Analogy of Inequality: Generic Predication

One "analogy" (Anderson calls it a quasi-analogy) which is not involved in the notion of analogy of being but which ought to be understood if for not other reason than to exclude it from the analogy of being is the so-called analogy of inequality. It is also referred to as generic predication, although it also seems to encompass specific predication. It is the combination of ontological equivocity (or existential diversity) with conceptual univocity, and it is done all the time as we abstract from the diversity of being we encounter with our senses into genera and species and the other accidents related to substances.*

Univocal Concept of "Man" Predicated of Three Different Men
Analogy of Inequality (Generic Predication)

So, for example, the mental concept or notion of "man" is univocal, but it is used via analogy of inequality (or generic/specific predication) to refer to Socrates, to Plato, and to Hitler. In each an every case the "concept" man refers to the same thing: it is univocal in meaning; there is a conceptual identity in man in each and every case, be he evil or be he good. This univocal concept is applied to ontologically equivocal or existentially diverse men. Hitler is distinct from Socrates is distinct from Plato: ontologically they are distinct or existentially diverse. And yet they all share in the one concept of "man." They are equivocal existential or ontological instantiations of the univocal mental concept of "man." The concept "man" may be said univocally, but the man Socrates is not univocal with the man Plato. We may say the same of trees: "tree is said univocally of all trees, but trees are not univocal [in actual existence]." Anderson (1967), 4.

The analogy of inequality or generic predication is not limited to substances, genera, or species, but it is also found in categories that are described with adjectives. Accordingly the univocal concept of circular may be predicated of both a bucket looked at from a birds-eye view, an abstract geometric shape, or the outline of a quarter.

Univocal Concept of "Circular" Predicated of Bucket, Geometric Shape, and Quarter

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*The univocal concept or conceptual identity in the analogy of inequality refers to "universals or logically common notions abstracted from sense particulars, i.e., from individuals in the world of physically material existence." They may also include categorical ideas, generic or specific. Anderson (1967), 3, 4. Anderson calls the analogy of inequality a "sort of quasi-analogy." Id. 13.

Univocal, Equivocal, and Analogical Terms, Concepts, and Beings

The word analogy is used in all sorts of manners and in all sorts of disciplines. It is obviously used in philosophy and theology, but is used also in logic, in biology, in literature and poetry, and in law, as well as other disciplines. The shared meaning among all its uses would appear to be "likeness in difference." Anderson (1967), 2. As we discussed in our last post, analogy stands midway between two opposites: univocity and equivocity. Before venturing off into understanding the various uses of the term analogy so as to distinguish them from the term "analogy" as used in the concept of analogia entis, we therefore have to grasp the concepts of univocity, equivocity, and analogicity. What is it that we mean by the word univocal? What is it that we mean by the word equivocal. How do they differ from the word analogical?

The words univocal, equivocal, and analogical can be used in reference to terms (words), to mental concepts (conceptually),* and to being (ontologically).

The word univocal comes from Latin univocus: a combination of uni (meaning "one" or "singular") + vocare or vox ("to say" or "to call" or "voice"). Terms that are univocal are unambiguous and are always used in the same sense. They may be defined negatively to equivocal words by saying that they are unequivocal. This notion of univocity as to terms can be extended to mental concepts and to being (or other transcendentals such as the good, the one, the true).

The word equivocal likewise comes from the Latin aequivocus: a combination of aequi (meaning "equal") + vocare or vox ("to say" or "to call" or "voice"). Terms that are equivocal are ambiguous and are used in entirely different senses, often referring to concepts with no relationship at all. Like univocity, this notion can be extended to include both mental concepts and being (and other transcendentals).

Terms that are analogical fall between the extremes of univocal terms and equivocal terms. The term "tree" is used univocally of the oak as it is of the elm. The term "ball" may be used in an equivocal manner it can be referred to a spherical toy as well as to a dance. The term "healthy" may be used of an animal, of its food, of its habits, or of its general state or condition. The term "healthy" has neither equivocal or univocal use, but rather is used analogically. There are differences and samenesses in the manner in which it is used depending upon whether it is used with reference to the animal, to its diet, to its habits, or to its condition.

