Understanding Intersecting Forms of Oppression using Models and Sets

A classmate asked me to expound upon my final statements in class today in a blog post because they were presented a little nebulously.  This post is an attempt to clarify from my point of view, specifically from the view of a mathematician.  

We can differentiate different aspects of our identity into categories.  This post will use the examples of Class, Race, and Sex.  We can treat these categories as sets, having certain elements that correspond to an individual's identity.  Furthermore, we can assume these social sets are partially-ordered sets (aka posets) under the binary relation of privilege.  There is a "greatest element" in each set, which is the most privileged element.  For the simplicity of an example, we can use three elements for each set: Class = {Lower, Middle, Upper}, Race = {Black, Asian, White}, and Sex = {Female, Intersex, Male}.

Any type of model that we create will have to make assumptions about the group it describes and hence will have to choose an element from each social set; this will create a new set which describes the assumptions for a model.  Since the topic of our analysis is oppression, preliminary models require choosing one non-privileged element of a social set, while assuming privileged elements for all other social sets.  This essentially means that to start with, we only examine one variable at a time.  Thus, the set of assumptions for preliminary models follows as such: { {Upper, White, Female}, {Upper, White, Intersex}, {Upper, Black, Male}, {Upper, Asian, Male}, {Lower, White, Male}, {Middle, White, Male} }.  There are 6 models here, and we can call this set 'x'.

Now, we move to the topic of analyzing intersecting forms of oppression.  This task is not as simple as analyzing two preliminary models because assumptions contradict.  For example, let us look at the black female.  The preliminary model for blackness assumes maleness.  The preliminary model for femaleness assumes whiteness.  As we can see here, an assumption for each model contradicts an assumption in the other, rendering these models incompatible.  Thus, we must now go past the preliminary models and create new models, new sets of assumptions, that are not constrained to contain only one non-privileged element.  This expansion results in the following set of expanded models for the intersection of two oppressed groups: { {Upper, Female, Black}, {Upper, Female, Asian}, {Upper, Intersex, Black}, {Upper, Intersex, Asian}, {Lower, Male, Black}, {Lower, Male, Asian}, {Middle, Male, Black}, {Middle, Male, Asian}, {Lower, Female, White}, {Lower, Intersex, Asian}, {Middle, Female, White}, {Middle, Intersex, White} }.  There are 12 models here, and we can call this set 'y'. The set of expanded models for the intersection of three oppressed groups is as follows: { {Lower, Female, Black}, {Lower, Female, Asian}, {Lower, Intersex Black}, {Lower, Intersex, Asian}, {Middle, Female, Black}, {Middle, Female, Asian}, {Middle, Intersex, Black}, {Middle, Intersex, Asian} }.  There are 8 models here, and we can call this set 'z'.

The number of elements in a set can be denoted by absolute value bars and is called a set's cardinality.  Because sets x, y, and z have no overlapping elements, we can see the total number of models created by finding the union of these three sets' cardinality, namely | x U y U z | = 6 + 12 + 8 = 26.  A simpler way to calculate this is just through knowledge of combinatorics: | Class | * | Race | * | Sex | - 1 = 3 * 3 * 3 - 1 = 27 - 1 = 26.  Why do we need to subtract 1?  Because there is no need to take into account the default model, namely {Upper, Male, White}; this model is already how we view things and thus is not included in the creation of any of our sets.  We defined a model as requiring at least one non-privileged element.

All of the above is by no means an actual, strict way of analyzing intersections but rather presents the basic concepts at hand.  It is just an example.  Obviously, there are more categories than just Class, Gender, and Sex, and each category actually contains more elements than given.  Regardless, we can see that models cannot be 'additive.'  Any metric for oppression is defined under a certain model, and since no two models are compatible, an understanding of a metric is not transferable between models.  From a mathematical point of view, addition is just an binary operator that maps two elements from a set onto another element in the same set (for example, under the set of integers, the addition operator takes the arguments 3 and 4 and maps them to 7).  A way of understanding that oppression is not additive is that since different metrics of oppression arise from different models, they cannot be placed in a set under which the addition operator is defined (at least in any reasonably coherent way).