Augustine. If someone were to say to you that numbers were impressed upon our spirit not as a result of their own nature, but as a result of those objects which we experience with the bodily senses, what answer would you make? Or do you agree with this?
Evodius. No, I do not. Even if I did perceive numbers with the bodily senses, I would not be able to perceive with the bodily senses the meaning of division and addition. It is with the light of the mind that I would prove wrong the man who makes an error in addition or subtraction. Whatever I may experience with my bodily senses, such as this air and earth and whatever corporeal matter they contain, I cannot know how long it will endure. But seven and three are ten, not only now, but forever. There has never been a time when seven and three were not ten, nor will there ever be a time when they are not ten. Therefore, I have said that the truth of number is incorruptible and common to all who think.
A. I do not disagree with your answer, for you spoke truly and clearly. [p. 54]
Of course it’s true that arithmetic and math are rational, but it doesn’t follow at all that we know nothing about them by way of our senses. The most obvious reply is that we all learn numbers by way of our senses: we are taught what “one” and “two” are by our parents (or others), who show us what these terms mean. We learn simple addition by way of our senses as well: we are shown one item, and two more are added to it, and we can then count that there are three; in this way we learn that 1 + 2 = 3. Obviously that is just a beginning, and of course reason comes into play in our comprehension of math. But it seems quite mistaken to suppose that we don’t begin to learn about this by way of what we can see and touch.
I think that a useful counter-example may be seen in this article, in which we learn about the Pirahã tribe in Brazil, whose concept of numbers is limited to “one,” “two,” and “many.” As the article says by way of example, they are unable to reliably distinguish between four and five objects in a row. But if “the truth of number is incorruptible and common to all who think,” in the way that St. Augustine apparently suggests, then it seems that the Pirahã tribe must not be able to think. But this is absurd: they are human beings created in the image of God. Therefore we know that they can think. Hence we must say that Augustine’s claim that “the truth of number” is “common to all who think” is incorrect.
St. Augustine argues against an empirical component to our ideas of numbers in a peculiar way. He says that the infinite divisibility of a body argues against means that we must “concede that no body is truly and purely one” (ibid., p. 55). But what does that have to do with whether we may distinguish the idea of one by way of what we see? I don’t think that it has anything to do with it. At the very least it seems to me to be obvious that infinite divisibility doesn’t mean we can’t look at any particular body and say that there is just one of them. The fact that a rock might be divisible doesn’t mean that it’s not a single rock. But Augustine says no: “The perception of one does not occur through any bodily sense” (ibid).
Similar Platonic influence seems to me to be evident in chapter X of Book II, where it appears that he views truth as a sort of subsisting thing somehow. He argues that for a given fact, its truth is not something that one man can hold in opposition to another; rather, its truth is available to all:
A. Can we deny that this fact is true and one, yet common for all who know it? Each man sees it with his own mind, not with mine, yours, or anyone else’s; yet what is seen, is present for all to see in common. We cannot deny this, can we?
E. Of course not.
A. Can anyone call truth his own, when it is present unchangingly, for all to meditate upon who have the power to meditate?
E. No one can truly call truth his own. Truth is one and common to all, just as much as it is true.
A. I shall not ask you any more questions of this kind. It is sufficient that you see and grant, as I do, that it is certain that these judgments are rules and, as it were, lights of virtue; and that true and unchangeable things, whether individually or all together, are present in common for all to meditate upon who have the power to perceive with mind and reason. [p. 61-62]
In chapter XII, he says that immutable truth exists, and it seems that he means that it has some sort of actual being:
You will not deny, therefore, that immutable truth, comprising everything that is immutably true, exists; and you cannot say that immutable truth is yours, or mine, or anyone else’s. It is present and shows itself as a kind of miraculously secret, yet public, light for all who see what is immutably true. [p. 66]
This doesn’t seem to me to be the best account of what truth is. It seems to me that Aquinas’ view, and Aristotle’s, is more reasonable: namely, that something may be said to be true when it conforms to reality.