Bounded Sets, Centered Sets, and Missional Modalities

Let it be known that I don't get along well with mathematics. You might recall the scene in the movie Apollo 13 where the ship has just experienced a massive explosion and is losing power and oxygen. The astronauts and NASA decide that the astronauts need to move from the main portion of the ship to the lunar module in order to conserve precious resources to enable a return trip to earth. The astronauts have only a few minutes in order to make the transition from one ship to another, and their lives hang in the balance. In order to make the transition properly, Jim Lovell, played by Tom Hanks, has to perform quick, complex mathematical calculations, and not trusting himself given the stress of the situation he radios NASA to verify his calculations. When I watched this scene for the first time I turned to my wife and said, "If my survival ever depends upon my abilities in higher mathematics, I'm dead."

This doesn't mean that I can't appreciate the insights of math, however, and I believe that the discussion of bounded and centered sets has an important contribution to make to an interdisciplinary approach to missional thinking.

Paul Hiebert, a Christian anthropologist and missiologist, discusses mathematical set concepts in his book Anthropological Reflections on Missiological Issues (Baker Books, 1994). His entire discussion on this topic, found in chapter 6 with the title "The Category Christian in the Mission Task", is helpful, but given the space limitations of a blog I will limit my discussion to bounded and centered sets, and their application to missional thinking.

Hiebert draws upon studies in mathematics where categories are created that define a set which entail certain structural characteristics and boundaries. He contrasts bounded sets with sharp boundaries, and centered sets that have boundaries but the emphasis is placed on that which centers the set rather than the boundaries around it.

Hiebert lists five characteristics of bounded sets:

1. The category is created by listing the essential characteristics an object must have in itself to belong to the set.
2. The category is defined by a clear boundary...The central question, therefore, is whether an object is inside or outside the category.
3. Objects within a bounded set are uniform in their essential characteristics - they constitute a homogeneous group.
4. Bounded sets are essentially static sets.
5. Bounded sets, as we use them in the West, are ontological sets. They have to do with the ultimate, changeless structure of reality, which is defined in terms of unchanging, universal, abstract categories. (Hiebert, 112-3)

If we consider the concept of "Christian" as a bounded set, Hiebert notes some interesting results. First, since we must classify objects in the set by their essential nature, in this case, whether someone is a Christian, in the absence of omniscience and a window into the human heart, we focus on external characteristics, such as assent to doctrinal orthodoxy, or adherence to certain moral behaviors, or both. Second, with a bounded set sharp boundaries are drawn between Christians and non-Christians. Hiebert states that with this emphasis, "we would work to maintain this boundary, because the boundary is critical to maintaining the category." From this perspective great emphasis is placed on determining who's in and who's out of the clearly bounded set.

In contrast to bounded sets Hiebert later moves to discussion of extrinsic well-formed (centered) sets. This he defines as a grouping of things "on the basis of how they relate to other things, not what they are in and of themselves" (emphasis in original).

Characteristics of centered sets are:

1. A centered set is created by defining a center or reference point and the relationship to that center.
2. Centered sets do not have sharp boundaries that separate the set from those outside it. The boundary emerges automatically by the relationship of the object to the center.
3. The variables of centered sets are membership and distance from the center.
4. Things headed away from the center can shift and turn toward or away from the center. (Hiebert, 123-4)

Hiebert then discusses the concept of "Christian" as a centered set. From this perspective Christians primarily define themselves as followers of the biblical Christ as the defining center of their lives. Second, and very importantly, Hiebert notes that while there is still a clear separation between Christians and non-Christians "the emphasis, however, would be on exhorting people to follow Christ, rather than on excluding others to preserve the purity of the set."

Hiebert then applies the concept of centered set to missions and states that "our primary aim would be to invite people to become followers of Jesus, not to prove that other religions are false. We would stress our personal testimonies of what Christ has done for us more than argue the superiority of Christianity."

As missional thinkers draw upon insights from various disciplines, including mathematics as applied within the context of missiology, set theory can help us rethink our concepts of "Christian", "Christianity", "church" and "missions". There are helpful aspects found in both bounded and centered sets. In terms of a bounded set concept, perhaps the primary concept most western evangelicals would consciously or subconsciously adhere to, the church must have some kind of boundary, defined in a variety of ways, including relationships, beliefs, and practices. These boundaries must be carefully defined and maintained, and yet balance is key to such efforts. As Roger Olson has insightfully noted, "The bounded set model ends up allowing little or no distinction between the center (the gospel) and the boundaries (orthodoxy). It also leads inevitably to obsessive boundary maintenance and inquisitorial judgments about whether persons and groups are Christian or not." (Roger E. Olson, The Mosaic of Christian Belief: Twenty Centuries of Unity & Diversity, [InterVarsity Press, 2002])

As we critically reflect in missional fashion in light of changing cultural circumstances in the western world, might it be possible that the church has overemphasized a bounded set mentality within a Christendom culture, and now the time has come to consider a centered set concept? How would our understandings of what it means to be a Christian, to be the church, and to engage missionally (not to mention our understanding of and relation to "the religious Other") be different if we spent less time building the fences of the boundaries and more time facilitating a journey to the Lord that is the center of the Kingdom set?