not have been able to arrive at a complete and accurate understanding. I would have given answers based solely on my memory, which is fallible and prone to error. I needed to step inside the activity of learning to read the information myself and attempt to solve the problems.
19. Commitment to Universals – We affirmed not only the universal axioms of mathematics, but eternal realities such as truth, goodness, love, and the soul.
20. Deference for Tradition – Mathematics is an old study; we honored its function and role in the universe and in the history of man. We endeavored to participate in the Great Conversation (about mathematics) with the past.
21. Humility – Humility was absolutely essential before we could learn anything. We had to acknowledge how much we did not know. I needed to admit that I had forgotten some of the strategies in solving the equations. Charlotte needed to admit that these new concepts were a challenge and that she needed help.
22. Imagination – Here we emphasize the importance of
the imagination for a fuller, more complete knowledge of ourselves and the world. We affirm the vital relationship between reason and imagination in the activity of knowing. 23. Wisdom – Though my work on the article was set behind, it was wiser for me to invest in the lesson with my daughter because it was the right thing to do. All knowledge has an ethical and spiritual dimension (all Truth is God’s truth). So all knowledge, in some way, relates to wisdom. Time spent with her was the wiser choice for many reasons, but to name two—we are a little closer now, and she is growing in her knowledge of math.
24. Faith – We needed faith in God, and in His eternal mathematical laws. By studying them, we believed that we might come to know reality a little more fully, and through that reality, know something more of Him and ourselves. 25. Love – Because I love Charlotte, and care enough for her to learn algebra, she now understands it. If I had insisted on her reading the pages on her own, as mere facts separated from reality, existence, and relationship, she would not have come to a full knowledge of it.
We shall now consider three salient concepts from above that are vitally important in the activity of knowing: Universals and Truth, Participation, and Language and Imagination. We will begin with universals and truth because they influence and inform the other concepts.
The first slip into modernism might well be located in the figure of William of Occam in the early 14th century. Occam established the doctrine of nominalism, which denies that universals and/or abstract objects have any existence or reality. The doctrine suggests that only particular, concrete things are real, and that universal terms and concepts have no existence (other than as mere names for classes of particular things). As Richard Weaver suggests, the issue at stake is whether a source of truth exists that is higher than, and independent of, man. The consequence of nominalism is that it banished reality perceived by the intellect and the spirit, and reduced reality to only what is perceived by the senses. And with this change in the assumption of what
is real, the entire orientation of culture took a turn toward modern empiricism.1
The effect of nominalism is the diminishment, if not the devastation, of our ability to know reality in a more comprehensive way. The denial of universals carries with it the denial of everything transcending sensory experience, and with this, the denial of truth. Astutely, Weaver recalls the story of the witches from Shakepeare’s Macbeth, who tempt Macbeth with the idea that man can realize himself more fully if he will only abandon belief in the existence of transcendentals.2 By denying transcendent reality
and objective truth, the witches spoke delusively and presciently—instead of man realizing himself more fully, he is actually sundered from knowledge and reality. For it is the transcendent entities that complete the fullness of reality and knowledge, giving life and being to all things.
James S. Taylor aptly states that the fullness of knowledge is a kind of natural, everyman’s metaphysics of common experience. It is a way of restoring the definition of reality to mean knowledge of the seen and unseen. Its restoration is essential for reawakening the intuitive nature of human beings who are able to know reality in a profound and intimate way that is prior to, and in a certain sense, superior to reductionistic, empirical knowledge.3
Let us now turn to the vital role of participation in knowledge. In “Meditation in a Toolshed,” C. S. Lewis relays an enlightening experience of standing in a dark toolshed. He says that the sun was shining outside and through the crack at the top of the door, a sunbeam pierced through. Everything else in the shed was pitch black. Particles of dust were floating in the beam. The beam appeared striking and beautiful. Importantly, he was looking at the beam, not seeing things because of the beam.
Then, Lewis moved into the beam so that the beam fell on his eyes. Instantly, he says, “the whole previous picture vanished. I saw no toolshed, and (above all) no beam. Instead I saw, framed in the irregular cranny at the top of the door, green leaves moving on the branches of a tree outside and beyond that, the sun. Looking along
the beam, and looking at the beam are very different experiences.” The modern method of acquiring knowledge is akin to looking at the beam; but to partake in the fullness of knowledge implies standing in the beam and looking along the beam. Here are two different ways of knowing. Both are valid, yet the second way implies participation inside; it facilitates passage into the glorious realm of universals, the transcendent realities that comprise the fullness of our knowledge, being, and purpose. From mere matter to intellect, spirit, and truth.
Let us conclude with language and imagination. Remember the opening anecdote where I was sitting in the kitchen with the morning sun and my coffee? By the active use of language and imagination, I imbued the experience with meaning. With modern reductionism, it is usually assumed that there is little connection between the physical causes of things and their meaning. But, as Owen Barfield illuminates, the meaning of a process is the inner being which the process expresses.5 And it is language and imagination, through symbol and metaphor, that connect the inner beings of things to their processes and to man.
So then, a thing functions as a symbol when it not only announces, but represents something other than itself.6 We owe the existence of language to this process: memory and imagination convert the forms of the physical world into mental images, images which function not only as signs and reminders of themselves, but as symbols for concepts.
If this were not so, they could never have given rise to words, which make abstract thought possible. If we really think about this, it implies that this symbolic significance is inherent in the forms of the outer world themselves.7
Thus, Barfield reveals, if language is meaningful, then nature is also meaningful. He quotes Emerson, “It is not only words that are emblematic; it is things which are emblematic… Man is placed in the center of beings and a ray of relation passes from every other being to him. And neither can man be understood without these objects, nor these objects without man. It is precisely in this ‘ray of relation’… that the secret of meaning resides.”8
Perhaps it is just this ray of relation dispersing through each other and the world, our experience and our soul—the interaction of coffee, sunlight, algebra, and spirit—the joy of participation and the fullness of knowledge—which grants meaning to all that we hold dear: that which we write, that which we hope to know, and those whom we love.