Notes on Dialectical Method in Metaphysics
Wherein I return to my Thomistic roots...
Readers of this blog may or may not be aware that my original training as a thinker is in the discipline of Thomistic philosophy. Though I have written little directly from this point of view on this blog so far, much of my writing on politics, economics, Marxism, mysticism, and so forth, is informed in the background by a perspective more or less rooted in the Catholic philosophy of Thomas Aquinas. This post is an exploration of certain methods applied especially in a Thomistic metaphysics leading into something like mystical theology. Much of this also forms a background for my engagement with Hegelian, post-Hegelian, and Marxist philosophy — but I won’t be getting into that here.
1. Charles DeKoninck, arguably the greatest Thomist philosopher of the 20th century, began to develop a line of thought on the notion of a “dialectic of limits” that has, I think, been relatively unexplored by his Thomist disciples. His theory of the dialectical method contains in it a stringent critique of the Hegelian dialectic as well as its most noteworthy descendant, Marxism, but also appears to be an attempt to engage positively on some level with the same Hegelianism. In the preface to a collection of his father’s essays, Thomas DeKoninck even writes that Charles, “though frequently critical of Hegel, perceived a possible rapprochement,” and that an attempt at such engagement was made especially in his two essays, “The Dialectic of Reason as a Critique of Reason,” (1945) and “Concept, Process, and Reality” (1949). In those essays, DeKoninck asserts that the dialectical method which he expounds there is ultimately derived by way of Thomas Aquinas from Plato and the Neoplatonists, among whom Ps.-Dionysius the Areopagite is especially mentioned. Hegel himself likewise inherited the dialectical method from Plato and, it has sometimes been argued, from Neoplatonists such as Dionysius and Nicholas Cusanus. Thus it is unsurprising that some measure of rapprochement might be possible between Thomism and Hegelianism, likely requiring a degree of adaptation and correction on both sides. Notwithstanding his critiques of Hegel — indeed, depending on them — I believe DeKoninck’s work may contain at least the seeds of such an effort of mutual engagement.
But there is another, related reason for the possibility of a positive engagement between DeKoninck’s Thomism and Hegelian and post-Hegelian (e.g. Marxist) philosophies, namely DeKoninck’s uniquely positive engagement with Darwinism and the scientific theory of evolution. Indeed, DeKoninck paid an especially close attention to the modern development of natural science, and it might be claimed that his biggest philosophical project was in reconciling modern scientific development with the principles of natural science and metaphysics that were contained in traditional Thomism. It is perhaps in the area of natural science that Thomism must accept the above mentioned “corrections,” if they could be called corrections at all. The strength of DeKoninck’s philosophy is to show that the discoveries of modern science, far from undermining the principles of the Thomistic-Aristotelian philosophy of nature, actually confirm and cohere with it in new and interesting ways. Indeed, the Thomistic-Aristotelian philosophy of nature actually leaves plenty of space within itself for scientific development, as a necessary consequence of its own commitment to the relative indeterminacy of matter itself. Precisely because material being, the object of natural science, is ontologically indeterminate and thus open to a kind of development, so must the sciences adopt a stance of openness to continual adaptation and development. It is with this disposition that, above all, DeKoninck approached the theory of evolution in his three-part unfinished essay “The Cosmos” as well as other works, where evolution is perceived as not-at-all the devastating blow to theism that it has so often been seen to be, but as a wonderful manifestation of the very principles which he, a Catholic and a Thomist, affirmed so confidently. While ever the critic of Marxism and dialectical materialism, I believe this gave his philosophy something of a “materialist” edge that makes a fruitful but critical dialogue with materialist philosophies quite possible. This is an avenue of exploration I hope to tread in further research.
But today I will bracket the question of evolution and materialism, though it is not totally unrelated to what I wish to discuss primarily: namely, the “dialectic of limits” as a method of use to the sapiential sciences, especially metaphysics — but a method which leads into the apophatic silence of that mystical wisdom which is beyond all science and beyond all discourse.
