Buchier’s Ordinal Metaphysics and Process Theology

by Peter H. Hare and John Ryder

Peter H. Hare is Professor of Philosophy and Associate Dean of the Division of Undergraduate Education at SUNY/Buffalo, Buffalo, New York. John Ryder is Lecturer in the Department of Philosophy at SUNY College at Cortland, Cortland, New York.

The following article appeared in Process Studies, pp. 120-129, Vol. 10, Number 3-4, Fall- Winter, 1980. Process Studies is published quarterly by the Center for Process Studies, 1325 N. College Ave., Claremont, CA 91711. Used by permission. This material was prepared for Religion Online by Ted and Winnie Brock.


A discussion between Peter H. Hare and John Ryder concerning Justus Buchler’s Metaphysics of Natural Complexes and the relationship of his thoughts to process theology.

Students of Whitehead can find much of interest in the metaphysics of Justus Buchler. Buchler, like Whitehead, subjects traditional substance-quality metaphysics to a devastating critique. If we regard, as surely we must, such rejection of substance-quality metaphysics as one of the distinguishing traits of process metaphysics, Buchler is a process metaphysician. But Buchler, again like White-head, does much more than find fault with traditional metaphysics -- he elaborates an alternative system of categories.1 Because his alternative categorial scheme is very different, the points Buchler makes in criticism of traditional metaphysics are interestingly different from those made by Whitehead. Indeed, though Buchler draws on the insights of various metaphysicans including Whitehead, his categories are genuinely original.2 Consequently, Buchler’s metaphysics offers to Whiteheadians the illumination of a novel perspective on the shared goal of the rejection of traditional substance. Furthermore, this shared rejection of substance-quality metaphysics leads to a shared rejection of classical Christian theology, and it is Buchler’s original perspective on the rejection of such traditional theistic doctrines as creation ex nihilo which John Ryder explores below. After his account, I will explore the relevance of this account to the possible development of an ordinal, process theology based on Buchler’s categories.


In his Metaphysics of Natural Complexes, Justus Buchler presents and develops the categorial framework of a general metaphysics. One of the primary functions of a system of this generality is its applicability to a wide range of more specific subject matters. A general ontology is designed to provide a framework for interpretation of such areas as experience, science, art, ethics, and religion. It is the task of this paper to consider some of the consequences of Buchler’s ordinal metaphysics for one component of most religious systems, God. Our scope will in fact be limited to two specific issues: the existence of God and God as creator.

The discussion will be framed for the most part by the categories of natural complex, ordinality, prevalence, scope, contour, and integrity. For Buchler, everything is a natural complex, including such things as material objects, fictional characters, ideas, relations and laws. To say that something is a natural complex is to say that it is not simple, that it consists of subaltern traits. A natural complex is an order of complexes; it locates (i.e., it is a sphere of relatedness for) its subaltern traits. Not only does a complex locate traits, but it is itself a trait located. Every complex is an order that locates traits and is itself located in an order, a context. That every complex is located in some order or orders is Buchler’s principle of ordinality. When a complex maintains traits in a particular ordinal location, it is said to prevail, to be prevalent, in that order.

Complexes may prevail in any number of orders, and for each order in which a complex prevails it has an integrity. A clock, for example, has an integrity as a time piece, a piece of furniture, and a wooden object, among others. The totality of a complex’s integrities is its gross integrity, its contour. In addition to its integrities, a complex has subaltern traits which do not influence its ordinal locations. The individual splinters of wood in our clock are such constituents. These constituents fall within the scope of a complex. Each of the categories just discussed, i.e., complex, ordinality, prevalence, scope, contour, and integrity, will bear on the forthcoming discussion of God and God’s characteristics.

In an ordinal metaphysics, "whatever is, in whatever way, is a natural complex" (MNC 1). God, then, is a natural complex. This of course does not imply an affirmative answer to the question "Does God exist?" God is a natural complex in so far as it prevails in some order or another. The order in which it prevails might be the order of literature, or the order of complexes that have had an important influence on the course of human history. To say that God prevails in these orders would not provide the kind of answer called for by the question "Does God exist?" The question must itself be understood in ordinal terms. To ask if God exists is to inquire into the ordinal locations of a discriminated complex. In particular, the question might concern the location of God in the order of complexes to which devotion is due, or the order of complexes that create other complexes. "Does God exist?" is a question that wishes to identify a specific integrity of the complex God.

