Vitae philosophorum

For when once we have said that an infinite number of particles, however small, are contained in anything, it is not possible to conceive how it could any longer be limited or finite in size. For clearly our infinite number of particles must have some size; and then, of whatever size they were, the aggregate they made would be infinite. And, in the next place, since what is finite has an extremity which is distinguishable, even if it is not by itself observable, it is not possible to avoid thinking of another such extremity next to this. Nor can we help thinking that in this way, by proceeding forward

We must consider the minimum perceptible by sense as not corresponding to that which is capable of being traversed, i.e. is extended,[*](That which admits the successive transitions from part to part. As Bignone remarks, a mathematical series, whether of integers or fractions or powers, might be so described. But Epicurus is obviously dealing with areas and surfaces; since generally to us the visible will also be extended.) nor again as utterly unlike it, but as having something in common with the things capable of being traversed, though it is without distinction of parts. But when from the illusion created by this common property we think we shall distinguish something in the minimum, one part on one side and another part on the other side, it must be another minimum equal to the first which catches our eye. In fact, we see these minima one after another, beginning with the first, and not as occupying the same space; nor do we see them touch one another’s parts with their parts, but we see that by virtue of their own peculiar character (i.e. as being unit indivisibles) they afford a means of measuring magnitudes: there are more of them, if the magnitude measured is greater; fewer of them, if the magnitude measured is less.

We must recognize that this analogy also holds of the minimum in the atom; it is only in minuteness that it differs from that which is observed by sense, but it follows the same analogy. On the analogy of things within our experience we have declared that the atom has magnitude; and this, small as it is, we have merely reproduced on a larger scale. And further, the least and simplest[*](i.e.uncompounded. But v. Arnim’s ἀμερῆ, void of parts, is more suitable.) things must be regarded as extremities of lengths, furnishing from themselves as units the means of measuring lengths, whether greater or less, the mental vision being

Further, we must not assert up or down of that which is unlimited, as if there were a zenith or nadir.[*](Objection was taken by Aristotle to the atomic motion of Democritus, on the ground that it implied a point or region absolutely high, and an opposite point or region absolutely low, these terms being unmeaning in infinite space (Aristotle, Phys. iii. 5. 205 b 30; iv. 8. 215 a 8). See Classical Review, xxxv. p. 108.) As to the space overhead, however, if it be possible to draw[*](This verb (ἄγειν) is technical in Euclid.) a line to infinity from the point where we stand, we know that never will this space —or, for that matter, the space below the supposed standpoint if produced to infinity—appear to us to be at the same time up and down with reference to the same point; for this is inconceivable. Hence it is possible to assume one direction of motion, which we conceive as extending upwards ad infinitum, and another downwards, even if it should happen ten thousand times that what moves from us to the spaces above our heads reaches the feet of those above us, or that which moves downwards from us the heads of those below us. None the less is it true that the whole of the motion in the respective cases is conceived as extending in opposite directions ad infinitum.

When they are travelling through the void and meet with no resistance, the atoms must move with equal speed. Neither will heavy atoms travel more quickly than small and light ones, so long as nothing meets them, nor will small atoms travel more quickly than large ones, provided they always find a passage suitable to their size, and provided also that they

Moreover, when we come to deal with composite bodies, one of them will travel faster than another, although their atoms have equal speed. This is because the atoms in the aggregates are travelling in one direction[*](When the atoms in a composite body are, during a continuous sensible time, however short, all moving in one single direction, then the composite body will be travelling from place to place and have a relative velocity.) during the shortest continuous time, albeit they move in different directions in times so short as to be appreciable only by the reason, but frequently collide until the continuity of their motion is appreciated by sense. For the assumption that beyond the range of direct observation even the minute times conceivable by reason will present continuity of motion is not true in the case before us. Our canon is that direct observation by sense and direct apprehension by the mind are alone invariably true.