2. In “The Dialectic of Limits as a Critique of Reason,” DeKoninck presents the method of limits in terms drawn from calculus, which is, as it were, the most famous and the most paradigmatic employment of this method. There are any number of examples of this method. Between 1 and 2, there is an infinite series of divisions by 1/2. That is, if you add 1 + 1/2 + 1/4 +1/8 + 1/16 + … etc., you will come closer and closer to 2, but you will in fact never reach 2. The number 2 can only be reached in this process “at infinity,” which is in fact never. Another example of the same process: given a polygon inscribed within a circle, if you continually double the sides of the polygon you will create new polygons of an ever-increasing number of sides, perpetually approaching the circumference of the circle itself, reaching identity with the circle only at the point of infinity — which is never. The paradox, of course, is that one is indeed always approaching this limit point of identity, but never actually arriving at this point, precisely because it is the process of multiplying/dividing a finite number can go on forever.
DeKoninck emphasizes — in contrast to Hegel and the Marxists (a point I will explore in a later post) — that this method can never actually attain the limit, i.e. it can never attain an actual identity between, e.g., a polygon and a circle, or a curved and a straight line, etc. The significance of this method lies not in what it reveals about any identity beyond multiplicity of the objects known, but in what it accomplishes for the faculty of knowledge itself. That is, this method reveals not the identity (a kind of unity or oneness) of the objects of knowledge, but rather attempts to arrive at, or rather approach, a unity in our means of knowing that multiplicity of objects. By way of the process of continually multiplying the sides of a polygon, we can approach a mode of knowing that encompasses both the circle and the polygon; but this mode of knowing cannot collapse the definitions of circle and polygon into each other without contradiction.
This is a function of the limited capacities of the human mode of knowing, as contrasted, say, with an unembodied intellect such as an angel, or ultimately such as the divine intellect itself. Because the human intellect relies upon the particular data drawn from the world by means of the senses, it requires distinct means of knowing — i.e. distinct concepts — for each of the objects which it knows. To the degree that the human intellect attempts to know multiple objects through one concept, it must sacrifice the concrete determinacy of those objects to the indeterminacy and vagueness of the more universal concept. E.g. the concept of a “figure” certainly encompasses both the circle and the polygon, but not as circle and as polygon; by contemplating the concept of a figure I lose the specificity of “circle” and “polygon” as distinct objects in themselves. To know those more specific objects, I require distinct concepts — concepts, to be sure, which include “figure” in their definition, but distinct concepts nonetheless. Indeed, there is an asymmetry of definition between the universal and the particular: the particular includes the universal in its definition (a polygon is a many-sided figure), but the universal does not include the particular in its definition (a figure is not some kind of polygon, as there are figures, e.g. circles, that are not polygons).
An angelic intellect is not subject to these limitations. By the contemplation of the single universal concept of a “figure,” the angelic intellect would thereby also grasp the infinite variety of specific objects to which that universal may be applied. The angel can have a perfect understanding of both “circle” and “polygon,” and all the many variants of the polygon, as distinct and determinate objects, by the contemplation of the single concept of “figure.” The angel requires no additional concept other than “figure” in order to grasp the distinctness of circles and polygons. This is because the angel’s knowledge is not dependent upon abstraction from particulars in the first place, as the human intellect is dependent upon the senses. Moreover, the angelic hierarchy is characterized by the ability to grasp more and more particulars by means of fewer and fewer concepts, according to the greater perfection of each angel within the ascending hierarchy.
