Science in Christian Perspective

Dialogic: A Systems Approach to Understanding
PAUL T. ARVESON
Naval Ship Research and Development Center
Bethesda, Maryland

From: JASA 30 (June 1978): 49-59.

A systems approach to philosophy is introduced in which various types of thinking or mentalities are organized according to their logical form, rather than their content. Special attention is given to the two-dimensional form, called dialogic. Examples of this logical structure in atomic physics, Aristotelian metaphysics, and Christian theology are shown, and a type of complementarity in communism is discussed. A three-dimensional form (trilogic) is suggested based on three types of relationships in the doctrine of the Trinity. Various guidelines are offered to distinguish the Christian-dialogical view from others, and to apply this view to philosophical problems. This systems approach attempts to provide a practical understanding of basic philosophical concepts, and to encourage respect for persons different from oneself.

Introduction

In the first half of our century, analytic or "critical" philosophy dominated Western culture. Its declared task was to arrive at precise definitions of a few legitimate terms of philosophy, and to do away with vague and unverifiable speculations.¹ During this period, the physical sciences also experienced a huge growth of knowledge, but the prevailing natural philosophy (materialism and empiricism) provided a basis to keep all this scientific knowledge somewhat unified. Everyone had a source for the assurance that there was a "rational explanation for everything." Truth could be found simply by observation or experiment.

However, within the last twenty-five years, many people in various disciplines have begun to criticize the inadequacies of critical philosophy and empiricism. (Michael Polyani's important book Personal Knowledge: Towards a Post-Critical Philosophy² is a survey of these inadequacies.) I think that one basic problem with such philosophy was that-in the hands of naturalistic and agnostic men-it tended to escape the traditionally ultimate questions of the meaning of life, death, personal significance and purpose, by simply relegating them to the realm of vague speculations. Thus, Wittgenstein concludes his Tract at us by announcing: "What we cannot speak about we must pass over in silence."

While the general questions of life were thus "passed over" in philosophy, they emerged in other fields such as psychology, fiction literature, and modem art-not to mention the more antirational movements of our times. World-views that were rarely heard of in the West now confront us and our children on the street-corners and in the media. Daily we are reminded of some new moral problem or ethical dilemma, or of some new guru's doctrines. Having been left uncultivated, the intellectual common ground is being taken over by weeds.
But while "legitimate" philosophy decreased, knowledge continues to increase, in both form and variety. Today there is more and more scientific information, but less and less understanding. A glance at the titles in any recent issue of Science or Nature reveals this fragmentation of knowledge; many of the words in an issue's titles are meaningless to any one individual.

We must, of course, accept the fact that such specialization of labor is inevitable. But everyone (including every scientist) needs to have some sense of unity, significance, and meaning in his life. We now realize that the bare empiricism of the old philosophy is inadequate. But what new source of rational unity can be offered in its place? Or should existentialism and antiscience be allowed to displace rationality altogether?

A Systems Approach to Understanding

By the 1960's, many new secular alternatives to analytic philosophy began to appear which attempted to maintain rationality without falling into the narrowness and pessimism of the critical philosophers. One of these new alternatives is called general systems theory.⁴ It claims to be a return to synthetic philosophy, an alternative to reductionism and dualism, a new view of the unity of the world.⁵ These claims clearly seem to be more in line with a Christian world view. (In fact, it may be fairly stated that many of the basic concepts in systems philosophy can be found in the Bible; this paper will bring out some of them.) But although there are many concepts affirmed in common by the Bible and systems philosophy, the latter still holds the old atheistic starting-point.⁶ Therefore it fails to find a sufficient common referent to truly give unity to the world and a place for the whole person. Or, to put it another way, the modem secular philosopher faces the problem of explaining how the world-system created itself and "emerges" to "higher levels."⁷

It is not my purpose here to criticize modem philosophy, nor am I qualified to do that. I do feel that other Christians in the American Scientific Affiliation and elsewhere should be more aware of the shift in direction that philosophy is taking, and offer responses to the new ideas and not old ones. Ironically, we have just recently been offered Dooyeweerd's excellent and comprehensive critique of Western "theoretical thought" from a reformed Christian point of view,⁸ but it mainly addresses the reductionistic and analytical views that are now largely behind us.

I am grateful for the many Christians in the sciences who are concerned about the "integration" of their faith and their work. The Journal ASA exists as an expression of this concern, and there has been an increasing number of excellent Christian books about the unity of scientific and biblical knowledge. For instance, Bube has developed an explicit Christian view of hierarchical systems, complete with diagrams.

These Christian approaches to systems philosophy are commendable. But much more work of this kind is needed. I believe that many Christians in science have been too silent or cautious in proportion to the quality and range of biblical answers available. The difficulty often is in simply being able to relate Christian views in concepts or forms that can communicate to modern people. And it is even more important for evangelical Christians to understand the basic kinds of philosophical and religious competitors that they may encounter in today's world, so that they are not deceived by them.

The systems approach that I describe involves a method of analyzing beliefs in terms of their logical structure. The advantage of this approach is that it avoids details of content and thus is simple to develop. The disadvantage is that it may be too simple; any such general organization is bound to oversimplify particular views greatly. Nevertheless I feel that some formal or systematic approach is necessary because of the need for Christians to have even a rough understanding of their philosophical and logical place in our world.

The illustrations to be developed here may at least serve the purpose of teaching aids: to clarify our basic beliefs and to show how they differ from others that are being offered. Christian doctrine may be understood, according to this approach, by seeing its place in a brief analysis of alternative thought-forms or mentalities, organized according to their logical structure without immediate regard for their particular content. Traditional classroom surveys of philosophy focus primarily on content and its development, without too much attention to the logical form that this content takes, However, I have found that philosophies fall into a small number of basic patterns which can be represented by a point, line, square, or solid figure: that is, by forms having different numbers of dimensions.

