Thomistic Note: The Use of Triplex Via Throughout the Various Forms of Analogy

Introductory Remarks

While recently correcting exams in an overview course of philosophy for new master’s-level theology students, I found myself continually making a similar remark to my students: Remember that you can apply the three “tools” of causality, negation, and eminence not only to the case of analogical predication of the names of God, but really in all cases of analogy. Eventually, because I also was receiving follow-up questions from students about this topic, I thought that perhaps I should investigate this point speculatively so as to lay out its importance more clearly. The present reflection has this task as its end.

Not everything can be done in a single essay, and this particular one has pedagogical ends, due to the conditions that gave rise to it. For that reason, I must leave in the background all of the many sources that have influenced me over the years on the topic of analogy and which I consult whenever this topic comes up. However, because more advanced readers might be interested in the background to what my thought is, allow an opening remark in which I might reference certain texts that have influenced my conception of the notion of analogy.

At the center of the many Thomistic articles and texts that have been written on analogy, the essay by Yves Simon, “On Order in Analogical Sets,” stands in a preeminent place. A significant portion of my outlook has been very influenced by this work, which, alas, is not as appreciated as perhaps it should be. (In the words of a venerable old Thomist member of the American Maritain Association: Simon is ignored because he committed the “sin” of not merely undertaking textual explorations.) The particular view that I have concerning the relationship between order and “imperfect abstraction” comes from him. Of course, this implies that I stand in the line of Cajetan and John of St. Thomas, with the alterations made by Simon. As a young man, I was introduced to Cajetan’s De nominum analogia through the somewhat pedagogical work of James Anderson, as well as the excellent study by Joshua Hochschild and the works of Steven A. Long.

Moreover, although I don’t share some of his criticisms made against this tradition, there are elements in the theory of John Deely’s “The Absence of Analogy” which have exercised a kind of influence on my thought, above all in his view of how “analogy” refers to a process by which terms come to be modified in their meaning (though I am not sure what I think about his positions regarding the immediate connection of this process to language, for I think the latter embodies also a purely intellectual “analogical process” within mental language itself—and in the end, I think that Deely could perhaps agree to a truce at least on this point).

I have been less influenced by some of the Thomists who have critiqued Cajetan, such as McInerny, Burrell, Montagnes, et al. Moreover, I think that the supposed theory of analogy found in someone like M.-J. Le Blond is problematic for reasons that I have discussed elsewhere. Finally, I have only somewhat engaged with the texts of those in the line of Przywara, which involve many issues of metaphysics and phenomenology which are of interest to the topic of analogy, though it also opens upon a broad scope of topics and authors that one must take care not to simplify by way of simplistic summary. (Ultimately, I suspect that—like Le Blond, though with far different and more solid sources—one should count Przywara as being a sui generis account that must be contextualized as scholastic adjacent. This requires, therefore, profound labors to properly fuse horizons, where such fusion is possible.)

Among the texts that I can consult on occasion and often feel that I should consider even more, I would be remiss if I did not add the textual resources found in the volume on analogy by Klubertanz and the massive De analogia of Ramirez, which stands on my shelf deserving even more use than it gets!

I should make another remark regarding certain historical points. On some points, I at least agree with the diachronic notes that have been made about analogy in Thomas’s own writings by John Wippel. Moreover, I think that the work of Dominic D’Ettore on the history of analogy during the period first following upon Thomas’s death is a very important unfolding of the philosophical and theological problems associated with analogy. Also, work on analogy in the Scotist tradition by authors like Thomas Ward and, especially, Garrett Smith are very important correctives to certain simplistic narratives, sometimes even engaged in by authors who are generally dear to me.

