The Thomist 77 (2013): 531-58 PROPORTIONALITY AND DIVINE NAMING: DID ST. THOMAS CHANGE HIS MIND ABOUT ANALOGY? JOSHUA P. HOCHSCHILD Mount St. Mary's University Emmitsburg, Maryland THERE IS A QUASI-"GENRE" of passages in which Aquinas distinguishes varieties of analogy in a theological context. In several works across his career, he introduces analogy as the crucial part of an answer to a question about how to understand the relationship between creatures and God. The elaborations of analogy in these various passages share at least three common features: (1) they locate analogy between univocation and equivocation; (2) they classify at least two, and sometimes more, different kinds of analogy, often with examples of each kind; and (3) they indicate that one of the kinds of analogy thus distinguished is the one most relevant to understanding divine naming. 1 Six such passages which are often discussed are (in chronological order): I Sentences, d. 19, q. 5, a. 2, ad 1; I Sentences, d. 35, q. 1, a. 4 (in this case, no examples are given); De Veritate, q. 2, a. 11; De Potentia Dei, q. 7, a. 7; Summa Contra Gentiles I, c. 34; and Summa Theologiae I, q. 13, a. 5. Scholars today typically treat one text in this genre-one of the most detailed and apparently comprehensive passages on 1 Different commentators have explored individual texts with great care. To give just two examples: I Sent., d. 19, q. 5, a. 2, ad 1 is the main subject of Lawrence Dewan, "St. Thomas and Analogy: The Logician and the Metaphysician," in idem, Form and Being: Studies in Thomistic Metaphysics (Washington, D.C.: The Catholic University of Anterica Press, 2006),81-95; De Potentia, q. 7, a. 7 is treated at length by Mark Jordan in "The Names of God and the Being of Names," in Alfred Freddoso, ed., The Existence and Nature of God (Notre Dame: University of Notre Dame Press, 1983). 531 532 JOSHUA Po HOCHSCHILD analogy in all of Aquinas-as idiosyncratic and unrepresentative of Aquinas's thought. The prevailing view is that question 2, article 11 of De Veritate represents an approach to analogy which Aquinas only temporarily entertained, and soon abandoned. As John Wippel describes this view in his magisterial treatment of Aquinas's metaphysics: "lVIost more recent scholars regard this particular discussion of Thomas as uncharacteristic his earlier and later thinking on analogical predication of the divine names, and hence as not reflecting definitive position.,,2 It is intriguing to find it so widely accepted that Aquinas changed his mind about analogy-indeed that changed it twice, soon before and soon after writing one of his most extensive elaborations of a classification of analogy. In this paper I will discuss Aquinas's classification of analogy in De Veritate, and summarize reasons that recent scholars have given for regarding this classification as atypicaL While the text does appeal to the notion of "proportionality" in a way that the other texts do not, we will see that the other texts are diverse enough that De Veritate hardly seems to deserve to be singled out. Then, by offering some philosophical clarifications about the notion of proportionality, I will show that the teaching of De Veritate is, in principle, philosophically consistent with Aquinas's teachings on analogy other places, and further that there are good theological and philosophical reasons why Aquinas might emphasize different things in this passage than he might in other passages that are otherwise similar. The hypothesis that Aquinas changed his mind about analogy turns out to be unnecessary once we take sufficient account of his attention to dialectical context. 2 John Wippel, The Metaphysical Thought of Thomas Aquinas (Washington, DoC: The Catholic University of America Press, 2000), 5530 As Wippel's footnotes make clear, the modern consensus has roots in the work of Klubertanz, Lyttkens, and especially Montagnes, the last to be discussed belowo PROPORTIONALITY AND DIVINE NANlING 533 L DE VERITATE, Q. 2, A 11 AND ITS COUSINS In the Disputed Questions on Truth) question 2, article 11, Aquinas raises the question of how a predicate, this case "knowledge" (scientia), can apply both to creatures and to God. The burden of his answer-as always when he poses this sort of question for himself-rests squarely on notion of analogy. In the body of the article, he first explains analogy in general, introducing it as a mean between univocal and equivocal predication. He then distinguishes several varieties of analogy in order to indicate which one is relevant to the case of predicating names of both creatures and God. It is the second part of the discussion, about different varieties of analogy, that concerns us. Aquinas first distinguishes two sorts of analogy, according as whether the agreement between the analogous things is (1) an agreement of proportion or a determinate relation (e.g., 2 is the double of 1; urine is healthy as the cause of health in the animal); or (2) an agreement of proportionality, or relation of proportions (e.g., 6 is to 3 as 4 is to 2; or "sight" is predicated of the intellect because understanding is to the intellect as physical sight is to the eye). This latter sort of agreement, agreement of proportionality, is further subdivided into: (2a) metaphor, when the word as applied to one analogate implies something that cannot be affirmed of the other (as is the case when the term "lion" is predicated of God); and (2b) another sort, not given a technical name but obviously a more proper or genuine form of analogy, obtaining when what is implied by the term as affirmed of one analogate can be appropriately affirmed of another analogate. Giving examples for each type and subtype, Aquinas concludes by answering his question, that knowledge can be predicated of God in the way mentioned, "according to an agreement of proportionality," in the nonmetaphorical, or properly analogical, wayo The classification of analogy in this text can thus schematized as follows (including Aquinas's own descriptions and examples): 534 JOSHUA Po HOCHSCHILD CLASSIFICATIONS OF ANALOGY IN DE VER1TATE (1256-59), Q, 2, A, 11, CORP. Designation Description Examples (1) agreement of agreement between two " 2 is the double of 1 proportion things with a m "being" [predicated of determinate distance or relation substance and accident] @ "healthy" [predicated of urine and animal] (2) agreement of agreement between two " 6 is related to 4 proportionality proportions because 6:3::4:2 9 "sight" [predicated of eye and intellect] (2a) metaphor the definition of one "lion" [predicated of implies something that lion and God] cannot be in the other (metaphor) (2b) the definition implies .. "being," "good" nothing that cannot be [predicated of creature in both and God] Like the passage summarized here, the other five passages mentioned above distinguish different sorts of analogy in order to show which sort applies to God. All of them but the one from distinction 35 of book 1 of the Sentences commentary also illustrate these different sorts with examples, and do so with the apparent intention of explaining and articulating some important points about analogy, rather than simply recalling or eliciting assent to already accepted doctrines. For my purposes it will be sufficient for me to summarize the teachings of these other five texts in the same simple table format. PROPORTIONALITY AND DIVINE