Alfred J. Freddoso
Brown University

In the Logica Ingredientibus Abailard attacks the theory according to which universals are collections of individuals. This paper argues that Abailard's principal objection to this 'collective realism', viz, that it conflates universals with integral wholes, is actually quite strong, though it is generally overlooked by recent commentators. For implicit in this objection is the claim that the collective realist cannot provide a satisfactory account of predication. The reason for this is that integral wholes are not uniquely decomposable. In support of thesis the author first explicates the medieval distinction between integral and subjective parts and then discusses its application to collective realism.

In his Logica Ingredientibus Abailard attempts to refute certain realist theories of universals which were prominent at his time. One of these theories, which I will call collective realism, holds that universals are collections of individuals and that such collections are things in their own right distinct from the individuals that they comprise. Abailard has this to say of the proponents of collective realism:

    They do not in any sense call Socrates and Plato in themselves species. Rather, they claim that all men collected together are the species which is man and that all animals taken together are the genus which is animal, and so on for the others.1

Now certain of the arguments that Abailard directs against collective realism have been judged by commentators like Martin Tweedale and Desmond Henry to be inconclusive at best.2 I concur with them on this matter. What I wish to suggest in this paper, however, is that Abailard's basic objection, viz. that the collective realist conflates universals with integral wholes, is actually quite strong. For, I believe, implicit in this objection is the claim that the collective realist cannot give an adequate philosophical account of simple subject-predicate sentences like 'Socrates is a man'. On the plausible assumption that any adequate theory of universals must yield a satisfactory account of predication, this Abailardian objection constitutes a serious and perhaps even fatal blow to collective realism. In section I of this paper I will characterize the two senses of 'predicable of many' which Abailard distinguishes and correlate them with the common medieval distinction between integral and subjective parts. Then, in section II, I will show how this distinction forms the basis for the strong, though generally overlooked, objection alluded to above. /528/


Shortly after characterizing collective realism Abailard continues:

    ... we might ask how the whole collection of men, which is called a species, can be predicated of many, so that it might be universal, even though the whole is not predicated of each individual (LI, p. 14, 33-35).

The point of this remark is that it is not immediately obvious how the collections posited by the collective realist meet the condition set down by Aristotle's definition of a universal as that which is predicable of many. Abailard goes on to insinuate that the only strategy open to the collective realist is to construe his collections of individuals as integral wholes and the individuals that they comprise as integral parts. In that case there is a sense in which such collections are predicable of many, since an integral whole is truly predicable of an exhaustive collection of its (proper) parts. We can roughly characterize this notion of collective predicability of many as follows:

    (P1) An integral whole W is collectively predicable of x1, x2 .... and xn just in case x1, x2 and xn constitute an exhaustive collection of the parts of W.

(The footnotes contain a more precise analysis of this notion.)3 The idea of collective predicability is, I think, intuitively clear. A whole cannot be truly said of any of its (proper) parts taken singly or even of any nonexhaustive collection of those parts. However, the whole can be truly said of a collection of those (proper) parts which completely constitutes or exhausts it, since an integral whole just is such a collection of its parts.

One problem that might be raised here is that what (P1) describes is not correctly thought of as predication, since an integral whole is identical with, rather than predicable of, an exhaustive /529/ collection of its parts. Thus, (P1) evinces a conflation of the 'is' of predication with the 'is' of identity. Now, given the way the term 'predication' is normally used in contemporary philosophical discourse, heavily influenced as it is by the function-argument model, this objection is surely correct. However, it is beyond doubt that some--and arguable that most--medieval philosophers use the schema 'A is predicable of B' in a wider sense which includes the so-called "'is' of identity." This fact lends support to the claim, made in several places by Desmond Henry, that the 'e'-functor of Stanislaw Lesniewski's Ontology is better suited to represent the copula of the medieval logicians than is any single formal element in classical Russellian logic.4 Since (P1) thus conforms to common medieval usage, we can regard it as philosophically legitimate in the present context. This at least gives the collective realist a chance to show that his collections are universals in the commonly accepted Aristotelian sense.