Zero-Dimensional Thinking

In zero-dimensional thought there are no permanent values or categories, such as good and evil, subject and object, true and false. Among Eastern cultures, such a "synthesis" has been expressed in the highly refined literature of Zen Buddhism. Zen poets take great pains to make theft mentality clear through oblique illustrations.¹⁰ Such poems or anecdotes usually involve attempts to circumvent the laws of logical thought.

In the West, synthesis or "monism" has been expressed in various ways since the pre-Socratic Greeks. Xenophanes identified the sum total of reality with God (Pantheism). Parmenides referred to the One, which fills the universe with Being fully and uniformly, so that everything is actually static and identical ¹¹ Heraclitns spoke of the universe in terms of a flux of changes or opposing forces, like a flowing river or the unresolved tension in a bent bow. He identified the world with fire, the element of continuous change.¹² In recent times Hegel and the communist philosophers have revived the Heraclitean form of synthesis.

But no matter how such a monistic universe is described-as God or identity or change or contrarietyit is logically and formally the same. Since there are no distinct, stable categories or boundaries, all true monistic syntheses are like an isolated point: it has no dimensions, no direction, no magnitude, no ends, no parts, not even position. Thus, it cannot properly be called a "system". Since it has no relations, the Buddhists properly identified their Zen with nothingness. Buddha also taught that the less said about it, the better.¹³

One-Dimensional Thinking: Monologic

Ordinary propositional thought, or classical logic, is one-dimensional. This means that it can be represented by a line or axis, along which one value is defined (truth-value).

                                                         A------------------------  -A

In this figure, A and -A constitute a pair of opposite or antithetical propositions. We say that if a proposition is true, then it is always true and its opposite is always false. We say that a certain thing either fits into a certain category, or it does not. There is no third possibility. These general rules constitute examples of the "laws of thought"; they are implicit in the Bible as well as in all other propositional literature, and they are stated in any classical logic text.¹⁴ I have given some examples from John's first epistle in the table below.

All propositional statements may be said to presuppose one or more of these laws, so that they cannot be negated in the context of a proposition. For example, the assertion "There are no absolute truths" is a self-contradictory and therefore a meaningless statement.

Philosophies fall into a small number of basic patterns which can be represented by a point, line, square, or solid figure: that is, by forms having different numbers of dimensions.

Because of this self-enforcing nature of the laws of thought, logic cannot be attacked directly. Therefore those who wish to affirm a zero-dimensional synthesis can do so only indirectly. We are told that "the Buddha preached for forty-nine years and in all that time found it not necessary to speak one word.¹⁵ In the West we have Kratylus, the Sophist follower of Heraclitus, "who finally thought that nothing should be spoken but only moved his finger.¹⁶ If such a position were carried to its conclusion, a person could not even think in his own head. It becomes a way to die before your time! Only when the axis of truth-value is accepted is it possible to communicate, live, and share in a society.

One-dimensional thought forms the simplest logical system, which has recently been called "monologic".¹⁷ This system has generally proved adequate for conceiving and communicating most concepts in all languages and throughout history. It is the foundation of rationality, and it can never be supplanted as a basis for intelligible thinking.

However, it is becoming realized that ordinary monologic does not form a completely closed and self-sufficient system. One of the most frequently noted examples of this fact is Kurt Godel's proof that even in a system as simple as arithmetic it is not possible to define and demonstrate all its essential propositions, without recourse to another independent system.¹⁸ There is another alternative to synthesis that can expand the applicability of systematic thinking without loss of rationality. That alternative should now be clear: it is to add another dimension to logic.

Two-Dimensional Thinking: Dialogic

This next dimension of thinking may best be introduced by describing some of the problems which led to its present formulation. People often seem to be tempted (in their use of ordinary monologic) to fall into one of three kinds of extreme or unbalanced thought-patterns or pitfalls, which I will call the "imperialist", the "conformist", and the "alternating."

                                                                             Fig 1

In the "imperialist" case, people may be tempted to claim views which are all-inclusive or comprehensive. This tendency leads to reductionistie thinking: often called "nothing-buttery" or "nothing-but-ness", in which alternative views are rejected as unimportant or meaningless.'9 Among Christians this tendency may cause overemphasis on certain doctrines, which then leads to the denial of other doctrines that are equally important. This kind of thinking is manifested in, for example, the notion that only saved people are capable of giving love. Or in teaching which emphasizes one area (such as prophecy or salvation or baptism or personal devotions), to the neglect of another (Bible history, sanctification, grace, social justice, respectively). These doctrines are not meant to be in opposition, but they often seem that way in the teaching or life of the Church.

The "conformist" pitfall has been aptly described in a little book by Francis Schaeffer, The Church Before
the Watching World. He gives one example of the "conformist" pitfall and its consequences as follows:

There are some Christian groups who see doctrine as being just statements of certain dogmas worded specifically according to their own terminology. If a person varies at all from this particular formulation, he is ruled out. These groups insist that there is no room for variation at all . . . . Oftentimes if a person is raised in this kind of thinking, what occurs is that as soon as he feels in any way that he cannot subscribe to the wording as it is given, then he is severely tempted to let the pendulum swing completely away from that position....Not knowing that there is some freedom within the proper form, they throw Christianity away entirely. Out of such groups there is a constant stream of people turning completely away from the Christian position.²⁰

