knew not, and thus determinateness continually vanishes from his thought. f. In the sixth place, the definition of the infinite is also of importance, for in the infinite Spinoza defines more strictly than anywhere else the Notion of the Notion. The infinite has a double significance, according as it is taken as the infinitely many or as the absolutely infinite (_infra_, p. 263). “The infinite in its kind is not such in respect of all possible attributes; but the absolutely infinite is that to whose essence all belongs that expresses an essence and contains no negation.” In the same sense Spinoza distinguishes in the nine-and-twentieth Letter (Oper. T. I. pp. 526-532) the infinite of imagination from the infinite of thought (_intellectus_), the actual (_actu_) infinite. Most men, when they wish to strive after the sublime, get no farther than the first of these; this is the false infinite, just as when one says “and so on into infinity,” meaning perhaps the infinity of space from star to star, or else the infinity of time. An infinite numerical series in mathematics is exactly the same thing. If a certain fraction is represented as a decimal fraction, it is incomplete; ⅐ is, on the contrary, the true infinite, and therefore not an incomplete expression, although the content here is of course limited. It is infinity in the incorrect sense that one usually has in view when infinity is spoken of; and even if it is looked on as sublime, it yet is nothing present, and only goes ever out into the negative, without being actual (_actu_). But for Spinoza the infinite is not the fixing of a limit and then passing beyond the limit fixed—the sensuous infinity—but absolute infinity, the positive, which has complete and present in itself an absolute multiplicity which has no Beyond. Philosophic infinity, that which is infinite _actu_, Spinoza therefore calls the absolute affirmation of itself. This is quite correct, only it might have been better expressed as: “It is the negation of negation.” Spinoza here also employs geometrical figures as illustrations of the Notion of infinity. In his _Opera postuma_, preceding his Ethics, and also in the letter quoted above, he has two circles, one of which lies within the other, which have not, however, a common centre. [Illustration]