You may have heard comments about “bounded sets” and “centered sets” in missions conversations. Since introduced by Paul Hiebert in 1978, these terms have been part of many missiological discussions. Frequently, in a somewhat reductionistic way, “bounded sets” are seen as Western and traditional and “centered sets” are seen as more progressive.
Let’s review what we are talking about. Bounded sets are defined by the boundaries used to describe the set. For instance, either conversion or baptism might be the boundary for a bounded set of the category “Christian.” According to this way of categorizing people, in order to be considered a Christian, you would have to have a conversion experience or be baptized. Often the list of characteristics that define a Christian are expanded to include things like: going to church regularly, not drinking alcohol, having assurance of salvation and espousing orthodox theology on all major doctrines.
In contrast, centered sets are defined by the relationship to the center of the set. In this way of categorizing people, Christ would be the defining center for those who are considered “Christian.” As long as there was movement toward Christ one would be part of the set. The set would not be defined by how much one knows about the Bible, whether one is a church member or not or whether one has forsaken certain vices or not. Instead, the defining factor would be whether one worships Christ and is growing in obedience and love to him.
Though Hiebert uses “bounded sets” and “centered sets” as short hand in his writings, that is only part of the theory. Hiebert expanded his application of set theory in an article in the July 1983 edition of International Review of Missions and further updated that article in chapter 6 of his 1994, Anthropological Reflections on Missiological Issues. Here we see a complete explanation and application of set theory to the categories “Christian” and “church.”
Four Types of Sets:
In his fuller explanation, Hiebert used the term “intrinsic sets” to refer to what we often call “bounded sets” and the term “extrinsic sets” to denote what we call “centered sets”. But rather than just using these two types, he identifies four types of categories:
Two variables are essential to defining a category. The first has to do with the basis on which elements are assigned to a category:
Intrinsic sets are formed on the basis of the essential nature of the members themselves – on what they are in themselves. …
Extrinsic, or relational, sets are formed, not on the basis of what things are, but on their relationship to other things or to a referent point. …
The second variable in forming categories has to do with their boundaries.
Well-formed sets have a sharp boundary. Things either belong to the set or they do not. The result is a clear boundary between things that are inside and things that are outside the category.
Fuzzy sets have no sharp boundaries. Categories flow into one another. For example, day becomes night, and a mountain turns into a plain without a clear transition.
Anthropological Reflections on Missiological Issues, 1994, p. 110, 111 (italics his).
So we have four types of categories or ways of grouping things:
- Intrinsic well-formed sets
- Extrinsic well-formed sets
- Intrinsic fuzzy sets
- Extrinsic fuzzy sets
All cultures use all four types of sets (see Hiebert, 2008, Transforming Worldviews, 34, 35). Reducing these four types of categories to only two (one with and one without boundaries) causes confusion and misses important nuances of the four types. To some extent, the difference between these types of categorizations is a matter of emphasis. Extrinsic categories (centered sets) emphasize the relationship to the center. Intrinsic categories (bounded sets) emphasize essential characteristics. Well-formed categories emphasize the connection of members within the set. Fuzzy sets emphasize the flow between sets.
Both intrinsic (bounded) sets and extrinsic (centered) sets can have boundaries. Often centered sets are seen as not having a boundary. But Hiebert insists that they can:
It should be noted that both bounded and centered sets have clear boundaries. The difference lies in the presence or absence of a center. It is “fuzzy sets” that lack a clear boundary, but a discussion of these and how they relate to conversion and the church needs another paper.
New Horizons in World Mission, 1979, p. 237.
The difference is what defines the boundary and whether there is a focus on the boundary. Intrinsic (bounded) well-formed sets focus on the boundary (the point when one comes “in”) and carefully define the characteristics required to be part of the set. These characteristics are most often static and focus on the minimum required to be part of the set. In the category “Christian”, the focus is on the decisive moment when one enters into the set (point of conversion), and the maturing process after conversion may be ignored. When one has crossed the line (accepted Christ), then one is “in”.