Opposed to this notion of collective predication of many is the notion of distributive predication of many, according to which a whole is predicated truly of each of its parts taken individually. We might roughly characterize this notion as follows:

    (P2) A whole W is distributively predicable of x1, x2 .... and xn just in case, for any xi such that xi= x1or xi= x2 or . . .xi= xn, xi is (a) W.

At first glance (P2) will strike a contemporary reader as somewhat mysterious. Just what sort of whole, we want to ask, is involved here? Certainly it is not the sort of whole which, like an integral whole, is governed by standard mereological principles.

The medievals, however, commonly construed universals themselves as wholes that can be divided into parts. For example, in enumerating the types of division, Boethius includes under the category of substantial divisions both the division of an integral whole into its (proper) parts and the division of a genus into its species.5 One finds a similar distinction between integral wholes and what I will call "universal" wholes in John Scotus Eriugena's discussion of ousia in the Periphyseon.6 In his Opus Oxoniense Duns Scotus extends this idea of the division of a universal to the case of the division of a lowest-level species, e.g., man or human /530/ nature, into concrete individuals, in this instance into individual human beings.7

In order to render the distinction between integral and universal wholes somewhat clearer I will turn to what Duns Scotus has to say about the division of wholes within the context of his discussion of the individuation of material substances.8 This appeal to Duns Scotus is somewhat anachronistic within the framework of a discussion of Abailard, but Scotus' remarks are, I believe, very helpful to one who is trying to grasp the force of Abailard's main objection to collective realism.

Scotus distinguishes the division of a quantitative whole, which is at least one species o£ an integral whole, from the division of a universal whole. A quantitative whole, he claims, is divided into parts in such a way that the definition of the whole is not truly predicable of any of the parts taken singly, although the predicate 'is a per se existent' truly characterizes both the whole (before the division) and each of the parts (after the division). Such parts are called integral parts. A universal whole, on the other hand, is divided into parts in such a way that the definition o£ the whole is truly predicable of each of the dividing parts. Such parts are called subjective parts. Thus, when the lowest-level species man is divided into subjective parts, each part is such that the definition of the species is truly predicable of it, as in 'Every man is a rational animal' or 'Socrates is a rational animal'. Thus, Socrates and Plato and all other human beings are subjective parts of the universal whole man.

In the selection under discussion Scotus is trying to show that quantity is not the cause or principle of the individuation of material substances. He notes, however, that one might be misled into believing that quantity does play this role of individuator, by the following line of reasoning. Imagine the quantitative whole that /531/ includes all and only the bodies of presently existing human beings, and suppose that these bodies are lumped together in such a way that no one entire body is discriminable from the others. We might imagine, for instance, that all the bodies are broken down into their elemental chemical components and that these elements are lumped together indiscriminately. Now suppose that this quantitative whole is rearranged and divided in such a way that the division yields as parts all and only the human bodies with which we began our thought experiment. In that case one might be inclined to claim that what makes each human being distinct from all the others is the fact that he or she has (or is) a distinct part of the quantitative whole in question. Thus, the primary cause of the distinction of human beings from one another is the fact that each has (or is) a distinct part of quantity.

In arguing against this opinion Scotus insists that it is not precisely as a part of such a quantitative whole that an individual is a human being or even a human body. For even if we think of the quantitative whole in question as virtually containing all the human bodies with which we began, still the parts of that whole, as parts of an integral whole, are integral parts and "cannot receive the predication of the whole."10 Thus, human beings are not primarily or essentially distinct from one another in virtue of any quantitative division. If they do differ from one another in that each possesses a different part of quantity, this difference is metaphysically posterior to their constitution as distinct individuals in themselves. The metaphysically prior constitution of these individuals as distinct human beings is accomplished only by the division of the species man into subjective parts. For even if we assume that the two divisions, viz. the division of the quantitative whole in question and the division of the universal whole man, occur concomitantly, they only accidentally yield all and only the same parts. The reason for this is that the division of the quantitative whole could have yielded parts o£ a different type. For example, such a division might have yielded as parts just those individual chemical components alluded to above. However, the division of the universal whole man necessarily yields as parts individual human beings. Now the fact that integral wholes, unlike universal wholes, are not uniquely divisible or decomposable is, as we shall see, absolutely crucial to Abailard's critique of collective realism. For, by construing universals as integral wholes, the collective realist makes it virtually impossible for his theory of /532/ universals to serve as the basis of an intuitively satisfying account of predication.