The "alternating" pitfall is a third type of thinking that is often heard among Christians. Many appear to admit the internal evidence for "paradoxes" in Scripture, especially in the notion that God is sovereign over all things, and yet man is responsible for his actions. "Why does He yet find fault? For who can resist His will?"2' Not being able to satisfactorily reconcile such issues, and yet not bold enough to discard the whole system as irrational, we keep the two sides of the "paradox" away from each other. Usually this is done by simply teaching one side and then the other, alternately. This is an especially common pitfall among preachers. They will teach God's sovereignty one Sunday, and man's responsibility the next. Or the worthlessness of human effort one Sunday, and the infinite significance of human life the next. I have heard this kind of shifty, out-of-balance teaching applied to many other issues. It is a simple way to avoid controversy and confusion. Besides, preachers are taught that for impact, a sermon should have only one main point. But in doing this, Christianity may be accused of making dualism an article of faith. By our actions we deny the oneness of God's truth. Such "doublethink" amounts to an admission that something is logically wrong with the system.

It appears to me that the Scriptures contain a different kind of mentality: one which avoids the extremes of imperialistic reduction, an insistence on precise word-by-word conformity, or alternating from one teaching to another. This mentality was described by Schaeffer as one having both form and freedom:

Christianity is not to be considered as a single point or a narrow, repetitive line but as a circle within which there is freedom to move in terms of understanding and expression. Christianity is a circle with definite limits, limits which tend to be like twin cliffs. We find ourselves in danger of falling off on one side or the other; that is, we have to he careful not to avoid one sort of doctrinal error by hacking off into the opposite one.²²

This two-dimensional mentality may be illustrated by drawing a square with two separate onedimensional axes (A:-A, B:-B) at right angles:


                                                                                    Fig 2

The two axes are perpendicular, not parallel, which illustrates the idea that A and B are dissimilar concepts. But since they are related in some way, they cross to mark off a common area, as in the ordinary Cartesian coordinate system. In general, two-dimensional thought means a correlation existing between two different pairs of antitheses. "Different" can in general mean anything from total irrelevance to close kinship (consanguinity). The former case applies, for example, when two people are said to argue at "cross-purposes." Or it may apply to "paradoxical" situations in which a common relationship between two sides of an issue is not discovered. In the latter ease of close kinship, A and B are dissimilar in some sense, but also a clear relationship of common origin or referent of the two sides is apparent. In this case, we can describe this relation between A and B as a complementary pair of antitheses, in which both pairs of ideas have a common property and yet are dissimilar. ²³

In the dictionary, the concept of eomplementarity is also said to "provide something felt to be lacking or needed . . . to putting together two things, each of which supplies what is lacking in the other, to make a complete whole."24 (I would add that in general more than two things may be necessary to make a complete whole.) In writing, complementary concepts are often identified by the phrases "on the one hand ... on the other hand." The dissimilarity of two ideas is thus shown by the fact that it takes two separate statements to express them. Their essential unity is shown in the metaphor of handedness, since both hands are connected to the same body.
At this point I define three kinds of paired relationships between the four propositions (the leftright order of the whole pattern is unimportant). The two relations A:-A and B:-B are the antitheses; the relation A:B is the complement; and the two relations A:-B and B:-A are called EXAGGERATIONS. The diagram is easier to use in print if I remove the axes and separate each proposition into a box.

                                                                                                Fig 3 

This structure I call an expression of A and B in dialogical form, or simply as a dialogic.²⁵

I have chosen this term because it includes four useful connotations: 1) dia means two, and -tog means word; two words or statements are involved. 2) Dia + logic = doubling of the dimensions of classical logic. 3) Dialogic is juxtaposed to dialectic and competes with it; the former emphasizes kinship; the latter (in the Marxist sense) emphasizes contradictoriness. 4) Dialog (or dialogue) = a discussion between two people, which commonly results in an agreement in terms of a complementary pair of ideas (or else a standoff). The "dialogical model" of personal relationships is implied here. This is a principle developed out of the experience of dialogue by some modern theologians, especially Martin Buber.²⁶ Howe has described dialogue (using some of Buber's language) as "a reciprocal relationship in which each party 'experiences the other side' so that their communication becomes a true address and response in which each informs and learns."²⁷

Actually dialogue form was a popular method of writing among the Creeks after Socrates, and among the early scientists like Galileo. In recent times it has fallen into disuse, probably because it seemed "too personal" and "subjective" for modern science. A constructive dialogue often follows a pattern such as the following, where A, B, and their opposites are seen to fit into a dialogic:

Jack: I believe A.
Jill: But that implies -B. I believe B.
Jack: But that implies -A. I believe A. Jill: I believe B, but not its exaggeration -A. Jack: I believe A, but not its exaggeration -B. lack and Jill: Then we both agree on A and B, but reject the exaggerations -A and -B.

The dialogic pattern provides a simple way to express the outcomes of such dialogues in compact form. In fact at this point it becomes easier to reveal other properties of dialogic by giving some examples from
various systems. (At present I am concerned mainly with analyzing the logical form of these ideas, not with their details of content.)

