Introduction to the Philosophy of Saint Augustine (continued)
find there, and what cannot be found there, or rather what is not there at all. But whenever I know one, I certainly do not know this through my bodily senses, because by the bodily senses we know only body, which we have proved to be not one, pure and simple.
Moreover, if we do not perceive one by a sense of the body, we do not perceive any number by that sense, so far at least as concerns those numbers that we discern by our understanding. For there is no one of them that does not get its name from the number of times it contains one; and one is not perceived by the bodily sense. For the half of any particle makes up a whole of two such halves and has also its half; therefore, those two parts are in the body in such a way that they are not simply two. But on the other hand the number that we call two because it contains twice that which is simply one, its half part, is something which is itself simply one, and cannot have a half or a third or any part whatsoever, because it is simply and truly one.
23. Then again, whereas taking the numbers in order, after one we get two, which comparing with one we find to be its double; the double of two does not follow in immediate succession, but four, which is the double of two, follows after the interposition of three. And this rule extends to all the other numbers by a most certain and immutable law: that after one, that is after the first of all the numbers, itself excepted, the first is that which contains it twice; for two follows one. But after the second number, that is after two, it is the second, itself excepted, that is the double of it; for the first after two is three and the second four, the double of the second number. After the third, that is after three, it is the third, itself excepted, that is the double of it; for after the third, that is to say three, the first is four, the second five, and the third six, which is the double of three. So again after the fourth it is the fourth, itself excepted, that is its double; for after the fourth, that is four, the first is five, the second six, the third seven, and the fourth eight, which is the double of four. And so throughout all the other numbers you will find this that has been found in the first pair of numbers, that is, in one and two: that the double of any number is just as many numbers after it as that number itself is from the very beginning.
But now when we perceive this thing to be for all numbers fixed and inviolate, whence comes this perception? For no one has touched all numbers by any sense of the body, for they are innumerable. Whence then do we know this for all or by what so sure an appearance or image do we know so confidently this