We may depict this relationship by means or a table.

As already mentioned, the concepts of univocity, equivocity, and analogy, however, are not limited to words or terms. These concepts can apply to the mental concepts that man has, concepts that he has formed, for example, by abstraction from the experience of his senses. Even more importantly for our particular exploration of the analogy of being, the notions of univocity, equivocity, and analogy can be used in reference to being and the other transcendentals, good, unity, and so forth. Thus, there may be ontological univocity, ontological equivocity, and ontological analogy.

The combination and relationship of terms, concepts, and ontological realities is what results in different kinds of analogy. For example, if ontological equivocity is coupled with conceptual univocity, one has what is called the "analogy of inequality." If one combines conceptual analogy without ontological analogy, one has an analogy of attribution, the pros hen analogy. If one combines both conceptual analogy with ontological analogy, one has analogy of proportionality, which can be metaphorical or intrinsic in character. The latter kind of analogy of proportionality, intrinsic in character, is called analogy of proper proportionality.

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Source: Anderson (1967), 1-2.
*Although Anderson states: "There are no purely equivocal concepts; there are only some equivocal names." Anderson (1967), 5. I am supposing, then, that concepts can be univocal, and non-univocal only in an analogical sense, but never non-univocal in an equivocal sense. Id. 4. Even if we have one term used equivocally of two equivocal objects, the one equivocal term will take on two univocal concepts, one for each equivocal object. Thus if we use the word "bat" equivocally to refer to to that with which we hit a baseball and that mammal which flies through the air at night (equivocal objects), the word "bat" (which is a homonym) takes on two separate and distinct univocal concepts.

Aristotle's πρὸς ἓν analogy

In terms of how it was finally to be used in the concept of the analogy of being, the Aristotelian use of the term analogy must be understood as inchoate at best. As we saw in our last posting, in his Nicomachean Ethics Aristotle seems to have taken a notion of arithmetic or geometric origins and applied it to moral concepts (justice).

Aristotle also seems to be the first to tie the word analogy (or at least analogical thinking) to ontological questions, that is, to questions about being. Aristotle perceived different levels or different participations in being. In his Metaphysics, Aristotle astutely observes that "being can be said in many ways," τὸ δὲ ὂν λέγεται μὲν πολλαχῶς. Metaph. 4.1003a. Aristotle indeed extends this insight into the analogical feature of being in that, while he recognizes that being can be used in different senses, he also recognizes that the different senses of the word participate in "one central idea and one definite characteristic, and not as merely a common epithet," ἀλλὰ πρὸς ἓν καὶ μίαν τινὰ φύσιν καὶ οὐχ ὁμωνύμως. The word "being" is used of different things not like a mere homonym, a term with the same spelling and pronunciation but with a different meaning. The word "being" is used in a relational, analogical way, to describe a shared similarity or unity in unequal or even opposing opposing things. Indeed, "being" can be used analogically even to refer to "non-being"!

[S]o "being " is used in various senses, but always with reference to one principle. For some things are said to "be" because they are substances; others because they are modifications of substance; others because they are a process towards substance, or destructions or privations or qualities of substance, or productive or generative of substance or of terms relating to substance, or negations of certain of these terms or of substance. (Hence we even say that not-being is not-being.)

οὕτω δὲ καὶ τὸ ὂν λέγεται πολλαχῶς μὲν ἀλλ᾽ ἅπαν πρὸς μίαν ἀρχήν: τὰ μὲν γὰρ ὅτι οὐσίαι, ὄντα λέγεται, τὰ δ᾽ ὅτι πάθη οὐσίας, τὰ δ᾽ ὅτι ὁδὸς εἰς οὐσίαν ἢ φθοραὶ ἢ στερήσεις ἢ ποιότητες ἢ ποιητικὰ ἢ γεννητικὰ οὐσίας ἢ τῶν πρὸς τὴν οὐσίαν λεγομένων, ἢ τούτων τινὸς ἀποφάσεις ἢ οὐσίας: διὸ καὶ τὸ μὴ ὂν εἶναι μὴ ὄν φαμεν.