However, all of this is a bit of “throat clearing” in order to prepare for the main portion of this pedagogical essay. The overall trajectory will be relatively simple. I will merely outline a kind of approach to thinking through the process of analogical reasoning, gradually working into it by contrasting it to univocation and equivocation. Although I will be rehearsing certain things from the tradition of Cajetan and John of St. Thomas, mediated through Simon, the approach will be my own, attempting to capture the phenomenon of analogical reasoning and the intellectual stabilization of an analogical term. My primary goal, by the end, is merely to show how the logic of the triplex via is useful for unpacking the priority-posterioirty ordering that is found among analogates of any sort.¹

General Outline of Analogical Reasoning

Simon is very correct whenever he amusingly notes, at the beginning of the aforementioned essay, how it is the case that very often people do not suspect the difficulty involved when they learn early in their philosophical formation: analogy stands between univocity and equivocity. They effectively think that they can dust off the notion of analogy, show how it involves meanings that are neither completely the same nor completely different. And after a few well-planted distinctions, it would seem that everything will be in line and properly set in order…. Yet, if one is truly intellectually engaged, one will find for many years things to reflect upon regarding something that stands at the very center of the mystery of metaphysics and human cognition. The great complexity of this topic is what causes the somewhat vexing experience that all Thomists have had when speaking with fellow thinkers whom one would think would agree on a topic that is supposedly at the center of Thomas Aquinas’s thought: if you gather 5 Thomists and speak about analogy, you are perhaps likely to get 7 different articulations…

The human mind is made to seek out similarity and difference. This point haunted Plato, who was well aware of the fact that the mixing of sameness and difference seems ubiquitous among finite realities. And although he desired, in a kind of “mitigated Parmenidean” fashion, to make each of his Forms completely self-independent, one has the sense while reading the Parmenides and the Sophist that he is aware of the fact that the forms must intermingle, at least in discourse (though perhaps also in finite realities too). And, at the center of this intermingling are the forms of Sameness and Difference. Moreover, the process of knowledge is perhaps nothing other than a recapitulation of the transcendent intermingling of the Forms, at least, if one thinks about the way he speaks in the Timaeus regarding the way that the “circles” of the Same and the Different resound in the soul as we achieve knowledge.

Those who follow in the line of Plato’s illustrious student, Aristotle, will, however, push further in their analysis. From the perspective of first principles, sameness and difference have a further resolution: into being and non-being. The intellect is not nearly made for finding sameness and difference but, ultimately, being and non-being. Through speculative cognition, the intellect expresses for itself the being of realities, and through practical cognition (whether moral or artistic), it declares what should be in the world. At the heart of human cognition is the intellect’s élan to commune with being in all of its instantiations. The mind is as broad as the universe, and indeed, even broader than that...

This means that as the human intellect seeks to articulate its experience, it will rely upon affirmations of being and denials thereof. The classic division of terms into “univocal,” “equivocal,” and “analogical” will therefore reflect the intellect’s capacity for affirming the being and the (relative or absolute) nonbeing of the realities that it knows.²

Somewhat rarely is a univocal term purely univocal in our usage. Consider the following genera: house, dirt, plant, elephant, cat. Because of convention, we very often consider these terms in their immediate signification. Thus, we consider these terms along these lines:

• House: a structure for shared and regularized human life

• Dirt: pulverized and loose dry soil

• Plant: a living substance living by way of these or those organic photosynthetic processes

• Elephant: A large pachyderm with a prehensile trunk

• Cat: a domesticated feline animal

These various definitions are likely all in some way accidental, but they manage to isolate the meaning of the term in question. And, if pressed, we would seek to give precision to these definitions. While we so search to express their meaning, we will desire to find a signification that we can affirm of all cases falling under that particular term. We will be looking for that absolute character that enables us to say: grass, a tomato organism, an oak tree, etc. is a plant, full stop; a bungalow, a cape cod, a double-wide trailer, etc. is a house, full stop; and so forth. Although we might say that a given organism is, perhaps, more perfectly a plant (an Oak is more complex a plant than is grass), nonetheless, when we successfully find the definition of plant, we affirm that this equally holding for all cases, semantically abstracting from the particular species that belong to that genus.³ The common genus in each case is unqualifiedly affirmed: a bungalow is a house, an oak is an plant, but so too is grass.

