Jacques Maritain Center : Studies in Analogy / by Ralph McInerny


"Analogy" is Analogous

The claim that "analogy" is analogous has sometimes been made in comparing so-called analogy of attribution with so-called analogy of proper proportionality when the meaning of "primary analogate" in these two putative types of analogous name is questioned. The claim, it has always seemed to me, has a rhetorical if not intimidating ring to it. One is being told, presumably, what analogy is and when he seeks clarification about an element of the explanation he is told that it is analogous.Well, of course, one finds the word "dictionary" in the dictionary but if one were sent to the dictionary to look up the word "dictionary" it would be fair to ask if the trip is necessary. Similarly, if one could be expected to understand the claim that "analogy" is analogous, made in the course of an explanation of analogy, one would scarcely be in need of enlightenment in the first place.

    Despite such uses of it, I am convinced that the statement "'analogy' is analogous" makes perfectly good sense. What it comes down to saying is is that "analogy" has several meanings one of which is privileged and explanatory of the others. Now, as it happens, to say that is to invoke one of the meanings "analogy" has - a meaning which is not the first or privileged meaning of the term - in order to explain the relationship between the several meanings of "analogy." That is, the meaning of "analogy" which enables us to make sense of the statement that "'analogy' is analogous" has to do with the relation between many meanings of a common term. However, not every meaning of "analogy" has to do with the meanings of words.

    The preceding paragraph is exact, if complicated, but doubtless the reader will be more struck by its complexity than its exactness. In what follows, I shall attempt a circuit which will bring us back to our beginning; during that circuit I shall first say a few things about the paper of Professor Thomas which appears in an appendix and go on to attempt a succinct statement of what it means for a word to be analogous. That done, we can apply what we have said to the word "analogy."

    Professor Thomas' paper could serve, for those who are unacquainted with the literature of analytic philosophy, as an excellent introduction to this style of philosophizing. The precision with which Professor Thomas' paper progresses, its drive for clarity, its unassuming honesty and lack of pretentiousness, will be apparent to every reader. I will try to summarize the major moments of his analysis in my own less lucid way and indicate why he and I appear to be speaking of somewhat different things when we confront the claim that "analogy" is analogous.

    Because he wants to separate linguistic from ontological issues, Professor Thomas proposes the following formula for analogy: "the expression 'a' is like the expression 'b' with respect to C (where C is a property signified by 'a' and 'b' in a given context)." He then introduces the notion of complex property by pointing out that the property of being human (what "man" signified) can be analysed into the property of being animal and the property of being rational. With this as background, Professor Thomas soon finds himself in the embarrassing situation of seeming to have to agree that "man" and "horse" are analogous in meaning. The names of the species of a genus agree in signifying the generic property. What occurs to me here, of course, is that we are faced with talk about analogous meaning where no common name is involved. That is, "man" and "horse," being two different names, cannot qualify as examples of analogy if by analgous meaning we are speaking of the different significations of the same term. Professor Thomas seems at this point to indicate that he regards his analysis of "man" and "horse" to be an analysis of the customary view that "animal" is predicated univocally of horses and men. But what he began with was something like "x is is a man" and x is a horse" and not "man is animal" and "horse is animal." If "animal" too signifies a complex property, as it does, that complex property has not been analysed by Professor Thomas. In short, I have difficulty right at the outset with the values Professor Thomas will allow for "a" and "b" in his general formula. They are said to be two expressions and not two tokens of the sme expression. For the same reason, his definition of "to be univocal" seems to me too commodious for it can embrace what we nowadays call synonymous terms. (Aristotle's συνώνομα is, of course, translated by univocals.)

