The mere notion of a dichotomy is straightforward: a dichotomy is a classificatory scheme for a kind of object which represents the situation of an object between two idealized extremes. However, the scheme itself, and the situation space, can vary between dichotomies. I'll give a couple of examples:

• The light/dark dichotomy is primarily one-dimensional. As perceptions, light and dark partially inherit the complexity of our perceptive faculties, which allows for illusions, but it is mostly correct to say that any given experience of brightness can be situated at a consistent point in this dichotomy, with the space of all such points forming a single line. Physically, brightness can be measured, justifying the existence of this straight line.

• The male/female dichotomy (as in physical sex, rather than gender; suppose we're talking about cows, if you wish) is multi-dimensional. There are many different biological traits which distinguish between the idealized male body and the idealized female body: the presence of XY or XX chromosomes, of testes or of ovaries, of a relatively high or low level of androgens, the ability to ovulate, the presence or lack of functional mammary glands, and so on.

  But any given organism, even if they are readily classifiable as either primarily male or primarily female, may differ from the idealized version of their sex along at least one of these axes (after all, there are so many axes on which to differ). More importantly, even if they are not readily classifiable, they will exhibit each one of these traits at some place along this dichotomy, even if the mixture of these traits doesn't align with one particular sex.

  In this sense, the male/female dichotomy is, while the same as the light/dark dichotomy insofar as we are compelled to situate each instance (an experience of brightness, a sexed person) at a specific place along the dichotomies, different insofar as the situation of each instance does not consist of a single quantity, but rather a combination of many quantities.

Simple Dichotomies

We'll call any dichotomy that is used by situating instances at some place along the dichotomy, a simple dichotomy. For simple dichotomies, the primary classifying factor is the data corresponding to the situation space: with light/dark, this data is a single dimension, though it may be "fuzzed" by the complexity of our perceptive faculties; in such a case, we speak of a simple linear dichotomy, and with male/female, this data has multiple dimensions, in which case we speak of a simple multidimensional dichotomy.

Do not think that linear and multidimensional are opposites, though; the opposite of linearity is rhizomaticity. A simple rhizomatic dichotomy is one for which no internal structure, such as a straight line or multiple dimensions, may be elucidated. In such a case, we can only really use the idealized extremes to reflect more on any given instance, without placing that instance within the dichotomy. Of course, totally rhizomatic dichotomies are hardly of any use, and rare to see; the living/nonliving dichotomy, as applied to e.g. viruses and whatnot, is the closest thing I can think of right now (and it's only like this due to a lack of clarity about what constitutes life, though I wouldn't be surprised if it remained so under most reasonable definitions of "life"). To discuss this further, though, I'll need to introduce the next kind of dichotomy.

Complex Dichotomies

By way of an abstruse example:

• The analytic/continental dichotomy in philosophy is not simple. For, while there are idealized notions of analytic and continental philosophy (take Frege and Foucault), the average instance of philosophy (a particular philosopher, work, idea, school, etc.) cannot straightforwardly be situated in any one place along this dichotomy. Its place as regards this dichotomy must be determined in a manner that requires the notions of analytic and continental philosophy to interact with one another. This particular work which we wish to classify reads some philosopher, generally considered to be analytic, through this lens developed by primarily continental philosophers using analytic methods, and so on.

We'll call any dichotomy that is used not by situating instances at some place along the dichotomy, but instead by analyzing the interaction of the two idealized extremes in instances, a complex dichotomy.

The dichotomy of simple dichotomies, which has at either end the simple linear dichotomy and the simple rhizomatic dichotomy, is a somewhat (but not totally) complex dichotomy. Simple multidimensional dichotomies are an example of an interaction between linearity and rhizomaticity, as multidimensionality in the abstract is just bundles of linear relationships (see the example of physical sex).

Note: it is true that we may consider simple binaries, where no intermediate can even be conceived, and that this gives a simpler structure than linearity. I considered considering the linear-rhizomatic-binary trichotomy rather than the linear-rhizomatic dichotomy, but found that it didn't change much, as the property of being binary is, ontologically speaking, so easily destroyed; once destroyed, we can only really speak of it as a statistical model, as we do when we seek to sex organisms as either male or female, statistically assuming that one immediately observable sexual trait will allow us to infer others. There's plenty of interesting things to say about this, but it's irrelevant to this.