Some simple ideas on the Andorian basis for geometry

As we recall from our halcyon years of adolescent frustration, the world of geometry starts with a point.     It progresses from there to two points, which form a line segment.  (In actuality, since a point is infinitely small, it is impossible to have a line segment consisting of two points, but we need not go there for now.)   But it is clear that the "and" is needed to unite points into a line or line segment.  Similarly, the "or" is necessary to separate the points on a line segment from all the other points on a plane.   Thus, the "and" and the "or" must work in tandem to form the basis of geometry, and they also work in tandem to constitute the basis for all geometrical shapes.  The "and" and the "or" work together to form the boundaries of a triangle.  Similarly, when we calculate the area of a triangle, we are gathering together the points within a triangle (the "and"), determining how much space they cover, and delimiting them from the area outside a triangle (the "or").   The same can be said for all geometrical shapes.

Finally, the same can be said for absolutely anything that takes up space, whether it be a desk or a person.  In giving that entity an identity, or at least a physical identity, we are gathering all the points, cells, nails or what have you (the "and") that that entity occupies or contains, and delimiting them from what exists outside that entity.

Restatement of Andorian essentialism

Essentialism in general provides that the world is what it is because things have certain essences.  Plato called these essences forms.  Aristotle, while denying that forms existed separate and apart from the physical world, went about systematically describing its essence.  We can divide the world into categories of things, and there are categories within these categories.  For instances, there is the category: clothes, and within this category, there are pants, socks, gloves and shoes, and within the category "shoes" there may be Gucci shoes.

Andorian essentialism holds that the "and" and the "or" serve as the foundation for the world of categories.  The category "shoe" exists because of the "and": we gather together all the things we use to cover and protect and in some cases showcase our feet and call them shoes. It couldn't exist without the "and".   The "or" plays an equally important role in the formation of essences by separating and delineating them from each other.   Thus, shoes are given their identity, in part, by being limited to what is placed on or under feet for protection, decoration etc.  Shoes are not socks or pants.  We give shoes their identity by delineating them, limiting their essence, separating them from the essence or definition of "socks".  As is the case with the "and", a category could not exist without the "or".   Thus, Andorian essentialism holds that the "and" and the "or" serves as the basis for all that is.  They have the highest ontological status.  And so it is.