What is analogy? A Thomistic introduction

In what follows I would like to introduce you to analogy from a Thomistic perspective. I will begin with a look at analogy in general. Then I will discuss some different kinds of analogy. And, lastly, I will offer a few examples of what we can “do” with analogy.

Analogy in general

We can use the same word in different ways so that its meaning in one case will be completely different from its meaning in another case. If I say “The bow of the Titanic plunged beneath the waves” and “We will not bow to their demands,” the word “bow” in the first sentence does not mean at all what it means in the second sentence. We would say that the relationship between the two meanings of “bow” is equivocal, that is, the meanings have no connection whatsoever.

If I say “The volcano is in the middle of the island” and “Every island is surrounded by water,” the word “island” has the very same meaning in each case. We would say that the relationship between the meaning of “island” in the first sentence and its meaning in the second sentence is univocal.

But there is yet a third kind of relationship that the meanings of a word can have in different instances of its use. This third kind of relationship is called analogical and St. Thomas Aquinas notes that it stands midway between equivocity and univocity.¹ If I say “This Scotch is good” and “My wife thinks Kristin Lavransdatter is a good book,” the meanings of “good” in these two sentences are partly the same and partly different. In both cases “good” means that the thing in question has met certain expectations (or perhaps that it has achieved a certain perfection with respect to the kind of thing it is). But it should be evident to everyone that what makes a Scotch good will be different from what makes a novel good. Some people prefer Scotch with a peaty taste but no one would say that peatiness is what we should look for in a novel.

So, “good” has an analogous meaning in these sentences. It is not meant in a completely different way in them nor is it meant in exactly the same way.

Analogy, then, has to do (at least in part) with how the meanings of words relate to each other. Meanings are not orphan entities that float around out in the world all on their own. Meanings are at home in human minds. On the Thomistic (and Aristotelian) view, language’s purpose is to express our understanding of things to each other.² When I tell you that the Scotch is good I am expressing to you my understanding of it, or better, my judgment about it. I predicate “good” of the Scotch. Judgment, or predication, is an act of the mind. I express it linguistically when I say to you something like “This Scotch is good.”

In the mental act of judging (or predicating), “good” is not simply a word but a concept. A concept is an understanding – a mental or cognitive grasp – of reality. I understand that parts of reality are valuable or excellent, that is, that they are good. But, upon reflection, I also understand that “good” is true of different things in partly the same and partly different ways, as we saw above with the Scotch and Kristin Lavransdatter. So, I understand that “good” is an analogous concept. And the word “good” is only analogous because the concept it expresses is analogous. More generally stated: the analogical use of language depends upon or expresses the analogical character of our concepts.

There is a third act of the mind that is distinct from but builds upon understanding and judging, and this is reasoning. When I understand something, I form a concept of it. When I judge it, I predicate a concept of it. When I reason about it, I relate various judgments connected to it to each other. Sticking with our examples, you may form (or recall) the concept “good” while reading Kristin Lavransdatter and go on to make the judgment “Kristin Lavransdatter is a good book.” Perhaps you would then follow that up with this bit of reasoning:

(i) All good books are worth reading.

(ii) Kristin Lavransdatter is a good book.

(iii) Therefore, Kristin Lavransdatter is worth reading.

Traditionally, logic has been understood as the art and science of correct reasoning. Logic aims at understanding how to reason well. Because reasoning involves concepts and judgments, logic concerns itself with these too. Given that concepts can be analogous, it’s clear that analogy is a matter that is appropriately addressed in logic. But from that we should not conclude that analogy is only a logical matter.

As I said a moment ago, “good” is more than a word. It is also a concept. But it is also more than a concept. It is an aspect of reality or being itself. I am judging some part of being to be good, not some concept of being to be good. In the examples that we have been using, we have judged a particular book and a particular alcoholic spirit to be good. It is likewise these things that we regard as partly the same and partly different.

The point that I want to make here is that it is not only concepts that are analogous but things or beings too. In fact, just as we saw that linguistic analogy depends on conceptual analogy, we can now see that conceptual analogy depends on analogy between beings or what we could call ontological analogy. The philosophical discipline that considers beings as such (that is, beings as existing) is metaphysics. It follows that, besides being a logical matter, analogy is also a metaphysical matter and is appropriately addressed in metaphysics.

