Book 10
1.56
Besides, you must not suppose that there are parts unlimited in number, be they ever so small, in any finite body. Hence not only must we reject as impossible subdivision ad infinitum into smaller and smaller parts, lest we make all things too weak and, in our conceptions of the aggregates, be driven to pulverize the things that exist, i.e. the atoms, and annihilateAdmitting indivisible atoms, hard solid bodies can be explained; whereas, if atoms were soft and thus divisible ad infinitum, all things would be deprived of solidity (Lucr. i. 565-576). Just before Lucretius has argued that, if atoms did not set a limit to the division of things, production or reproduction would be impossible, since destruction is wrought more quickly than it is repaired, and endless future time could not undo the waste of endless past time. Possibly, however, Epicurus is thinking of an argument similar to that used by Lucretius in ii. 522-568—that a finite number of shapes implies and requires an infinity of atoms of each shape. them; but in dealing with finite things we must also reject as impossible the progression ad infinitum by less and less increments.
1.57
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 from one to the next in order, it is possible by such a progression to arrive in thought at infinity.Each visible body is the sum of minima, or least perceptible points, which, because they are of finite size, are also finite in number.