Metaph., 1003b.

This concept--of different-yet-somehow-similar things all are referable "to one" primary analogate from when all derive their core meaning--is analogical. In fact, it is a specific kind of analogy, one called (with reference to Aristotle) a πρὸς ἓν (pros hen) analogy ("pros hen" means "in relation to one"). More commonly, this sort of analogy is called (in the language of Cajetan) analogy of attribution (analogia attributionis). It is, as Aristotle put it, a concept between univocity and equivocity: analogy can be said to be a kind of mean between the extremes of univocity and equivocity, τὸ γὰρ ἀνάλογον μέσον. Nich. Ethic., 1131b.

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Source: Betz (2011), 46-47.

Analogy: ἀναλογία

We ought to perhaps start our journey into the concept of the analogia entis by etymology, though the etymological source of the word analogia (analogy) does not by any means admit us into the real meaning of this concept. In fact, it may serve to confuse. If for no other reason than perhaps to understand how these words analogia entis have a life separate and apart from their origins we ought to start with etymology.

The word analogy comes to us from the Latin analogia, but the word is Greek in ultimate origin. The Greek term ἀναλογία (analogia) means proportion. It is a compound word formed from ana (meaning "upon" or "according to") and logos (mean "reason," "word," or "speech"). When used by, for example, Plato and Aristotle, the term ἀναλογία means a proportion of mathematical kind. We find it used by Plato in his Timaeus and by Aristotle in his Nicomachean Ethics. We might quote from Plato's Timaeus:

[31c] for there must needs be some intermediary bond to connect the two. And the fairest of bonds is that which most perfectly unites into one both itself and the things which it binds together; and to effect this in the fairest manner is the natural property of proportion. For whenever the middle term of any three numbers, cubic or square, [32a] is such that as the first term is to it, so is it to the last term, and again, conversely, as the last term is to the middle, so is the middle to the first,—then the middle term becomes in turn the first and the last, while the first and last become in turn middle terms, and the necessary consequence will be that all the terms are interchangeable, and being interchangeable they all form a unity.

[31ξ] οὐ δυνατόν: δεσμὸν γὰρ ἐν μέσῳ δεῖ τινα ἀμφοῖν συναγωγὸν γίγνεσθαι. δεσμῶν δὲ κάλλιστος ὃς ἂν αὑτὸν καὶ τὰ συνδούμενα ὅτι μάλιστα ἓν ποιῇ, τοῦτο δὲ πέφυκεν ἀναλογία κάλλιστα ἀποτελεῖν. ὁπόταν γὰρ ἀριθμῶν τριῶν εἴτε ὄγκων [32α] εἴτε δυνάμεων ὡντινωνοῦν ᾖ τὸ μέσον, ὅτιπερ τὸ πρῶτον πρὸς αὐτό, τοῦτο αὐτὸ πρὸς τὸ ἔσχατον, καὶ πάλιν αὖθις, ὅτι τὸ ἔσχατον πρὸς τὸ μέσον, τὸ μέσον πρὸς τὸ πρῶτον, τότε τὸ μέσον μὲν πρῶτον καὶ ἔσχατον γιγνόμενον, τὸ δ᾽ ἔσχατον καὶ τὸ πρῶτον αὖ μέσα ἀμφότερα, πάνθ᾽ οὕτως ἐξ ἀνάγκης τὰ αὐτὰ εἶναι συμβήσεται, τὰ αὐτὰ δὲ γενόμενα ἀλλήλοις ἓν πάντα ἔσται.

Later in the same work, Plato again invokes the word analogia:

Thus it was that in the midst between fire and earth God set water and air, and having bestowed upon them so far as possible a like ratio one towards another—air being to water as fire to air, and water being to earth as air to water, —he joined together and constructed a Heaven visible and tangible. For these reasons [32c] and out of these materials, such in kind and four in number, the body of the Cosmos was harmonized by proportion and brought into existence.