Two (or three) kinds of analogy

In the Thomistic tradition a distinction is standardly made between two kinds of analogy: analogy of attribution and analogy of proportionality. I’ll start with the first.

In analogy of attribution, some quality or attribute is predicated of several things but of one intrinsically and of the others extrinsically. In this analogy the first is called the “primary analogate” and the others are called “secondary analogates.” To illustrate: health is intrinsic to plants and animals. To say that a plant or animal is “healthy” is to say that its biological functioning is such that it can readily achieve its natural goals. In regard to plants “healthy” might also refer to their color. If a basil plant is green, we might speak of its color as “healthy.” But color in itself isn’t healthy or unhealthy. The color of the basil, however, can be a sign of its health. So, “health” applies intrinsically to the basil but extrinsically to its color. The basil is the primary analogate and its color is the secondary analogate.

To take another example: we might say that some library is “full of wisdom” or that a person, say, Socrates, is “full of wisdom.” Wisdom, however, as a mental state, is intrinsic to Socrates but extrinsic to the library because libraries are not the kind of things that have minds. The reason that we might, nevertheless, predicate “wisdom” of the library is that the books it contains are instrumental causes of wisdom in the persons who are their readers. In this case Socrates is the primary analogate and the library is the secondary analogate.

Analogy of attribution evidently involves a kind of hierarchy. Health belongs more to the basil than it does to its color. Wisdom belongs more to Socrates than it does to the library. So, the basil and Socrates are in a certain sense “above” the secondary analogates. Furthermore, the predicates applied to the secondary analogates depend on the primary analogate. Without plants (or animals) color would never be considered healthy, for there would be nothing to which health intrinsically belongs; and without people libraries could not be thought to contain wisdom, for there would be nothing – in the sublunary world at any rate – to which wisdom intrinsically belongs.

Let’s move on now to analogy of proportionality. In this analogy relationships are compared to each other. The items in the relationships – the relata – are seen to be analogous because their relationships are. Represented symbolically, the analogy of proportionality would look like this: A : B : : C : D. In ordinary English this means A is to B as C is to D. Here is a stock example: Seeing is to the eye as understanding is to the soul, i.e.: seeing : eye : : understanding : soul. The two relationships are analogous and, thus, the relata are too.

The example I used at the beginning of this essay is also a case of analogy of proportionality: good : : Scotch : : good : Kristin Lavransdatter. You might object that this doesn’t fit the pattern of A : B : : C : D but would be more accurately expressed as A : B : : A : C. However, let’s recall that we discovered that “good” is realized in partly the same way and partly a different way in the relata, that is, in the Scotch and Kristin Lavransdatter. So, arguably, it would be misleading to use the same variable to symbolize “good” in this equation.

Both of the foregoing examples are instances of what is called analogy of proper proportionality. The predicates are meant literally of their subjects. Analogy of proper proportionality is contrasted with analogy of improper proportionality (or metaphor). In the latter the predicates are not meant literally. Winston Churchill was given the nickname “Bulldog” not because he was literally a canis lupus familiaris but because of his toughness. The idea is that toughness : bulldog : : toughness : Churchill. Presumably, toughness isn’t realized in bulldogs and Churchill in exactly the same way. So, we would not expect Churchill to manifest his toughness by growling and showing his teeth.

Unlike the analogy of attribution, the predicates applied to the subjects in an analogy of proportionality are understood to belong to both of them intrinsically. Seeing is something intrinsic to the eye, understanding is something intrinsic to the soul, good is something intrinsic to the Scotch, and so on. In analogy of attribution what is predicated of the analogates belongs intrinsically only to the primary analogate and extrinsically to the secondary analogates.

Also unlike analogy of attribution, analogy of proportionality does not necessarily imply a hierarchy. I noted two aspects of a hierarchy in analogy of attribution: first, the predicate applied to the primary analogate belongs more to it than to the secondary analogates; second, the predicate applied to the secondary analogates depends on the primary analogate. Neither is necessarily the case for analogy of proportionality. We could not say that seeing belongs more to the eyes than to the soul since the soul is just not something that sees (in the physical sense). And a Scotch can be good even if Kristin Lavransdatter is not and vice-versa. The analogates in analogy of proportionality do not have a primary/secondary relationship (or least this is not a necessary assumption in this kind of analogy).