Complementarity in Modem Physics

The concept of complementarity has received a great amount of attention since Heisenberg introduced it in quantum mechanics to express the dual wave-particle nature of light (photons). Since this subject is generally well known, I am presenting it as my first example of dialogie:
A single photon may be

                                         Fig. 4

In this diagram, the upper two statements describe the (complementary) outcomes of real experiments. The lower two statements describe the (paradoxical, contradictory) properties expected of classical waves and particles. The upper formulation is the accepted pair. In this instance, the complementary pair taken together makes a whole which has a quantitative meaning as well (namely, the Uncertainty Principle: the product of the photon's location and momentum has a limiting value called Planck's constant). It is this quantitative formulation which constitutes a new twentieth-century application of the concept of complementarity.²⁶

Notice that the two pairs of statements along diagonals are true antitheses. It can be seen that an overemphasis on, say, the precise localization of a photon tends to imply the notion that photons have discrete positions and hence are particles: this relation (A:-B) is an exaggeration. Likewise the relation B:-A is an exaggeration. Both of these exaggerations are ruled out by actual observations of light in the laboratory-more properly, by laboratory experiences involving light. The same is true of experiments with electrons or any other "particles". As Bohr describes it:

any measurement of the position of an electron by means of some device, like a microscope, making use of high frequency radiation, will ... be connected with a momentum exchange between the electron and the measuring agency, which is the greater the more accurate a position measurement is attempted.²⁹

There is no causal, physical law describing the relationship of position and momentum. Rather, the relationship is determined in part by what the experimenter chooses to measure. Thus, his choice of instruments and settings becomes an integral part of the phenomenon being observed. The universe exists only as a whole; on the atomic scale the effects of observation become relatively large enough to cast doubt on the location of an "object". (At least this is the widelyheld "Copenhagen interpretation" of atomic physics.)

Classical concepts were of course developed on the basis of experience in our ordinary scale of distances and energies. When two of these concepts are simultaneously applied to photons, however, the result is a "paradox": the relation -A:-B. The dialogic formulation offers a way to show how such paradoxical concepts may be redefined and thus reconciled.

Others have derived somewhat different implications from this example of complementarity. In my view, physical complementarity is not an expression of polarity or dualism, and the unity it offers is not mystical or inscrutable, as Bohr's later views seem to imply. His neo-Kantian notion of "reciprocal limitation" is a dualism in which particle and wave models are considered mutually exclusive concepts. Bohr says that these classical concepts are the only ones available to describe the atomic world, due to the given structures of the human mind. Certainly it is important to realize that human mental concepts can force nature into conceptual molds that can limit our further knowledge and even deceive us. Barbour attributes this self-deception not to the mind's structures but to a limitation of human imagination that can perhaps be overcome in succeeding theories.³⁰ But I believe an even stronger case can be made for the validity of twodimensional concepts. As Leibnix often warned his contemporary scientists, it is the classical concepts that are unintelligible! (If there is a classical "particle", what is its inside made of? If there is a classical "wave", what is waving?) The complementarity concept-though difficult to grasp at first-may he ultimately more intelligible because it avoids these classical problems. It simultaneously meets the requirements for expressing the unity and yet the distinctness or diversity in physical phenomena as a whole.

The Composite in Early Greek Science

Although it has received this new recognition in physics, complementarity or two-dimensional thought is not new. It was perhaps first expressed around 350 BC by the Greek naturalists in order to reconcile a paradox in natural philosophy: the paradox of intelligibility versus "saving the appearances." Briefly the problem they faced was this: in the world of our experience we see everything in a more or less rapid state of change; nothing appears constant. But words and ideas in human languages can change only slowly. How can we describe nature in a way that is true to the changing appearances, yet in a way that is expressed in fixed word-forms so as to be intelligible to others?³¹

The pre-Socratic philosophers divided sharply on this issue. Parmenides argued for intelligibility: he said that everything is one Being, fixed and unchanging; all change is an illusion. But this left the changing appearances unaccounted for. Heraclitus argued for the appearances: he said that everything is in constant flux or tension; nothing is fixed. But this left the real nature of the world totally inexpressible (remember his follower, Kratylus!)
Plato suggested a solution for this "paradox" in terms of ideals and Particulars: every particular thing is an imperfect representation of its ideal form which exists in an unchanging realm of Ideals, or Ideas, to which our human words refer. These two concepts were thus not strongly tied together-which led Plato and his followers to drift into an "imperialist" mentality which exalted the heavenly realm of Ideals over the imperfect, worldly realm of Particulars. To this day "Platonism" remains with us as an example of an unbalanced tendency towards idealism.

Aristotle was probably the first philosopher to explicitly specify a way to satisfy the scientific requirements for an intelligible explanation of appearances in the natural world of Particulars. He combined the two equally important terms of Parmenides and Heraclitus into one "composite" (synalon). He declared that any practical description of nature must contain both terms as inherent aspects of reality.³² Aristotle used many names for this composite pair of terms: BeingBecoming, Species-Genus, Actuality-Potentiality, Continuity-Alteration, Form-Matter, Agent-Patient, etc. Regardless of the terminology used, the basic structure is the same. It may be briefly expressed in dialogic form in various ways, such as the following:

 

                                                                                        Fig. 5

In the historical development of Greek naturalism, theories alternated back and forth in the lower (paradoxical) terms until a composite solution was finally discovered. Aristotle's careful examination of the problem and its solution are fully explained in his Metaphysics³³ Here is a particular application of this composite description as it might be applied to a wellknown phenomenon:

                                                                                  Fig. 6

It can be seen that (although my dialogie formulations are brief and perhaps oversimplified), the diagonal propositions in the above figures are antithetical, while the composites consist of the upper two propositions which are not antithetical. The composite is not an attempt to reconcile concepts that are truly opposites; if it were, this would be an attempt to violate ordinary monologic.

Aristotle's two-dimensional solution of this problem was an extremely important achievement in the early history of science. Those who rejected either the intelligibility or the appearances requirement fell by the wayside as regards physical science. History shows that these other streams of thought failed to bear any scientific fruit.³⁴ But Aristotle's composite-based inquiry went ahead; its basic method (induction-deduction or empirical-rational) was in hand. Through the continual interplay of these two kinds of inquiry, the content of scientific knowledge continues to grow.