NAt\1ING 535 CLASSIFICATIONS OF ANALOGY IN FIVE THEOLOGICAL TEXTS L I Sent. (1252-56), d. 19, q. 5, a. 2, ad 1 Designation Description Examples (1) according to the intention refers to many " "health" [predicated intention, and not by order of priority and of animal, urine, according to being posteriority, but has being and diet] only in one (2) according to many equated in common ., "body" [predicated being, and not intention, which does not of corruptible bodies according to have the same being in all and incorruptible intention bodies] (3) according to neither a common intention '" "being" [predicated intention and nor same being, a common of substance and according to being nature with greater and accident] lesser perfection 2. I Sent. (1252-56), d. 35, q. 1, a. 4 Designation Description Examples (1) agreement in some one thing, according to an order of priority (2) one is an appropriate imitation of the other 3. De Potentia Dei (1259-1268), q. 7, a. 7, corp. Designation Description Examples (1) predicated of two two things must be @ "being" [predicated with respect to a third preceded by something of quantity and to which each of them quality with respect bears some relation to substance] (2) predicated of two one of the two must " "being" [predicated because of a precede the other of substance and relationship between the quantity] two 536 JOSHUA P. HOCHSCHILD 4. contra Gentiles (1259/60-1264/65) I, c. 34 Designation Description Examples (1) many-to-one '" "healthy" [predicated of medicine, food, and urine in relation to animal] (2) one-to-another .. "being" [predicated of substance and accident] (2a) order of reality same as '" "being" [predicated order of naming of substance and accident] (2b) order of reality " "healthy" different from order of [predicated of nammg medicine and animal] 5. Summa Theologiae (1266-68), I, q. 13, a. Designation Description Examples (1) many-to-one " "healthy" [predicated of medicine and urine in relation to body] (2) one-to-another s "healthy" [predicated of medicine and animal] To present the teaching of the texts in this format is to distill theoretical structures from the prose and larger context in which they are presented; later we need to take some account of what is ignored in this summary. Acknowledging that inherent limitation, we can say each table here portrays Aquinas's own presentation of divisions of PROPORTIONALITY AND DIVINE NAMING 537 analogy. In each case, the table preserves Aquinas's designations for the distinguished (where given), his explanations or descriptions for each (again, where given), and the examples uses to illustrate each type of analogy (once again, where given). The first thing to note about the classification schemes of these five other texts is that in no obvious way do they provide a uniform background against the De Veritate passage jumps out in stark relief. The most uniformity is in the three passages-from De Potentia Dei, Summa contra Gentiles and Summa Theologiae-which use essentially the same terminology to make (what seem to be) the same sorts of (Though even here, ScG employs an apparently significant subdistinction not employed in De Pot. or 5Th.) AJI three of these texts use terminology that differs from that of the two Sentences passages of De Veritate. It also appears that what differs among the six passages is not just the terminology but also the of conceptual distinctions that are being made. The first passage has three different divisions according to different answers to the overlapping questions of whether the analogy is or is not "according to intention" and "according to being." In the second passage, reference to one thing is contrasted with imitation. In De Veritate, as we have seen, the contrast is between proportion and proportionality. In the three texts, we have variations on many-to-one versus one-to-another relations. As further evidence that these are not just different verbal formulations for the same consistent theoretical distinctions, we may notice that different phenomena find a place in different divisions. So, for instance, the first Sentences passage, and only this passage in the group, a place for what is formally a case of univocation3 (type "body" predicated of corruptible 3 Univocation can be a form of analogy from a "metaphysical" as opposed to "logical" point of view: while a stone and a man are equally bodies ("body" behaves logically univocally, signifying corporeity in both the stone and the man) they are not equal bodies-indeed, the actual significate of "body" in man (his corporeity, which is 538 JOSHUA P. HOCHSCHILD and incorruptible bodies). Only the classification in De Veritate finds a place its classification scheme for metaphor (2a). Complicating matters even further, the passages make different uses of examples. In the first Sentences passage, divine names are said to like "being" as said of substance and accident, but the divine names are distinguished from "being" as said of substance and accident in the Summa contra Gentiles and De Veritate. Likewise "being" and "healthy" illustrate the same type of analogy in the De Veritate examples, but they illustrate different types of analogy in the first Sentences passage) and the contra Gentiles. Even those texts that are fairly similar in their formal divisions use examples quite differently. In De Potentia, "being" is an example of types of analogy, but in the Summa contra Gentiles "healthy" is an example of both major divisions (1 and 2b) while "being" is only an example of one kind (2a). In the Summa Theologiae, "healthy" illustrates both kinds, and "being" is not used as an example at all. Since in each classification the last mode of analogy characterized is supposed to apply to the relation between creatures and God, we find divine names likened in one passages to "being" (I Sent., d. 19), while in another passage divine names are said to operate otherwise than "being" (ScG), and in two passages divine naming operates like some cases of "being" but unlike others (De Verii'. and De Pot.). Given the obvious diversity of Aquinas's classifications of analogy, it is not surprising to find scholars either arguing that there is a lack of a consistent teaching, or employing creative interpretation to some passages more compatible than they may first appear. What would be surprising, at least to someone first introduced to these texts, would be the notion that De Veri tate stands out as the one text which differs from the others and is therefore unrepresentative of Aquinas's views. his human soul, given the thesis of the unicity of substantial form) is of a higher grade of reality than the actual significate of "body" in the stone. See Armand Maurer, "St. Thomas and the Analogy of Genus," The New Scholasticism 29 (1955); 127-44. PROPORTIONALITY AND DIVINE NAMING 539 And yet this is the case made by several scholars starting in the 1950s-not incidentally, often as part of a criticism of Cajetan's analogy theory, cites the text from De Veritate as an authority. Studies by Hampus Lyttkens and George Klubertanz are important sources for 4 but one of the most influential interpreters of these passages is Bernard Montagnes.5 II. MONTAGNES'S APPROACH TO AQUINAS'S CLASSIFICATIONS OF ANALOGY lvl.ontagnes interprets the texts at issue as different attempts to answer a consistent question about what kind of unity between creatures and God. Finding