Centered set thinking
#####################

:date: 2016-01-11
:category: faith
:tags: blue ocean, centered faith, christianity

.. zotero-setup::
   :style: chicago-author-date

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 :xcite:`[@schmelzer:2008not]`, although
originally this theory originated from
:xcite:`[@hiebert:1994anthropological]`, and Schmelzer uses the
simplified version of the theory probably from
:xcite:`[@mclaren:2002more]` 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.

.. _Utraquism:
    https://en.wikipedia.org/wiki/Utraquism

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 :xcite:`[@hiebert:1994anthropological]` 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.

.. FIXME Add more about idolworshippers as the biggest enemies of
    the God’s people in the Old Testament.


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.

.. image:: {static}/images/centered_set_01.svg
    :width: 250pt
    :align: center
    :alt: 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. [#]_

.. [#] 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.”

.. Add a little bit about certainity of election, assurance of
    salvation. Also, once-and-forever salvation,
    now-I-am-saved-and-what-next. Horrible method of
    evangelization which look like a sale of detergent, because
    assent to the salvation and sinner’s prayer is ALL what
    matters. “Salvation is free gift offered here for you, how
    can you not accept it when it is free?”
    Now sure how much of Bonhoeffer’s The Cost of Discipleship
    should be added.

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).

.. image:: {static}/images/centered_set_02.svg
    :width: 250pt
    :align: center
    :alt: Centered set

:xcite:`[@mclaren:2002more]` 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.

.. bibliography::