[38] See Chap. V. 60. The anomalies, or, rather, the contradictions which we seem to find in the applications of the idea of the infinite, when any thing is presented to us as infinite which we afterwards discover not to be so, originate in the application of this idea under different conditions. This variety would not be possible if the idea represented any thing determinate; but as it only contains the negation of limit in general joined to being in general, it follows that we subject this negation to particular conditions in each case, and therefore when we pass to other conditions, the general idea cannot give us the same result. 61. A line drawn from the point where we are situated in the direction of the north, and produced infinitely, gives us an infinite and a not-infinite. This contradiction is only apparent; there is really only the difference of result caused by the condition under which the general idea is applied. When we consider a line infinitely produced towards the north, we do not apply the idea of the infinite to a lineal value in the abstract, but to a right line starting from a point and produced only in one direction. The result is what it should be. The negation of limit is affirmed under a condition; the infinite which results is subject to that condition. It may be said that there is no medium between the infinite and the not-infinite; but it is easy to solve this difficulty, if we observe that yes and no, to be contradictory, must be referred to the same thing, which is not the case when the conditions of the object are changed. 62. If instead of a line produced in one direction only, we had wished to apply the negation of limit to a right line in general, it is evident that we should have been obliged to produce the line in the two opposite directions: which would have given us another infinite under a new condition. We have before seen that not even in this case can we have a lineal value strictly infinite; because this right line only forms a part of the sum of lines which we can imagine. Is it then infinite, or is it not? It is both, if we make the proper distinction. It will be infinite, or we shall have the idea of infinity or negation of limit, applied to a right line _alone_; but if instead of one _right line alone_, we take a lineal value, without any condition, the supposed line will not be infinite; the negation of the limit is not applied under that condition; the result must therefore be different.