We are now in a position to examine the full context of Abailard's main objection to collective realism. Turning to collective realism he says:

    But now we should attack the theory about collection just presented. And we might ask how the whole collection of men, which is called a species, can be predicated of many, so that it might be universal, even though the whole is not predicated of each individual. Even if it is agreed that it is predicated of different things in virtue of its parts, viz. in that its individual parts correspond to those very things, this has nothing to do with the commonness of a universal, which according to Boethius ought to be wholly present in each individual. This is why (a universal) is distinguished from a common thing which is common by reason of its parts, e.g., a field, the different parts of which belong to different people (LI, p. 14, 2-40).

Now Martin Tweedale simply quotes this passage and, after noting the aptness of the field analogy in characterizing collective realism, goes on to consider Abailard's weaker objections.11 The implication is that in the above passage Abailard is only describing and not criticizing collective realism. But it is clear from the opening sentence that Abailard looks upon the point he is making as an objection, indeed the first objection, to collective realism. In fact, the sentence following the quoted passage begins "Furthermore ..." and goes on to express the first of his admittedly weaker objections.

Now one might be inclined to regard the objection under discussion as itself rather inconclusive. For, it seems, the collective realist can simply reply that, pace Boethius and the others, universal wholes are in fact a species of integral wholes. However, we do not have to strain to see something more in what Abailard says. The quoted passage obviously provides the ground for the distinction /533/ between collective and distributive predication which I elaborated on above. And just as clearly, it seems to me, it challenges the collective realist with the following question: if universals are indeed integral wholes, then what sort of analysis of simple predication can collective realism provide? That is, what alternative can the collective realist provide to Boethius' dictum that a universal is wholly in (i.e., is distributively predicable of) each of its individual instances?

The ties between a philosophical account of predication and the theory of universals are intimate. One common realist strategy is to claim that, unless universals exist, we cannot account for the truth of simple predications like

    (1) Jimmy Carter is a man.

For the correct philosophical analysis of (1) is

    (2) Jimmy Carter exemplifies the universal man.12

(2) reveals that (1) is implicitly relational. 'Jimmy Carter' picks out a concrete individual and 'man' picks out a universal to which that individual stands in the relation (or quasi-relation) of exemplification. Hence, if there are no universals, then no sentence like (1) is true. Now on the standard realist theories--and these are what Boethius has in mind--a universal is taken to be one in many. That is, each individual human being, for instance, exemplifies numerically the same universal man. Thus, the humanity of Jimmy Carter is identical with the humanity of each other human being. Hence, the very same universal is distributively predicable of each human being taken singly. However, Abailard is claiming, the collective realist has closed off this avenue by insisting that individuals of the same species or genus do not literally share any entity in common. Thus, (2) as commonly understood, is not available to the collective realist as an analysis of (1). Abailard's challenge, then, is that the collective realist provide a satisfactory analysis of schemata like

    (3) ________ is a man

--an analysis which is both consistent with and based upon his theory of universals.

At first glance the collective realist seems to have an easy answer to this problem. He can simply claim that the analysis of (3) is provided by /534/

    (4) ________ is a (proper) part of the integral whole man.

But a moment's reflection reveals that such an account is deficient. For, as we saw above, an integral whole may be divided in any number of nonequivalent ways. Thus, the integral whole man may be divided in such a way as to yield, say, Jimmy Carter's left ear as a dividing part. But if (4) is the analysis of (3), then we are entitled to infer that Jimmy Carter's left ear is a man--which is patently absurd.

For one of the consequences of our previous discussion of integral and universal wholes is that an integral whole is not uniquely determined by any one sortal predicate and thus is not uniquely decomposable. Let 'a' and 'b' stand for two distinct sortal terms. Then if we take collections to be integral wholes, the following principle seems to be beyond reproach:

    (P3) The collection of a's is identical with the collection of b's if and only if the collection of a's contains no more and no less than the collection of b's.

Thus, the collection of human beings is identical with the collection of parts of human beings on the reasonable assumption that the one contains no more and no less than the putalive other. By the same token the following principle is clearly false:

    (P4) If G is the collection of a's and x is a (proper) part of G, then x is an a.