Given the necessity of understanding the question "Does God exist?" within the terms and categorial framework of an ordinal metaphysics, it may be better to dispense with the question altogether -- dispense with it, that is, only in the terms in which it is usually couched. In an ordinal metaphysics, existence outside of some order is an unintelligible notion. To ask if God exists is to ask whether God prevails in order x or order y. God is already discriminated, and to that extent must prevail in some order. To take the question of the existence of God at face value, we would have to answer yes to it. God does exist, at least in the order of myth, or that of symbol. But these are not the sorts of responses that fully satisfy the question. The question "Does God exist?" is not equivalent to the question "Does God prevail?" Outside of prevalence in some order, though, the term "existence" can have very little meaning in an ordinal metaphysics. Thus Buchler says that "the question whether God exists or does not is a symptom of deficiency in the categorial equipment of a metaphysics" (MNC 8). It is better, i.e., less ambiguous and more clearly meaningful, to ask what orders God is located in rather than if God exists. A complete answer to this question would amount to an articulation of the contour of the complex God.

How can the question of the ordinal locations of God be answered? One way would be to look at several of the traditionally assigned attributes of God and consider whether these attributes can be consistently held along with the workings and conditions of ordinality. One such characteristic would be God as creator ex nihilo. If God is a creator ex nihilo, then certain things must be true. It must be true, for example, that at the point when God had not created the world, there was nothing other than God alone. If an ordinal metaphysics allows for this possibility, then it may allow for the possibility of God’s being located in the order of complexes that create, or create ex nihilo. If this characteristic of God is found not to be possible in an ordinal metaphysics, then it is not possible that God is located in the order of complexes that create ex nihilo. If God cannot be located in this order, then God cannot be a creator. The same methodology must be applied to all the traditional traits of God. Once that is done, a picture will emerge of the nature of the God that an ordinal metaphysics can recognize. We will not pretend here to offer an exhaustive analysis of the characteristics of God. Rather we will treat only one of them. This will clarify at least a bit what an ordinal metaphysics does or does not allow for.

To say that God is a natural complex is to say a number of things, or a number of different kinds of things. Consequences follow in different branches of inquiry. One of the kinds of consequences that follows from God’s being a natural complex is ontological. If God is a complex, then, by definition, God is not simple or indivisible. As a complex, God, to use an awkward phrase, is composed of constituent complexes. The constituent complexes are what constitute God. This in itself is contrary to one of the more prevalent features of the God of much of monotheism, viz., its simplicity. Further consequences follow from this ontological point, one of which has to do with God as creator. If God is a creator ex nihilo, then there was a point where God had not yet produced his creation, or at least this is the popular conception. Leaving aside the difficult question of how there could be a "before" if time was not "yet" created, there are still difficulties in the notion of a creator God. Presumably, when God had not yet created the universe, there was nothing in existence other than God. But if God is a natural complex, there must be complexes other than God for there even to be God. If God is a complex, then this complex locates other subordinate complexes. That is, it has constituents. These constituents cannot be the same as God, since God, as a complex, is the order within which they are located. In order for God to be, certain subordinate complexes must be as well.

An ordinal metaphysics places further stipulations on the nature of any given complex. Not only must the complex locate subordinate subcomplexes, but it must itself be a subcomplex of another, perhaps more pervasive, complex. All complexes both locate and are located. If God is a complex, then God is located in at least one order. Here again, the image of God (as cause) standing alone, prior to everything else (its effects), is untenable. An order is defined by Buchler as "a sphere of (or for) relatedness. It is what ‘provides’ extent, conditions, and kinds of relatedness" (MNC 95). An order necessarily distinguishes complexes in certain ways and along certain lines; it necessarily delimits complexes and the relations among them. Complexes are what they are by virtue of their ordinal locations. The multiplicity of orders, which includes the idea of orders as delimiters, is what provides the many-faceted nature of complexes. The ordinal location or locations of a complex are what provide, or constitute, its integrity or integrities. The contour, or gross integrity, of a complex is what determines it as that and just that complex. Buchler characterizes identity as "the continuous relation that obtains between the contour of a complex and any of its integrities" (MNC 22). In an ordinal metaphysics, the very notion of identity, of a complex being the complex that it is, is a function of the stipulation that every complex must both locate traits and be located in an order of traits. For God to obtain at all, it is necessary that it both locate traits and be itself ordinally located. Neither of these conceptions seem to be compatible with a creator ex nihilo.

