Introduction to Hypertheology

(Please read this brief introduction first. It will help you greatly in learning how to read the diagrams that follow).

Hypertheology is an outline for a systematic Christian theology that uses hypertext (HTML) to facilitate its presentation. Hypertheology emerged from a study of underlying logical structures in philosophy, theology and other systems. It was observed that religious and philosophical systems, in their logical structure, can be classified in a way that is analogous to the dimensions of geometry (0, 1, 2, or 3). This classification scheme only has to do with logical forms, not with substances or essences, so this scheme is not about monism, dualisms etc., which refer to numbers of things. The following paragraphs describe examples of logical systems in terms of their dimensions.

Zero Dimensional Logic
Buddhism is based on zero-dimensional logic. It may also be found in the writings of some of the Pre-Socratic Greek philosophers such as Heraclitus, the mystic Meister Eckhart and others. Pure zero-dimensional logic recognizes no fundamental distinctions, no antitheses, no parts or aspects of ultimate reality; hence this view is geometrically equivalent to a point:

.

One Dimensional Logic
Classical logic (or "monologic") is based on an antithesis between true/false, right/wrong, good/evil etc. This structure provides the fundamental basis for rational discourse. It specifies laws of thought (which Aristotle described as identity, non-contradiction, and the excluded middle). Because of this axis of antithesis, conventional logic may be said to be one-dimensional, like the two poles or ends of a line:

A _____________________ not-A

 

Two Dimensional Logic
Many structures in theology, philosophy and other subjects exhibit a complex and often confusing relationship that is sometimes described as "paradoxical" or even "contradictory." However, these views may actually be complementary rather than contradictory. The key to resolving many apparent conflicts is to realize that the full teaching fits into a two-dimensional framework. The total view is formed by two separate, "orthogonal" lines of monologic, that is, two separate theses/antitheses:

                                    B
                                    |
                                    |
                          A ________|________ not-A 
                                    |
                                    |
                                    |
                                  not-B 
 

In order to fit the text conveniently onto a table, the two lines of the diagram are turned 45 degrees so that now the antitheses are on diagonals:

                               A       B
                                \     /
                                 \   /
                                  \ /
                                   X
                                  / \
                                 /   \
                                /     \
                            not-B      not-A
 

The following table format is used to represent the resulting dilogic diagram:

A and B

A
B
-B
-A

Presented separately, theses A or B offer only partial statements of "desirable" ideas; this often leads to misinterpretations and exaggerations. Taken together, the two theses (A and B) balance each other and serve to moderate each other's exaggerations. The 2-dimensional structure above represents simultaneous affirmation of two "complementary" theses. (The left-right position of theses is unimportant.)

Such a relationship is here referred to as "dilogic". A significant feature of dilogic is that the exaggeration of A implies the negation of B, and vice-versa. Except for this feature, the connections between A and B are not logically determined; they are free from logical constraints and must be discovered "empirically" through discourse. A and B are simply said to "complement" one another so as to make up a more complete or balanced view.

Note that although the heading above is labeled "A and B", in general two-dimensional logic is not simply a way of saying "Both A and B." That would "flatten" the logic into the 1-dimensional antithesis "Both A and B" -- "Neither A nor B".  True two-dimensional logic requires assertion of two distinct antitheses "A|not-A" and "B|not-B". The heading may be an entirely different term that embraces the sense of the whole 2-dimensional relationship.

Please note that dilogic is not to be confused with "dialogic" which has a somewhat different meaning.

What is the significance of the colors?


Applications to Theology

Anyone approaching the subject of theology must first of all recognize human limitations. Whenever we talk about theology, we must remember that we really don't know what we are talking about. In Orthodox Christianity, the apophatic tradition of theology is based on the recognition that God's essence is unknowable or ineffable and on the recognition of the inadequacy of human language to describe God. However, though humans may not be able to say anything positive about God, they can consider texts that claim to be revealed by God. Hence often the prophets and Christian apostles claimed to know something.