Complementarity in Communism

Marx and Lenin appropriated the old Greek term "dialectics" to describe their own logical system, but their use of this term is quite different. Lenin defined dialectics as "the study of contradiction in the very essence of objects ."³⁵ Thus this "system" is a restatement of Heraclitus' conception of the world as a flux of opposites-a form which earlier was identified as zero-dimensional.

Modern Leninist dialectics, however, is much more sophisticated and subtle than Heraclitus' monism. Lenin, Engels, and other communist philosophers apparently saw the need for more logical structure in their philosophy, and tried to develop it. Mao Tse-Tung recognized the importance of complementarity in this connection. Referring to an ancient Chinese proverb, he wrote,

We Chinese often say, 'Things that oppose each other also complement each other.' That is, things opposed to each other have identity. This saying is dialectical and contrary to metaphysics [i.e. correct]. 'Oppose each other' refers to the mutual exclusion or the struggle of two contradictory aspects. 'Complement each other' means that in given conditions the two contradictory aspects unite and achieve identity. Yet struggle is inherent in identity and without struggle there can be no identity.³⁶

In this and other passages, Mao uses the term "earnplement" in a subtly different way from that defined by Aristotle's "composite." (And presumably different also from the original Chinese proverb from the 1st century AD, or else Mao would have exploited this historical precedent in far more detail.) The "unity" or "identity" Mao refers to in the quote above is only relative, temporary, and conditional. But the contradiction-the struggle of mutually exclusive opposites-is absolute, universal, and eternal. Therefore the two dimensions of the complementary pair, identity and contradiction, are not equally important or balanced in the dialectical system. Consequently there is an "imperialist" tendency for the system to revert to a pure Heraclitean monism of eternal contradiction. This leads to a denial of any "metaphysical" basis for a continuity or common ground along which change can occur (Aristotle's Form, Being, etc.) Thus Mao's dialectic has not really succeeded in developing a two-dimensional structure.

Mao offers only two senses in which to affirm the "identity" of mutually opposing things: (1) the existence of a thing presupposes the existence of its opposite-a moot point; (2) in given conditions, each of the pair transforms itself into its opposite.³⁷ For instance, a communist would say that there is an "identity" between the bourgeoisie and the proletariat in the sense that they can change into each other, e.g. when a revolution "happens to occur." Thus the two classes remain in a state of struggle before and after the revolution. Hopes for eventual peace and the "dissolution of the state" will always remain precisely that, for there is no formal basis for such a strong kind of unity within the dialectical system. Actually the term "polarity" seems to be more appropriate to describe Mao's "identity". Communists reject, under the epithet "metaphysical", any notion of the essential, absolute unity of humanity which cuts across class distinctions. The latter is the strong form of unity-agreement, kinship-affirmed in such statements as "all men are created equal," or "He made from one every nation of men to live on all the face of the earth."³⁸ Absence of a concept of essential unity appears to be a weakness and danger in the formal structure of communist philosophy.

Dialogical Thought in Christian Theology

The Bible reveals a God Who has a personality characterized by holiness and love. Often in isolated passages of Scripture these two character traits seem to be contradictory: we read of a God Who loves Israel more than any other people, yet Who can break forth in holy wrath, destroying all but a small remnant. How can these two opposing patterns of God's character be satisfactorily reconciled?

Some sections of the Bible give answers to this question. Job saw the greatness and yet the closeness of God, as revealed in the last chapter of his book. The atonement of Christ is another example. It is summarized in Rom. 3:26 as follows:

[Christ's crucifixion] was to demonstrate His righteousness, because in the forbearance of God He passed over the sins previously committed; for the demonstration, I say, of His righteousness at the present time, that He might be just and the justifier of the one who has faith in Jesus.

All our systems and models are only metaphorical tools of communication. They can never contain the full knowledge of God, or "absolute certainty."

Here Christ is presented as the just, Who in His divine holiness cannot tolerate evil and convicts all men of sin. Thus for all men the legal death penalty should follow. But also Christ is the Justifier Who, out of His love for all men, takes their death penalty upon Himself, that they may live. In Christ men can be justified, yet without negating or compromising the perfect justice of God. Its Christ God's holy wrath is fully satisfied, yet without destroying all men in its wake. All this can be summarized in dialogic form: 

                                                 Fig 7

Here we can see that holiness and love counterbalance each other: we would not desire either one by itself. If God's love were unconditional, if He could condone sin against His own laws, then He is not a faithful God; He is capricious. We would have no assurance of His faithfulness to save and keep us, if His other laws are not important to him. On the other hand, if God's holiness meant only His wrath and consistent application of His laws to sinners, then a personal relationship between a sinner and God would be impossible. God would be only an unapproachable ideal or "Other". As far as man is concerned, such "holiness" would amount only to alienation-an evil thing.

Therefore, not only are holiness and love non-contradictory, but they must be held together simultaneously
to understand the character of the biblical God. This is an example of a dialogical or complementary concept in Christian theology.

There are many other examples that could be elaborated showing these dialogical structures in Christian doctrine. One of the most "paradoxical" doctrines, the sovereignty of God and the free choice and responsibility of persons, has already been shown to have a formal connection with the idea of complementarity in modem physics. This connection was suggested in an article in the Journal ASA by Bube, written some twenty-two years ago.³⁹ Similar connections have been recognized by others. Schaeffcr, in the book mentioned earlier, shows that similar relationships exist among many of the major Christian doctrines. He uses the terminology of two cliffs; when Christians are challenged to defend the truth of one Biblical concept, there is often a tendency to "fall off the cliff" on the other side, that is, to negate another Biblical concept.⁴⁰ The dialogical structure provides a way to see both concepts simultaneously and thus to keep doctrines in their proper balance.