different answers to the same question, Montagnes proposes an account of how Aquinas's views In his interpretation, the historical progression of the texts reveals two movements in Aquinas's thought. First, a unity of likeness (in the Sentences commentary) is replaced by a unity of proportionality (in De Veritate). Second, a unity of proportionality is replaced by talk of reference to one or "analogy of relation" (in subsequent texts). Montagnes understands the first move (from likeness to proportionality) as prompted Aquinas's realization that likeness could imply a common form, some one thing in reference to which both analogates are defined, or one defined in terms of the other. Since sharing a common factor would 4 Hampus Lyttkens, The Analogy between God and the World: An Investigation of Its Background and Interpretation of Its Use by Thomas of Aquino (UppsaJa: AImqvist and Wiksells Boktrycheri AB, 1952); and George p, Klubertanz, Saint Thomas Aquinas on Analogy: A Textual Analysis and Systematic Synthesis (Chicago: Loyola University Press, 1960), 5 Bernard Montagnes, La doctrine de l'analogie de l'fitre dOapres Saint Thomas d'Aquin (Louvain: Publications Universitaires; Paris: Beatrice-Nauwelaerts, 1963), For English translation see Bernard Montagnes, The Doctrine of the Analogy of Being according to Saint Thomas Aquinas, trans, E. M, Macierowski (Milwaukee: Marquette University Press, 2004), 540 JOSHUA p, HOCHSCHILD ultimately imply Aquinas experimented with the four-term proportionality relationship as a way of describing likeness that safeguards divine transcendence. The second move (from proportionality to analogy of relation) Montagnes argues is by further realizations about the metaphysics of participation. Proportionality may have safeguarded transcendence, but at the expense of the intrinsic connection and direct relation between creature and creator. According to Montagnes, the development of Aquinas's metaphysics, especially understanding of causality and the notion of the act of being, prompted him to replace "proportionality" explanation with an account in terms of participation. 6 6 Here is Montagnes summarizing his view in his own words: "In order to ' , , bring to the fore the philosophical significance of the doctrinal progress it reveals, we can say that the De Veri tate functions as an extension of the Sentences, There Thomas accepts the same formalist conception according to which the principle relation of beings to God is that of imitation, but he grasps the danger that it presents: more or less to confuse the creature with the creator and to succumb to the univocity to which our conceptual processes incline us, There is only one means to eliminate this danger: to accentuate the distance, to deny all direct likeness, to refuse every sort of determinate relation, At what price, then, does one safeguard the divine transcendence? By radically separating beings from God, by accentuating the distance to the point of rupture, by running the risk of equivocity and agnosticism, Neither theologically nor philosophically is this a satisfactory solution: it annihilates our knowledge of God; it eliminates the unity of being, The cause of this is the underlying metaphysics which inspires the solution, To escape this impasse, one had to conceive being no longer as form but as act, and causality no longer has the likeness of the copy to the model [i,e, original] but as the dependence of one being on another being which produces it, Now this is exactly what efficient causality implies: exercised by a being in act, it makes a new being exist in act, which being is not confounded with the first, since the effect and the cause each exist on its own account, but which communicates with it in the act, since the act of the agent becomes that of the patient, At the same time the act is that which the effect has in common with the cause and that by which it is not identified with it, Thus, it is by a veritable communication of being that God produces creatures and creative causality establishes between beings and God the indispensable bond of participation so that there might be an analogy of relation between them, It will no longer be necessary to have recourse to analogy of proportion[ality], and Thomas will never come back to the theory of the De Veritate" (Macierowski, trans" 78; corresponds to French edition, 9192]), PROPORTIONALITY AND DIVINE NAMING 541 To appreciate the influence of Montagne's interpretation, we may note briefly how it has been received, by two recent interpreters of Aquinas. John Wippel follows Montagnes's approach to accounting for the diversity among these passages, differing mainly in that he finds a closer affinity between the earlier appeal to likeness and the later understanding of participation rooted a causal connection.7 According to Wippel, the earlier (I Sent" d. 35) distinction sharing a common factor imitation is just an alternative formulation of what is later referred to in terms of the distinction between analogical relations that are many-toone and those that are one-to-another. 8 Wippel agrees with Montagnes that the De Veritate appeal to proportionality leaves God too distant from creatures; as a proposed solution to the problem of the relationship between creatures and God, it is not as successful in staving off agnosticism as other formulations. 9 So, according to Wippel, it makes sense that Aquinas would move to a preference for analogy of one to another, because in such cases the causal connection guarantees a likeness, which need not be a specific or generic likeness, between cause and effect, Like Montagnes then, Wippel finds that Aquinas, in grappling with the relationship between creatures and God, gained a better understanding of "the ontological situation" after De Veritate,JO abandoning analogy of proportionality in favor of analogy of direct attribution founded in a causal relation. Gregory Rocca also reviews Aquinas's invocations of analogy in characterizing the relationship between creatures and God, and he too finds Thomas experimenting very briefly with the notion of proportionality, but then settling on analogy of 7 Wippel, Metaphysical Thought of Thomas Aquinas; see especially his treatment of divine names (543-75) and the analogy of being (73-93), along with the chapter on participation (94-131). 8 Ibid., 547. Wippel finds in another text (De Veritate, q. 23, not considered here) a softer, nonexclusive appeal to proportionality. 9 Ibid., 554. 10 Ibid., 568, 575. 542 JOSHUA P. HOCHSCHILD or a relation to one.]] Like Wippel, sees consistency of emphasis on a direct relation between God and creatures, allowing intrinsic causal connections, in texts before and after De Veritate. For Rocca, Aquinas struggled with the problem of describing God's relationship with creatures, eventually finding a solution "retooling" the notion of "proportio" to cover a broader range of relationships than strict proportionality had allowed.]2 Rocca admits, Aquinas's reasons for shifting his preference from analogy of proportionality to analogy of analogy attribution (or what Rocca prefers to call "referential are only "implicit,,,13 Rocca supplies two: first, proportional similarity functions "as a genus or quasi-genus" and such a generic notion "must . . . eventually be grounded in the multivocal analogy of direct rapport"; second, there seems to an epistemological dependence of knowledge learned VIa proportionality on knowledge learned more directly.14 11 Gregory Rocca, Speaking the Incomprehensible God: Thomas Aquinas on the Interplay of Positive and Negative Theology (Washington, D.C.: The Catholic University of America Press, 2004). 