Christian theology is an ancient field of discourse drawn from an even more ancient text (the Bible). Its creeds have been refined through 2000 years of study, argument and competition with unorthodoxy. Hence an important feature of orthodox Christian theology is its attempt to balanced ideas derived from all the biblical texts; unorthodox views tend to exaggerate one subset of texts. In theology, we often find two complementary theses that must be mutually inclusive to express the richness of the full biblical views. However, they may still appear very different from one another, and attempts to merge the theses into one statement are generally unsuccessful. That is why it has been found helpful to extend the textual relations to a second dimension.

Three-dimensional logic
The richness in theological expression in some cases even extends to a third dimension. Some of the central doctrines of theology require an additional dimension to bring out their full interrelationships. This 3-dimensional structure ("trilogic') follows the same rules as the 2-dimensional dilogic structures, i.e. there are three hyperlinked 2-dimensional dilogics, which can serve to represent the 3-D relationships.

Hypertext has proved to be a useful tool for illustrating these ideas, because it allows more flexibility of connections than the printed page. Likewise, the term hypertheology is meant to recognize the interrelationships of ideas that are easier to present in an interactive, hypertext format. For this reason, these ideas were formatted in HTML for presentation on the Web.

In the dilogic diagrams, the two upper statements represent positive or orthodox theses; the two lower statements are exaggerations that result in the negation of one of the theses. In some cases, arrows will be seen at the right and left sides; these link to two other dilogic diagrams that, taken together, express one of the three-dimensional doctrines. Take some time to consider the relationships as you examine each category.

You will discover that in many cases the dilogic structure reveals a rich structure and subtlety in many ancient ideas. Awareness of the full expression of these multidimensional concepts dispels some of the accusations of irrationality or contradiction in these views which can occur from seeing them as one-dimensional.

T. F. Torrance on the rediscovery of the Trinity

Sources

The concepts of complementarity and dilogic are not new. The Tao of ancient Chinese thought has long recognized the desirable "balance" or "moderation" to avoid idealistic extremes, as expressed by the yin/yang symbol. In the West Aristotle introduced a similar concept (the composite, synalon ) in the Physics. Augustine and Calvin have described ideas in which dilogical structures are implicit. Dilogic also has some similarities to previously described concepts including polarities and C. G. Jung's quaternities. In 20th century physics, complementarity was adopted as the paradigm for describing phenomena in quantum mechanics by Niels Bohr, but this is a strong, mutually-exclusive form of complementarity between the "idealized" wave and particle descriptions of quantum phenomena. Recent recognition of the usefulness of dilogical thought in Christian theology is based on the teachings of Francis Schaeffer, an evangelical Presbyterian theologian who helped a lot of people in the US and Europe in the critical period of the 1960's and 70's. His small book The Church Before the Watching World (Inter-Varsity Press, 1971) was a primary stimulus for this work. Dr. Richard Bube, as a Stanford professor of physics, also recognized the value of dilogical structures in his writings for the American Scientific Affiliation and elsewhere. Specific references, where available, are given in the "more" links on each dilogic diagram.

Your formulations of these great ideas may not agree with this author's, but these are offered so that you can begin to think dilogically about ideas in general, for such structures are widespread in literature.

Viewing the Dilogic Diagrams

Each dilogic diagram contains five links to other documents. The "overview" link gives a discussion that relates the two complementary ideas in the diagram. The four "more" links in each section of a diagram provide additional details and references that are specific to that section. Some of these documents may be blank and under construction.

Some dilogic diagrams are combined in a group of three which have the same category. These "trilogic" diagrams are linked together by arrows on the sides of the diagram. Click on the arrows to move among the three related diagrams. Also, in these cases there will be a "3-D Overview" document that describes the relationship among all three terms. This document can be reached from any of the three dilogic overview links; the Overviews contain an additional link to go the the 3-D Overview.

Using the Index

The index of diagrams (see link below) is divided into general categories. Click a link to go the dilogic diagram on this subject.


See INDEX of diagrams

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This and associated pages [except for quotations as noted] 2012 Paul Arveson.

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