    In the second major moment of his paper, Professor Thomas considers what happens when we substitute "analogy" for the variables in his formula numbered (3). Before he can do this, however, he has to consider some first-order terms of which we can say that they are analogous. Here he considers an example where we have tokens of the same expression: healthy1 and healthy2. "On closer scrutiny 'h1 and h2', respectively, turn out to be elliptical for 'x is the cause of health' and 'y is the sign of health' where health in the expanded expression is being employed in the primary sense (i.e. as predicated of living organisms)." He then enumerates three characteristics of "analogy of attribution" to which he will later refer as ABC. Terms analogous in this sense have meanings of the form "...R..." and the place before the symbol of relation can be filled by a variable whose value is an individual while the place after the symbol of relation can be filled by "a monadic predicate term employed in its primary sense." That third characteristic seems faulty to me for reasons I will give later. On the basis of this similarity of form on the part of meanings of a term said to be analogous, Professor Thomas concludes that "h1 is like h2" because they share the three characteristics enumerated. If now we should introduce "w1" and "w2" analysed in the way "h1" and "h2." have been, Professor Thomas asks if they share the three characteristics (ABC) in exactly the same way as "h1" and "h2" or not. "Since 'a1' (analyzable into 'h1' and 'h2') and 'a2' (analyzable into 'w1' and 'w2') share the characteristics ABC both are univocal in that respect. We have worked out way back to a view of analogy of attribution, at least, that is based on univocity, a position which presumably the dictum 'analogy is analogical' was originally calculated to avoid." But is that the import of the dictum? Surely not, I should say, and Professor Thomas, forseeing this, continues on a different tack. This time, he will compare "analogy of attribution" and "analogy of proper proportionality" to see if their comparison enables us to avoid univocity in speaking of analogy. His point here turns out to be that analogy of attribution and analogy of proper proportionality have at least one characteristic in common, that this is grounds for univocal  community between them and that, finally, this casts doubt on the dictum that "analogy" is is analogous. The characteristic they share, hoever, namely Rxy, is so general that Professor Thomas notes it would warrant saying that all dyadic relational terms are analogous. After careful and painstaking analysis, Professor Thomas concludes that he has been unable to find a way to avoid appealing to univocity in speaking of analogy and that this must cause doubts about the claim that "analogy" is analogous.

    Despite the misgivings I have indicated, I found Professor Thomas' paper a joy to read. any student of analogy will recognize the problems raised by Professor Thomas as inevitable. I want now to address myself to one of his final remarks. "It would appear that we need something sufficiently like analogy to warrant saying 'analogy is analogous' rather than 'analogy is univocal' or 'analogy is equivocal' but not so like it as to blur the distinction between the commune analogicum and the genus univocum." I hope my approach to it will not seem needlessly oblique.

    The immediate signification of a word is called its ratio and it must always be something complex.{1} Professor Thomas introduced the notion of complex property which, in the example he used, analyses into a genus and specific difference. I prefer to speak of the complexity of what the word signifies in terms of res significata and modus significandi; perhaps Professor Thomas could express this in the following way. Any term signifies a property in a certain fashion or manner. Thus, we might say that "man" and "humanity" signify the same property but in different ways, concretely and abstractly, respectively. Other examples would be "healthy" and "health." If Professor Thomas will accept this, I can go on to give definitions of univocal, equivocal, synonymous and analogous terms. (1) Two tokens of the same term are univocal if they signify the same property in the same way in the uses which interest us.  Alternatively, we could say that two things are univocal if two tokens of the same term are predicated of them and the tokens signify the same property in the same way. (2) Two tokens of the same term are equivocal if they signify different properties in the uses which interest us. Or, things are named equivocally when tokens of the same term are predicated of them and the tokens signify different properties. (3) Tokens of different terms are synonymous if, though they are tokens of different terms, they signify the same property in the same way in the uses which interest us. Or, something is named synonymously if tokens of different terms are predicated of it and the different terms signify the same property in the same way. (4) Tokens of the same term are analogous if they signify the same property but in different ways and one way of signifying the property is primary and privileged because it enters into our explication of the other ways of signifying the same property, in the uses which interest us. St. Thomas sums up what we have been attempting in these definitions by saying that univocal things are divided by differences, equivocal things by res significatae and analogous things by modi significandi.{2}

    What the foregoing implies, of course, is that the analogous term, being a term, has certain characteristics in common with any term whatsoever. Thus, any word within an appropriate range signifies a ratio which can be analysed into res and modus. Univocity, equivocity and analogy come in when we consider the word as predicable of several things. If someone could manage to discuss analogical signification without any reference to univocity or equivocity, he might come up with the res/modus analysis as something peculiar to and constitutive of analogy as such. Then, when he came to see that these are involved in univocal and equivocal predication as well, he would be in a position similar to that of Professor Thomas when he reached the point of extracting Rxy from his analyses of analogy.