12 "What Aquinas' ultimate solution hiuges on, even in its earliest stages, is his ability to retool and expand the meaning of propOitio, which from its infancy in Greek philosophy had been closely tied to finding the exact ratios between finite numbers, and to be comfortable enough with its extended sense not to forget it when confronted with God's infinity, for as we have seen, he only decides for proportionality when he also ignores the broad sense of proportion. This broad sense of proportio as 'direct relation' is the bridge that allows theological attributes to cross from us to God and, more generally, is the philosopher's stone Aquinas utilizes to transmute analogia as four-term proportionality into analogia as referential multivocity" (ibid., 123). 13 Ibid., 125. Cf. K1ubertanz, Saint Thomas Aquinas on Analogy, 94-95: "Nothing can be explicitly found in the existing texts which gives any reason for St. Thomas' temporary adherence to proportionality." 14 Rocca, Speaking the Incomprehensible God, 125-27. Rocca seems to downplay (as an occasional "secondary formulation") those places where Aquinas makes clear that there is proportionality in the analogy between accident and substance (ibid., 125, and n. 77)0 His point seems to be that the relation of proportionality here depends on a more fundamental and direct relation, which on page 132 he describes in terms of imitation. PROPORTIONALITY AND DIVINE NAMING HI. AN ALTERNATIVE ApPROACH TO INTERPRETING DE VERITATE, Q. 2, 11 543 In summarizing their accounts of the significance of De Veritate among Aquinas's accounts analogy in divine naming, scholars sometime describe Aquinas as reversing his position about the priority of proportionality or attribution. But, to be precise, it is not the case that Aquinas in texts other than De Veritate makes the same distinction he makes there, and then prioritizes analogy of attribution (analogy of direct proportion) over analogy of proportionality, Instead, what we find is that Aquinas explicitly invokes "proportionality" to classify a privileged kind of analogy in De Veritate, and does not invoke proportionality at all-either as a privileged or as a nonprivileged form of analogy-in some of the other key texts. In other words, rather than reversing priority of a consistent classification scheme, Aquinas appears simply to drop the classification scheme of De Veritate and replace it with a different classification scheme (or schemes). If this is a "reversal" it is a more subtle or quiet one. One might also note there are a couple common but questionable assumptions behind this strategy of interpreting De Veritate relative to the other comparable texts. The first is that in each text Aquinas attempts to give the comprehensive essential classification of analogy. Only from this assumption would it follow that different classifications are not compatible. But alternatively one could assume that Aquinas does not mean each classification to be comprehensive, or they are comprehensive in different ways, perhaps because the classifications are made in terms of different kinds of criteria, serving different purposes. Thus we see another assumption at work these interpretations: the various passages are each attempts to answer the very same question. Montagnes makes explicit, insisting that the texts are "strictly 544 JOSHUA P. HOCHSCHILD parallel,"15 not just in the sense that I taken them, as having parallel structures of but as dialectically parallel, For is "a" problem of divine naming and De Veritate's "solution" to that one problem is only a provisional one "displaced" the mature "definitive" of later texts. \.Xlippel retains this assumption, although IS more aware that the dialectical contexts of the relevant texts differ: notes that in "the more mature" examples, Aquinas's consideration of divine names comes after discussion quidditative knowledge of God. 16 Rocca is also more attuned to the fact that different passages may have different dialectical even so, he retains the assumption that various texts should be read as evidence of Aquinas returning to the same basic question and negotiating a choice, between analogy as attribution and analogy as proportionality, as providing the answer to that question, 17 An alternative hermeneutic strategy is available: to take each text as designed to make' those distinctions relevant to addressing a given problem, and to assume that the given problem is not necessarily the same in each case. For a proper appreciation of the dialectical context of Aquinas's distinctions, it is not necessarily enough to look at title questions of the relevant articles in which they are made, medieval teachers knew very well, a given proposition can only interpreted in light of the larger dialectical context in which it arises, Aquinas's different claims about how something can be predicated of God and creatures thus do not have to be interpreted as, and should not be assumed to be, different attempts to address the same one question, There may be a cluster of questions, or a general question which could be answered on different levels depending on what specific dimension of question is most relevant in a given situation, 15 Montagnes, Doctrine o( the Analogy o( Being, 63-64 (French ed., 66-67). 10 Wippel, Metaphysics o(Thomas Aquinas, 543-44. j 7 Rocca, Speaking the Incornprehensible God, 118. PROPORTIONALITY AND DIVINE NA1vlING 545 If this is the case, classification schemes that are very different may in fact be philosophical compatible, and need imply no inconsistency or development. J 8 IV. CLARIFICATIONS ABOUT PROPORTIONALITY Before proceeding alternative hermeutic strategy and attending to particular dialectical contexts, it is also important to establish some theoretical clarifications about 18 In general, we must remember that Aquinas's discussions of analogy are always occasional-analogy is usually brought in as a solution to a particular problem, a problem that is itself located in a larger dialectical context. It is inappropriate, then, to ask what Aquinas's theory or doctrine of analogy was, if that implies a fully explicated, stand-alone theory, though we can still ask what he taught about analogy. We only have to remember that what Aquinas taught about analogy cannot be separated from the question of how he taught it. (It may not be incidental to his teaching on analogy, after all, that he did not choose to write a treatise on analogy, and it may even be that a systematic textbook treatment of the topic would somehow falsify the wisdom contained in Aquinas's more organic discussions.) And how Aquinas teaches about analogy is largely a question of where he teaches about it-that is: in what kinds of texts, in what dialectical circumstances, does Aquinas find it useful to bring up analogy, and what role does analogy play in those dialectical circumstances? (There are so many occasions, so many places where analogy is either briefly invoked or elaborately discussed, that it is difficult to take account of them all. Klubertanz's study is still the most comprehensive review of relevant texts, although other