οὕτω δὴ πυρός τε καὶ γῆς ὕδωρ ἀέρα τε ὁ θεὸς ἐν μέσῳ θείς, καὶ πρὸς ἄλληλα καθ᾽ ὅσον ἦν δυνατὸν ἀνὰ τὸν αὐτὸν λόγον ἀπεργασάμενος, ὅτιπερ πῦρ πρὸς ἀέρα, τοῦτο ἀέρα πρὸς ὕδωρ, καὶ ὅτι ἀὴρ πρὸς ὕδωρ, ὕδωρ πρὸς γῆν, συνέδησεν καὶ συνεστήσατο οὐρανὸν ὁρατὸν καὶ ἁπτόν. καὶ διὰ ταῦτα ἔκ τε δὴ τούτων τοιούτων [32ξ] καὶ τὸν ἀριθμὸν τεττάρων τὸ τοῦ κόσμου σῶμα ἐγεννήθη δι᾽ ἀναλογίας ὁμολογῆσαν . . . .

It is an error to start the journey of understanding the analogia entis with a concept of analogy that is based upon mathematical or geometric proportion. The biggest single impediment to understanding the term analogy (when used in the concept analogy of being) is failing to see the term analogy itself analogical, at least analogical relative to its original sense of proportion.

Plato and Aristotle both use the term analogia in the meaning of "sameness of ratio," so that A:B :: C:D (e.g., 2:4 :: 8:16). This analogia or proportion may be discontinuous (because there are no shared terms among the four components) or continuous if there is a shared term. For example, a continuous analogia would be A:B :: B:C (e.g., 2:4 :: 4:8). In the Timaeus, however, Plato appears to be using the term as a continuous geometric analogia.

Aristotle in his Nicomachean Ethics (1131a31) imports the term analogia into the concept of justice, using this mathematical proportion as a term for justice.

Justice is therefore a sort of proportion; for proportion is not a property of numerical quantity only, but of quantity in general, proportion being equality of ratios, and involving four terms at least.

ἔστιν ἄρα τὸ δίκαιον ἀνάλογόν τι. τὸ γὰρ ἀνάλογον οὐ μόνον ἐστὶ μοναδικοῦ ἀριθμοῦ ἴδιον, ἀλλ᾽ ὅλως ἀριθμοῦ: ἡ γὰρ ἀναλογία ἰσότης ἐστὶ λόγων, καὶ ἐν τέτταρσιν ἐλαχίστοις. ἡ μὲν οὖν διῃρημένη ὅτι ἐν τέτταρσι, δῆλον. ἀλλὰ καὶ ἡ συνεχής: τῷ γὰρ ἑνὶ ὡς δυσὶ χρῆται καὶ δὶς λέγει.

Aristotle later tells us (1131b13) that this analogia is borrowed from the geometers.

This kind of proportion is termed by mathematicians geometrical proportion; for a geometrical proportion is one in which the sum of the first and third terms will bear the same ratio to the sum of the second and fourth as one term of either pair bears to the other term. Distributive justice is not a continuous proportion, for its second and third terms, a person and a share, do not constitute a single term.

καλοῦσι δὲ τὴν τοιαύτην ἀναλογίαν γεωμετρικὴν οἱ μαθηματικοί: ἐν γὰρ τῇ γεωμετρικῇ συμβαίνει καὶ τὸ ὅλον πρὸς τὸ ὅλον ὅπερ ἑκάτερον πρὸς ἑκάτερον. ἔστι δ᾽ οὐ συνεχὴς αὕτη ἡ ἀναλογία: οὐ γὰρ γίνεται εἷς ἀριθμῷ ὅρος, ᾧ καὶ ὅ. τὸ μὲν οὖν δίκαιον τοῦτο, τὸ ἀνάλογον: τὸ δ᾽ ἄδικον τὸ παρὰ τὸ ἀνάλογον.

But Aristotle seems to use the term in other ways as well: as an arithmetic analogia, as distinguished from a geometric analogia.

For example, let 10 be many and 2 few; then one takes the mean with respect to the thing if one takes 6; since 6 —2 = 10 — 6, and this is the mean according to arithmetical proportion.