It is precisely the falsity of (P4) which renders (4) inadequate as an analysis of (3).

Now the collective realist might try to remedy this defect by adding to (4) a conjunct that delimits the type of (proper) part of the collection man that can count as a man. Perhaps he might try

    (5) ________ is a (proper) part of the integral whole man and ________ is a rational animal.

However, such a move is clearly unsatisfactory, since the added conjunct is of the same form as the analysandum and thus raises exactly the same problems.

To avoid this difficulty the collective realist might claim that all we really have to add to (4) is the weaker conjunct

    (6) ________is rational.

Initially this move seems promising, since 'rational' is not a sortal term. That is, perhaps the collective realist can provide an acceptable analysis of (6) and then attempt to reduce predications involving sortal terms to predications involving only nonsortal terms. However, even if we put aside doubts about the possibility of such /535/ a reduction, this move is doomed to failure, given the collective realist's contention that universals are collections. For, on his theory, the universal rational is, presumably, just the collection of rational beings. Thus, an account of (6) presupposes an account of

    (7) ________ is a rational being

--an account which is itself based on collective realism. However, 'ratiOnal being' is a sortal term, and thus (7) presents us with exactly the same problems as does (3).

At this point the collective realist might be tempted to try a more radical strategy. He might simply deny that a theory of universals must provide an analysis of predication. Perhaps his most attractive alternative is to claim that a theory of universals is intended to explain the role that abstract singular terms like 'humanity' and 'rationality' play in our language. According to collective realism, such terms are, he might continue, the proper designators of universals, i.e., of abstract collections of the appropriate type. Now simple predications of the form illustrated by (3) are logically prior to the notion of the collection of men, or humanity. For such collections are constituted by predefined individuals, i.e., individuals that are already human beings. Thus, the theory of universals presupposes an account of predication and should not itself be required to provide such an account. Therefore, Abailard's challenge is misdirected.

Two comments--one historical and one systematic--should be made here. First, this suggestion clearly takes us far beyond what Abailard tells us about collective realism and to that extent represents a retreat from the position held by the historical collective realists. This in itself indicates that Abailard's objection is more cogent than is generally recognized. However, even though we find in Abailard's treatment of collective realism no mention of abstract terms or of problems regarding paronymy, the issues involved were being discussed at Abailard's time.13 Thus, it is not completely unreasonable to think that the collective realist might have made a move like the one under discussion.

Second, the strategy in question rather perversely inverts the relation between universals and concrete individuals as conceived by classical realist theories. According to the latter, individuals are in some sense or other constituted by--and are thus metaphysically posterior to--universals. Here, however, the collective realist /536/ is suggesting that the constitution of individuals must be taken as metaphysically prior to the existence of universals, since the latter are just collections of predefined individuals. Thus, this strategy constitutes a radical departure from traditional philosophical intuitions about the significance of a theory of universals and has the further undesirable consequence of leaving us in the dark with regard to the analysis of predication.

But prescinding for the moment from this difficulty, can such a strategy be successful on its own grounds? I think not. For even if we agree that a theory of universals need not provide the basis for an adequate account of predication, the collective realist is still constrained to explicate the relation between individuals and the collections they constitute. But here the problem of the decomposability of integral wholes emerges once again. For the collective realist cannot subscribe to the following principle:

    (P5) x (partially) constitutes the collection of men (humanity) if and only if x is a man.

The reason is, again, that, on any plausible understanding of constitution, (P5) allows us to infer that Jimmy Carter's left ear is a man. Only the weaker (P6) is acceptable:

    (P6) If x is a man, then x (partially) constitutes humanity.

But (P6) seems to leave open the possibility that a nonman bears the same relation to humanity as does a man. And such a result is surely counterintuitive, since it destroys the intimate connection between concrete terms and their abstract counterparts. At this point the collective realist might respond as follows: there is an asymmetry between men and nonmen (e.g., parts of men) with respect to the constitution of humanity. For an individual man like Jimmy Carter necessarily has the property of constituting humanity, whereas his parts have this property only contingently, since they are only contingently his parts or parts of a human being at all. And this is a difference that allows us to preserve the close connection between men and humanity while denying that such a connection holds between humanity and any nonmen.

