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 previous descriptions, which was largely dependent upon the thought of Thomas Aquinas, by channeling the thought of Bernard Lonergan, through his magnum opus Insight[i], and Erich Przywara, through his magnum opus Analogia Entis[ii].
We first note that by considering an object in terms of human understanding, if that object is physical then it is perceived by the senses, received in the mind as an object of understanding. In that way, we will take it to be that it is grasped first as a thing, that is a “unity, identity, whole in data, … grasped, not by considering data in an abstractive viewpoint, but by taking [it] in [its] concrete individuality and in the totality of its aspects … extended in space, permanent in time, and yet subject to change.”[iii] In terms of what can be said of this object, in being grasped as a thing, is that it is an “already out there now real,” i.e. a body[iv]. In terms of its sensible qualities, it is understood in terms of aspects of its data that includes being an individual that is part of a continuum at a particular time and place. We will identify such particular data as pertaining to the sensible matter of the thing as an individual. For Lonergan this type of data belongs to the empirical residue[v] which we will borrow as the term referring to any data that pertains to an individual thing’s sensible matter. Such data may be characterized and ordered in accord with Aristotle’s categories[vi]
- Qualities: color, shape, abilities, etc.
- Relation: similarities and differences
- Action and Passion: performance and susceptibilities
- Place and Time: habitat, seasonal changes, being here, happening then, etc.
- Posture: mode of motion and rest
- Habit: possessing, for example, eyes, ears, fur, claws, etc.
Prior in understanding to such sensory data, that belong to the empirical residue, are two more fundamental categories that pertain to a thing in proper order
- Substance: genus, species, instance
- Quantity: size, weight, etc.
It is in grasping a thing in terms of these last two categories that that thing is being understood in terms of its intelligible matter. It is in making this distinction that we seek to identify how to separate what constitutes the objective of scientific and mathematical thinking as it pertains to a thing as opposed to that which we come to in the mode of simple common sense through the senses. For that, we will need to clarify how the intelligible can be separated from the sensible. For that we will need to recall and elaborate upon our current understanding of abstraction.
Recall that to grasp a thing in terms of particular features it possesses independent other features may be done so by abstraction if one may do so according to the formula: A is understood separate from understanding B even though A and B are in fact joined in reality[vii]. In the case of our understanding a thing in terms of how the categories pertain, grasping the thing strictly in terms of its intelligent matter is to understand it as abstracted from the individual sensible matter. In order to clarify how this understanding operates with regard to how A may be grasped separate from B and in distinction to how A and B are joined in reality, we recall the two main principles of abstraction:
- Principle of Independent Intelligibility: “The aspect which is considered separate must not depend for its intelligibility on the other aspects from which it is mentally separated.”
- Principle of Dependent Existence: “The aspect which is considered separate cannot be asserted to exist apart from the thing and its other aspects with which it really does exist.”[viii]
In concentrating our attention on the intelligible material as grasped in the thing as an object of abstraction, this understanding is grounded upon these two principles.
In order to arrive at what we may refer to as a scientific understanding of the thing, being what is comprehended of a body as perceived through the senses, the existential nature of the thing is grounded upon the actuality of the sensed body. As initially understood, the qualities, etc. that are understood to pertain to the thing (shape, colors, sounds, etc.) as perceived in that body is, what Lonergan calls, experiential conjugates[ix]. These being in the mind what pertains to the sensible matter of the thing and therefore concerns the correlates in the data of the empirical residue. In abstracting from these to the intelligible matter of the thing leads to understanding the thing quantitatively, through measuring, which pertain to the data as limitations (mass, weight, speed, vector quantity, energy, etc.) and relate as correlations (understood classically as laws). This is due to its being what it is in actuality (its essence-in-existence) upon the qualities that quantity bears upon (shape, size, and other measurable aspects). In particular, we will define the capability of a thing to bear quantities in accord with its essence to be ordinable.
These quantitative features as they pertain to the thing, being in active relation and coherence to the measurements of the body perceived and empirically verified, are what Lonergan refers to as explanatory conjugates[x]. These form the basis for the formation of scientific theories. As such, they arise from an inductive (a posteriori) activity of the mind in which understanding of the data of a thing as object is grounded in the actuality of the body. This is a motion in the intellect that goes from effect to cause. Following Przywara[xi], this can be characterized as a morphological view of understanding in which intelligible matter arises as abstracted from the sensible.
Within this process of arriving at the explanatory conjugates in the morphological formation of scientific theories, there is a return to the sensible matter via empirical verification in the laboratory. That these occur regularly itself verifies the integrity of abstraction as grounded in the principles of independent intelligibility and dependent existence. In turn, these principles are grounded upon the more fundamental:
Principle of Non-Contradiction: Nothing can simultaneously both be and not-be. Equivalently, nothing can be understood in anyway as being simultaneously both true and false.
Intertwined with this empirical verification is the further endeavor to predict novelties from the theories. This assets a reciprocal relationship in which that which is understood in intelligible matter has implications in the sensible. This is an understanding, on the level of the ideative, that arises in the formulation of theories grounded in principles. Empirical predications, as instances of the theory in reality, are initiated by deductions from the theory, which is a motion in the intellect from cause to effective. Following Przywara[xii]again, this is the eidetic mode of understanding by which is made possible the movement from intelligible matter to the sensible matter.
The integrity of the thing understood from the body in act is best seen through its hylomorphic simplicity as the composite of, equivalently, matter and form, potency and act, or essence and existence. We will refer to a thing viewed in its hylomorphic capacity as a formation. In comparison of each mode of composition, the composite of form inhering in matter is, as we have seen, a hierarchical ordering of intelligible and sensible matter which can be understood separately by abstraction and which, in the key of essence and existence, attains to essence beyond existence. Thus this rhythmic interplay of the morphological and the eidetic can be scored as Przywara’s fundamental “essence-in-and-beyond-existence”[xiii]. In the mode of potency-act, a formation in its intelligibility becomes free to be understood in its full spectrum of potentialities only limited by the formation grounded in its existential act which tethers the thing to reality and which, in turn, is held in harmony between the two poles of potency-act/form-matter/essence-existence by (the principle of) non-contradiction. Analogously, there is the twin poles in level of intelligence between the eidetic and morphological in which each acts in harmony both in distinction and in unity without contradiction.
In the next installment, we continue to fill in Przywara’s pendulating movement from the morphological to the eidetic and back as the disclosure of truth through Lonergan’s account of the operations of thought as they occur in the levels of intelligence and reflection. This will set the stage for an account of the nature of knowledge that is mathematical as well as its relationship to and its distinction from that of the scientific.
[i] Bernard Lonergan, Insight: A Study in Human Understanding, Collected Works of Bernard Lonergan, vol. 3, 5th Ed., University of Toronto Press, Scholarly Publishing Division, (Frederick Crowe and Robert Doran eds.), 1992
[ii] Erich Przywara, Analogia Entis: Metaphysics – Original Structure and Universal Rhythm, translated by John R. Betz and David Bentley Hart, Ressourcement: Retrieval and Renewal in Catholic Thought series, Eerdmans Publishing, 2014
[iii] Insight, p. 271
[iv] Ibid p. 276
[v] Ibid p. 336, for example
[vi] Ibid p. 420
[vii] Thomas Aquinas, Summa Theologica I q. 85, 1 ad 2; In Boethius’s De Trinitae V, 3
[viii] Thomas C. Anderson “Intelligible matter and objects of mathematics in Aquinas”
[ix] Insight, pp. 102-105, 271
[xi] Analogia Entis, pp. 134-135
[xiii] Ibid p. 124