texts could be added, e.g. Thomas Aquinas, In Aristotelis Libras Peri Hermeneias et Posteriorum Analyticorum Expositio II, lect. 17, n. 4.) While the present article deals with a set of theological texts, it should not be forgotten that analogy plays a role in a variety of other kinds of texts, including treatises, like De Principiis Naturae, and commentaries on Aristotle (e.g., on the Metaphysics and Ethics), as well as theological texts where divine naming is not the primary focus. Any careful examination of Aquinas would also have to take account of where analogy does not appear, or where the topic appears under different guises without being labeled "analogia." (It is not often appreciated, for instance, that Aquinas discusses analogy, as a kind of unity, in De Principiis Naturae, a work of natural philosophy, while his De Ente et Essentia-which considers the diverse meanings of being, and its application not only across the categories but also to a self-subsisting nature-never refers to these relations [of words, or of things 1 as cases of analogy; indeed in this metaphysical and theological work the word "analogia" and its cognates make no appearance at alL) 546 JOSHUA P. HOCHSCHILD notion of proportionality and its relation to the logical and metaphysical orders. (1) First, as noted, proportionality involves a four-term O'-"H .. "H~ describing a relation of relations: A is to B as C is to D. Originally a mathematical notion, this was extended to nonmathematical domains as a way of describing likenesses that do not involve a common form or a generic similarity. Two things are proportionally similar not insofar as they each have a share in the same quality, but insofar as they find in relations or proportions are similar-A is proportionally to C insofar as A is to B as C is to D. Contemporary philosophers have referred to phenomenon as morphy."19 Two things are understood to be isomorphic not if they share a common trait, but if they play similar roles or find themselves in similar relationships to other things in their respective domains. 20 In short, four-term proportionality is a 19 L lv1. Bochenski, "On Analogy," The Thomist (1948): 425-77, §17. (I cite this work by section number as it has been reprinted, with corrections, in Albert lvlenne, ed., Logico-Philosophical Studies [Dordrecht: D. Reidel, 1962]; and in James F. Ross, ed., Inquiries into Medieval Philosophy: A Collection in Honor of Francis P. Clarke [Westport, Conn.: Greenwood Publishing Co., 1971]: 99-122). Cf. 1. M. Bochenski, A History of Formal Logic, trans. Ivo Thomas (Notre Dame: University of Notre Dame Press, 1961),397, commenting on a discussion of "systematic ambiguity" from Principia Mathematica: "all the statements in question evidently share the same formal structure. We have in fact a case of isomorphy. It is remarkable that the name used for this kind of isomorphy, 'systematic ambiguity', is an exact translation of the common Scholastic expression aequivocatio a consilio, synonymous with 'analogy'; for isomorphy is precisely analogy." 20 It may be possible to argue that some proportional relationships are in lact reducible to identity (mathematically, 2/4 equals 4/8) or that there in fact is a common quality ("half," shared by 2 with respect to 4 and by 4 with respect to 8), but: (1) the assertion of identity is not the same as the assertion of isomorphy (something is lost theoretically, even if not quantitively, in reducing 2/4=4/8 to 1/2= 1/2); (2) the identity is not the basis of the isomorphy or proportionality (.5 = ,5, but that doesn't make them proportional or isomorphic); and (3) it is not always necessary to insist on identity to perceive isomorphy or proportionality (the spine of a mammal and the shell of a lobster play similar roles for those creatures, though clearly not identical roles; and even in mathematics there are proportional relationships that are not reducible to equations, for instance circumference:area::surface area:volume). PROPORTIONALITY AND DIVINE NAMING 547 way of describing a relation of likeness that need not involve a common quality or form shared by the relata. (2) Now suppose that two proportionally similar or isomorphic things receive the same name-as, for example, we can use the term "river" to denominate both the Thames and one of the blue lines on my map of Oxford. the order of imposition, this obviously involves the extension of a term from one semantic context to another: the Thames is a river in the primary sense, and the blue is a the sense that it is related to other on the map as surrounding topography. But if even in analogy of proportionality I extend a term from one analogate to another, in a loose sense even analogy proportionalty involves "attribution" or denomination of one thing by reference to another. Of course, the ability to denominate the secondary analogate by "reference" to primary analogate is itself based on the discernment of a proportional similarity or isomorphy between the secondary analogate (the blue line) and the primary analogate (the real river). Thus, applying a common name to proportionally similar things always involves, in the order of imposition, attribution or reference to one. (3) Now note further isomorphy or proportionality between items in their respective structures may or may not imply an intrinsic connection, or causal relation, between those items. There may be a causal connection, as in the case of the map, which was produced intentionally to represent the mapped territory. But there need not be any causal connection. Consider two classic examples of proportionality, that a captain is to his ship as a governor is to the commonwealth, and that physical vision is to the eye as intellectual vision is to the intellect. In these cases, the proportionally related things have no metaphysical connection. The captain (or his relationship to the ship) is in no way causally linked to the governor (or his relationship to the commonwealth); and physical and intellectual vision are similar without one causing, or otherwise being intrinsically related, to other. So we must further remember that discerning a formal relationship of proportional 548 JOSHUA P. HOCHSCHILD likeness between two things does not address the metaphysical question of whether those two things are causally related. (4) If, in at least some cases, there is no intrinsic or metaphysical connection between two proportionally related things, it is still the case that two noncausally related but proportionally similar analogates may be intrinsically denominated a common term, that is, denominated by that term on account of a relevant proportional "formality" found in each analogate. Intellectual and physical sight are not intrinsically related, but we extend the term "seeing" from the primary analogate (the eye which sees) to the secondary analogate (the intellect which understands), we denominate the intellect as "seeing" because of its own intrinsic act grasping intellectual objects. Even' in the order of imposition, denominating the intellect as seeing we make reference to an extrinsic (and metaphysically independent) primary analogate (the eye's physical vision), it remains the case that in the order of signification the analogical term ("seeing") is predicated of the secondary analogate intellect) on account of that secondary analogate's own act (the intellect's understanding). sum, we must not confuse the metaphysical issue of an intrinsic connection between two things, and the semantic issue of the intrinsic denomination of something, 21 (5) Furthermore, those cases in which there is a causal connection between two proportionally similar things, there would ipso facto also be a "direct" relation (of cause to effect), Two things whose formality of likeness is proportional may as a matter of fact be related (as cause to effect), so that in addition to their proportional relationship we may say that one is directly related to another. Thus, Aquinas holds that the being of accidents is caused by the being of substance, but he also holds that accidents have their own intrinsic being which is proportionally similar to the intrinsic being of substances. 