“Let every good and true Christian understand that wherever truth may be found, it belongs to his Master.” With these words in book II of On Christian Doctrine, the great Bishop of Hippo, St. Augustine, summarized his endorsement of pagan literature in Chirstian education. As the Israelites took jewels from Egypt, he says in an interesting example of his method of interpreting the Old Testament, let us accept the best and most valuable ideas from Greek and Roman writers while carefully rejecting their devotion to a pantheon of false gods.
This tolerant view from the most influential Christian of his time (the most influential Christian, in fact, of any time since the first century) set the curricular tone for higher education in Europe for the next several hundred years. And yet Augustine, throughout On Christian Doctrine, advocates searching for all God’s truth – in Greek philosophy, in the study of nature, in the skills and knowledge of the arts and crafts, and elsewhere – only for the sake of understanding the Scriptures. How are we to understand the timing of the festivals in Deuteronomy, for instance, without some understanding of the motions of the moon? Fair enough.
But, Augustine (I’m conversing with him now), properly understanding the Scriptures entails living out their precepts in mundane life: doing well at work, trading fairly, caring for our families and for our bodies. Doesn’t this mean we should learn as much as we can, for all truth is God’s Truth, in order to live well, to work well, to interact with others well, to teach, to protect, to heal, to judge, to govern, to serve? Everything I learn, when I refer it to God, gives me deeper understanding of God’s wisdom and leads me to love and honor Him more. And if I need to go on, I could remind you that God encouraged and honored the pagan education of Joseph in Egypt and Daniel in Babylon, and these curricula included training in false religions and astrology. I’m grateful that you endorsed the study of science, history, philosophy, and poetry, but I think you’re only half right about the purpose and application of these pursuits.
Augustine (I’m talking to the reader again now) came by his position honestly: in his Confessions, he explains that Plato (or actually probably some neo-Platonists) taught him much that prepared him for the gospel. And as a good Platonist, Augustine had an interest in numbers. Now I’ve written previously in these posts (probably somewhere under Euclid) about whether ancient and medieval mathematicians did or didn’t accept the existence of fractions. I’ve talked with professors of math and science who insist that they did. But all the medieval music theorists I’ve read talk about comparisons of string lenghs as if fractions don’t exist. Ratios, yes; fractions, no. One string may be twice as long as another, but that doesn’t mean they had a conception of a fraction, of a number less than 1.
It’s next-to-impossible, of course, to find a smoking-gun admission on a concept that a culture doesn’t have. I don’t expect any ancient author to prove my position right by saying, “I don’t believe in fractions.” If the concept isn’t there yet, they can’t think about it either to believe or not to believe. Plato never said, “I don’t believe in x-ray machines,” even though he clearly didn’t. But I think I’ve found the clearest passage I’ve ever come across to confirm my historical understanding contra that of my well trained friends who have assured me I’m wrong. In chapter 38 of book II of On Christian Doctrine, he says that nine is one-and-a-half times the number six. So surely, my colleagues would say, he recognizes that one-and-a-half is a number. But before that sentence ends, Augustine adds that nine is “not the double of any number because odd numbers have no half.” Odd numbers have no half. How can he say in one phrase that nine is one-and-a-half times six and in the next that three is not the double of any number? We could point out to him that three is the double of that one-and-a-half that he just mentioned. He might agree at some level and might even recognize some sort of existence for one-and-a-half. But for Augustine, as for other ancients (at least the Platonists) and for my medieval music theorists, one-and-a-half is a relationship; it is not a number. Augustine's sentence just doesn’t make sense any other way.
So now I can confidently say that my friends who have tried to correct me are only half right.
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