Even the principle of ontological parity creates trouble for a creator God. Much if not all of the more Platonic strain in the history of Christian thought turns to a large extent on a principle of ontological priority, but this is not the source of the trouble suggested here. Even though the principle of ontological priority has played such a crucial role in our philosophic and theological development, there is an equally strong tradition wherein the notion of degrees of being does not figure quite as prominently. The point at which the principle of ontological parity interferes with a creator God is in the context of the idea of existence itself. Whatever is, is a complex, and no complex "is" more than any other. Many things, and many different kinds of things, cart be said "to be." It has become traditional philosophically to erect as a model of existence a rather crude spatiotemporal paradigm. But this is clearly too restrictive. There are many kinds of complexes that do not seem to fit this paradigm, but yet must be said "to be." Possibilities are one such kind of complex. There has also been a strong tendency in philosophy to consider "being" as in some sense equivalent to actuality. This conception places possibility in some sort of ontological limbo. A more coherent way of looking at all of this is to say that actuality "is" no more than possibility "is." A possibility is no less of a complex, with all of the appropriate ordinal conditions, than is actuality. If either can be said "to be," then so must the other.

If God were a creator, then the possibility of what he creates obtains along with him. It would not do to suggest that God creates this possibility as well, since that would only push the question back one step. The question would then have to do with the possibility of this creation, and this could easily lead to an infinite regress of the possibility of the creation of the possibility of the creation of. . . . The possibility of creation must be understood as a complex, located in certain orders, and as obtaining along with, and in relation of some kind to, God. Again, the idea of a creator ex nihilo is severely hampered by the categorial demands of an ordinal metaphysics.

There is one further point that would be worth making here. It has to do with an issue already raised, viz., the identity of a complex. It was pointed out earlier that Buchler locates the identity of a complex in the continuing relation "between the contour of a complex and any of its integrities." I will try to show why this way of characterizing identity is important for the coherence of an ordinal metaphysics, and in particular how identity in this sense allows for some of the more characteristic features of Buchler’s treatment of the question of God. The issue of identity should also show the importance of a principle mentioned earlier, viz., that all complexes must themselves be ordinally located.3

One of the more interesting points that Buchler makes in connection with God is that:

In the metaphysics of natural complexes it could be said that God prevails, not for this reason or that, but because God is a complex discriminated, and every complex prevails, each in its own way, whether as myth, historical event, symbol, or force; whether as actuality or possibility. (MNC 8)

On the basis of this, it would be appropriate to say that God prevails in the orders of literature, mythology, historical influences, etc. At the same time, there are orders in which God does not prevail, such as the order of complexes that create other complexes ex nihilo. The body of this paper has been an attempt to show that God could not possibly prevail in this order. The curious thing about this, though, is that the orders in which God cannot prevail are precisely those orders which seem to frame the historically most characteristic and persistent traits of God. If God cannot prevail in the order of complexes that create ex nihilo, as well as others which could be elaborated, then God cannot be a creator, etc.

Yet it seems necessary, especially in light of the principle of ontological parity, to say that God does prevail in some of the other orders already mentioned. However, if God cannot create and do many of the other things customarily attributed to the Divinity, one wonders whether the God that does prevail in the orders of historical influences and literature is the same God that cannot prevail as creator, etc. If the two "Gods" are not one and the same, that is if we are doing something more than viewing the same complex in a number of its ordinal locations, then the point of saying that God does prevail in this or that order loses much of its force. Yet it does look as if it is not the same complex under discussion in the two cases. The complex "God" that prevails in these orders is the God who has created what is, who may perhaps preserve its prevalence and towards whom persons strive.

It is crucial for an ordinal metaphysics to be able to show that the complex seen in terms of each of these orders, including those in which it prevails and in which it is not located at all, is the same one. This is accomplished by the particular way in which identity is characterized. Another point of considerable relevance here is that complexes are indefinitely ramifiable, which is to say they are amenable to indefinite inquiry and analysis (MNC 24, 56 & 102). In so far as they are ordinally located they are relational, and in so far as they are relational, their traits and integrities are inexhaustible.

What this point amounts to is that an elaboration of the traits of a complex must include both the traits of the complex in terms of each of its ordinal locations as well as each of its ordinal locations as among its traits. It would be curious to suggest that at a given point all the ordinal locations of a complex, all of its integrities, have been exhaustively delineated, since this would imply that all possibilities for the complex have ceased to obtain. If the integrities of a complex are indefinitely ramifiable, then so are its traits. The important implication of this, at least for our purposes, is that a discussion of the traits of a complex, if it hopes to achieve any sort of adequate scope, cannot limit itself to a consideration of a complex only in terms of one of its ordinal locations. A proper response to the question "What are the attributes (traits) of God?" must include those traits that obtain for the complex in terms of a number of its ordinal locations. God, then, could not be adequately characterized solely as a creator, preserver, judge, goal etc. The description must include those traits relevant in other ordinal locations as well. God is also a major force in human political and social history, in literature, etc.

