logic> dichotomies

Why does something – anything – happen? This is a wonderful question and it is amazing how little we discuss such things.

It is also a modelling question. We cannot of course know the world and its reasons directly. But we can suppose. We can develop ideas that seem to explain, or at least predict.

The normal way of thinking about causality is what I call mechanical logic. Or to stress the fact that it is an interlocking package of beliefs, I also call it RAMML – standing for its key components of reductionism, atomism, mechanicalism, monadism and locality.

But here I am setting out an alternative organic logic. A view of why things happen that depends on asymmetric dichotomisation.

In the mechanical world, collections of parts combine according to their properties to construct outcomes. A cause produces an effect in machine-like, step-by-step, fashion.

However in the organic view, parts and wholes swim into existence together as aspects of a single holistic system. The causality is bootstrapping or self-organising. And every development begins in some vaguer state. Formed structure arises out of a pool of potential. You don’t need concrete materials – already existent atoms or components – to get the ball rolling.

separation~integration Holism is a reasonably familiar idea. Vagueness much less so. But the real heart of the story here is the dichotomous nature of the developmental process. Things happen first by separation and then by a mixing of the separated. And the dichotomisation is asymmetric. The only possible way to divide a vague state of potential is to separate in two complementary ways. Every move creates a counter-move; every action, a reaction. To make a figure, you must also make a ground.

Other terms for this central process of asymmetric dichotomisation might be a symmetry-breaking or phase transition. Or we could talk about dialectics, antimonies, synergies, yin-yang or paticca samuppada (dependent co-arising). There are many discourses that recognise there is something different about organic causality.

But I prefer to use dichotomy as this is the most ancient and general term. And then asymmetry stresses the fact that the initial symmetry of vagueness is not just broken, but broken in distinctive fashion.

what is a dichotomy in simple terms?

symmetrical breakDichotomy is Greek for cut in two. But split an apple in two and you simply have two halves of one thing. This is a symmetrical division. Greek philosophy developed by breaking something like an apple into two quite different seeming things.

substance~formSo Plato and Aristotle would ask what is the essence of an apple? Is it a particular kind of stuff? A lump of some substance? A collection of atoms? Or does its essence lie in its form? Is appleness all about the way some stuff is arranged? Does the essence of being an apple reside in a particular set of qualities that must be possessed, such as  being juicy, crunchy and round?

The Greeks came up with many enduring metaphysical dichotomies. Substance~form was a biggie. Other still familiar ones are atom~void, stasis~change, chance~necessity, being~becoming, particular~universal, part~whole, discrete~continuous, quantity~quality, body~mind...the list goes on. And today we could add many more. Such as  local~global, integrate~differentiate, information~entropy, figure~ground. Even mechanical~organic.

You can see from this list that it is not much of a dichotomy to say x and not-x. Like fat and not-fat, or fast and not-fast. Or even fat~thin, fast~slow. A dichotomy strikes a chord when the two extremes seem both complementary and different – asymmetric. The two are opposite in some deep qualitative way, not merely in a quantitative fashion. Yet even being so different, they are necessary to make a complete, integrated, whole.

So the local is pretty much defined by the fact it is not globally spread. The stationary is pretty much defined by the fact it is not moving, Substance would be pretty much defined by the fact it is a stuff without yet the imprint of a particular form. By the same token, the global has nothing that seems tied to some local happenstance. The changing is defined by the fact it is managing to leave something standing behind. Pure form is that which is so insubstantial as to appear almost as a wish or an idea - a latent desire of nature.

In each case, one is defined as the complete absence of the other. And yet it is hard to imagine any real thing which does not have both combined. An apple must be composed of both substance and form. For an apple to be moving, there must be a world that is standing still (rather than moving with it and so leaving the apple looking as though it stands relativistically at rest). For an apple to be located as a particular instance of an apple, there must be a global context that is all the other places that the apple is not (yet where it could have been as a crisp possibility).

Once you start looking for them, dichotomies are everywhere. You might think that this is merely evidence of a particular metaphysical affliction - dichotomania! We humans like dividing nature by simple numbers. There are the three dimensions of space,the four corners of the earth,the five powers of Taoist wu-hsing (wood, fire, earth, metal and water), the seven deadly sins - you name it.

But I hope to show that only dichotomies are fundamental. All other divisions into a this and a that and then some number of others are superficial and unstable. The larger sets will always reduce to a more fundamental dichotomistic description. Space for example becomes the dichotomy of space~time - or the located and the changing. The five (or however many) elements reduce to the larger dichotomy of substance~form - all the many kinds of stuff and then also all the many kinds of possible organisation.

Mathematicians might note that this is exactly the conclusion of category theory. Every kind of mathematical construct reduces to an object and process, or object~process.