21 Making a similar point, Rocca calls this "analogy's metaphysical neutrality" (Speaking the Incomprehensible God, 129). "For Aquinas, analogy formally understood as such is also a logical entity that is neutral as regards the ontological question of whether a subject possesses an analogous predicate intrinsically or not" (ibid., 13 n PROPORTIONALITY AND DIVINE NAMING 549 Likewise, while "healthy" is treated as an example of analogy of attribution, it would be easy to argue organs deserve to be called "healthy" not just by reference to the health of the organism of which they are a part, but also by reference to their own intrinsic good function, which is proportionally similar to the good function of the organism as a whole, But such a case, the intrinsic health of the liver is understood to directly, causally related to the intrinsic health of the organism as a whole (indeed, as both helping to cause, and as being caused by), in a way that, for instance, the governor of the state is not causally related to the captain of the ship to which is proportionally related. So possible that, not only in the order of imposition, but of reality, proportionality does not rule out a direct or relation between the two proportionally related things. (6) A relationship of proportionality, which is not a determinate relationship but a relation of relations, IS nonetheless compatible with the way Aquinas talks about analogy of "one to anotheL" Some scholars have attempted to treat "one-to-another" and "many-to-one" (or "two-to-a-third") as substantive divisions in the mechanism analogical naming or as relevant to metaphysical relationship between analogates, as if an analogy's being "one-to-another" automatically implies something about the nature of the relationship obtains between two analogates, Wippel, for instance, assumes that Aquinas expresses a preference for analogy of one to another, as if that an affirmation of causal connection and a rejectlOn of proportionality.22 This confusion may have its roots in Montagnes, who begins recognizing the modest logical implications of the distinction but attempts to link it to a fundamental development in Aquinas's theory of being,23 But 22 Wippel, Metaphysical Thought of Thomas Aquinas, 561, 565, Cf. John F, Wippel, "Metaphysics," in The Cambridge Companion to Aquinas, ed, Norman Kretzmann and Eleonore Stnmp (Cambridge: Cambridge University Press, 1993),92, 23 Montagnes, Doctrine of the Analogy of Being, 71-72. Steven A, Long's Analogia Entis,' On the Analogy of Being, Metaphysics, and the Act of Faith (Notre Dame: University of Notre Dame Press, 2011), otherwise representing a strong critique of 550 JOSHUA P. HOCHSCHILD the view that describing analogy as "one to another" implies something about the metaphysical relationship of the analogates is simply not warranted by Aquinas's actual usage. Whenever Aquinas appeals to the distinction between "one-to-another" and "many-to-one" in analogy (as the examples used in ScC I, c. 34; STh I, q. 13, a. 5; and De Pot., q. 7, a. 7 show), all that the distinction addresses IS the question whether, between two analogates, one of is primary by reference to which the other is secondary, or both are secondary and need to be understood by reference to some other, primary, analogate. Whether there is a causal relationship between the analogates, and whether the analogates are related proportionality, are metaphysical questions, entirely independent of the semantic question of whether one of the two analogates is primary. In other words, identifying an instance of analogy as "one to another" neither entails a causal connection between analogates) nor rules out a proportional relationship between analogates. 24 V. PROPORTIONALITY AND PARTICIPATION On the basis of these general theoretical clarifications about the nature of proportionality, it is possible to read the discussion of analogy at De Veritate, question 2, article 11 not .Montagnes, nonetheless perpetuates this confusion by treating "analogy of one to another" as a kind of analogy, and one of a piece with analogy of "effect to cause" and "analogy of proportion" (e.g., 33-34, 54, 58-59, 63, 76, 79). Ralph McInerny seems to understand the notion of analogy of one to another correctly (The Logic of Analogy: An Interpretation of St. Thomas [The Hague: Martinus Nijhoff, 1961], 82), although he implicates Cajetan in misreading it as a more substantive division, despite Cajetan's De Nominum Analogia, §18, which explains that the distinction between analogy of one to another and analogy of two to a third does not address what sort of cause produces the analogy, only whether the prime analogate is among those being considered, or the analogates considered are all secondary. 24 The reflections in this section help to account for why the notion of proportionality has such a complicated history in relation to the notion of deliberate equivocation or analogy as a mean between univocation and equivocation. For a brief account of this history see Joshua P. Hochschild, The Semantics of Analogy: Rereadirtg Cajetan's "De Nominum Analogia" (Notre Dame: University of Notre Dame Press, 2010),4-10. PROPORTIONALITY AND DIVINE NAMING 551 as an experiment with an alternative approach to analogy, briefly entertained and then abandoned, but as an analysis of analogy on one level that is compatible with the analyses of analogy given in other places. For purposes of this argument, only brief attention to the relevant contexts is necessary. The divisions and examples in the passages from the two latest texts and STh) appear in similar situations, that is, early in general theological works. are to lend support to the theological method being defended and the method of learning about God by reasoning from effects to causes. Not surprisingly, then, their emphasis is on the causal relationships between analogates.25 epistemological metaphysical issues related to divine naming these passages should not be expected to address. contrast, the point of the passage from distinction 19 book 1 of the Sentences is to clarify the differences and relations between truth God and truth in creatures. Aquinas's divisions and examples there allow him to argue that there is not only one truth (first division of analogy), nor are there many different truths generically the same (second division), but there is one primary truth to which other truths are related although they are not generically the same (third division). The classification framework gives more detail, because the issue is not a general one of a theological method (reasoning from effects to cause), but a very specific metaphysical question about whether and sense something is actualized in both God and creatures. The fact of a relationship of causal dependency between analogates, which Aquinas's later texts emphasize as part of a method of theological inquiry, is less relevant here. Instead, the distinction is designed to make clarifications about 25 It is also worth pointing out that the divisions of analogy are relatively short discussions compared to the reflections on language developed immediately prior to them; Jordan points out that they each serve as a kind of "coda" to prior discussions of how the divine names work (SeC I, cc. 30-33; STh I, q. 13, aa. 1-4; d. De Pot., q. 7, aa. 1-6, followed by discussion of analogy in q. 7, a. 7; see Jordan, "Names of God and the Being of Names," 168-69; and 186 n. 14). 