However, there are serious problems with this response. First, it helps the collective realist only in the case of those universals which are had necessarily if at all. But it does not hold for universals in categories other than the category of substance--universals, that is, which are possibly such that they are had contingently. /537/ Thus, the response is unacceptable if collective realism purports to be a general theory of universals.

Second, the response may not help the collective realist even with respect to those universals which are had necessarily if at all. For many philosophers, Abailard included,14 have defended mereological essentialism. That is, they have held that a thing necessarily has just those parts which it actually has. Now to say that Jimmy Carter necessarily has the property of constituting humanity is, on the standard possible-worlds understanding of necessity, just to say that he has the property of constituting humanity in every world in which Jimmy Carter exists. But if mereological essentialism is correct, then each of Jimmy Carter's parts has exactly the same property--and thus the supposed asymmetry between men and nonmen vanishes. Thus, even to safeguard the little he may have gained from his response, the collective realist must argue that mereological essentialism is false or at least not true of all integral wholes.15 However this matter turns out, Abailard's first objection to collective realism has been shown to run deeper than has commonly been thought.

One last point. A contemporary reader may agree that the collective realist cannot adequately respond to Abailard's objection by relying on the logical tools available in the eleventh and twelfth centuries. He might go on to argue, however, that what the collective realist needs is the contemporary notion of a set. For a (first-level) set is a collection of individuals which may be thought of as uniquely determined by some constitutive property and thus as uniquely decomposable. Armed with the notion of a set, the collective realist could claim that universals are sets rather than integral wholes. In this way he could escape the problems that arise in virtue of the fact that integral wholes are not uniquely decomposable.

There are, I think, cogent reasons for believing that the collective realist could not accept this alternative to his theory. The /538/ most obvious reason is that the view of sets just mentioned seems to involve a commitment to both sets and constitutive properties, since the latter are not in all cases reducible nonparadoxically to sets or set-theoretic notions. For they must be metaphysically prior to sets in order to serve as properties that play an essential role in the constitution of sets. However, the collective realist apparently wants to show that all universals are collections.16

But the most interesting aspect of this contemporary suggestion is the following. As we have seen, Abailard's first objection to collective realism is that it conflates two distinct notions of a whole by taking universals to be integral wholes. In an exactly similar way certain modern authors, most notably Lesniewski, have argued that the classical Cantorian notion of a set conflates distributive and collective concepts.17 In fact, Lesniewski sees this conflation as the underlying cause for the emergence of Russell's paradox. This leads him to the conclusion that standard contemporary set theory is merely an ad hoc response to that paradox and that philosophically preferable responses are possible. Now this is a rather controversial claim which I do not intend to discuss further. However, it is interesting to note that the medieval distinction between integral and universal wholes corresponds almost exactly to Lesniewski's distinction between collective classes, which he treats in his Mereology, and distributive classes, which he treats in his Ontology. Moreover, from what we have seen, it is not implausible to think that Abailard would view the notion of a set with the same suspicious glance that he directs at the collective realist's notion of a collection.


*To be presented in an APA symposium on Medieval Philosophy, December 28, 1978. Eileen Serene will comment.

1. Peter Abailard, Logica Ingredientibus (hereafter: LI), Beiträge zur Geschichte der Philosophie und Theologie des Mittelalters, XXI (1933): 14, lines 8-11. LI contains the only discussion of collective realism in Abailard's works. All translations are my own, although I have consulted the translations of Richard McKeon in Selections from Medieval Philosophers (New York: Scribner's, 1929), vol. II, pp. 208 ff, and Martin Tweedale in Abailard on Universals (hereafter: AU) (Amsterdam: North-Holland, 1976), chap. III, esp. pp. 113-115.

2.Cf. AU, pp. 113-115, and Desmond P. Henry, Medieval Logic and Metaphysics (hereafter: MLM) (London: Hutchinson, 1972), pp. 121/2. `

3. Because of the problem of the decomposability of integral wholes, to be discussed below, the following three definitions are needed to clarify the meaning of (P1):

    (D1) x is a proper part of y =df  x is a part of y and it is not the case that y is a part of x.

    (D2) x and y share a part in common =df  For some z, z is a part of x and z is a part of y.