In many cases there is a sort of mixed analogy in which analogy of attribution and analogy of proportionality are combined. Consider Debussy’s La mer, which was apparently inspired by the view of the Mediterranean from Cannes, where Debussy visited as a child. Debussy tries to capture the beauty of the sea in his music. But the music itself has a fair claim to beauty too. Although it requires some qualification, I think it is reasonable to see the beauty of the sea as a cause of the beauty of the music. Moreover, the beauty would seem to belong to both the sea and the music intrinsically and not just because of their relationship; I could recognize the beauty of one without connecting it to the beauty of the other.

According to this example, therefore, beauty : the Mediterranean : : beauty : La mer. What moves us to regard them as beautiful is, presumably, that the mere perception of them is pleasing to us. As Thomas says, “the beautiful is said to be that which pleases us when we apprehend it.”³ However, it is not the same things that delight us about the sea and about music. How they are beautiful differs. Very clearly, then, we are dealing with an instance of analogy of proportionality (and, more specifically, proper proportionality). But the same relationship also has a feature of analogy of attribution. There is a hierarchy among the analogates insofar as the beauty of the one (La mer) in some sense depends on the beauty of the other (the Mediterranean).

Doing things with analogy

There is a lot that we can do with analogy but here I will only mention a few things. First, analogy is helpful when we are trying to explain something. If A and B are analogous and you understand A but not B and I understand both, then I can help you understand B by pointing out its analogous relationship with A.

The analogical relationship between things can also be the basis for what logicians call an “argument by analogy.” The purpose of an argument by analogy is to show that the analogates, because they have certain similar features, will probably have another similar feature that may not be altogether evident. Thus, someone might have argued in 1939 that because of its similarities with World War I, World War II would likely have a similar outcome for Germany.

In analogical argumentation you will want to avoid the fallacy of false analogy. Consider that just because A and B are alike in one or more respects, they will not necessarily be alike in all respects. Suppose I were to argue in the following way:

(i) The sun and the moon are both visible in the sky.

(ii) The moon orbits the earth.

(iii) Therefore, the sun orbits the earth.

Even if we didn’t already know the conclusion to be false, I suspect most of us would have seen that the likeness stated in the first premise was insufficient to support the inference that is made in the conclusion. This shows us that when we argue by analogy we need to be careful not to go beyond what is licensed by the likeness.

Analogy plays a role too in what we think and say about God. In this life we do not enjoy the beatific vision. We have no direct cognition of God. What we know about him, we know through the created world. This is true both for what we know about God by reason and for what we know about him by revelation.⁴ Natural and supernatural knowledge of God come to us in different ways, but both are mediated by creatures. Because God is infinite and creatures are finite and God, thus, radically transcends the world, our knowledge of him at present will be imperfect because creatures, as St. Thomas says, are only able to represent him imperfectly.⁵ In this life we can “see” God only “through a glass darkly.”⁶

However, if God is the creator of the world and we can regard the items that populate the world as his effects, then we are justified in supposing some likeness between creatures and God. This is so because effects, precisely as effects, will always bear some trace of their cause.⁷ The impression of a signet ring on wax, for example, will be like the signet ring itself. To be sure, not every likeness of effect to cause will be so perspicuous. However, I cannot consider all the complexities of causal relationships here. I only wish to indicate how creatures, despite their radical difference from God, could, nonetheless, disclose him to us to some degree. Creatures will be both like and unlike God and will, consequently, stand in an analogical relationship with him. Although we do not have direct cognitive access to God, what we know about creatures will tell us something about God to the extent that they are like him.

But we must be careful to notice how the similar feature will be realized in God in a very different way. As the Fourth Lateran Council teaches, whatever similarity (similitudo) there is between God and creatures, there will always be a greater dissimilarity (maior dissimilitudo).⁸

• For further reading on analogy, I recommend H.D. Gardeil, Introduction to the Philosophy of St. Thomas Aquinas, vol. IV, Metaphysics, trans. J.A. Otto (St. Louis: Herder, 1956), pp. 119-152 and Edward Feser, Scholastic Metaphysics: A Contemporary Introduction (Heusenstamm: Editiones Scholasticae, 2014), pp. 284-291.

(An earlier version of this essay appeared last October at The Josias under the title “Analogy and Predication.”)

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