Sets and Logic

In response to an email from a friend the other day, I described myself as a ‘barrage balloon, loosely tethered to the body of Christ’. Which led me to wondering about  the way that the Christian church thinks about itself as a group. Set theory is a concept in mathematics whereby certain numbers or other entities belong to a group, or set. A bounded set would describe a group with clear "in" and "out" definitions of membership, such as “all integers divisible by 5”. It seems to me that the church historically has organised itself as a bounded set, or better, a series of bounded sets called denominations with more or less overlap. The set bounded by both Catholicism A (all integers divisible by 5) and Anglicanism B (all integers divisible by 2)  has as its shared membership A Ç B,  (to which the numbers 10 and 20 belong, but 15 and 6 do not) perhaps defined by the Creed or the Eucharist, for example. Those who share the same beliefs and values belong to the set and those who disagree are outside it. This is the methodology that most of the historic churches have adopted towards interfaith dialogue. I think it’s a mistake.

In response to postmodern thinking, a ‘centred set’ does not limit membership to pre-conceived boundaries, defined by liturgy or tradition, for example. Instead, a centred set is conditioned on a centred point and membership is contingent on those who are moving toward that point. Elements moving toward a particular point are part of the set, but elements moving away from  it are not. Thus, membership of a centred set called ‘believers’ would be dependent on moving toward the central point or focus of belief. Jesus, in other words. One is then, in my view, more properly defined by one’s focus and movement toward Christ rather than by a limited set of shared beliefs and values. Hopeful travel, as C S Lewis put it, is better than arrival.