The divine intellect surpasses all angelic intellects in grasping everything absolutely — the whole compass of being and non-being, that which exists and that which does not, that which is actual and that which is potential, in all of its infinite variety and particularity — through one concept alone, which is identical with the divine essence itself. In Thomistic language, which is DeKoninck’s language, one would say that the divine concept is “universal in representative power”: it is a single universal that, rather than (like the human concept) representing things only vaguely and indeterminately, represents them in all their specificity and determinacy. That is, its representative power is equal to the scope of its embrace — by contrast to the human concept, whose representative power actually decreases as its scope increases. Thus DeKoninck:
The problem of the One and the Many is usually confined to the manner in which things in themselves are one and many. Yet there is also a question of a One and Many with regard to the cognitive means by which we reach what we know. The latter (we shall call it the noetic as opposed to the natural problem) is amply treated by St. Thomas who, in this connection, draws from Platonic, and more particularly from Neo-Platonic sources. His teaching on this subject is as follows. For each object distinctly known we require a distinct means of knowing. Thus, the concept by which we reach the object “circle” is other than that by which we attain “triangle.” It is true that both objects may be known simultaneously by some common concept such as that of figure, but the genus “figure” cannot represent them distinctly. Whenever, by means of one concept, we actually consider many objects, we inevitably do so at the expense of distinction. In fact, distinct knowledge requires in us a multitude of cognitive means directly proportioned to the multitude of objects we know. This dispersion of our means of knowing is due to the empirical nature of our mind. Any finite intellect, knowing things in its own mode, requires a manifold of intelligible species, but the number of species, the extent to which the intellect is broken up and scattered about within itself, will be in proportion to its specific degree of perfection. Thus, if our mind were of a more exalted nature, a single concept such as figure might well represent simultaneously the several irreducible kinds of figure with even sharper distinction than that attainable by separate concepts used in succession. Indeed the Divine Intellect knows all things by means of the single intelligible species which is Its indivisible Essence.—The general concept by which distinct objects are known in confusion only, is called universal in predication (“secundum praedicationem”), whereas the intelligible species which represents distinct objects in their very distinction is said to be of universal power (“universalis virtute,” akin to Cassirer’s “concrete universality”). (“Concept, Process, and Reality,” in The Writings of Charles DeKoninck: Volume Two, 408-409.)
However, the same conditions which limit the human mode of knowing also provide the basis for the method by which the human intellect can attempt to surmount its limitations. The dialectic of limits is at once the sign of the limitation of the human intellect and the means by which it transcends itself, or approaches such transcendence. This dialectical method is applicable not only to mathematical objects but to natural objects as well. Between any two natures — between cat and dog, or between the lowest amoeba and the rational nature of man — there is a potentially infinite number of variations. The spectrum between the amoeba and man is just as potentially infinite as any variable quantity ordered to a limit, such as that embodied in the series 1, 1+1/2, 1+1/2+1/4, etc., ordered to the number 2 as its limit. To seek that limit point where, per impossibile, the amoeba and the human being might arrive at a perfect identity of natures is in fact to seek and approach a mode of knowing by which the whole spectrum of the biological universe might be grasped by a single means of knowing. I say it is only to approach such a mode of knowing, and that it is seek a limit point where identity is achieved per impossibile, because again such a limit is unattainable to the human mind in fact. Nonetheless, the potential infinity (rather than actual infinity, which is impossible) that is embodied in this process is a powerful tool in the mind’s ascent towards an ever higher, and ultimately divine, mode of knowing, where the endless variety of creatures — including those they do not exist — are comprehended in a single act of knowledge.
At the same time, while I claim that this dialectical tool is “powerful,” it is also uniquely humble or humbling, as it serves to remind man of the insurmountable limitations of his intellectual faculties. The limit is unattainable; he cannot attain the infinite which this process so evidently tends toward — he cannot fulfill the desire for infinity that is so intimately inscribed in his very own mode of knowing. This is why DeKoninck says that the dialectic of limits stands as a “critique of reason.” An infinite distance cannot be traversed even by the unending (and thus only potentially infinite) addition of finite natures upon each other. Thus, the same method which displays such a dynamic tendency and desire for the divine knowledge must also “despair,” as it were, of attaining such knowledge in actuality by its own powers; it can only be a participation, and to be sure, an ever greater and more perfect participation — but divine knowledge as such remains infinitely far off. This method must therefore terminate, not in the infinity which it always desires, but in a kind of dumbfounded silence.
Thus, DeKoninck summarizes the point:
This effort of the intelligence toward unification is, at bottom, only an attempt to reduce the multiplicity, not of the natures conceived, but of the means of knowing them. And that is its only point: to arrive at a higher view, more unified, consequently, more penetrating of the diversity of natures; to tend toward this unity and this penetration that simple coordination, however perfect, could never give us. In a sense, this view is only a limit that one never ceases approaching but never really attains. What we can do in this sense is only a shadow of a mode of knowing at the least superhuman. The view to which we can approach is only a tendency, an effort, an attempt at assimilation. Once more, it is only a shadow, but it is truly a shadow of intelligence properly so called.