However, as I already noted, each of these (explicitly chosen) cases involves a kind of implicit discrimination that we make because of the force of custom. In point of fact, each of these terms are subject to a kind of equivocation (which we will discuss as metaphor). Rarely, however, is an equivocation completely “by chance.” Indeed, for this reason, whenever we speak of equivocation in common speech, we almost always are actually speaking about metaphor, as should become clear as we continue this article. Most cases of pure equivocation are linguistic happenstance of homonymy: “saw” as applying to both tool and as past tense of the verb to see; “rose” as applied to the plant and to the verb to rise; “tire” as applied to the rubber “attire” for a wheel and as related to exhaustion. Other pure homonyms would include: tear, bow, mint, and bat. In such cases, the unity of meanings exists only in the term itself, foremost as expressed by the mind, but also importantly as stabilized in a spoken or written term.

In such cases of pure homonomy, the difference of meaning (and hence too the difference of being) is quite absolute: there is nothing common that can be affirmed outside of the very extrinsic fact that these multiple realities are gathered together in relation to a given term. Therefore, here affirmation of commonality is most minimal and denial most maximal.

We do, of course, find ourselves faced with the need to disambiguate such pure equivocation from time to time. However, very often it is the case that at least some kind of etymology hides a transfer of term from its primary meaning to some other secondary meaning. And in this case, we find ourselves in a very important situation of equivocation which, in fact, is already on the way toward analogy, namely: metaphor. In rhetoric we can distinguish between metaphor and simile, and also discuss particular kinds of metaphors such as synecdoche, metonymy, catachresis, (I would argue as well, at least in a way) irony, etc.⁴ For our purposes, we will treat these all in the very general sense of the Greek basis of this term (μεταφέρω), connoting the idea of transferring something from one place (or owner) to another.

Although the case of etymology is very interesting,⁵ let us instead return to some of the univocal examples given above. In context, we very often use each of these terms (or something paronymously derived therefrom) to indicate some transferred meaning. For each of the terms listed above, we can consider the following examples of transference:

• This structure houses 100 boats. (Very proximate in meaning.) In the storehouse of his mind, he had many memories. (Transference, treating knowledge like a kind of quantifiable “area”.)

• He did not want to dirty himself by talking to the wrong kind of people. (Treatment of “dirtiness” in a broader sense concerning social situations.)

• The steel plant had a very high production capacity. (A transference based upon the way that a steel plant is a kind of fixed location for producing things, like how vegetative plants are fixed beings that organically produce their life cycle. In fact, the term “plant” is subject to many metaphorical aspects over the course of its history.)

• Nobody was discussing the elephant in the room. (Because some situation or problem is a “big deal”, we speak of it as though it were a huge elephant.)

• This or that person can be very “catty” toward other people. (Based upon the scratching action of cats, we say that people have this kind of hurtful capacity to be “catty”.)

Metaphor structures a huge amount of our discourse. (Technically, even in that last sentence, “structure” and “huge” are metaphors.) Brief reflection upon our language bears witness to the fact that it is carried along very often by a whole series of metaphorical transferences, affecting even the use of prepositions. Think of the three very different senses of “in” used in the following statements: the book is in the room; I am in love with her; the memory was in my mind.⁶ In cases of metaphor, we find ourselves to be using both affirmation and denial in order to stabilize the likeness and dissimilarity between the realities to which we apply the term in question.

Now that we find ourselves deploying a more intermingled kind of affirmation and denial, I would like to introduce the classic triplex via of causality, negation, and eminence most regularly associated with the Proclean theologian-philosopher Pseudo-Dionysius.⁷ Most often, these three aspects of analogical predation are associated with our knowledge of God: we can analogically predicate names to God, because He is the cause of this or that perfection; but, we deny that He has this perfection in a way that accords with the finite mode in which it is realized in finite beings; rather, we say that he super-eminently has this perfection. This is all good and true, but this use of the triplex via has application in all of the forms of analogy, even metaphorical “improper” analogies. The application to the case of God is just the most transcendent and loftiest case of such application.

