the total line represents the total duration, the parts of the line must, it seems, correspond to parts of the duration, and the points of the line to moments of time. The indivisibles of duration, or moments of time, are born, then, of the need of symmetry; we come to them naturally as soon as we demand from space an integral presentment of duration.—But herein, precisely, lies the error. While the line AB symbolizes the duration already lapsed of the movement from A to B already accomplished, it cannot, motionless, represent the movement in its accomplishment nor duration in its flow. And from the fact that this line is divisible into parts and that it ends in points, we cannot conclude either that the corresponding duration is composed of separate parts or that it is limited by instants.
The arguments of Zeno of Elea have no other origin than this illusion. They all consist inZeno transfers to the moving body the properties of its trajectory: hence all the difficulties and contradictions making time and movement coincide with the line which underlies them, in attributing to them the same subdivisions as to the line, in short in treating them like that line. In this confusion Zeno was encouraged by common sense, which usually carries over to the movement the properties of its trajectory, and also by language, which always translates movement and duration in terms of space. But common sense and language have a right to do so