    (D3) x1, x2 .... and xn exhaust the integral whole W =df  (i) For any xi such that xi = x1 or xi = x2 ... or xi = xn, xi is a proper part of W; and (ii) for any y, if y is a proper part of W, then for at least one xi such that xi = x1 or xi = x2 ... or xi = xn, y and xi share a part in common.

I am indebted to Richard Potter for helping me in formulating these definitions.

4. Cf., e.g., MLM, pp. 53-54.

5. Commentaries on Porphyry's Isagogue, in McKeon, op. cit., vol. I, pp. 87-89.

6. Periphyseon: Liber I, ed. and trans. I. P. Sheldon-Williams (Dublin: Institute for Advanced Studies, 1968), p. 149.

7. Opus Oxoniense (hereafter: OO), ed. Marianus Fernandez-Garcia (St. Bonaventure, N.Y.: Franciscan Institute, 1914), Book II, dist. III, ques. IV, p. 250. Of course, just how literally one is willing to construe a universal as a whole having parts is a function of one's theory of universals. Thus, William of Ockham, who denies the existence of extramental universals, claims that the parts of a universal, i.e., the species of a genus or the individuals of a lowest-level species, "are considered parts only in a broad and extended sense of the term." Cf. his Summa Logicae, ed. P. Boehner, S. Brown, and G. Gal (St. Bonaventure, N.Y.: Franciscan Institute, 1974), Part II, chap. 6, p. 268, 30-31.

8. OO, Book II, dist. III, quest. I-IV, pp. 223-276.

9. This leaves open the possibility that certain objects, e.g., human beings and perhaps plants and animals, have nonquantitative as well as quantitative parts. However, even if they do have such parts, what Scotus says about quantitative wholes seems applicable to integral wholes in general.

10. OO, Book II, dist III, ques. IV, p. 249.

11. AU, p. 114. The "weaker" objections include the following: that every integral whole would count as a universal; that each 'lowest-level species would, per impossibile, contain many species of the same type; that each commonly acknowledged universal would actually be a collection of many universals of the same type; and that a genus would not be the same as its species in the sense stipulated by Boethius. Although the first and third of these objections are not, I think, as ineffectual as some have thought, the collective realist seems to be able to respond to all these objections in a somewhat plausible manner. For the purposes of this paper I am assuming that all these responses are adequate and urging that Abailard still has a devastating critique of collective realism.

12. The use of the abstract term 'humanity' is more appropriate in this context. However, the collective realist--as presented by Abailard--does not use such abstract terms. Nevertheless, I will suggest below a strategy involving abstract terms which the collective realist might resort to in the face of Abailard's demand that he provide an analysis of predication.

13. Cf., e.g., Anselm, The De Grammatico, ed. and trans. Desmond P. Henry (Notre Dame, Ind.: University Press, 1964), in which Anselm formulates a rather sophisticated theory of paronymy.

14. Cf. Abailard, Dialectica, ed. R. M. de Rijk (Assen, 1956), p. 423, 29-30. For a contemporary defense of mereological essentialism cf. Roderick Chisholm, Person and Object (Lasalle, Ill.: Open Court, 1976), chap. III and appendix B.

15. One further alternative with respect to the property of being a human being is to espouse mind-body dualism and claim that each human being is identical with his immaterial mind. In such a case perhaps a human being would not be an integral whole at all. However, such a move would be applicable to only one or at best a few universals. Thus, it would be of little help to the collective realist in his quest to delineate a general account of the relation between universals and the individuals which constitute them.

16. Of course, there are also standard problems regarding identity conditions which militate against the claim that all universals are sets. Perhaps the most successful contemporary analogue of collective realism is the theory of universals formulated by Nicholas Wolterstorff in On Universals (Chicago: University Press, 1972). Wolterstorff identifies universals with kinds, i.e., intensional collections, of apects of individuals rather than of individuals themselves. Perhaps a theory such as Wolterstorff's could escape Abailard's critique, but this does not alter the fact that Abailard's basic objection is cogent as applied to collective realism itself.

17. For an account of Lesniewski's views, cf. Eugene C. Luschei, The Systems of Lesniewski (Amsterdam: North-Holland, 1962), esp. chap. 4.