is so, every definition must be adjectival, must be made up of abstractions. In other words, it is impossible to give a true definition of an uncreated thing, if by an uncreated thing is meant the universe, the system of reality itself, which is the presupposition of all definition. Yet Spinoza bases his philosophy upon the de- finition of an uncreated thing and believes that he has deduced all from this definition. Spinoza's imperfect recognition of the system which is presupposed in all demonstration appears to me to be due (in great part at least) to the way in which mathematical problems were regarded by him as by most of his contempo- raries. The ancient geometers found that there were many problems which could not be solved directly by the aid of Euclid's definitions and postulates. In plane geometi Euclid postulated the straight line and the circle. But many problems (such as that of the area of a circle or the relation of its radius to its circumference) depend for their exact
