I am very taken with the unique kind of abstraction Plato has in mind with his notion of Form or Idea, although my understanding of it is certainly not as clear as Plato’s seems to be. Geometric figures provide a fairly good illustration. The Idea Triangle, for example, is itself neither equilateral, isosceles, right angle, etc., nor even the impossible Penrose triangle.
Yet, it is a kind of metaphysical umbrella for each and all of these. The relationship seems to resemble members of a class except that each individual triangle “participates” in the Form Triangle, that is, derives its “triangle-ness” from the Form. Since the Form is not a specific kind of triangle, while a drawing of a triangle is necessarily specific, the Form triangle, (and every other Form) is visually elusive. The capitalization, italics and quotation marks above are indicators of philosophical thin ice and suggest caution. Add to this Euclidian complications of formal geometry, where lines have no width and points have no dimensions, and you have major difficulties for any artist who would take inspiration from the Forms.
Plato had no such misgivings. To the contrary, he raised the ante. First, by extending the notion of Form to cover more ambitious abstractions such as Love, Truth, Beauty, Justice, etc.; and second, by claiming a separate existence for the Forms - eternal, unchanging and independent of human thought or perception. This is the aspect of the Forms that is especially appealing to me.
I take heart, perhaps mistakenly, from Mathematical Realism which has a distinct Platonic flavor: mathematical entities exist, it is claimed, independent of human endeavor, waiting to be discovered. The internal angles of a triangle (any triangle on a Euclidian plane) will add up to 180 degrees, whether there are rational minds around to appreciate this ‘fact’ or not. The geometric relationship represented by Pi (π) existed during the time of our caveman ancestors, but had not yet been discovered. On this view, that there exist an infinity of prime numbers is “objectively true.” Mathematical Formalism, on the other hand, makes the arguable but uninteresting claim that mathematics (and logic) is merely the practice of manipulating and transforming strings of symbols according to fixed rules. Mathematical entities thus are constructed, not discovered, and mathematical statements, strictly speaking, are not really about anything.
As a painter in the Platonic tradition (with reservations), I am attracted to the geometric Forms. I have the feeling that they somehow allow contact with an eternal, unchanging realm that stands behind mere appearances, a realm that waits to be discovered. A simple line drawing of a circle or rectangle transforms a landscape, abstract or still life into something more. I once entertained the notion that the “Ladder of Love” in Plato’s Symposium, with some adaptations could be transformed into a “Ladder of Geometry.” The goal and method remain the same. Begin in the here and now, and by means of training, attention and philosophical concentration, ascend through various levels of increasing abstraction until one reaches the Form, the Idea, the thing itself whether it be Love, Truth, Beauty or the Triangle. The realm of Forms is eternal and unchanging – the exact opposite of our present situation in the realm of “coming to be and passing away.”
Any representative member of a given level should point towards the level beyond. The object-oriented love for a particular person points a more generic love of persons in general, which eventually leads to the ultimate abstraction of Love itself, which needs no object. There are, of course, many rungs in this ladder. The trick is not to be diverted by objects of beauty on the lower levels. Such distractions capture our attention and deflect our momentum. Although I aspire to this goal of the eternal and unchanging, at the end of the painting process, when I remove the masking and protective films and see the whole piece for the first time, I find, all too often, that I remain rooted in the earthly realm of change, a horizontal movement at best. My aspirations were pure but I must have “taken a few wrong turns,” as Dylan would say. After all these years, you would think my sense of direction would be more dependable.
For Plato, at least in The Republic, art is an unprofitable and distracting exercise of the senses and not to be taken seriously. The art he has in mind here is mimesis: imitation or the creation of likenesses. Its subject, the here and now, is a mere shadow of the Forms, and the art object is a mere copy of that shadow. It is thus twice removed from reality. For Plato, mimesis is seen an indulgence of our desires and a hindrance to progress on the upward path to knowledge. For Aristotle, by contrast, mimesis is a vital tool for giving an account of the world and an essential part of the knowledge process. I find myself in Aristotle’s camp on this issue. “There are as many paths as there are pilgrims,” goes an old Buddhist saying. This is especially true in art. There is probably no artistic style, approach, or starting point that doesn’t have the potential to lead the artist or the viewer to new insights and the possibility of seeing beyond themselves.