552 JOSHUA P. HOCHSCHILD sameness difference both on the metaphysical and on the of the semantics of terms, The dialectical purpose of the passage from De Veritate is quite different again, Here, Aquinas sets up the discussion to u\.oJe .... Hu the possibility of a relation between creatures and God which is not a "determinate relationship" (habitudo determinata), In other words, although problem is posed in terms of predication (and so of logic or semantics), the main theological point addressed in the article is not that God and creatures are commonly named analogy, but that analogically common naming need not imply a "determinate relation" of God to creatures. This is evident from the objections: the first five of the eight objections deny, in different ways, the possibility of comparing, or finding likeness between, God and creatures, This general objection is made appeal in turn to: Scripture (obj. 1), God's infinity (obj. 2), God's simplicity (obj. 3), and the infinite distance between creature and God (objs. 4 and 5). In reply to such objections, Aquinas needs to talk about the possibility of a likeness or comparison between God and creatures that does not imply a determinate relationship. The evidence for the possibility of some likeness between God and creatures is easy to give, from Aristotle's Metaphysics (sed contra 1) and from Genesis 1:26 (sed contra 2). And in the body of the article, the reality of likeness is further advanced by appeal to the facts, not argued for here, that God can know creatures through his essence, and that we can learn about God from creatures. For Aquinas, a "determinate relation" apparently implies that the relata could share something in common or be considered as elements in a common domain; if such a relationship held between God and creatures it would be a threat to divine transcendence. So Aquinas here invokes "agreement of proportionality" in the body of the article in order to explain the possibility a relation, a comparison of between God and creatures which is not "determinate" in this way, that which still allows a gap or distance between PROPORTIONALITY AND DIVINE NAMING 553 the items; God creatures are similar, in different domains. It is worth noting this general point whatever relation obtains between God and creatures must be "nondeterminate") remains consistent in Aquinas's later theological 26 And understanding such a relationship in terms of proportionality, or a similitude of is also never abandoned. though the notion proportionality is rarely invoked in other attempts to classify types of analogy, that notion remains common currency in Aquinas's discussions of the relationship between God creatures. Take, for instance, question 14 in the Prima Pars (STh I, q. a. 3, ad 2), where Aquinas addresses a sophism regarding God's knowledge. We cannot conclude the assertion that "God is finite to himself" that God is actually finite, because saying that "God is finite to himself" was only meant as a way of saying that God was to grasp himself as finite creatures can grasp themselves. What we say about God's knowledge, in other words, presumes a proportional relationship between God and his knowledge, creatures and their knowledge. Likewise, in question 3 of the Prima Secundae (STh I-II, q. 3, a. 5, ad 1), a conclusion about the comparison of human and intellect is corrected by restating the schema of proportionality. Human practical intellect is God only insofar as "it stands in relation to what it knows as God does to 26 E.g., STh I, q. 12, a. 1, ad 4: "Proportion is twofold: in one sense it means a certain relation of one quantity to another, according as double, treble, and equal are species of proportion. In another sense every relation of one thing to another is called proportion. And in this sense there can be a proportion of the creature to God, inasmuch as it is related to Him as the effect to its cause, and as potentiality to its act; and in this way the created intellect can be proportioned to know God." Cf, De Pot., q. 7, a. 10, ad 9. It might appear that 5Th I, q. 13, a. 6 denies this, asserting a straight proportion between creatures and God, but surely Aquinas does not here mean to contradict what he said earlier at STh I, q. 12, a. 1, ad 4. At issue in this subsequent article is the question of what counts as the primary analogate in divine naming, which Aquinas takes as an occasion to distinguish between the order of imposition and the order of signification; the question of the nature of the causal relationship between creature and God is not at stake here. 554 JOSHUA P HOCHSCHILD what knows." In short, when Aquinas it necessary to clarify relationship between creatures and God, and especially to be precise about we can learn about the one from the other, he continues to assert a relation of proportionality.27 But then, it is not difficult to read question 2, article 11 of De Veritate as consistent with the other passages we find on analogy, and the question of whether one particular passage's teaching is so peculiar as not to fit with the others need not arise. In De Veritate, the motivating theological points are ones are consistent throughout Aquinas's career; in that sense, we do not have to treat De Veritate as idiosyncratic or unrepresentative of Aquinas's thought. Admittedly, only goes so If we no longer have reason to say that Aquinas abandoned the central metaphysical position articulated in De Veritate, it is still correct to note that he seems to have abandoned, or at least de-emphasized, the explicit invocation of "proportionality," or the four-term notion of relations of proportions, when making recourse to analogy to account for divine naming. One could hypothesize that this shift is simply due to Aquinas's experimentation with different terminology over the course of his career, perhaps finding help in a variety of sources and experimenting with different ways in which terminology from different sources can be combinedo28 But apart from such fundamentally philological factors, which may indeed be relevant, I want to draw on the clarifications about proportionality articulated above to discern at least one principled philosophical reason why Aquinas might find that the relationship of "proportionality" serves his purpose particularly well in De Veritate, while it is not adequate for his purposes in 27 Another point that Aqninas never abandons, indeed, which he seems to emphasize in later works, is the relation of imitation between creatures and God. It is cited in De VeriL, q. 2, a. 11, ad 1, on the authority of Pseudo-Dionysius. 