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. 157. The idea of the infinite is not intuitive. We have no intuition of an object either absolutely or relatively infinite. 158. The idea of the infinite is an indeterminate conception formed by the union of the two indeterminate ideas of being in general, and the negation of limit in general. 159. The indeterminate conception of the infinite gives us no knowledge of any thing infinite. 160. The anomalies and apparent contradictions, which we find in the application of the idea of the infinite, vanish when we reflect that the difference of the results depends on the different conditions under which we apply the idea of the infinite. Things which would be infinite under one condition cease to be so when considered under other conditions: the apparent contradiction is caused by one not remarking the change of conditions. 161. We have the conception of infinite number, for we can unite in our mind the two indeterminate conceptions of number and the negation of limit. 162. We have the conception of infinite extension, for we can unite the two indeterminate ideas of extension and the negation of limit. 163. The possibility or non-contradiction of conceptions in the purely ideal order does not prove their possibility in the real order. When the conceptions are realized, their reality is not in an abstract extension or an abstract number, but in individual extended beings, or individual numbers: the determinateness implied by the reality may involve contradiction to the true infinity, although it be impossible for us to discover any contradiction in the indeterminate conception, which abstracts the conditions of their realization. 164. Although we have the conception of infinite extension, it is impossible for us to imagine it. 165. No extrinsic or intrinsic repugnance can be discovered in the existence of infinite extension. 166. We cannot know by purely philosophical means whether the extension of the universe is infinite or finite. 167. Although an absolutely infinite number may be indeterminately conceived, it is not susceptible of any arithmetical or geometrical expression: no series of what mathematicians call infinite expresses an absolutely infinite number. 168. The intrinsic impossibility of an _actual_ infinite number may be demonstrated from the intrinsic repugnance of the _co-existence_ of certain things which may be _numbered_. 169. The idea of the absolutely infinite real being cannot be indeterminate: it necessarily involves positive and formal perfections.