Since some of these relations between Christian doctrines are important to us, I have illustrated them
briefly, using some of Schaeffer's terminology as well as my own. In all cases the "orthodox" position, as I understand it at least, is expressed in the upper pair of statements. Of course these are not meant to be "creeds"; there may be better ways to formulate these doctrines than the ones given. The reader may wish to formulate his or her own views in dialogical form.

At this point it can be seen that the three pitfalls mentioned earlier are all attempts to squeeze two-dimensional concepts into a one-dimensional formulation. This is done either by emphasizing one aspect of the complementary pair over the other (the "imperialist" pitfall), or by defining orthodoxy/ heresy as agreement/ disagreement with one particular statement of doctrine (the "conformist" pitfall), or by affirming only one of the two aspects at any one time (the "alternating" pitfall). In all of these cases, a one-dimensional but distorted formulation is the result.

Three-Dimensional Thinking-and Beyond?

For the past few years I have been "collecting" dialogical patterns such as the ones above, wherever I discovered them. After finding a large number, the natural step was to attempt to organize them into more general types. To do this required closer attention to the content of complementary ideas, since they all have the same two-dimensional form. This amounts to the development of a kind of general systems theory.

It is the Christian system in particular that I have 'attempted to organize in this way. After spending considerable time struggling with various arrangements of basic concepts in Christian doctrine, it became clear to me that at least one additional dimension would be necessary to express the full relationships among these doctrines. With the addition of one more dimension I arrived at a three-dimensional system, naturally called trilogic.

                                                            Fig  8, 9

Trilogic retains the same kinds of logical relations as in dialogic, except that there are three mutually orthogonal axes instead of two, and the complementary relation between three concepts A, B, and C encloses a volume rather than an area. There are three "degrees of freedom" and three kinds of "cliffs", or error-boundaries in this system. Figure 1 is a sketch of the relationships in geometrical form; a sphere rather than an octahedron is drawn to clarify the illustration.

In this figure the three axes are A:-A, B:-B, and C:-C. The octant (ii section) ABC, which faces the viewer, contains the positive complementary trio of concepts A+B+C; the other seven octants contain more or less "heretical" combinations of views in which one or more of the primary concepts A, B, or C are negated.
(This property shows that the more freedom there is in doctrinal preferences, the more kinds of "heresies are possible also.) This structure constitutes the form of trilogic. If the Christian system is the source of content, I would suggest that the three primary concepts to organize much of the doctrinal material would be variations on the theme of unity, equality, and diversity; these are the three relations described in the Westminster Confession of Faith with respect to the Trinity.⁴¹

I have only begun to explore the implications of these relationships. At this point all I can say is that trilogical formulations of Christian doctrines in the terms suggested appear to offer a remarkably complete framework for a Christian worldview, which includes views on epistemology, metaphysics, physics, values, and other aspects of philosophy.

It may be unnecessary and undesirable to extend multidimensional logic to more than three dimensions The aim was to clarify issues, not complicate them. Besides, it becomes difficult to depict four-dimensional patterns on plane paper!

There are many situations in which we can see many "levels" of meaning or valid models of a phenomenon or doctrine; for example the atonement of Christ, which has aspects of legal, personal, theological, and social significance. Another example would be Dooyeweerd's fifteen "modal aspects" or viewpoints of the world .⁴² It is not necessary to invoke complicated multidimensional structures to elucidate such concepts. They can all be understood in terms of a trilogical system with unity, diversity, and equality as the relations among the levels. In practically all cases the number of aspects or levels in such models is not tightly defined, but open to expansion or reduction somewhat. The only necessary relations are that: (1) there is a diversity of true ways of looking at reality; (2) each of the several viewpoints is equally important or valid; (3) reality is truly a unity which includes all the levels: they are all created, among other things.

The Purposes of Multi-Dimensional Thinking

It is apparent that philosophical systems have differences of form as well as differences of content. Understanding the logical form taken by a system helps us to understand its content. The most fully complementary systems appear to allow a place for unity, diversity, and equality relations in the system's content; two (or more) concepts have some underlying unity so that they truly fit together, yet they also have an essential difference, so that they counter-balance each other to prevent false exaggerations. And they share equally in this balance; one concept does not predominate over the others.

The trilogical geometrical pattern is a model of these fully complementary systems. It consists of three axes in different directions; they all intersect at a common origin, and they all are mutually orthogonal and equal in length. Such a model can be used to illustrate the relationships in any system of concepts having the same form.
Do these complementary concepts really "solve" anything? I believe so, at least in the sense of providing some of the needed unity or rational integration of knowledge. But I suggest some guidelines to keep in mind when dialogic is applied to philosophical problems. (The same guidelines apply to trilogic.)

First, the dialogic form may help in determining whether any solution is possible. For example, a given "paradoxical" pair of concepts are really either contradictory or they are not.⁴³ If they are contradictory, e.g. the concepts "personal" and "impersonal", then no rational synthesis is possible. An attempt to summarize the ideas into dialogical form may help to determine which is the case. A restriction of this kind is also affirmed by Barbour in which he says:

Complementarity provides no justification for an uncritical acceptance of dichotomies. It cannot be used to avoid dealing with inconsistencies or to veto the search for unity. . . Coherence remains an important ideal and criterion in all reflective inquiry.⁴⁴

With due regard for coherence, I would suggest that if valid complementarity is really present in a model, then there is already a unity, viz. a common referent. There may not be semantical or mathematical unity; these may be found eventually, but they are not essential to the heuristic value of the model. The common referent is the bond or source of coherence in complementary concepts. It may be a specified subject (e.g. a photon), or a specified worldview or paradigm. Both sides of the complement must share equally in this subject-matter; as Barbour puts it, each side must have the same "logical type." Naive mixing of unrelated concepts is a common error. One example of this is the unqualified use-by Barbour and practically everybody else-of the term "religion."

