A Centered-Set View of Christian Missions
Years ago, Paul Hiebert spoke of Evangelism and Conversion in terms of Centered-Sets rather than bounded sets, or even simple open sets. We don’t really know who is saved and who is not. God alone knows. I am not being a Calvinist here (which I am not). I am just saying that God alone knows the heart… we don’t. Because of that, in Evangelism we don’t know where the person was before we witnessed to them, and we don’t know are after (with respect to God). Hiebert suggested then that we should see the set of mankind as a bounded set with Christ in the center. We don’t know the exact boundary between a person and Christ, but we know that the redeemed can be thought of as closer. As such, Evangelism should be seen as moving people toward Christ. As such, statistics are a bit artificial. We can’t really measure “being closer to Christ then they were before.” See Paul Hiebert, “Anthropological Reflections on Missiological Issues,” Chapter 6.
Missions is also a thing that is hard to place boundaries on. Any definition for missions tends to cross off things that we all pretty clearly accept as missions. For example, many of the definitions would exclude Paul and Barnabas (as I have noted before). They did not serve internationally, and barely qualified as working cross-culturally. Even things like being cross-cultural may not apply to Missional Churches, or Diaspora Missions, for example. Stephen Neill years ago, however, pointed out the warning that if everything is Missions, then nothing is. I think this is valid, but it becomes difficult to find a consistent boundary.
So maybe it is better to have a centered set where the center is most clearly Christian Missions, and as one moves further from the center, it becomes less so, but with no clearly boundaries of when it moves beyond.

Using this, one might say that loosely to be described as being in the center is the most clearly missions. One could define
is “Cross-cultural Missions.” This is the most common understanding of missions. It is serving God oversees or across cultural lines in a variety of types of ministries to expand the Kingdom of God.
is a category that I like to use when I talk about Missions. Maybe because of my Baptist roots, I like to look at missions from the perspective of the local church. When the church reaches out beyond itself for the growth of the Kingdom of God (without expecting its own growth) this could be called Missions. This would include both local church planting as well as long-distant or cross-cultural ministry.
is the broadest category that could include all forms of ministry of the church. This could be said to be the Missio Ecclessiae. the full ministry of the church in response to God’s ministry work (Missio Dei). Essentially anything that lines up with God’s will and work could be said to be carrying out missions in this sense. This is where things get a bit questionable since Stephen Neill’s warning start to truly apply. Still, doing the mission of the church (Missio Ecclessiae) is indeed Missions in some sense.
The boundaries, except for the outermost are porous because there are no clear boundaries. I noted Paul and Barnabas before. They were clearly Pioneer Missionaries. However, they were not international missionaries and were barely even cross-cultural (in my context more like going from one part of the Philippines to another). So where do they fit? The fit inside of the circle, but almost don’t really fit inside of the circle. The problem goes away somewhat when one recognizes that the boundaries are approximate and loosely defined. Diaspora missions is often International but to one’s own culture, so it is also hard to fit clearly. Centered set doesn’t solve everything but does help gives some insights I believe.
A similar set of circles could be done for types of ministries as well. Churchplanting, Evangelism, and Discipleship are clearly mission work. Holistic ministry (especially in places where the gospel has had limited impact) is also in a broader circle of mission work. I teach missions in a seminary in a different country (from my own). That is missions, I think, but a different circle. Social justice, Bible translation, Missionary member care, and others also fit into missions but the definition is becoming gradually looser and poorly defined. Rather than saying certain types of work is missions and others are not, one should look at it from a centered-set perspective.