Let me oversimplify in a useful way:
- Facts are local.
- Understanding is global.
- Knowledge is something of a bridge from facts to understanding.
And, yet, we should not imagine that facts and knowledge exist only to serve understanding. Nor should we imagine that understanding is fully, or even mostly, what can be found in a (pseudo-)Platonic scheme.
We live in a dynamic Creation, one driven forward by evolution and development. The trick for a Christian, for one who believes in an afterlife in the world where the resurrected share God’s life, isn’t to develop a set of schemes which can be applied to all things and situations to understand—such is a false understanding of understanding. The trick is to understand the story and not to reduce it to just some things that had to happen to compensate for a fall from a state of perfection.
When we have a story which works—and we currently don’t—we work to integrate into that story new events and new knowledge of things and their relationships. When the story breaks down, we have to pick up the pieces, Biblical revelation and human traditions to the extent they remain valid, and then we have to create a new story as did Christians from the time of Augustine (call it the Fall of Rome if you wish) to the High Middle Ages (1150-1300 or thereabouts).
In the succeeding centuries, Christians fell down upon the job. They fought Galileo, a man who was an orthodox Augustinian thinker and even more consistently empirical than was the great African. That was the problem. `Empirical’ means having to pay attention and respond to events and natural revelations which might be very disturbing. Most human beings, including Christian theologians and even saints, prefer to have a set of canned truths by which they can understand and even judge all of Creation. That’s not real understanding. Even in mathematics, axiomatic systems aren’t created from nothingness but rather distilled from years or even centuries of exploring specific areas of mathematics. Even this seeming ideal of idealistic thought is no such thing—great advances in mathematics have often come when a scheme of thought produced results which indicated the scheme needed to be expanded or enriched or changed in fundamental ways. I don’t agree with those who see mathematics as a cultural activity but I do agree with a similar but grander view of mathematics being one area of activity of the human communal mind as it expands, enriches and complexifies itself—first of all, in response to reality, but then in response to the internal developments of that mind and the communities of which the mind is a part.
So, those thinkers such as Reuben Hersh and Raymond Wilder who see mathematics as a cultural activity, and argue intelligently for that view, are more right than wrong but not right enough. They aren’t right enough because they have no reason to pursue a grander vision than simply understanding the community of mathematical thinkers—a noble task in itself but only part of the greater task of understanding all human communities as they enrich and complexify themselves in response to what lies around them…and then inside of them. Human understanding is the story of human individuals and communities shaping their selves in honest and faithful response to God’s Creation.
As I see it, a higher level understanding which is the setting for all lesser understandings, comes from a proper perception of the world as a story, the world as being the universe and all creatures living, evolving and developing, according to the moral purposes of its Creator. This obviously can only happen if we pay attention to the universe, to God’s creatures. As Aquinas told us:
[J]ust as a disciple reaches an understanding of the teacher’s wisdom by the words he hears from him, so man can reach an understanding of God’s wisdom by examining the creatures [God] made… [Page 17 of St Thomas Aquinas’ commentary on 1 Corinthians, according to a translation by Fabian Larcher, OP, and now available in hardcopy at Priory of the Immaculate Conception, which is a Dominican House of Studies in Washington, DC. It might still be available as a downloadable pdf if you search the Internet.]
Examine the creatures God made if you wish to understand the thoughts of God in His freely chosen role as Creator of this particular world in a very specific Creation. And then make sense of it in light of your understanding of the Creator God of Jesus Christ or another God or even Reason if you wish. In any case, the idea is to wrap the best available knowledge of your day and age in a narrative, purposeful and even morally purposeful to many of us.