Secondly, the history of philosophy shows a few cases of related concepts which cannot satisfactorily be reduced to one concept, yet which seem to be mutually necessary and valid. We may have to reconcile ourselves to the fact that the unity or coherence of such concepts is complementary, and that such a situation is final, It may not be possible to find a monological statement of these concepts. A more positive way to say this is that the form of a concept may be as much a part of the solution as is its content. (Form and content are complementary, too!) For instance, the Christian doctrine of the free will of persons and the sovereignty of God has been debated for two thousand years, encountering all of the "pitfalls". But it should not be difficult for Christians to accept the final complementary (yet still rational) nature of this particular doctrine. There appears to be no expression which does complete justice to the Creator-creature relationship in a simple sentence. (Theologians have offered a reason for this: man cannot by feigning autonomy, place himself in a vantage-point that is outside both the Creator and the creation, so as to discover some kind of commonality between them, or something "in back of God ."⁴⁵)

Thirdly, dialogic must be carefully distinguished from other formal approaches to philosophical problems. Dialogic is not Hegehan synthesis, nor is it communist dialectic. These forms appear to lack a real concept of the unity of the world and the stability of truth. Dialogic, when dealing with problems of the created order, cannot he an expression of relativism, dualism, "biperspectivism",⁴⁶ or polarities or reciprocal concepts that are mutually exclusive. These are all forms of "paradoxical" relations in which a common referent (such as createdness) is not clearly present.

We may say that such-and-such a subject has different meanings on different levels, but "God will destroy both one and the others."⁴⁷

Conclusion

The Christian world-view may be modeled as a logical structure which recognizes the essential relationships of unity, diversity, and equality in all creation. As such, it is eminently qualified to offer to the world a fully-integrated view of creation in the form of a general system.⁴⁸ In contrast to secular system philosophies, this Christian view does not have to search for a source of unity across the levels or "modal aspects" of life's experiences. It already has that unity: in "the divine Origin of all meaning, Whose absoluteness reflects itself in the human ego as the central seat of the image of God."⁴⁹

In particular, this view recognizes the unity, diversity and equality of all kinds of persons: man/woman, believer/ unbeliver, black/white, liberal/ conservative, evolutionist/ antievolutionist, and so forth. Tolerance and respect for people different from ourselves is mandatory because we have an essential unity and equality before our Creator. Views which lack such a strong source of unity and kinship find no basis for such tolerance. Likewise Christians who forget their own Creator or distort their own world-view can become intolerant and destructive. It is important for us to know, practice and communicate a full expression of the Christian world-view. Not only its full content, but its fully-developed form and mentality, may be different from that found in the world's philosophies.
It is also vital to remember that all our systems and models are only metaphorical tools of communication. They can never contain the full knowledge of God, or "absolute certainty". But they can be means to glorify Him, if offered with a clear conscience. The Apostle's formal doctrinal exposition in Romans ends with a rather informal conclusion:

   0 the depth of the riches and wisdom of God! How unsearchable are His judgments, And how inscrutable His ways!⁵⁰