    Let me now make a hysteron proteron move. Professor Thomas, in his paper, noticed that the meanings of the names of species of the same genus have a common element and restated that to read: species1 is like species2 with respect to that common element. On that basis, he briefly entertained the possibility that "man" and "horse" might be said to be analogous but dropped it in deference to the traditional view that "animal" is univocally and not analogously predicated of its species. My point earloier was that the remark about "animal" is not what mitigates against speaking of "man" and "horse" as analogous. Rather it is the absence of two tokens of the same term. But let us take what is indeed a term common to man and horse, namely, "animal." This term signifies a ratio which is generic to man and horse and the community involved causes us to say that "animal" in this situation is a univocal term. Now, according to our definition of univocal terms, this means that "animal" as predicated of man and horse signifies the same property in the same way. Despite the univocity of the generic term, thaere has been continued discussion of the so-called "analogy of genus" which answers to Cajetan's analogy of inequality and to the analogia secundum esse sed non secundum intentionem of a famous text of St Thomas.{3} How can the generic notion be equally shared by species which are unequal with respect to animality itself? The question is only posed now; I raise it to show that Professor Thomas' difficulty is not a private one.

    Like most of us Professor Thomas finds "healthy" a convenient example when speaking of analogy. Personally, I do not share his apparent conviction that the traditional division of analogy into attribution and proper proportionality can stand up to close scrutiny from either a theoretical point of view or from that of textual analysis of Aquinas. But perhaps Professor Thomas is simply accepting the division as good money. We begin with a list of statements.

    (1) The dog is healthy.
    (2) Food is healthy.
    (3) A cold nose is healthy.
In our three statements the predicates are tokens of the same term and we want to analyse the meaning of these instances of "healthy." If  "healthy" were predicated univocally of the dog, food and a cold nose, it would signify the same property in the same way, i.e. the same rem significatam and the same modum significandi. We can say that in each of these instances "healthy" signifies the same property, the same rem significatam, namely, health. The way health is signified by "healthy" differs, however; in (2) it signifies the cause of health and in (3) a sign of health. Professor Thomas wrote, we remember, that "health in the expanded expressions is being employed in the primary sense (i.e. as predicated of living organisms)." Now, it seems to me he should have spoken, not of the primary sense of health, but of the primary sense of healthy, the meaning it has in (1). In (1), "healthy" signifies health in a certain way, namely, the subject of health. If "health" is given a meaning such that it is clear that  only a living organism, as a whole can be the subject of such a property, then "subject of health" is the meaning of "healthy" in (1), And that, as Professor Thomas indicates, is a privileged way of signifying the property for the precise reason that that way of signifying it enters into our explication of other ways of signifying the same property.   

    Let us attempt to cast the content of the preceding paragraph into the terminology of Professor Thomas and then into that of St Thomas. Professor Thomas wrote that the meanings of "healthy" in our (2) and (3) exhibit the common form "...R..." I see no reason not to include its occurrence in (1) under the same form if we can interpret "...R..." as "habens respectum ad sanitatem" or "habens sanitatem" or "id quod habet sanitatem." The participle habens and the phrase id quod habet provide both "a place marker for an individual variable" (or, perhaps better, give the variable) and indicate its relation to the property which would go in the slot after R. However, and this was Professor Thomas' point, in explicating the meaning of "healthy" in (2) and (3) we would come up with something like "that which is a cause of health in such things as dogs" and "that which is a sign of health in such things as dogs" where it becomes clear that the explication of the way health is signified when "healthy" is predicated of the dog does not involve reference to other ways of signifying health. Nevertheless, of all these rationes of "healthy" we can say that they signify the same res but in different ways. 

