Centered set thinking

Po 11 ledna 2016

The centered-set theory

Before explaining my further thoughts on the unity of the Church, let me explain what I think about the application of the set theory to the understanding of the Church. The following thoughts are heavily based on (Schmelzer 2008), although originally this theory originated from (Hiebert 1994), and Schmelzer uses the simplified version of the theory probably from (McLaren 2002) or some other books by this author, not from the Hierbert's article itself. I present here the original version. “Centered set” versus “bounded set” terminology comes originally from the mathematical set theory (originally by Georg Cantor).

  Strict Fuzzy
Limit Bounded set Fuzzy set
Center Centered set Fuzzy center

This part of the set theory deals with the means how to define a set and thinks about primary two ways. One is the to define a limit (“if a vehicle has four wheels it belongs to the set of cars”), which is the way more traditional way how to define set. When this style of categorization works then it works pretty well: a person is at least biologically either a man or a woman (ignoring psychological problems of transgender people), or she is either Christian, Muslim, Jewish, or an agnostic. There are people taller than 180 cm and the rest, etc.

This hard version of the bounded set (bounded by the defining characteristics) has been under violent attack of the current thinkers mostly because they observed that many (if not most, or even all) groups in the real world are not that neatly delineated and that ignoring the inherent ambiguity of the world leads to sometimes terrible results. For example, to use the example relevant to the Czech history, one of the founding problems of the Central Europe is the insistence on the exact definition of the nation. Of course, there are many reasons why the historical events happen, but one of the sources of the Central European nationalism (crowned by its extremes like Nazism) was the idea that nation can be exactly defined by the characteristics of its members, namely their language. Otherwise, it would be possible to find a lot of shared between German-speaking and Czech-speaking citizens of the Czechoslovakia or the Austria-Hungary, it would be perhaps even possible to speak about one nation speaking two languages, but that went completely against the concept of the nation as a set of people speaking the same language and so it was never even seriously considered.

In order to return to the more ecclesiastically relevant example, this persistence on the precise and unequivocal characterization of the group was something which prevented development of the parallel slightly different version of then Roman Catholic church in Bohemia of the 15th century (Utraquism), because it was not acceptable for two members of the same church to accept the Lord’s Supper in a different manner.

After discoverting these problems using obvious examples, couple of ways out of this conundrum were developed, two of which I will mention here. One is just thinking in terms of the fuzzy logic. Although, the sets are still determined based on the characteristics of its members, it is now possible to understand membership not in terms of “either-or” but more like partial membership. It is suddenly possible to be partially (perhaps even expressed in percents) member of the one group and yet in the same time being partially members of the opposite one. To return to the previously mentioned sets, there is now plenty of psychological research showing that the distinction between males and females in terms of their character traits can be better understood in terms of the fuzzy logic. So, more than person being either a pure man or pure woman (and being subject of ridicule if his personality is not clearly alienated with either stereotype) it is useful to put individuals somewhere on the scale. There are obvious males who are driven very much by relationships, and females who are much more action- and purpose-driven than would be “appropriate” for their respective gender stereotypes. And I am purposefully abstaining from any comments on the sexual behavior.

Again turning towards the church scene, there is now large interest in the theology of the third way, a group of churchmen of the 16th century who were neither strong Protestants nor strong Catholics; for example a large part of the Anglican church, or their patron saint could be Erasmus of Rotterdam. Czech Utraquists would fir the bill as well. It suddenly seems that the difference between Catholicism and Protestantism (which itself is very poorly defined) is not that endless abyss as it was seen in the modern times. Although some differences are real and profound, there are many persons and theological systems which are more like bridges over that abyss.