Let us consider the examples above. Technically, the question of causality is quite difficult here. At most what we can refer to in each of these examples is some kind of “formal similarity.” (And, as we will see in case of proper proportional analogy, this is quite fine for engaging analogical reasoning.) However, negation and eminence are indeed very readily deployed here. For example, in a case of speaking about “an elephant in the room,” we deny formally that this is an elephant-animal but, instead, only something that is metaphorically “large” like an elephant. What is more, we very clearly assert eminence, to the maximal point: “elephant” is super eminently applicable to the animal, and only very very partially applicable to the human situation used in the example here.

Now, this kind of application of the triplex via works also in another important case of equivocation, which brings us into the domain of what has come to be called analogy (even though in its original meaning analogy applied only to proportional analogical structures): the analogy of attribution or “pros-hen equivocation,” a kind of managed equivocation, which has a central and focal meaning. The classic example is, of course, health. Thus, we can say that grapes are not healthy for dogs; that a certain consistency of urine or blood is healthy; or that the dog itself is healthy. Technically, however, we cannot say that either the grapes or the urine (or blood) are healthy (or unhealthy) in the strict sense that holds for the case of the dog itself. Grapes can be called “unhealthy” only in reference to what it is for a dog to have a healthy constitution and in so far as grapes cause a lack of health. Similarly, it might be very healthy for a dog to have a certain report for his blood work, but that same kind of blood work would be indicative of illness in a human. In any case, though, it is not the qualitative state of being healthy; rather, such blood work or urine is a sign or effect of health (as specified for dog health).

Here, as well, we can use the triplex via to spell out some of the relationships between the particular “analogates” and the “analogue” (health) that unites them together. Causality is truly operative here. We are able to say that the grapes are a “cause” (I would say material cause) of a lack of health. Moreover, we can say that health in the organism is a cause of “healthy” urine or blood. But whenever we say this, we also come along to say that we must quite importantly deny that health is found in urine or grapes in the same way as it is found in the very activity of being a healthy organism. Moreover, because we must recognize the primacy of the analogate that is health in a dog organism, we affirm the eminence of this prime analogate. In fact, the eminence is so great that there really is only one meaning that is formally good, with all the other meanings being derivative upon that particular meaning. (And, thus, too, technically, none of those other cases of “health” are real instances of health.)

This is where we find that there is difficulty applying such attributional analogy even to the case of the categories of being: substance, quality, quantity, action, etc. Each of these indicate a particular way of being, and we cannot say that only substance really is being, with all of the other categories basically fading away and not formally having the character—unique in each case—of “that which is”. Therefore, even at this level of the categories, we must bring in the analogy of proportionality, returning somewhat to the structure of cognition involved in metaphor–but here with some important differences. When we attribute “being” to quality, we indicate various modes of something being “such or such”; when we attribute “being” to quantity, we indicate various ways of being by which parts can be spread outside of each other; etc. In each of these cases, there is a likeness that is not univocal, but which suffices for gathering together a set of analogates. However, there is an order among these analogates: substance comes first, quantity and quality both depend upon substance, though it is arguable that in physical substances, quality depends upon quantity, etc.

In other words, the analogically common notion of “being” applies to each analogate (substance, quantity, quality, etc.) in different ways, according to different rationes, but in a way that really and formally applies to each analogate. Hence, we will here need to establish an analogy that takes up a series of proportions in order to express the meaning of the general term (which only imperfectly abstracts from the specific instances thereof)—being : substance :: being : quantity :: being : quality :: being : action…

Here too, we can apply the triplex via in order to help us order this set. Thus, substance is the cause of all the other accidents technically by way of material causality (as the subject of inherence) but also as the radical principle of the esse (or existence) in each of those accidents. Moreover, we could say that there is a kind of causality operative between the various qualities of a being and particular ways in which it is said to be in action. And so forth. Moreover, we can deny that the being of quantity (which is nothing other than the exteriorizing of parts outside of each other) is as rich as that of substance (which is the unified being of an operative subject), the latter having being in an eminent sense. We see here, therefore, some ways that causality, negation, and eminence can play out in order to parse the priority and posteriority which is an essential property of analogical unity. (And this work of “parsing” is necessary in order for us to actually think through a case of analogy in act, thereby recognizing what the tradition has come to call the “imperfect” abstraction of the analogue from its analogates.)

