Jacques Maritain Center : Studies in Analogy / by Ralph McInerny


On the Meaning of "'Analogy' is Analogical"*


John E. Thomas

In his recent book The Logic of Analogy,{1} Ralph M. McInerny makes the repeated claim that "'analogy' is analogous." In the pages that follow this claim will be examined in some detail and an attempt made to fill out McInerny's terse account. The issues raised by the dictum "'analogy' is analogous" are extremely difficult and complicated. This present paper, therefore, does not pretend to solve these problems. The reflections of this paper are offered rather in the hope that the problems may be somewhat clarified and the issues at stake brought once again into clear focus.

    To facilitate the examination of the meaning of "'analogy' is analogous," we shall take as our point of departure Austin Farrer's view that analogy presupposes complexity in the things compared.{2} The adoption of this insight commits us to the following general formulation of analogy: "x is analogous to y with respect to z." If we substitute for the word "analogy" the word "like" we shall be further committed, at least tentatively, to treat analogy as a species of likeness. It will somewhat simplify matters if the linguistic issues are kept distinct from the ontological issues. We have in mind here McInerny's distinction between dicuntur and sunt and betwen rationes and entia. This qualification demands a revision of the proposed schema so that it reads: 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).{3} Such a general formulation of analogy is calculated to rule out, at least for purposes of the present paper, the need to consider things claimed to analogous.

    The view of analogy proposed here is very much like a definition per genus et per differentiam in the following way: both proceed on the assumption that some properties signified by expressions are complex in the sense of being analyzable into two or more properties. We offer as a paradigm for complex property the property of being human signified by the word "man." This property can be analyzed into the property of being animal and the property of being rational (signified, respectively, by the expressions "animal" and "rational" in terms of which "man," traditionally, has been defined).

    In addition to providing a paradigm for complex property (and indirectly for complex expression) demanded by the rubric "x is like y with respect to z," the word "man" is useful in carrying the inquiry into the meaning of "'analogy' is analogous" one stage farther.

    Employing the Lxyz formula let us consider what it would mean to say "man" and "horse" are analogous in meaning. Let "man" signify the properties of being an animal and of being rational (dubbed respectively A and R) and let "horse" signify the properties of being an animal and being a quadruped (dubbed respectively A and Q). We are now in a position to claim that "man" is analogous to "horse" with respect to A. Customarily, however, the expression "animal" as predicated of horses and men is acknowledgedly univocal.{4} We cannot, therefore, harmonize the general schema of analogy with the claim that "animal" is univocal, for on the latter assumption the comparison of "man" and "animal" is an instance of the rubric "x is the same as y with respect to z" rather than of the rubric "x is like y with respect to z." Nevertheless our example seems to meet Aquinas' criterion that analogy be a via media between univocity and equivocity.{5} To be univocal two expressions must have exactly the same signification i.e. signify exactly the same properties, (e.g. "a" signifying FG and "b" signifying FG). By parity of reasoning two expressions are equivocal if they signify no properties in common (e.g. "a" signifying FG and "c" signifying LM). The example offered above avoids both extremes, the expressions "man" and "horse" are partly univocal (i.e. they have A in common) and partly equivocal ("man" signifies R and "horse" signifies Q). The admission of partial univocity, however, seems to be ruled out by McInerny's caution (which seems to be well founded in the Thomistic tradition) ..."we must never confuse the ratio communis of an analogous name with the ratio communis of the univocal name."{6} Granted this proviso, the likeness at the basis of analogical comparisons cannot be univocity. This insight could be made more explicit in the case of the example under consideration as follows:

(1) m and h are analogous in meaning if m signifies A1R and h signifies A2Q and A1 is like but not identical with A2 i.e. [L(A1, A2)] & (A1 ≠ A2).

The clause [L(A1,A2)] & (A1 ≠ A2) tells us (a) A1 is like A2 (in some undefined sense of "like") and (b) specifies that however "like" is to be defined it must not be defined in terms of identity. The clause fails, however, to furnish any positive clue whatsoever about the nature of likeness which would qualify for incorporation into an adequate definition of analogy.