οἷον εἰ τὰ δέκα πολλὰ τὰ δὲ δύο ὀλίγα, τὰ ἓξ μέσα λαμβάνουσι κατὰ τὸ πρᾶγμα: ἴσῳ γὰρ ὑπερέχει τε καὶ ὑπερέχεται: τοῦτο δὲ μέσον ἐστὶ κατὰ τὴν ἀριθμητικὴν ἀναλογίαν.

N.E., 1106a36. As Carl A. Huffman interprets it,* "[i]t appears that from the more precise definition of 'equality of ratio' [proportion] there developed a looser sense in which any similarity, which could be defined in accordance with a mathematical account (ἀνα λόγον.), could constitute an analogia." "In its broadest sense," Huffman continues, "Aristotle uses analogia to refer to any similarity in the relationships between two pairs of things." It is in this broader sense that Aristotle uses the term analogia to compare the scales of a fish as feathers are to a bird. Aristotle, History of Animals, 486b17.

The notion of analogy that is used in the concept of analogy of being, however, is transmathematical. Not only is it transmathematical, it is not a protraction or extrapolation of the mathematical concept of proportion. We do not simply extend out or protract the meaning of the mathematical term "proportion," a term which is univocal, and in some sense derive a meaning of "super-proportion" to understand the use of the term. Multiply a univocal term by a million and you still have a univocal term. The term analogy as used in the concept of analogy of being is not some sort of "inflated univocal notion." Anderson (1967), 1.

The notion of analogy of being is, rather, metaphysical, ontological (it relates to being), beyond time, space, and quantity, and so it is not constrained or bounded by any dimensional qualities. "[O]ntological analogies cannot be mere extrapolations from the real of mathematical ratios." Anderson (1967), 1.

We do best then to forget the etymological roots of the word analogia, for it is sure to steer us wrong. It is a false friend.

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*Carl A. Huffman, Archytas of Tarentum: Pythagorean, Philosopher, and Mathematician King (Cambridge: Cambridge University Press 2005), 179-80.
*Anderson (1967), 1.

Lucta Iacobi

This blog begins with a confession of ignorance, ignorance of a particular concept, namely, that of the analogy of being, the analogia entis. I have a sense--from whence it comes I know not, but I trust it comes from God--that the principle of the analogy of being is fundamental, important, foundational. I have a cursory, shallow, topical understanding of it, enough to have piqued my interest, but insufficient for me to have grasped it. So this blog is dedicated to my efforts--whether the prove availing or not I do not know--to grasp, to comprehend, to embrace to the extent I am able, this doctrine and its importance to philosophical and theological thought and to the spiritual life.

The blog will have no order, no grand organizing principle. It will be a catch-as-catch-can, as disordered and unruly as a wrestling match. It will be a struggle by a feeble albeit willing mind to grasp a philosophical and theological concept that is both comprehensive and sublime. Perhaps towards the end we may expect some synthetic grasp of the whole. I sense that the analogy of being is a window that allows us to peer into created reality, and from that created reality, by the use of reason, advance to the threshold into the very life of the divine, to grasp in some manner the praeambula fidei and that God is the ground of all being, indeed self-subsisting being itself, the ipsum esse per se subsistens, God. From this jumping off place, we fall, as it were, by the revealed invitation of the unseen but intelligible God on the other side of that threshold into the very arms of God himself, handed over from the introduction of reason to embrace the gifts of Faith, of Grace, and thereby enjoy the divine Love, a Love which enraptures us into the divine maelstrom of Truth, Good, Beauty, Unity, and Being Himself. The anologia entis, then, is an introductory to the God whom I love. This is the God who gives meaning to my life, the God of Abraham, of Isaac, and of Joseph. The God who revealed himself in Christ to be Triune: Father, Son, and Holy Spirit.

I anticipate a struggle, a long one. For that reason I have named it Lucta Iacobi, "Jacob's Fight." The reference is to the 32nd Chapter of Genesis, where Jacob fights an angel. Anybody who wants to join in the fight, or offer help, I welcome.