We can also think of cases that have no kind of evident efficient, final, or materiality; and even in these cases, the structure of the triplex via is present. Thus, the various degrees of life (plant, sense, intellectual) each have something formally-causally similar with each other, even though we must apply denial and eminence in order to distinguish and order these analogates. Similarly, the notion of duration can be parse as time, aeviternity, and eternity; sin can be parsed as original and actual, with the latter being divided into the analogates of mortal and venial sin; and so too for efficient causality as transitive and immanent. Many other examples could be drawn, but in each of these cases, there at least remains an analogical formal-causal link between the analogates. And this link is parsed by the means of the “no” of denial and the “YES, INDEED” of eminence.

This note cannot solve every issue related to analogy. But it is my hope that I have made some small contribution to the understanding of this topic for those who have read it. Interestingly, whenever Cajetan speaks of the “comparison” that is necessary among analogates (arguing against certain possible objectors), he does note the role of participation for understanding at least one kind of analogical comparison relationship. As soon as one hears the language of “participation” being used, one rightly senses the formal-causal (whether intrinsic or extrinsic) kind of an analysis that is most at home in Platonism and Neo-Platonism. Cajetan would not be numbered among those who hyper-valorize the Platonic elements in Thomas. But he was a disciple of the truth, and he here hits on a very important point that I think can connect the analogy of proper proportionality to the Neo-Platonic elements in Thomas, especially those drawn from Pseudo-Dionysius. The role of TRUE⁸ metaphysical participation is reflected in the prior-posterior ordering that takes place in all analogy (whether the technically-equivocal case of attributional analogy or in the case of properly proportional analogy), and this ordering is very well articulated, in all cases of analogy, by the use of the triplex via of causality, negation, and eminence.

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1. Originally, I had planned to draw out a series of examples from the end of an article by John Cahalan, who has gathered together a very useful listing of properly proportional analogues and analogates in John C. Cahalan, “Thomism’s Conceptual Structure and Modern Science,” in Facts are Stubborn Things: Thomistic Perspectives in the Philosophies of Nature and Science, ed. Matthew K. Minerd (Washington, DC: American Maritain Association, 2020), 40–68 (here, 66–68)↩︎

2. The reader will notice that the context of this essay is much more concerned with the cognition and logic of analogy, allowing the background metaphysics to remain somewhat unstated, although it is the important foundation for the very possibility of analogy in a realistic sense.↩︎

3. The well apprised reader will sense in the background here of the somewhat problematic case of the so-called “analogy of inequality.” I am setting that aside here.↩︎

4. I am taking my references here from the neat and useful little book Adina Arvatu and Andrew Aberdein, Rhetoric: The Art of Persuasion (New York: Bloomsbury, 2015).↩︎

5. And can have important philosophical use, as one sees in someone like Heidegger, though others, including Thomas Aquinas, have not been deaf to the usefulness of this kind of linguistic tool.↩︎

6. For a thoughtful reflection on this topic, see George Lakoff and Mark Johnson, Metaphors We Live By (Chicago: The University of Chicago Press, 2003). Also, for a more recent work that probes the borders of the scholastic notions of equivocation, metaphor, and analogy, see Douglas Hofstadter and Emmanuel Sander, Surfaces and Essences: Analogy as the Fuel of Thinking (New York: Basic Books, 2013).↩︎

7. For a history of this “threefold way,” see Fran O’Rourke, “The Triplex Via of Naming God,” Review of Metaphysics 69 (March 2016): 519–54.↩︎

8. This is emphasized because, in the case of much of Platonism, although participation and “imaging” is real, nonetheless, Platonism, through its extreme realism, tends toward a kind of nominalism as regards “participated’ realities. (Thus, in addition to Parmenides and Pythagoras, a bit of Heraclitus and Cratylus remain in Plato’s metaphysics of finite beings.)↩︎