If one introduces at this point Buchler’s account of the nature of identity, the question of the sameness of a complex across its ordinal locations should be answered. A complex has an integrity for each of its ordinal locations, and identity, to repeat a phrase cited twice already, is the "continuous relation that obtains between the contour of a complex and any of its integrities." The identity of a complex is not a function of this or that integrity. If it were, then we would be forced to say that a complex in one of its ordinal locations is not the same one as the complex considered in another of its locations. Since identity is a function of the relation between the contour, or gross integrity, of a complex and any of its integrities, the possibility of speaking of the "same" complex across ordinal locations is assured. Consequently, the categorial relations of an ordinal metaphysics allow us to say of God that while it cannot be a creator, etc., it, the same God, is locatable and identifiable in other ordinal locations.

It is clear, then, that whatever character an ordinal metaphysics may recognize God as having, it does not include God as a creator ex nihilo. As I have indicated earlier, it does not follow from this that it would be appropriate to say that "God does not exist." God prevails in any number of ordinal locations, but not as a creator. Peter H. Hare’s remarks that follow consider in further detail the possibilities of examining the traits and functions that can be ascribed to God, which is to say the possibility of an ordinal theology.


John Ryder has argued that Justus Buchler’s metaphysical principles do not allow God to have at least some of the traits he is thought by traditional Christian theists to have. More specifically, using Buchler’s categories of natural complex, ordinality, prevalence, scope, contour, integrity, and relation, he argues that God cannot be creator of the world. Ryder’s careful account of the conflict between Buchler’s metaphysics and the metaphysics of Christian theism is surprising. I find it surprising not because his exposition of Buchler’s views is inaccurate. His exposition is faultless. Nor do I find it surprising because I do not think worthwhile the examination of the implications of Buchler’s metaphysics. Certainly Buchler’s ambitious and original categorial scheme deserves attention, much more attention than it has received. What I find surprising is that Ryder should consider it remarkable that the metaphysical principles of Buchler, or those of any other philosopher, are violated by Christian theology. In the history of metaphysics it has been common -- it has been the norm even -- to have metaphysical principles violated by Christian theology. For example, a metaphysician will commonly assert as sound metaphysical doctrine that every event has a cause, and yet will also assert, as a doctrine of Christian theology, that God’s acts do not have causes. Or, as sound metaphysical doctrine it is asserted that everything that manifests design must have a designer, and yet as sound theological doctrine it is also asserted that the design manifested in God is without designer. Or, it is asserted as sound metaphysical doctrine that all existence is contingent, and yet as sound theology it is asserted that God’s existence is necessary, i.e., noncontingent. This fundamental sort of inconsistency seems to be endemic among metaphysicians.

In other words, it would have been remarkable if Buchler’s metaphysics had not been found to contradict basic tenets of Christian theology. It would have been remarkable not just because Buchler is working in the tradition of American naturalism but also because, as I have just pointed out, such a conflict is common among many sorts of metaphysicians, not just among naturalistic metaphysicians.

Although I applaud the accuracy of Ryder’s account of the relations between some of the tenets of Christian theology and Buchler’s categorial scheme, I worry that Ryder may unintentionally give the impression that Buchler’s metaphysics is narrowly naturalistic and strongly antitheological in character when quite the opposite is the case. It seems to me that, all things considered, Buchler’s categorial scheme is a naturalistic metaphysics that is unusually open to theological development. To be sure, Buchler’s metaphysics quite appropriately rules out certain theological tenets of the sort Ryder describes. But Buchler’s is not a militantly naturalistic metaphysics of the sort one finds espoused by Sidney Hook, for example. Indeed, I venture the opinion that Buchler’s is the most broad and open naturalistic metaphysics yet produced. That breadth and openness is one of his system’s most characteristic features, and I would not like to see that admirable breadth and openness obscured by Ryder’s emphasis on the conflicts between Christian theology and Buchler’s system of categories.