    We can now ask what, for Aquinas, is the ratio analogice communis? In answering the question we can indicate the root of our dissatisfaction with Cajetan's division of analogous names into analogy of attribution and analogy of proper proportionality. Consider the following passage.

Sciendum est quod, quando aliquid praedicatur univoce de multis, illud in quolibet eorum secundum propriam rationem invenitur, sicut animal in qualibet specie animalis. Sed quando aliquid dicitur analogice de multis, illud invenitur secundum propriam rationem in uno eorum tantum, a quo alia denominantur.{4}
Why does St Thomas speak of the ratio signified by "animal" predicated of man and horse as a ratio propria? As a generic notion, we should expect him to call it a ratio communis. It is the generically common notion that is here called a proper notion; the proper notion common to man and horse insofar as they are called animals involves a res and modus: the usual and therefore proper way of signifying animality. What now does ratio propria mean in the statement about analogy? What is analogically predicated of many things is said to be found in only one of them according to its i If we consult Cajetan's commentary on the article in which our passage occurs, we encounter an identification of ratio propria and the res significata of the term, an identification whick eventually leads Cajetan to reject St Thomas' description of analogy. Actually, Cajetan says, it is a description only of analogy of attribution. Why? Because analogy of attribution is such that the perfection signified by the name (the res significata) exists in only one of the analogates and the secondary analogates are named by the name in question only by extrinsic denomination. It is precisely this Cajetan takes St Thomas to be saying when he writes "illud invenitur secundum propriam rationem in uno eorum tantum, a quo alia denominantur." Of analogy in the strong sense, Cajetan's analogy of proper proportionality, we musst say what St Thomas here says of univocity: "illud in quolibet eorum secundum rationem propriam invenitur." Fortunately, however, there is no need to do such violence to the text.

    In the case of the analogous name, can we identify its ratio propria and its ratio communis as we did in the case of the generic and univocal name? Let us return to "healthy" and ask what its ratio communis would be. I suggest the following: habens aliquem respectum ad sanitatem. The basis of this suggestion is the oft-repeated ratio communis entis: habens esse or id quod habet esse. What the ratio communis gives us is the res significata, health or esse, and what Professor Thomas might call a variable whose values would be determinate modi significandi. If that is the ratio communis of the analogous name, what is its ratio propria? I suggest that it is the res and a determinate way of signifying it: e.g. "subject of health" and "id cui debet esse in se et non in alio." With these explanations, there is nothing restrictive or mysterious about Aquinas' "illud invenitur secundum propriam rationem in uno eorum tantum." Invenitur does not as such require a restrictive and determinate ontological situation; after all, that is in which the ratio propria of "healthy" is found is still denominated extrinsically by the term. In some analogous names, it may well be that a number of modes of signifying the res involve the intrinsic possession of the res, but that is not the import of "illud in quolibet eorum secundum propriam rationem invenitur" nor is it precluded by "illud invenitur secundum propriam rationem in uno eorum tantum."

    The foregoing interpretation of the ratio communis and ratio propria of the analogous names seems best to me; nevertheless, mention might be made of the way in which the ratio propria of the analogous name is common to all the rationes analogically signified by the name. That is, the privileged way of signifying the res enters into our explication of the other meanings of the name and can therefore be said to be either what the name means or an element of what it means.  

    With particular reference to Professor Thomas' paper, I would not want to interpret the statement "analogy is analogous" to mean the denial that different instances of analogous naming are instances of the same kind of naming. It seems to me that what St Thomas comes up with in his logical analysis of analogously common names is exemplified by any term he takes to be analogous. That is, I take the description of analogy found in Ia, 16,6 to be saved and saved in exactly the same way by every instance of analogous naming. I see nothing to prevent our saying that "analogous" in "Healthy is analogous" and in "Being is analogous" is univocal. If "analogy is analogous" were a denial of that, the statement would seem to me simply an invitation to vertigo. What then does the statement mean?

