We continue to sketch an account of creational thinking as a way of understanding mathematics and its relationship to reality. In our narrative so far, we had begun to develop a perspective of objects of reality as creative by adopting a hylomorphic view of them as the sensible and intelligible united in matter. As objects […]
Tag: Mathematics
Creational Thinking – Part II: Things, Abstractions, and Formations
We begin our journey in developing a notion of creational thinking by giving an account of physical objects in hylomorphic terms and describe how by abstraction human understanding distinguishes such an object in terms of the sensible and the intelligible. In the course of laying out such an account, we will be expanding upon our […]
Creational Thinking – Part I: Introduction
In a previous series of posts (beginning here https://thinkingbeautifully.org/mathematical-understanding-as-seen-within-a-framework-of-beauty-part-1/), I described a particular perspective on thinking beautifully in mathematics. In that description, I aimed to channel the thinking of Medieval thinkers such as Thomas Aquinas and Bonaventure, but also by incorporating the thinking of such twentieth century philosophers as Bernard Lonergan and Michael Polanyi. Unfortunately, […]
Mathematical Understanding as Seen Within a Framework of Beauty (part 4)
Following upon my previous posts, where I began to explore the possibility of framing mathematical understanding within the Thomistic modes of beauty proportio and claritas, I now consider the third mode of beauty, that of integritas. This mode brings beauty in mathematical understanding to its fulfillment and serves to complete and unite the other two […]
Mathematical Understanding as Seen Within a Framework of Beauty (part 3)
In the first two parts of this series, I began outlining how mathematics and mathematical understanding can be framed within the Thomistic modes of beauty: proportio, claritas, and integritas. In particular, I defined mathematics as the science whose subject-matter is measurable orders: objects understood as parts united into whole, having a distinction of same or […]
Beauty for Truth’s Sake (Book Review)
“Music, architecture, astronomy, and physics — the physical arts and their applications — demonstrate the fundamental intuition behind the Liberal Arts tradition of education, which is that the world is an ordered whole, a ‘cosmos,’ whose beauty becomes more apparent the more carefully and deeply we study it. By preparing ourselves in this way to […]
Mathematical Understanding as Seen Within a Framework of Beauty (part 2)
In part 1 of this series, I began to explore how mathematical reasoning can be understood within a Thomistic framework of beauty as expressed in the modes proportio, claritas, and integritas. In that post, I arrived at an initial description of the subject-matter of mathematics as pertaining to quantitative being understood as parts ordered into […]
Mathematical Understanding as Seen Within a Framework of Beauty (part 1)
In a previous series of posts (part 1 being here: https://thinkingbeautifully.org/form-beauty-and-euclids-elements-part-1/) I began to describe how mathematics could be understood as an endeavor of human discovery and invention by showing how form and the pursuit of beauty underlies successes in such efforts. In particular, I focused on the opening of Book I of Euclid’s Elements […]