Thursday, 7 September 2017

On the logical form of maximal inclusivity

It strikes me as obvious, even a truism, that people find it important to feel that they belong to a larger group or community of some sort or another.  I will, at any rate, take that as given.  So, a sense of inclusion is psychologically valuable to many.  There are, no doubt, those who prefer to be alone, and we all have times when we need solitude, but overall, one wants to be part of a community.

It seems, further, that in many cases the sense of belonging is engendered by a shared characteristic of some sort: all who believe that P, or accept that Q, or who are R, bond over P, Q, or R, and form a community on that basis:

“All of us, here, are P/Q/R”.

As valuable as such congregating may be in creating a sense of inclusion, it also entails exclusion, for:

“You must be F to belong here”

is logically equivalent to:

“If you are not-F, you do not belong here”.

The risk as that those who are F will clash with those who are not-F, over resources, or legislation, or simply broader social norms.  On risk is the urge to segregate: let the Fs live here, the non-Fs there.  This is the dark side of the craving for inclusion.  For example, suppose a child grows to reject the religious upbringing of her parents but still wants to feel a sense of belonging to her family and community.  It would be a shame for her to have experience rejection on that basis, so we want families, for example, to have a broader sense of belonging/inclusion that a shared religious belief or practice.  Accordingly, I think it worthwhile ask what greater inclusion would look like.

Which leads me to wonder what the maximally inclusive community would be.  Is there a conception of inclusion that is sufficiently broad that it could include everybody?  I will eave aside for the moment whether such a broad definition of community would satisfy the psychological need for a sense of belonging.  My question is whether it is logically possible to define a community that would not be exclusive, something along the lines of:

            “All are welcome here”.

Right of the bat, this seems like a paradoxical formulation.  Suppose we had a community defined by this principle: would it welcome those who actively wish to destroy the community?  Could they really be welcome there?  It is hard to see how a community could, in general, be robust enough to survive if it had to invite in those who wished to destroy it, as they could not be integrated into the community as a whole.

What is nice, however, about “all are welcome here” is that it is a, relatively, content-free criterion of inclusion.  Any community built on a specific belief, practice, or physical trait, is inherently alienating because many will not share that belief, practice, or trait.  So a content-free, or formal criterion of community would likely be the most inclusive.  We can start with the idea of a community that is welcome to anyone who doesn’t wish to destroy the community itself:

(Ax)(Ac)[~D(x, c) à W(x, c)]

Where:
D(x, y) = x works to destroy y
W(x, c) = x is welcome in community c

This seems necessary but not sufficient.  After all, the most exclusive community imaginable could still satisfy this requirement: e.g. a very religiously intolerant group would still count as maximally inclusive so long as it was unwelcome to those who are religiously tolerant.

Okay, so let us focus on the concept of welcoming, which is a naturally inclusive idea.  Consider a community that is open to anybody who is him/herself maximally welcoming, or, put differently, a community that welcomes any who welcomes any:

(Ax)(Ay)(Ac)[W(x, y) à W(x, c)]

Of course, such a community must only include those who are maximally welcoming, so let's make this a biconditional:

(Ax)(Ay)(Ac)[W(x, y) <-> W(x, c)]

So long as “x welcomes y” entails that x does not try to murder, humiliate, cheat, or otherwise harm y”, then it seems that such a community could be defined without welcoming in murderers, thieves, and those who otherwise wish to destroy communities.


Thus, perhaps it is logically coherent to imagine a community that is maximally welcoming without immediately inviting self-destruction.  Such a formal principle is useful because it provides a criterion for determining when a community is as open as it can be.

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