REFERENCES

¹Ervin Lazlo, introduction to Systems Philosophy: Toward a New Paradigm of Contemporary Thought, (New York: Harper & Row, 1973), p. 1-2.
²Michael Polanyi, Personal Knowledge: Towards a Post-Critical Philosophy, (Chicago: The University of Chicago Press, 1958), Paperback ed. published by Harper Torchbooks (New York, 1964).
³Ludwig Wittgenstein, Tract atus Logico-Philosophicszs, trans. by D. F. Pears and B. F. McGuinness (London: Routledge & Kegan Paul, 1961). The first German edition was published in Annalen der Naturphilosophie in 1921.
⁴Ludwig von Bertalanffy, General System Theory, (New York, George Braziler, 1968).
⁵Lazlo, op. cit. and The Systems View of the World: The Natural Philosophy of the New Developments in the Sciences (New York: George Braziller, 1972). These two books contain large bibliographies of contemporary literature on systems theory.
⁶Namely, atheism itself, as Romans 1:17 says. I believe that theism/atheism is the basic presuppositional watershed, not some other such as belief in an "open" or "deterministic" universe.
⁷Terms such as these are frequently used in modern theories of "hierarchical structures", but I think that they only beg the question. See, e.g. Lazlo, introduction, p. 174ff;
Polanyi, op. cit., p. 382ff; Bube, The Human Quest, p. 33; Whyte, L. L. et al,, Hierarchical Structures, (New York: American Elsevier, 1969).
⁸Herman Dooyeweerd, A New Critique of Theoretical Thought, tr. by D. H. Freeman and W. S. Young (Philadelphia: Presby. & Reformed Pub. Co., 1969).
⁹R. H. Bube, The Human Quest (Waco, Texas: Word, Inc., 1971). Other books include Buhe's The Encounter Between Science and Christian Faith, D. M. MacKay's The Clockwork Image, John Stott's Your Mind Matters, and Malcom Jeeves' The Scientific Enterprise and Christian Faith.
¹⁰For a good sampling of these, see Zen Flesh, Zen Bones, A Collection of Zen and Pre-Zen Writings, compiled by Paul Reps (New York: Anchor Books).
¹¹Leonardo Taran, Parmenides (Princeton, 1965).
¹²Wheelwright, Heraclitus (Princeton, 1959).
¹³Reps, op. cit., pp. 35, 38.
¹⁴Morris R. Cohen and Ernest Nagel, An introduction to Logic and Scientific Method, (New York: Harcourt, Brace, & World, 1934), p. 181ff.
¹⁵Reps, op. cit., p. 49.
¹⁶Aristotle, Metaphysics, 1010a12.
¹⁷By R. Buckminster Fuller, among others.
¹⁸Ernest Nagel and J. R. Newman, Godels Proof. (London: Routledge & Kegan Paul, 1959). For a detailed discussion of its implications, see Thomas F. Torrance, Theological Science, (London: Oxford University Press, 1969).
¹⁹"Nothing-buttery" is discussed in Donald M. MacKay, The Clockwork Image: A Christian Perspective on Science, (Downers Grove, Ill.: Inter-Varsity Press, 1974), ch. 4. "Nothing-but-ness" is from Viktor R. Frankl, "Reductionism and Nihilism", in Beyond Reductionism: New Perspectives in the Life Sciences, Arthur Koestler and J. R. Smythies, eds. (London and New York, 1969), p. 398.
²⁰Francis A. Schaeffer, The Church Before the Watching World, (Downers Grove, Ill.: Inter-Varsity Press, 1971), pp. 83ff.
²¹Romans 9:19. Paul's answer to his own question is probably the clearest given in Scripture. He points out that God not only "finds fault," but also gives undeserved grace and mercy. However, he still leaves unclear what our sense of free will is. This concept must be drawn from other passages.
²²Schaeffer, op. cit., p. 105.
²³1n this passage I have tried to choose words which conform to the headings in the Abstract Relations section of Roget's Thesaurus, because this is the most well-known organization of concepts in the English language. The relations referred to here are Roget's numbers 10, 11, 12, 14, 15, 18, 27, and 46.
²⁴Randorn House Dictionary of the English Language, Un
abridged, (New York: Random House, 1967.)
²⁵Kirk Farnsworth's diagrams ("Psychology and Christianity: A Substantial Integration," Journal ASA 27, 2 (June 1975) ) resemble these in appearance, and they were also drawn from Schaeffer's thought-but they have no further relation to my diagrams. Aristotle's "square of opposition" comes closer, but it deals with statements differing in quantity, not subjects or qualities (Some A are B, all A are B, etc.) A discussion of the latter is given in logic texts such as M. Cohen and E. Nagel, op. cit.
²⁶Martin Buber, I and Thou, (New York: Charles Scribner's: 1970). His discourse begins: "The world is twofold for man, in accordance with his twofold attitude. . . - The basic words are not single words but word-pairs." See also Between Man and Man (Beacon Press), and Maurice S. Friedman, Martin Buber, (New York: Harper Torchbooks, 1955).
²⁷Reuel L. Howe, The Miracle of Dialogue, (New York: Seabury Press, 1963), pp. 38, 50.
²⁸Niels Bohr, "Discussion with Einstein on Epistemological Problems in Atomic Physics," in Albert Einstein-Philosopher
Scientist, ed. by Paul A. Schlipp (New York: Harper & Row, 1959). Bohr emphasizes the intense face-to-face dialogues that accompanied the development of these theories of atomic physics.
²⁹ibid, p. 208-209.
³⁰Ian G. Barbour, Myths, Models, and Paradigms: A Comparative Study in Science and Religion, (New York: Harper & Row, 1974), p. 76.
³¹This problem and its Aristotelian solution is outlined in more detail in Henry Veach, "Aristotelianism," in A History of Philosophical Systems, ed. Vergilius Ferm (Totowa, N.J.: Littlefield, Adams, 1968). 
³²Aristotle, op. cit., 1029a3-7 et at. 
³³Aristotle, Metaphysics, 995a24ff (Book B). 
³⁴Gordon H. Clark, "The Beginnings of Creek Philosophy," in V. Ferm, op. cit., p. 80. 
³⁵V. I. Lenin, Collected Works, Russian ed. (Moscow, 1958), Vol. 38, p. 249. 
³⁶Mao Tse-Tung, "On Contradiction", in Four Essays on Philosophy, (Peking: Foreign Language Press, 1968), p. 68. 
³⁷ibid, pp. 60-67. 
³⁸Acts 17:26. 
³⁹R. H. Bube, "Relevance of the Quantum Principle of Complementarity to Apparent Basic Paradoxes in Christian Theology," Journal ASA, Dec. 1956. 
⁴⁰Schaeffer, op. cit., pp. 86, 105. 
⁴¹Westminster Confession of Faith (1647), Chapter II, 3. For a profound commentary on this doctrine, see George P. Fisher, An Unpublished Essay of (Jonathan) Edwards on the Trinity, (New York; Charles Scribner's, 1903).
⁴²Herman Dooyeweerd, in the Twilight of Western Thought,
(Nutley, N.J.: The Craig Press, 1972), p. 7.
⁴³The word "paradox" is ambiguous in this connection. The dictionary allows either real or apparent contradictions to be called paradoxes.
⁴⁴Barbour, op. cit., p. 77.
⁴⁵Dooyeweerd, op. cit. p. 1ff.
⁴⁶From Lazlo, Introduction to Systems Philosophy, pp. 152ff.
⁴⁷From I Corinthians 6:13. In other words, the notion of metaphysical "levels" in creation may be useful, as long as some levels are not made irrelevant to or exempt from the Lordship of the Creator.
⁴⁸1 Corinthians 12 offers another example of these three relationships as expressed in social living in the Church.
⁴⁹Dooyeweerd, op. cit., p. 31 et at. Also see C. van TB, A Christian Theory of Knowledge, (Grand Rapids: Baker Book House, 1969), p. 51: ". - . there is a non-Christian as well as a Christian dimentionalism."
⁵⁰ Romans 11:33.