So as a way of modelling the world, chopping it up in ways that make it comprehensible, the dichotomy is fundamental. Two-ness rules for a sound reason. We can claim further proof of this from information theory. Binary choices are the most efficient possible way of dissipating uncertainty - this is the famous 20 questions principle.

However the big claim here is that a dichotomy is not just a division imposed on nature by a modelling mind – a useful generalisation we create to make the world seem a simpler place. It is a causality, a model of why things happen. Dichotomisation is the actual process by which a world makes itself.

So the reason we find ourselves dichotomising is not because we have made some free choice. If thinking is a process, then dichotomising is going to have to be the most effective and natural way of our thoughts forming. And indeed that is essentially the story when it comes to accounting for the evolution of human brains and human minds.

It is dichotomies everywhere you look. The left and right brain as figure and ground style hemispheric processing. The what~where division and the sensori~motor division. The split of speech into syntax~semantics and words~rules. The overall divide of cognition into attention~habit and ideas~impressions. The nature~nurture or biology~sociocultural dichotomies. All mental distinctions and abilities arise through the dichotomisation of less well-formed potentials. So we don't impose dichotomies on nature. Instead by dichotomising we are going along with the flow of nature.

Finally I will argue that the many dichotomies – and the list is vast – all reduce back to a single ur-dichotomy. Well really it is a pair of dichotomies at right angles to each other – asymmetrically arranged!

The really important dichotomies are substance~form, local~global, matter~mind, atom~void, figure~ground and discrete~continuous. As we will see when we get to scale hierarchies and semiotics, all of these are really different ways of saying much the same thing. And local~global emerges as the ur-dichotomy because naked scale is the most basic measure of all existent things.

But if there is an ur-dichotomy that is the fundamental description of the way things are, there must also be an orthogonal axis of description to track their development. As Aristotle argued, the world is composed of both being and becoming. The synchronic and the diachronic view. So we have to have a second ur-dichotomy that describes the developmental trajectory. And this is the vague~crisp.

the two "ur-dichotomistic" axesThe ur-dichotomy is dichotomised to give us local~global, the view of the instant, and vague~crisp, the view of the journey. And in terms of the 1,2,3 story, local~global is the scale-breaking, the triadic hierarchy, the crisply developed end-state of any process of development.  Vagueness is the monadic oneness that lies before the dichotomisation, before any development has got going. Think of this as a cone. Two ur-axes are needed to describe it. And there is a progression from simplicity to complexity. As a system, it is all perfectly logical and beautifully complete.


Before setting down the axioms of organic logic, first a quick comment about notation. The tilde or squiggle here “~” was suggested to me by Scott Kelso. I have adopted it to stand specifically for an organic dichtomy where a potential has become separated, however not actually broken. As we can see, there are then just three other possible ways of viewing a dichotomous division. And we would want a different notation to mark each.

To start with, there would be two forms of a broken or mechanical dichotomy – one monadic, the other dualistic. The monadic view says that reality has to be one thing or another. This is a binary choice and it can be marked with a Sheffer stroke – “|”. So if we write substance|form, then we are saying that an apple must be fundamentally one thing or the other. Either its essence is a substance, a set of molecules or some such stuff, or its essence is its particular qualities, the result of some special state of organisation.

But we can also take a dualistic stance and say that reality is fundamentally both. We would mark this dualistic position with a slash – “/”. So when we say mind/body, we are following Descartes in saying that reality breaks into both categories of existence. They are both equally fundamental. Even if this claim then raises some causal paradoxes, like how are the two realms then connected?

For the sake of completeness, we may as well throw in a fourth symbol, the hyphen, to mark the most general case where we are not really making any strong claim about the nature of the relationship between the two poles of a dichotomy. So substance-form and mind-body would just say that reality seems to be broken in this kind of way but we are not yet saying anything definite about how the division works.

the twelve axioms of organic logic

Now we are at the heart of the whole site. These are the twelve axioms of organic logic that I wish to defend.

1) Dichotomies have vague beginnings.
2) Dichotomies are dynamically developing not passively existent.
3) Dichotomies develop in asymmetric fashion.
4) Dichotomies thus depend on scale.
5) Dichotomies always develop in both their directions at the same time.
6) Dichotomies are separations not breakings.
7) Dichotomies involve separation but also the mixing of the separated.
8) The middles of dichotomies have scale symmetry.
9) Dichotomies have only two poles because three or more is unstable.
10) Organic causality is hierarchical or holistic.
11) Organic logic is dichotomous with mechanical logic.
12) Organicism is only modelling.

Continue to the axioms of organic logic and then the search for the ur-dichotomy.

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