[An Introduction to Philosophy by George Stuart Fullerton]@TWC D-Link bookAn Introduction to Philosophy CHAPTER VI 10/27
We cannot say, for example, that, when the point has moved over one half, one fourth, and one eighth of the line, it has completed its motion.
If even a single member of the series is left out, the whole line has not been passed over; and this is equally true whether the omitted member represent a large bit of line or a small one. The whole series, then, represents the whole line, as definite parts of the series represent definite parts of the line.
The line can only be completed when the series is completed.
But when and how can this series be completed? In general, a series is completed when we reach the final term, but here there appears to be no final term.
We cannot make zero the final term, for it does not belong to the series at all. It does not obey the law of the series, for it is not one half as large as the term preceding it--what space is so small that dividing it by 2 gives us [omicron]? On the other hand, some term just before zero cannot be the final term; for if it really represents a little bit of the line, however small, it must, by hypothesis, be made up of lesser bits, and a smaller term must be conceivable.
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