Another way how to overcome the problems with the strict definition of the bounded set lies in the complete change of the way how to define such set. Instead of looking for a group of characteristics (precise or fuzzy) which should be present in each member of the set, it could be possible to define a set by the relationship towards the common center. It seems to me for example that for the medieval Christians the membership in their nation was not that much about showing some characteristics but rather worship and honor towards the shared saint. So, the basic semi-official definition of the Czech nation was that it is “domestic staff [čeládka] of the Saint Wenceslaus” and similarly were defined worshipers of Saint Boniface (Germans), Saint Steven (Hungarians), Saint George (English), etc. And while keeping on the Czech theme, it was apparently not that big problem that some servants of the Saint Wenceslaus were celebrating svatý Václav in Czech, and some Heiliger Wenzel in their native German. Only with the advent of the modernist thinking there was apparently strong desire to get more precise (and thus bounded) definition of the nation and number of thinkers (especially known among them are Germans Johann Gottfried Herder and Johann Gottlieb Fichte) develop the bounded set theory of nation as a set of speakers of the same language, which got so ingrained in our thinking that (at least for me as a native from the Central Europe) now it seems completely outrageous to think about nation as anything else than the language defined bounded set.

Actually one of the best examples of the historical use of the centered set was the understanding of religion by traditional Jews. There is no properly developed definition of Judaism in the Old Testament in the similar manner Christians defined their faith in the great creeds of the early ecumenical councils, and with the only exception of the Maimonides’ Thirteen Principles of Faith (from the late 12th century) Jews never developed anything resembling a creed (the only profession of faith being the biblical Shema Yisrael). It is no mistake that the First Commandment is resolutely center based “I am the Lord your God, who brought you out of the land of Egypt, out of the house of slavery. You shall have no other gods before me.” (Exodus 20:20f).

It must be emphasized that centered set in itself is in its original Jewish formulation strictly non-fuzzy. Most of the Old Testament is concerned with struggle of the Jewish community to keep strictly faithful to the LORD God only and refuse any other centers of their faith (aka polytheism and idolatry). For Jew, there is absolutely no alternative to the absolute allegiance to the only god, The LORD God. Although (Hiebert 1994) considers the fuzzy variant of the centered set Church, we will ignore it here as I do not think it brings much interesting to the debate.

Application of the set theory to the understanding of the Church

So, how we can apply this theory to our understanding of the Church? Let us consider first example of a group of Christians viewed through the bounded set lenses.

Traditional bounded set

In this illustration of the bounded set we can easily say that “A” and “B” (although we are bit worried about the later) are members of the set, whereas “C” isn’t. There can be some discussion about “D”, but in the end by sharpening the rule we can certainly find some decision on which side of the line he belongs.

This is the traditional distinction used in the most Christian thinking. The traditional evangelical formulation that somebody either is or is not born again (another qualifying characteristics could be whether they are baptized). You either are or you are not with the substantial consequences attached to such membership. [1]

[1]Romans 10:9: “because, if you confess with your mouth that Jesus is Lord and believe in your heart that God raised him from the dead, you will be saved.”

Centered set is quite different. It is characterized by its center (Jesus) and individual elements are not qualified as members but each of them has some level (including none) of relationship with the center.

And to make things even more interesting, let us add arrows to signify the orientation of each member of this group not only its distance from the center. Suddenly the image (with each person in more or less the same position) provides quite different picture. “A” even though is closer to the center (perhaps he is even a pastor from the traditionally religious family) is going in the completely opposite direction out from the Lord Jesus. “B” is rather close to the Jesus and she goes in more or less right direction. Suddenly “D” who was more or less suspicious and on the edge and even more “C” who was originally considered completely out of the group are suddenly better oriented than “A” and “B” although they target Jesus from larger distance (perhaps they are converts coming to the Jesus from the atheistic background).

Centered set

(McLaren 2002) makes this picture even more complicated by assuming that Jesus as the center is constantly on the move, so rather than just pointing to the place where the Jesus is now it may be better to go to the place where Jesus will be in the future.

Hiebert, Paul G. 1994. Anthropological Reflections on Missiological Issues. Grand Rapids, Mich: Baker Academic.
McLaren, Brian D. 2002. More Ready than You Realize: The Power of Everyday Conversations. English Language edition. Grand Rapids, Mich: Zondervan.
Schmelzer, David. 2008. Not the Religious Type. Carol Stream, Ill.: TYNDALE.

Category: faith Tagged: blue ocean centered faith christianity