    In his The Logic of Analogy McInerny speaks of the... "commune analogicum which is opposed to the genus univocum."{7} We shall attempt to understand this within the framework of our proposed schema. Could the ratio communis of analogous expressions be analogy?{8} As unpromising as this idea sounds let us pursue it a little farther. For [L(A1, A2)] & (A1 ≠ A2) let us substitute AN(A1,A2). The introduction of this clause in (1) would involve treating the genus of animal as analogical. McInerny does speak of treating genus, in certain contexts, largo modo, though it is quite clear that the genus of animal would not be included in this category. At this point we shall persist in drawing out the lessons of our chosen example while recognizing that it constitutes an extension of McInerny's genus largo modo. The difficulties with treating analogy as the ratio communis of analogous expressions can be brought out in the following manner. Generalizing (1) we arive at the following definition of analogy:

(2) Two expressions x and y are analogous if x signifies G,F and y signifies G2H and [L(G1, G2)] & (G1 ≠ G2).

If for [L(G1, G2)] & (G1 ≠ G2) we substitute AN(G1, G2) we derive the following formula:
(3) Two expressions x and y are analogous if x signifies G1F and y signifies G2H and AN(G1, G2).
A number of difficulties emerge in connection with (3). First, the definition is overtly circular in that it defines analogy in terms of itself. Second, if one attempts to avoid the circularity by an appeal to differences of types claiming that the clause AN(G1, G2) is concerned with analogous properties rather than analogous expressions, it is difficult to see what has been gained. Presumably what it means to say G1 and G2 are analogous is that G1 and G2 are analyzable respectively into, say, LM1 and M2N. Such an interpretation is open to two objections. In the first place, even if it does not mean the same to say that properties are analogous as to say expressions are analogous, the notion of analogous properties is no clearer than the notion of analogous expressions. No clarity has been achieved by the introduction of the clause AN(G1, G2). In the second place, the same difficulties recur in the case of M1 and M2 as with G1 and G2. To subject M1 and M2 to the same analysis of G1 and G2 would lead to an infinite regress. nor could the regress be avoided by claiming that the expressions "s" (signifying G1) and "t" (signifying G2) are analogous, since the same claim would now have to be made for, say, "v" (signifying M1) and "w" (signifying M2) and so on ad infinitum.

    Third (and this is directly related to this last comment) if we are to succeed in specifying a meaning for "'analogy' is analogous," it would seem that the expression "analogy" itself must be included among the possible substitution instances for x and y in (3). Failing this we should be specifying what it means to say that two expressions other than the word "analogy" (but falling under the general definition of analogy) are analogous. The moral of this being that a part of what is meant by "'analogy' is analogous" is that the expression "analogy" itself can be a substitution instance for x and y in (3). We shall now explore this possibility in some detail.

    On the basis of the submission just made the claim "'analogy' is analogous" involves a comparison of two occurrences of the expression "analogy" itself. Let us begin with a comparison of "a1" and "a2" (two occurrences of "analogy" in the sense of analogy of attribution). We shall first analyze "a1" along the following lines. The expression "healthy1" and "healthy2" are analogous by analogy of attribution. This claim is to be made good by showing that "h1" and "h2" conform to the Lxyz formula. There is, however, a prior question that demands attention, namely: In virtue of what characteristic or characteristics are "h1" and "h2" analogous by analogy of attribution?  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"{9} where health in the expanded expressions is being employed in the primary sense (i.e. as predicated of living organisms). We shall now attempt to specify the necessary characteristics of analogy of attribution.{10} They are: (A) "h1" and "h2" are dyadic predicate terms of the form "...R..."; (B) the first slot in "...R..." is a place marker for an individual variable; "C) the second slot in "...R..." is a place marker for a monadic predicate term employed in its primary sense.