To the degree that objects known by us are in a finite understanding, our concepts constitute an a priori structure that keeps us on this side of objects themselves. By objects themselves we here mean the object as known by the divine intelligence. But, again, we know, in a certain measure, this limitation: intelligence dominates its structure a priori, although the judgment that it makes on itself remains purely extrinsically critical and negative and can only pronounce its insufficiency. By contrast, using the method of limits, reason seeks to surmount the division in our knowledge, to surpass the finitude of our concepts always inferior to objects, and all that finitude entails of composition in our judgment and of formal discourse in our science; our intelligence finds itself instituting a positive and constructive critique of its own limitations. It tends, in a certain way, to repress reason, that is, it tends toward the condition of intelligence properly so called. What characterizes reason is the diffusion of its objects: there is need of formal discourse in order to attain their scientific coordination. Therefore it only imitates intelligence in a twisted manner; it does not surmount, even in a tentative fashion, the division of our concepts. On the contrary, in its critical movement toward a limit, our intelligence tends toward the universality of intelligences. Properly speaking, it tries to make itself similar to, so far as this is possible, the deiform intellect of separated substance, even to imitate in its fashion the supreme Wisdom which, in a unique intelligible species, contains the plenitude of all intellectual knowledge. (“The Dialectic of Limits as Critique of Reason,” in The Writings of Charles DeKoninck: Volume Two, 370-371.)
3. The idea of the universal is obviously central to this method. The method essentially consists in the search for a universal concept that embraces the whole variety of intelligible objects without sacrificing their specificity: a universal in representative power. Human knowledge does not ordinarily attain such a universal, yet it compensates for its inability to know things in such a way by undergoing the dialectical method, which DeKoninck emphasizes is inseparable from time: it is a movement, a process, just as a variable number is not simply a number but actually a moving process tending towards a limit. What the human intellect cannot possess in a single concept universal in power, it possesses through a temporal process of ordered succession among various specific concepts gathered under a single universal predicate. There is a dialectical motion between the universal predicate itself and its many and varied determinate subjects: between “figure” and “polygon” and between “figure” and “circle.” It is only within this essentially moving process that the ideal unity between two distinct concepts such as “polygon” and “circle,” grasped under a common universal “figure,” can be grasped at in at least a tentative manner.
A universal predicate, or a universal concept, is (for the human intellect) a necessarily vague and confused means of knowing; it only gains clarity when inserted into a dialectical relationship with the more specific concepts with which it may share the same subject, of which it may be predicated. “Figure” is vague and unclear until “polygon” is also predicated of the same subject. Thus, as such, “figure” does not contain anything very enlightening for the human faculty of intellect in attempting to know a given subject; it is relatively powerless in the pursuit of knowledge. I do not learn much about a particular figure, say a triangle, when I am told that it is a figure. I know more about the triangle the more specific is the concept which I can apply to it: i.e. it is a many-sided, or better yet, a three-sided figure. This, indeed, is a major facet of Aristotle’s critique of the Platonic Ideas or Forms, which are (according to the most common reading of Plato, anyhow) the effect of mistaking the more universal predicate of a given subject for the more real and thus more intelligible aspect of that subject; when in fact the more universal one ascends in the order of predication, the less on knows of the subject — unless, using the dialectical method elucidated above, one continually and without exhaustion returns to the particulars in “dialogue” with the universal. It is thus that one simulates the universal in representative power.
It is evident, then, that the trajectory of intellectual life is in some way towards the universal — but not a universal in the order of predication, except insofar as that universal is itself complemented by attention to particulars. In this way, it approaches the universal in representative power. This latter is therefore the true trajectory of knowledge, though it can only be approached as something in potency, and never attained as something in actuality. The paradox is that the universal in predication, on account of being a mere vague and indistinct abstraction, is at once disqualified from being the goal and end of the pursuit of knowledge, but is also an indispensable component of the mind’s approach to the universal in representative power.
