In the previous posts to this series, I set out to articulate a perspective on the opening of Euclid’s Elements as arising by abstraction of forms that arise from sensible perceptions of things experienced in the real world. I aimed to make the case that certain ones of his Definitions and the forms his Postulates take are justifiable and understandable in light of them as arising in this manner. In this concluding, I consider one further definition and postulate and then finish with how this perspective of the Elements may be seen as an expression of beauty in relationship to in the quest for human understanding of geometry.
In the previous installment (upon which this part depends), I gave what I feel is the correct beginning in how to arrive at and understand basic notions in mathematics. In doing so, I attempted to re-appropriate medieval concepts of matter, form, and abstraction in order to understand what constitutes the objects and subject-matter of mathematics. In particular, I emphasized the role quantity played and in what way things may be quantified. To that end, quantitative being became understood as substance as subject to quantity. I began here with this understanding and examine how the basic items of Euclid’s Elements are arrived at.
It takes time to absorb David Bentley Hart’s sprawling and difficult book, The Beauty of the Infinite: The Aesthetics of Christian Truth (Eerdmans, 2003). Most reviews that I have read are full of qualifiers, noting that there is far more to this book than can be captured in a summary, and often admitting candidly that the reviewer has not yet mastered the material.
Part of this is because of Hart’s writing style. He is not difficult in the way that many academic writers are difficult; his writing is not sloppy or intentionally obscure. Indeed, there is often a poetic, soaring and persuasive quality to his prose. His sentence structure sometimes rivals the apostle Paul’s for complexity, but when pondered everything he says is clear. He is difficult because he is holding so many strands of thought together and because he is in dialogue with such a wide variety of thinkers.
The book begins with an introductory section in which Hart helpfully defines his terms and outlines his project. He begins with a question: “Is the beauty to whose persuasive power the Christian rhetoric of evangelism inevitably appeals, and upon which it depends, theologically defensible?” The book can be understood not only as an attempt to answer this question but as an attempt to justify the centrality of the question for Christian theology.
Belden Lane’s Ravished by Beauty: The Surprising Legacy of Reformed Spirituality (Oxford 2011) is a lovely book. It is a book that uncovers beautiful dimensions to the Reformed tradition. It is accessible, winsome, personal and inviting. Lane does a particularly good job of summarizing some often overlooked and valuable aspects of the Reformed tradition. He dispels many stereotypes about this tradition, especially in its Puritan manifestations. This is a book that I might well use in class to introduce students to the discipline of theological aesthetics in a Reformed context.
If I were to use it in class, however, I would have to point out that this is also a fundamentally incoherent book. Lane is trying simultaneously to embrace and to reject the Reformed tradition, which creates problems for him throughout. He freely admits to being “at best, a reluctant Calvinist” [p.57] who is “repulsed” by doctrines of divine wrath and predestination [p.207]. This does not invalidate the book, but it does mean that readers need to be attentive.
What does it mean to think beautifully? Perhaps it means that our thoughts are elegantly expressed. Perhaps it means that our thoughts are focused on the nature of beauty. And perhaps it means that beauty can be a lens for all thinking about whatever is true and whatever is good.
We hope to express things beautifully on this website, and we will certainly be thinking a great deal about the nature of beauty. But the reason for the site’s name is centered on the last possibility: that beauty can be a lens for all thinking about whatever is true and whatever is good, and because it can function as such a lens for all real knowledge it can also be a meeting place for multi-disciplinary conversation among Christian scholars. Engineers and theologians, mathematicians and poets, historians and chemists may not share much in the way of language or method, but all those disciplines and many more take beauty into account.
I want to begin exploring, or perhaps recovering, a way of understanding the discipline of mathematics as one that integrally involves a perspective of beauty, not a “beauty cold and austere, like that of a sculpture,” (Bertrand Russell) but a beauty that irradiates from the form of anything that can be understood as having being. This view that I will articulate will be one which sees the development of any subject-matter as a dynamic interplay of human understanding and the rendering and communication of knowledge. I will focus, as my case study, on what is considered the earliest of paradigmatic works of mathematics: Euclid’s Elements. As we will see, I consider this as an exemplary work for demonstrating how form and beauty underlie mathematical reasoning.