    We have arrived where we began. I find in Professor Thomas' paper a statement he might have exploited to his profit. He is speaking of proper proportionality. "Both Aquinas' and Cajetan's treatment of proper proportionality is based on the mathematical model 2:4::3:6 with the appropriate weakening of identity of relations (here (half of')) to similarity of relations in fields of investigation where mathematical precision is impossible." What that remark calls to our attention is this: "analogy" had a use in mathematics which is prior to its use by the logician for whom it means a type of community of the name. St Thomas put it this way. "Dicendum quod proportio dicitur dupliciter. Uno modo, certa habitudo unius quantitatis ad alteram secundum quod duplum, triplum et aequale sunt species proportionis.Alio modo, quaelibet habitudo unius ad alterum."{5} Proportio is merely synonym for "analogy" and what this passage is saying is that "analogy" has a number of meanings. Its first meaning, and we can call this its ratio propria, is a "determinate relation between quantities." Usage evolves a ratio communis, "any relation between things," a determinate mode of which is the relation or proportion or analogy of creature to God as effect to cause. If this is correct, "analogy" has two meanings,  one of which is privileged since, if we are asked why we call the relation of creatures to God an analogy, we would invoke the quantitative mode to explain our usage. If now we should say "analogy is analogous" we have not yet given a meaning of "analogy" which explains the adjective in our remark. What St Thomas did was to employ the term "analogy" to speak about the relation between several meanings of a common term. And it is just this meaning of "analogy" which is invoked when we say that "analogy" is analogous. Let us spell this out."Analogy" means (1) a determinate relation between quantities: e.g. double, triple, equal; (2) any relation between things, a determinate mode of which is the relation of effect to cause; (3) the relation between several meanings of a common term where all the meanings are ways of signifying the same res significata and one way of signifying the res is privileged because it enters into the explication of the others, e.g. "healthy," "being," "analogy." That is to say, meaning (3) of "analogy" explains the way "analogy" signifies (1), (2) and (3). That is what is meant by the statement, "analogy is analogous." While complicated, the meaning of the statement is clear. Therefore, although the statement may continue to be used to obfuscate, to pospone explanations, it need not be so used. It has a definite and defensible meaning.


{1} Cf. In VII Metaphysic., lect. 9, n. 1460: "Dicit ergo primo quod omnis 'definitio est quaedam ratio,' idest quaedam compositio nominum per rationem ordinata..." - Ibid., lect 15, n. 1614: "Necessarium esse omnem definitivam rationem esse ex pluribus nominibus."

{2} "Ad secundum dicendum quod aliter dividitur acquivocum, analogum et univocum. Aequivocum enim dividitur secundum res significatas, univocum vero dividitur secundum diversas differentias; sed analogum dividitur secundum diversos modes. Unde cum ens praedicatur analogice de decem generibus, dividitur in ea secundum diversos modos. Unde unicuique generi debetur proprius modus praedicandi." - I Sent., d. 22, q. 1, a. 3, ad 2m.

{3} Cajetan, De nominum analogia, cap. 1; St Thomas, I Sent., d. 19, q. 5, a. 2, ad 1m.

{4} The following texts are of importance for settling the question of the "analogy of genus" raised earlier. Ia, 29,4. ad 4m; Quaest. quodl. III, q. 3, a. 1. The most lucid perhaps, is this: "Sed dicendum quod unum dividentium aliquod commune potest esse prius altero dupliciter:  uno modo, secundum proprias rationes, aut naturas dividentium; alio modo, secundum participationem rationis illius communis quod in ea dividitur. Primum autem non tollit univocationem generis, ut manifestum est in numeris, in quibus binarius secundum propriam rationem naturaliter est prior ternario; sed tamen aequaliter participant rationem generis sui, scilicet numeri; ita enim est ternarius meltitudo mensurata per unum, sicut et binarius. Sed secundum impedit univocationem generis. Et propter hoc ens non potest esse genus substantiae e accidentis: quia in ipsa ratione entis, substantia, quae est ens per se, prioritatem habet respectu accidentis, quod est ens per aliud et in alio." - In I Periherm., lect. 8, n. 6.

{5} Ia. 12.1, ad 4.

© 2011 by the Estate of Ralph McInerny. All rights reserved including the right to translate or reproduce this book or parts thereof in any form.

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