In a way, the Platonic drive for the universal idea has thus been salvaged, even after being tested by the fire of the Aristotelian critique. One might even argue that if Plato’s original Ideas or Forms could be reinterpreted not as mere universal predicates but as universals in representative power, then the Platonic theory of knowledge would suddenly acquire a new validity. The only remaining question would be to what extent Plato thought that such universals could actually be held in the mind of man. The Thomist theory proposes that such universals are limits of a process that is performed by the human mind, and it is only as such that it is right to claim that human knowledge arises by participation in them. Something like this interpretation is present, I dare say, in the Neoplatonists — and Charles DeKoninck himself admits as much — for whom the unattainability and ineffability of that which is most universal, the One, or the First Principle, receives a new emphasis. Neoplatonism in its various forms, even in the more intellectualist form it takes in Plotinus, tends to regard the highest reaches of intellectual attainment as beyond the capacity of reason and all its methods. In Dionysius the Areopagite, Christian Neoplatonism reaches its apex in the application of the dialectic of limits to the created natures from which the divine names themselves are derived, leading the intellect through the vast causeway of created being into the abyss of divine self-knowledge beyond all being, where the human intellect must fall into deep silence before the darkness of God’s infinity.
This method truly does aim for a universal idea, and it is therefore truly Platonic in this way — but Aristotelian in the way it clarifies how the universal idea cannot be attained in actuality, but only tended towards in a dynamic (potential) manner. This Aristotelian clarification does not merely negate the Platonic position, but actually serves to clarify the limits of what Platonic participation can mean; and this clarification is integrated into the Neoplatonic synthesis. For the universal idea aimed at by this process is not an abstraction — and yet it depends for its (always potential) realization on the abstract universals that are characteristic of human knowledge. In some degree, then, the intellect in aiming for such a universal in power is quite justified to turn to its own abstractions, the vague universal concepts which it derives from particulars, so long as it supplements these abstractions with continual return to the particulars themselves. In this way it “fills” the empty universal with content, discovering that this process of “filling” can indeed go on forever; and it is precisely this unending process, as a process, that reflects the divine universality which intellectual nature desires.
4. In the Thomistic framework, as I have stated many times already, the universal concept is not, for the human mind, a clear and distinct concept, but a vague and confused one. As such it is not, by itself, sufficient for the attainment of knowledge. Of all universal concepts, the most universal is that of being, which is therefore the most vague and the most confused. Indeed, Aquinas will insist, following both Aristotle and the Platonists in various ways, that being is so universal that it is not even contained in any logical category of determined being. “Being is said in many senses,” said Aristotle. This is one meaning of the claim that being is a transcendental. Of all concepts, it is the least determined, the least specific, and thus the least illuminating to the intellect which desires to know reality.
However, it is this same concept — being — that expresses the very subject of the first and noblest of the philosophic sciences, namely metaphysics. Perhaps this seems to be something of a paradox: that the noblest of the sciences has for its object the concept of being, which is the least clear and the least helpful of all concepts, precisely on account of being the most universal. Aquinas also states famously in the beginning pages of the De Ente et Essentia that being is the first concept that falls in the intellect. This is in line with its nature as a universal: the first things which the intellect knows are, in a way, the most universal, and the most vague; it is only subsequently, as the intellectual process unfolds, that this initial conception is clarified and specified as the intellect approaches the particular.
It is this process of approaching the particular that fills out the beginning concepts, which are the most universal, especially the concept of being, thereby — again — approximating the universal concepts that are held in the mind of supra-human intelligences, such as the angels and ultimately God. Thus, while the initial universal concepts that fall in the human mind, and especially the concept of being, are the least vague and the least powerful in their ability to represent reality adequately to the mind, it is precisely for the sake of rendering them so adequate that the intellectual approach to the particular must take place at all. In other words, even though the movement of the intellect from the beginning of its inception is in the direction of the particular and away from the universal — in the direction of the clear and distinct, away from the vague and confused — it is still true to claim that, ultimately, the goal of the intellectual pursuit is the completion and fulfillment of the initial universal, by rendering it into a more adequate and powerful representative of the whole of reality. The concept of being comes to mean a whole lot more precisely by being supplemented by the vast diversity of particularities which are discovered subsequently. This is why the science of metaphysics remains the highest of the sciences: because it brings the intellect back around to its very beginning, which is the universal concept of being, but with a fuller and more complete comprehension of that concept than what it started out with. T.S. Eliot says it well: “the end of all our exploring will be to arrive where we started and know the place for the first time.”
Have you read Guenon's "Metaphysical Principles of the Infinitesimal Calculus"? Relevant to section 2 here. Short read, but illuminating and helpful imo. I've never been much of a math guy