237 r. The Achilles argument is so named because Achilles is named in it as the example, and the argument shows that if he pursued a tortoise it would be impossible for him to overtake it. 255 r. Aristotle accordingly solves the problem of Zeno the Eleatic, which he propounded to Protagoras the Sophist.[68] Tell me, Protagoras, said he, does one grain of millet make a noise when it falls, or does the ten-thousandth part of a grain? On receiving the answer that it does not, he went on: Does a measure of millet grains make a noise when it falls, or not? He answered, it does make a noise. Well, said Zeno, does not the statement about the measure of millet apply to the one grain and the ten-thousandth part of a grain? He assented, and Zeno continued, Are not the statements as to the noise the same in regard to each? For as are the things that make a noise, so are the noises. Since this is the case, if the measure of millet makes a noise, the one grain and the ten-thousandth part of a grain make a noise. (_b_) ZENO’S ARGUMENTS AS DESCRIBED BY ARISTOTLE. _Phys._ iv. 1; 209 a 23. Zeno’s problem demands some consideration; if all being is in some place, evidently there must be a place of this place, and so on indefinitely. 3; 210 b 22. It is not difficult to solve Zeno’s problem, that if place is anything, it will be in some place; there is no reason why the first place should not be in something else, not however as in that place, but just as health exists in warm beings as a state while warmth exists in matter as a property of it. So it is not necessary to assume an indefinite series of places. vi. 2; 233 a 21. (Time and space are continuous ... the divisions of time and space are the same.) Accordingly Zeno’s argument is erroneous, that it is not possible to traverse infinite spaces, or to come in contact with infinite spaces successively in a finite time. Both space and time can be called infinite in two ways, either absolutely as a continuous whole, or by division into the smallest parts. With infinites in point of quantity, it is not possible for anything to come in contact in a finite time, but it is possible in the case of the infinites reached by division, for time itself is infinite from this standpoint. So the result is that it traverses the infinite in an infinite, not a finite time, and that infinites, not finites, come in contact with infinites.