    It is not difficult now to show that "a1" (the comparison of "h1" and "h2") conforms to the Lxyz formula. The substitution instances for x and y are dyadic predicate terms of the form "...R..."  ("h1" and "h2" are such terms) while z serves as a place marker for the characteristics ABC. Making the appropriate substitutions we get Lh1h2ABC which is clearly of the Lxyz form. What it means, then, to say that "h1" and "h2" are analogous by analogy of attribution is that they are similar with respect to ABC. Strictly speaking we should say that "h1" and "h2" are the same with respect to ABC, but if we do we run afoul of McInerny's caution..."we must never confuse the ratio communis of an analogous name with the ratio communis of the univocal name." Have we not done this very thing here? But this is not the only difficulty. So far we have not succeeded in comparing "a1" and "a2". We have been preoccupied with showing that "h1" and "h2" are bona fide instances of analogy of attribution. To facilitate a comparison of "a1" and "a2" we could analyze "wealthy1" and "wealthy2" along the lines of "healthy" above and let this count as an analysis of "a2". We encounter the same difficulty as before. 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 our way back to a view of analogy of attribution, at least, that is based on univocity, a position which presumably the dictum "'analogy' is an analogical" was originally calculated to avoid.

    Possibly the difficulty just raised could be avoided by pointing out that the dictum "'analogy' is analogous" does not legislate for causes where two occurrences of the expression "analogy" with exactly the same signification (viz. analogy of attribution) are in question but only for cases where different though related senses of "analogy" are involved. The word "analogous" in "'analogy' is analogous" tries to pick up this "different though related senses" just alluded to. Presumably, then, a comparison of "a1" (analogy of attribution) and "a3" (analogy of proper proportionality) would be a fairer sample of the situation for which the dictum prescribes. We shall now explore this possibility.

    If we take as definitive Aquinas' claim that analogy of proper proportionality is "a similitude of two proportions,"{11} we can then make some headway in preparing the ground for a comparison of "a1" and "a3".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.{12} In the familiar proportionality schema - God's essence is to God's existence as a man's essence is to a man's existence - given St. Thomas' proviso we are comparing R1 (the relation of the divine essence to the divine existence) with R2 (the relation of human essence to human existence). To facilitate the comparison one could substitute "... is appropriate to ..." for R1 and R2. Granted difficulties will be encountered in specifying a precise meaning for "... is appropriate to ..." nevertheless it serves meanwhile to focus attention on the fact that we are comparing two expressions of the form "... R ...". As with analogy of attribution we shall attempt to enumerate the characteristics of "a3" and to show that it conforms to the Lxyz formula. The characteristics are: (A) x and y in the Lxyz formula are place-markers for dyadic predicate terms of the form "... R ..."; (D) the comparison of such terms (e.g. "... is appropriate to1 ..." and "... is appropriate to2 ..." is with respect to "... R ... (contrast this with analogy of attribution where R1 = "... cause of..." and R2 = "... sign of..."); (E) the slots in "... R ..." are place markers for variables ranging over individuals, properties, activities and so on. That "a3" is of the Lxyz formula can be shown by making the appropriate substitutions thus L:(R1, R2) (ADE). We are now in a position to compare "a1" and "a3". They are similar with respect to A but different in the following respects - "a1" has characteristics BC and "a3", characteristics DE. We now run again into the old Phocian rampart ..."we must never confuse the ratio communis on an analogous name with the ratio communis of the univocal name." Working within the prescribed limits we have set for ourselves, we are committed to the view that "a1" and "a3" are the same with respect to A and clearly "the same with respect to A" or "x and y in the Lxyz formula are place markers for dyadic relations of the form '...R...'" are as univocal as one can get. Perhaps the way around this difficulty is to attempt to weigh the characteristics. That "a1" and "a3" exemplify the form Rxy is such a general property, that given this criterion alone all dyadic relational terms are analogous. But rather than eliminate this characteristic all together perhaps one or more of the other characteristics could be ranked higher in order of importance. On the face of it, it would be a tall order to arbitrate between BC and DE (since these are the respects in which "a1" and "a3" are claimed to differ). In principle, one line of analysis is closed to us, namely, the unpacking of AB and DE (treated as complex properties) in the quest for a common core. This is not to say that it is impossible to arbitrate between BC and DE or that in singling out BC and DE that the last word has been said on the selection of the characteristics of analogy of attribution and of analogy of proper proportionality. It is safe to say, however, that the task of weighting the given characteristics or the quest for further characteristics, if successful, would solve the problem of analogy. If one can contribute to that ultimate solution even if only by erecting the sign cul de sac over certain lines of investigation, then this will be its own reward.

