[CHAPTER XIX.]
SUMMING UP.
149. The examination of the idea of the infinite is of the greatest importance, because it is inseparably united with the idea of God.
150. We have the idea of the infinite; but the disputes concerning its nature, and even its existence, denote its obscurity.
151. The finite is that which has limits.
152. The infinite is not the same as the indefinite. The infinite is that which has no limits—the not-finite; the indefinite is that to which no limits are assigned—the not-defined.
153. The difference between the infinite and the finite is founded on the principle of contradiction: the finite affirms limits; the infinite denies them: there is no medium between yes and no.
154. Limit is the negation of a being, or of something real, applied to a being: the limit of a line is the point which terminates it; the limit of a force is the point beyond which it does not extend.
155. The idea of the infinite, denying limit, denies a negation; therefore it is an affirmative idea: the idea of the finite is negative, because it affirms a negation.
156. The idea of the infinite is applied to many orders of beings, and presents strange anomalies, which seem contradictions. A line produced to infinity in only one direction appears infinite, since it is greater than all finite lines; and it is not infinite, because it has a limit in the point where it starts. The same thing is verified in surfaces and solids. To explain these anomalies we must attend to the following observations.