More than any other feature of his system it is Buchler’s principle of ontological parity that ensures the openness of his metaphysics. According to that principle, "no complex is more ‘real’, more ‘natural’, more ‘genuine’, or more ‘ultimate’ than any other" (MNC 31). While this principle, of course, rules out any theology in which God is considered the ultimate reality, i.e., rules out traditional theism, it does not rule out other sorts of theology. When I speak of "other sorts of theology," I do not have in mind only a Deweyan or a Randallian sort of theology in which "God" is considered a human symbol of the unity of social ideals. It should go without saying that Buchler’s metaphysics leaves room for religious humanism. Buchler’s metaphysics, I am suggesting, leaves open the possibility of more than a humanistic sort of theology. I can find nothing in his metaphysics that requires that divine reality he reducible to human reality. It is a serious mistake to suppose that the fact that his metaphysical principles preclude traditional theism implies that they allow only humanistic conceptions of God. There is much metaphysical room between the extreme of traditional theism and the extreme of religious humanism. Humanism is by no means the only conceivable religion compatible with the principle of ontological parity. Let us consider the intriguing question of what nonhumanistic theologies Buchler’s metaphysics will allow.

Whitehead advised us to seek a concept of God according to which he is the "chief exemplification" of our metaphysical principles, not an exception to those principles "invoked to save their collapse" (PR 343/ 521). Whitehead may not have done a very good job of following his own advice, but it is good advice nonetheless. What might be the "chief exemplification" of Buchler’s metaphysical principles? Couldn’t we develop as such an exemplification a category of "divine proception"? "Proception" is the term Buchler uses to refer to the life-process of a human individual. I can find nothing in his principles which precludes a superhuman form of proception. There seems to be nothing in his characterization of individual experience that precludes a form of proception in which far greater than human powers are exercised. If proception in its human form involves the exercise of powers of assimilation and manipulation of natural complexes, could not a divine form of proception involve much greater powers of assimilation and manipulation? If the cumulative order of complexes which constitute the history of a human being is what Buchler calls the "proceptive domain," is it not metaphysically permissible to conceive of a much more inclusive proceptive domain, a "divine proceptive domain"? If human experience has what Buchler calls "proceptive direction," couldn’t we suppose that much more influential forms of proceptive direction can be found -- what might be thought of as a process form of Providence?

In short, I can find nothing in Buchler’s metaphysics that rules out -- or even discourages -- the development of an ordinal, process theology. Of course, process theology is associated with the work of Whitehead, and Whitehead has been severely criticized by Buchler for his arbitrary use of a principle of ontological priority.4 Yet there seems to be nothing in the nature of process theology which requires that some entities be considered "more real" than others. If process theology were freed from Whitehead’s "strain of arbitrariness," it would seem to be compatible with Buchler’s metaphysical principles.

The theological possibilities inherent in Buchler’s metaphysics can, I think, be illustrated in other ways. For example, Buchler has said repeatedly that metaphysicians should cure themselves of the bad habit of treating the spatiotemporal complex as the fundamental entitity. Surely this openness to realities that are not spatiotemporal invites the development of the notion of a divine reality that is located in various orders but not in a spatiotemporal order. If part of the motivation behind theistic theology lies in the need to believe that reality is not merely spatiotemporal, then a theology developed from Buchler’s metaphysics would satisfy that need without committing the theologian to the metaphysical absurdity of a God that is not a natural complex.

Another feature of Buchler’s metaphysics that invites theological development is his insistence on the reality of possibilities, a reality that follows from his principle of ontological parity. If part of the motivation behind traditional theology lies in the demand for a recognition of the genuine reality of possibilities and not merely the reality of here-and-now actualities, that demand could be satisfied without departing from Buchler’s metaphysics of natural complexes.

My thesis, then, is that one of the remarkable features of Buchler’s metaphysics is that it allows (by virtue of the principle of ontological parity) the development of a nonhumanistic theology, a development not allowed by other systems of metaphysics in the naturalistic tradition and a development that should be welcomed by process theologians.



MNC -- Buchler, Justus. Metaphysics of Natural Complexes. N.Y.: Columbia University Press, 1966.



1 For a comparison between Buchler’s and whitehead’s critiques of’ traditional substance, see Beth J. Singer, "Substitutes for Substance", Modern Schoohman. 53 (1975), 19-38.

2 For helpful discussion of the relations between Buchler and many other metaphysicians, see Stephen David Ross, Transition to an Ordinal Metaphysics (Albany: State University of New York Press, 1980), passim.

3 For a detailed discussion of Buchler’s treatment of identity, see Marjorie C. Miller, "The Concept of Identity in Justus Buchler and Mahayana Buddhism", International Philosophical Quarterly 16 (1976), 87-107.

4 See Buchler’s "On a Strain of Arbitrariness in Whitehead’s System", Journal of Philosophy 66 (1969), 589-601.