    The reader is likely to be as disappointed with this paper as a freshman with one of Plato's dialogues. The problem posed by the dictum "'analogy' is analogical" is still unsolved. It may be objected that the failure to avoid univocity in the foregoing account springs from (a) the classification of analogy as a species of likeness and (b) from the choice of the man-horse model which is acknowledgedly based on univocity. This objection is not without force. By way of rejoinder, however, it should be pointed out that the alternative classification of analogy as a species of equivocity does not avoid the difficulties encountered above. One would still have to show that "a1" and "a3" are not totally equivocal or that they have some property or properties in common. We are at once confronted with our self-appointed task of finding "something common" other than univocity. Furthermore, while it is true that the man-horse model is based on univocity, it primarily functions negatively to rule out identifying the ratio communis with the genus univocum.

    While no positive solution to the problems posed by "'analogy' is analogous" has been achieved in the foregoing pages, the following indications of the direction in which the solution should be sought may prove of value. First, the clue to the understanding of "'analogy' is analogous" is to be sought in a comparison of (at least) two occurrences of the expression "analogy" itself and two occurrences like "a1" and "a3" rather than two occurrences like "a1" and "a2". This insight emerged where it was suggested that the range of substitution instances for x and y in (3) be extended to include the expression "analogy" itself. Second, this last insight suggests another possibility - that the definition of analogy is self-referential. Third, clearly what stands in the way of specifying the meaning of "'analogy' is analogous" is the failure to solve the problem of the ratio communis of analogous expressions. 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. This sounds like an impossible task, but the limits within which the meaning of "'analogy' is analogous" must be clarified have been set by tradition and not by the present writer. The difficulties encountered in this paper are the direct consequences of these limits.

John E. Thomas
Philosophy Department
McMaster University
Hamilton, Ontario


* I am grateful to Professor Ralph M. McInerny of the University of Notre Dame for his helpful criticisms of an earlier draft of this paper. I must assume full responsibility for any obscurities that remain particularly where our views tend to differ.

{0} I am grateful to Professor Thomas for permission to include here this essay. He and I are continuing our discussion and expect to publish more later.

{1} Ralph M. McInerny, The Logic of Analogy (the Hague: Martinus Nijhoff, 1961) pp. 4, 33, 166 ff. It is clear from the last two references that McInerny is concerned with the expression "analogy."

{2} One can force the problems for this view in the case of God's nature which, according to tradition, is simple. We shall have to advocate at least a notional distinction of, for example, essence and existence in God if our analogical schemata are to have any purchase.

{3} The schema focuses attention on the properties as signified rather than the properties as exemplified.

{4} Speaking "secundum intentionem."

{5} Summa Theologiae I q 13 a 5.

{6} McInerny ibid., p. 79.

{7} Ibid., p. 135.

{8} Put this bluntly the proposal would be rejected by McInerny. Since. however, we are seeking to get at the adjectival form of "analogy" in "'analogy is analogous," if not analogy then something very much like it seems to be called for.

{9} For the justification for this analysis see Summa Theologiae I q 13 a 6, De nominum Analogia cap. 2 para. 8 and E. L. Mascall's Existence and Analogy (London: Longmans, Green and Co., 1949), p. 101 ff.

{10} I am not here prepared to do battle for these characteristics. They have been arrived at simply on the basis of generalizing examples taken from Aquinas, Cajetan and Mascall for the purpose of illustrating the sort of thing needed to clarify the meaning of "'analogy' is analogous."

{11} ..."similitudo duarum ad invicem proportionem"... De Veritate II, 11 c.

{12} Summa Theologiae I q 13 a 2 c.f. De Veritate 9 a 12 and 9 a 13 and De Nominum Analogia cap. 3, para. 24.

© 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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