All Zeno's arguments are based upon the one argument described above, which may be called the antinomy of infinite divisibility. For example, the story of the flying arrow. At any moment of its flight, says Zeno, it must be in one place, because it cannot be in two places at the same moment. This depends upon the view of time as being infinitely divisible. It is only in an infinitesimal moment, an absolute moment having no duration, that the arrow is at rest. This, however, is not the only antinomy which we find in our conceptions of space and time. Every mathematician is acquainted with the contradictions immanent in our ideas of infinity. For example, the familiar proposition that parallel straight lines meet at infinity, is a contradiction. Again, a decreasing geometrical progression can be added up to infinity, the infinite number of its terms adding up in the sum-total to a finite number. The idea of infinite space itself is a contradiction. You can say of it exactly what Zeno said of the many. There must be in existence as much space as there is, no more. But this means that there must be a definite and limited amount of space. Therefore space is finite. On the other hand, it is impossible to conceive a limit to space. Beyond the limit there must be more space. Therefore space is infinite. Zeno himself gave expression to this antinomy in the form of an argument which I have not so far mentioned. He said that everything which exists is in space. Space itself exists, therefore space must be in space. That space must be in another space and so _ad infinitum_. This of course is merely a quaint way of saying that to conceive a limit to space is impossible.