Creational Thinking – Part I: Introduction

In a previous series of posts (beginning here, 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, my grasp on the latter two thinkers was not sufficient to capture the depths of their ideas in developing the theory of mathematical knowledge that I am aiming for. I have since dug deeper in both of these authors’ works on human understanding, particularly Lonergan’s Insight, and I want to now expand upon my previous forays by articulating how mathematical knowledge fits into a larger mode of human understanding which seeks to see the human knower and knowable reality as united and understood in that unity as a divine creation. To that end, I will also be bringing in as an additional conversation partner, along with Lonergan, Erich Przywara through his magnum opus Analogia Entis

            In developing a perspective of mathematics that relates, reflects, and informs on our understanding of the universe as a knowable, created, physical reality, I will continue to do so within a framework that understands objects of physical reality as composites of matter and form, i.e. in hylomorphic terms. This can be further elaborated through the dynamic relationship between the object’s actuality and potency to be. Specifically, an object that comes to be in act is so as matter in form. The form determines what the thing is in essence from matter and, thereby, determines what it is and limits what it can be in its material potentiality. In turn, the matter provides the medium for the form, but limits the extent the form can be act. We adopt this hylomorphic perspective as a way to understand how objects within a physical medium are to be internally structured and in relationship with other objects. Furthermore, such an understanding has not only a horizontal/relational ordering, but also a vertical/hierarchical ordering in terms of the sensible and the intelligible. I have outlined how these perspectives can serve as a foundation of mathematical knowledge in previous posts. In the current series underway, I will be expanding this perspective to a framework of understanding that I will refer to as creational thinking

            The key to the beginning of creational thinking is the viewpoint of scientific understanding as being thoroughly grounded in the human knower and the efficacy of that knower’s relationship to physical reality as being knowable. In hylomorphic terms, again, physical objects are hierarchically ordered as being intelligible first and then as being sensible. Awareness of such a physical object is obtained in reverse order, first as a sensible object in terms of particular colors, features, capabilities, being here and now. That is in terms of its individual sensible matter, or, alternatively, in terms of its empirical residue, as Lonergan frames it.  But, in order to arrive at a scientific understanding of a physical object, it is to understand it within a theoretical framework of properties and relations that is intelligibly independent of the particular sensible features, yet existentially dependent on it as an individual. Materially, it is being understood in terms of matter as intelligible. As such it is understood more properly in terms of formal causes as limited by its material substrate. This last point will be important for our understanding of creational thinking as regards to mathematics as things understood mathematically will still be understood hylomorphically, though materially purely in a mode of intelligibility.

            Now, the key to understanding a thing in the mode of its intelligible matter is to understand it as separate from its sensible matter. This is achieved by way of the human cognitive power of abstraction. We have paid particular attention to this power in previous posts as it was articulated by Aquinas, but now we will be expanding our understanding of it in terms of Lonergan’s notion of enriching abstraction. This further elaboration will enable us to make a distinction between scientific theories that are empirically grounded (framed in terms of Lonergan’s explanatory conjugates) and more general mathematical theories while retaining their proper connections. Moreover, by deepening our understanding of the cognitive operation of abstraction, we will be in a better position to distinguish between the intelligible matter that pertain to scientific objects, which have their end in the empirical residue, and mathematical objects which are abstracted from the empirical residue, grounded completely in the intelligible matter. 

            At this point, I want to begin to place what has been said so far within Erich Przywara”s understanding and elaboration upon Aquinas’s essence and existence. In his Analogia Entis, Przywara begins the development of a metaphysics that distinguishes and yet relates creation and Creator by first developing a creaturely metaphysics that distinguishes and yet relates immanent form and ideative (morpheand eidos). This leads to a morphological metaphysics from below and an eidetic metaphysics from above. The former is one that seeks to understand things a posteriori, as from effect to cause, via induction, while the latter looks to see how things are understood a priori, as from cause to effect, by way of deduction. Przywara sees a proper creaturely metaphysics as the two forms of metaphysics functioning separately and in unity, so that neither is diminished, dissolved, or collapses to the other and yet together serves to fully ground human understanding.  It will be our aim to develop our notion of creational thinking as a kind of synthesis of Przywara’s creaturely metaphysics with Lonergan’s account of reflective understanding. In adopting this approach, the morphological/a posteriori will at first take priority in that things to be understood will be taken to be so first in a sensible way and then moving to the eidetic/a priori mode of understanding in its intelligibility through enriching abstraction. There can then be a return to the morphological from the eidetic through the process of formalization in which theories are established through definitions, axioms, and propositions, rendered sensible through language and representations both symbolically and iconically. We will elaborate on this way of “going forth and returning” utilizing Lonergan’s theory of judgement in intelligence and reflection. Through this we seek to find the distinction and relation between material, efficient, formal, and final causes in the understanding of creation. Furthermore, we will seek to portray this process of balancing the eidetic and the morphological in a “suspended middle” as a dynamic of human understanding in balancing between contemplation and craft. In that light, we may see this series of posts on creational thinking as an extended meditation on the following quote of David Bentley Hart:

“[A]s an instinctive Platonist, I naturally believe that every genuine act of human creativity is simultaneously an innovation and a discovery, a marriage of poetic craft and contemplative vision that captures traces of eternity’s radiance in fugitive splendors here below by translating our tacit knowledge of the eternal forms into finite objects of reflection, at once strange and strangely familiar.”[i]

            In the next installment, we will review how physical objects may be understood within a hylomorphic framework. We will also review our understanding of Thomistic abstraction and enhance it through Lonergan’s notion of enrichment.  We will then take that opportunity to examine how Lonergan construes abstracted intelligible matter in such a way as to provide a medium for both empirically verifiable scientific theories and the universality of mathematical theories.

[i] David Bentley Hart, “A Perfect Game”, reprinted in A Splendid Wickedness and Other Essays Eerdmans Publishing 2016 p. 44