Extrinsic (centered) well-formed sets instead focus on defining the center and the relationship of members of the set to that center. In the category “Christian”, defining who Christ is (according to Scripture) will be essential. Also, defining what it means to be moving toward (growing closer to) Christ will be required. Centered sets pay attention to a person’s movement toward Christ, the continuous maturing process, rather than the moment of conversion. In this type of thinking, it is much more important that one is growing in Christ than that one can tell you the time and day when one “prayed a prayer and made a decision for Christ.”
Both bounded and centered well-formed sets have clear boundaries. Hiebert explains:
While centered sets are not created by drawing boundaries, they do have sharp boundaries that separate things inside the set from those outside it – between things related to or moving toward the center and those that are not.
Centered sets are well-formed, just like bounded sets. They are formed by defining the center and any relationship to it. The boundary then emerges automatically. Things related to the center naturally separate themselves from things that are not.
In centered-set thinking, greater emphasis is placed on the center and relationships than on maintaining a boundary, because there is no need to maintain the boundary in order to maintain the set.
Anthropological Reflections, 1994, p. 124 (italics his).
The cohesiveness of a well-formed extrinsic (centered) set depends on not defining the line when one enters the set, but rather on defining the center. So in the category “Christian” with Christ as the center, the biblical definition of the person and work of Christ is the controlling center of the set. If one is worshipping, following and loving that “Center”, then one is in the set.
Fuzzy sets, on the other hand, whether intrinsic or extrinsic, lack a clear boundary or center. These types of sets describe categories where there is a more of a gradual transition from one set to another set, e.g. day becomes night. A bounded fuzzy set still focuses on the boundary but that boundary is not clearly defined. So from this “fuzzy” perspective, the category “Christian” might include or exclude a person depending on whether they have any spiritual or religious interest. But who determines how much spiritual interest is sufficient? This lack of definition is what makes it a fuzzy set.
A centered fuzzy set of the category “Christian” might include anyone who says they admire Jesus, regardless of what they might think about who Jesus Christ really is (good man, peace-maker, revolutionary, prophet, God-incarnate, etc). But there are many different understandings of who Jesus is in the world, and some of them are clearly contradictory. How can they all be valid? This lack of definition of who we mean when we talk about Jesus is what makes this categorization “fuzzy”.
Fuzzy sets are probably more appropriate for describing transitional categories, e.g. people who are in the process of exploring the gospel but have not come to a clear biblical understanding or commitment.
Hiebert appears to favor well-formed extrinsic sets for the categories “Christian” and “church.” He writes:
The worldview of Scripture, I believe, is based primarily on a centered-set approach to reality. Relationships are at the heart of its message, our relationship to God and our relationships, therefore, to one another. …
Furthermore, Scripture affirms clear boundaries at several key points. Christ is declared to be the only way to God. In the end people will be saved or lost, and sinners are called to turn radically away from their evil ways to righteousness and love. There is no both-and approach to these and other essential matters in the Bible.
Anthropological Reflections, 1994, p. 134 (italics his).
Hiebert’s application of set theory to missiological issues is extremely helpful. Well-formed centered set thinking can help us focus on the person and work of Christ in our conversations with seekers and new converts. In trying to help them understand what it means to be a Christian, we would emphasize movement toward Christ, both in their understanding of and their commitment to Christ.
But all four category types are needed in our missiological discussions. There is a place for bounded set categories, and also for fuzzy set categories, depending on what we are seeking to categorize. Just remember, in forming our categories, the Bible must inform and control our definitions.
For further reading:
In addition to the works cited above, I recommend a ThM thesis by Michael Hakmin Lee, “Assessment of Paul Hiebert’s Centered-Set Approach to the Category ‘Christian'” available at this link.
Here are links to a couple of Hiebert’s earlier articles:
But Hiebert’s fullest explanation and application of set theory is found in his 1994 book, Anthropological Reflections on Missiological Issues.