Augustine: Earlier Writings (continued)
ON FREE WILL Ig
multiple of unity, and unity cannot be perceived by the bodily senses. The half of any body, however small, requires the other half to complete the whole, and it itself can be halved. A body can be divided into two parts but they are not simply two.
[They may in turn be further sub-divided.] But the number two consists of twice simple unity, so that the half of two, that is, simple unity, cannot be sub-divided by two or three or any other number whatever, because it is true and simple unity.
23. Following the order of the numbers we see that two comes next to one, and is found to be the double of one. The double of two does not immediately follow. Three comes first and then four, which is the double of two. Throughout the numerical series this order extends by a fixed and unchangeable law. After one, which is the first of all numbers, two follows immediately, which is the double of one. After the second number, that is, two, in the second place in order comes the double of two.
In the first place after two comes three and in the second place four, the double of two. After the third number, three, in the third place comes its double, for after three four comes first, five second, and in the third place six, which is the double of three. Similarly the fourth number after the fourth is its double; five, six, seven, and in the fourth place eight, which is the double of four. And throughout the numerical series you will find the same rule holds good from first to last. The double of any number is found to be exactly as far from that number as it is from the beginning of the series. How do we find this changeless, firm and unbroken rule persisting throughout the numerical series? No bodily sense makes contact with all numbers, for they are innumerable. How do we know that this rule holds throughout? How can any phantasy or phantasm yield such certain truth about numbers which are innumerable? We must know this by the inner light, of which bodily sense knows nothing.
24. By many such evidences all disputants to whom God has given ability and who are not clouded by obstinacy, are driven to admit that the science of numbers does not pertain to bodily sense, but stands sure and unchangeable, the common possession of all reasoning beings. Many other things might occur to one that belong to thinkers as their common and, as it were, pubhc property, things which each beholder sees with his own mind and reason, and which abide inviolate and unchangeable. But I am glad that the science of numbers most readily occurred to you when you had to answer my question. For it is not in vain that the holy books conjoin number and wisdom, where it