28 Philip Reynolds has argued a similar case with respect to Bonaventure; d. "Bonaventure's Theory of Resemblance," Traditio 58 (2003): 219-56; and "Analogy of N ames in Bonaventure," lvlediaeval Studies 65 (2003): 117-62. PROPORTIONALITY AND DIVINE NAMING 555 the majority of other theological contexts in which he employs and theorizes about analogy. In the of passages we are discussing, Aquinas if ever remains only on the level of semantic analysis-his concern is not just the function of analogical names, but the natures of the things analogically named. Moreover, when two things are proportionally similar, the fact of their proportional similarity says nothing about the cause of that Two things may be proportionally similar because one was produced as a representation or imitation of the other-as the contours of a map have a proportional relationship to the territory they map, because the map-maker deliberately imitated the geography of the territory in his map. But, as we have already noted, two things proportionally similar may have no intentional, historical or causal connection between them. In short, the relationship of proportional similarity between two things does not imply that one of the two things has a causal relationship with, and so a degree of participation in, the other. As noted, the eye's vision and the intellect's vision are proportionally similar, one is not caused by, and is not properly said to imitate or participate in, the other,29 On the other hand, if one thing participates in (or is an imitation of) another, that does imply that the two are proportionally similar. Participation implies imitation or likeness between item participating and the item being participated in, and imitation or implies isomorphy, that is, unlike media or domains within which there are nonetheless comparable relations between parts, qualities or items of those media or structures. (A picture "imitates" a thing insofar as the relationships between parts of a picture "map" the relationships between parts of a thing pictured.) 29 One could make the case that both eye and intellect participate in or imitate divine vision/cognition-but discerning this would be a matter of advanced theological insight well beyond a characterization of the obvious relationship, more known to us, ben'lfeen intellectual and ocular vision; and obviously one can discern the proportional relationship between physical and intellectual vision without being aware of or believing in a common divine exemplar of each, 556 JOSHUA p, HOCHSCHILD Aquinas was well aware that the relationship of proportional similarity is necessarily implicit in imitation, Defining image as a kind of imitation or likeness, he says, it is necessary that there be some adequation in that quality [in respect of which there is imitation], either according to quality or according to proportion; as it is clear that, in a small image, there is an equal proportion of parts to each other as in the big thing of which it is the image,30 So proportionality does not imply a of participation, but a relation of participation entail proportionality, entailment relationship between participation and proportionality helps us appreciate how Aquinas characterize in different contexts, as he did, without having to inconsistent understandings of analogy, If he remained on the "formal" or semantic level of might have "proportionality" to characterize by analogical concepts, when he discusses analogy in theological and metaphysical contexts, he cannot aside the "material" or analysis, and so he is more likely to "participation" to describe analogical relationships between things. Proportionality is inadequate to explain the effect's imitation of its cause, which is usually Aquinas's concern. However, proportionality-likeness understood as isomorphy, or formal similarity between different kinds of or sets-is implicit in the effect's imitation of its cause, and does help us to understand how two things can be similar without having a "determinate relation" between them, Put another way, the metaphysics of participation emphasizes causal relationship, attention to the reason one thing fact "imitates" another. By contrast, the logic of proportionality describes why one thing appears as an imitation of another. Better than metaphysical relation of partIcIpation, proportionality describes the formality of nongeneric likeness or isomorphy, accounting for our ability to perceive or discern "imitation." And insofar as Aquinas consistently recogmzes relationship of 30 I Sent" d, 28, g, 2, a, L PROPORTIONALITY AND DIVINE NANlING 557 imitation or participation betViTeen creatures and God, he continues to their formal proportionality. CONCLUSION On the basis of these observations, we have seen that interpreting question 2, 11 of De Veritate as articulating a temporary or idiosyncratic view is unnecessary. The recent marginalization this passage from De Veritate is based on a speculative metanarrative about Aquinas's metaphysical development is not required by the is based partly on confusions about the nature of proportionality its implications in the logical metaphysical orders, and is inattentive to dialectical context. There is simply no need to say that Aquinas changed his about analogy of proportionality-though his mind had to be flexible enough to notice the different demands on an articulation of analogy different theological questions. Most of the time, Aquinas finds proportionality neither necessary nor sufficient for his theological purposes; the metaphysics of participation better answers to what is usually at issue, namely the causal responsibility for imitation, rather than the formal structure of similarity. However, when the reality of some causal relationship between God and creatures is already assumed, what is at stake is rather an account of how that relationship can be named and conceived in such a way as not to imply a determinate relation betViTeen creatures God, the notions of imitation or participation are inadequate on their own; these notions do not make explicit how it is possible to avoid the or more determinate relationship that Aquinas seeks to deny between creatures and God. In such a context Aquinas must have recourse to the notion of proportionality.31 31 Or, as at 5Th I, q. 4, a. 3, he must have recourse to the notion of "analogy" in its original Greek sense of proportionality (that is, as describing a type of unity or sameness which is not reducible to specific or generic unity or sameness), as opposed to the sense 558 JOSHUA P. HOCHSCHILD This is exactly what we find him doing in this passage from De Veritate, a text that is distinctive for its detail and language, but otherwise entirely with Aquinas says about analogy in divine naming in very different dialectical contexts.32 of "analogy," more common in his usage, of signification with associated meaning (constituting a middle ground between univocation and equivocation). 32 The author would like to thank the manuscript reviewers for The Thomist, as well as Thomas Joseph White and Stephen Brock, for comments on drafts, and David Burrell, Steven A. Long, and Thomas Osborne for helpful conversations about the central argument. Previous versions of this paper were delivered as the Aquinas Lecture at Emory University in September 2004, and for the Blackfriars Aquinas Seminar in February 2008.