logic

science

logic> dichotomies> ur-dichotomy

How many different dichotomies ought there be? There are hundreds, probably thousands, in everyday language. But ideally if we are talking about a logic – a universal notion of causality – all this variety would boil down to just a single ur-dichotomy. There might be many particular examples of this causal process, but only one actual general causal process.

Well, being a logic based on dichotomies, perhaps we should end up with just two fundamental dichotomies. There might be a pair of ur-dichotomies that are the same, but different(iated).

Anyway, this would be the natural expectation. A logic is a model of how things happen – how anything and everything must happen if it is to be a “logical” event within a “logical” world. So more than one (or perhaps two) ways for things to happen would be a sign that a model of causality was not properly self-consistent. It would probably be faulty, or at least still in need of further development.

Now ordinary mechanical logic does seem to boil down to a single view of the way things happen. In fact, it is a little ill-defined. But we could call it the ur-sequence. The sequence that is cause and effect. If we unpack this a little, we assume that we start with a set of parts. These combine in some fashion – dictated by their localised properties of course – and we end up with some “logical” outcome. That is, nothing happens that was not completely implicit in the collection of parts.

This is a view of causality that depends on locality and the reversibility of time. It is taken for granted that the parts undergoing their interaction are isolated from the wider world. At least for a moment there is no entanglement with other more distant systems (or at least no interactions that interfere). And because nothing essentially new is created in the mixing of the parts, the outcome is exactly reversible. What is constructed from parts can be deconstructed back into the same parts.

The conservation that derives from symmetry rules. Effects are exactly the sum of their causes. Nothing gets changed, just moved about.

This mechanical logic, this idea of cause and effect, works pretty well for science and philosophy. And quite brilliantly for technology. But it is interesting how it breaks down at the three limits of knowledge – the very small, the very large, and the intelligent.

Standard causality seems to fail at the Planck scale, the quantum realm. And it breaks down at the largest scale once we start wondering how an entire universe (or even multiverse) can come to be created. It is not logical that effects have something more than their causes – or in the case of a Big Bang universe, that there is all effect and no apparent prime mover cause. Finally mechanical logic appears to break down with the modelling of complexity, and more definitely when it comes to accounting logically for the presence of consciousness, subjective experience in a flesh and blood brain.

This is not just another idle dig at mechanical logic. Remember that one of the axioms of organic logic is that whatever the mechanical finds paradoxical or impossible, the organic must mandate. So the three extremes of the small, the large and the intelligent should be a good clue in our search for the ur-dichotomy.

But heck, let’s just answer the question right now. The ur-dichotomy is of course the local~global.

Well, at least it is one of them. The other is the vague~crisp. Matter~mind and substance~form are both quite close to being ur-dichotomies. However if both these can be reduced back to local~global, we will end up with only a single neatly matched and orthogonally oriented pair. Local~global and vague~crisp.

But first, let’s consider something of the variety of dichotomies. Let’s make a list of the ones that seem most key and see what patterns start to emerge.

what makes a good dichotomy?

What makes a good dichotomy is primarily one that embodies a clear asymmetry. A symmetric dichotomy, like positive~negative or left~right, seems trivial in that it is so easily erased. Each half pretty much instantly cancels the other out. Asymmetry is the way that the same can become apparently different. Taken to an extreme, such as matter~mind or substance~form, the opposing poles no longer even appear to be the same kind of thing. So, for example, substance cannot directly cancel form.

A good dichotomy also tends to have a clear sense of scale because a breaking across scale seems logically about the only way something which remains essentially the same can come to look as if it is also different.

Finally a dichotomy ought to be dynamic. A sense of motion, or rather development, is basic. Though equally we want to have some idea of how things end up. So we are looking for dichotomies that have dichotomised themselves sufficiently to create an equilibrium balance. They will be still changing, being essentially dynamic. But they will have changed to the point where further change ceases to make a visible difference.

So let’s consider a few groupings of dichotomies to see how they stack up. First a set of weak ones with which to warm up our conceptual muscles.

first some weak dichotomies

before~after
left~right
up~down
presence~absence
wet~dry
true~false
good~evil
beauty~ugliness
love~hate
conscious~unconscious
weak~strong
positive~negative

All of these seem rather symmetric or either/or. A something and then its straight negation. This is the case for any kind of to and fro motion like up and down, or before and after, where there is no real shift in scale. You make a hole of a certain size with a move. Then like presence~absence, reversing the move exactly fills it again. Something may get moved apart, a left becomes a right, but the change does not alter the something in any meaningful way.

Wet~dry or love~hate seem a little more complex. But then again dryness is an absence of moisture and wetness its presence. We could just about as well have said dry and non-dry. Love and hate also seem like simple extremes. At least they appear to lack any scale differences. Neither is really the larger or more encompassing emotion. And it is hard to see how they might relate, except perhaps in the sense that psychologically they could represent a move towards versus a move away.

We can see that all this group of dichotomies are opposed in some essential way. But either the opposition is just too simple (a presence ~absence, a to~fro) or the mechanism of the relation is not really clear. Good and evil are a classic pair of opposites, but how exactly are they opposites? What is the internal causal machinery by which they become opposed (and yet remain in some kind of real world interaction?).

So this group are all dichotomies. It is not as though we are talking apples~oranges. Or making some truly nonsensical pairing like wallaby~calcite, or hirsute~purple. They have a certain legitimacy as dichotomies. Yet still they are either too simple or too opaque.

A vast number of dichotomies fall into these two groups (too simple, too vague). Now let’s only consider dichotomies that I find tellingly strong.

vague~crisp as developmental dichotomy

vague~crisp
fuzzy~definite
hazy~clear
potential~actual
becoming~being
development~equilbrium
open~closed
diachronic~synchronic
symmetric~asymmetric

This set of dichotomies all have something in common. They speak of a developmental trajectory from some kind of idea of pure and perhaps restless potential towards a state that is more definite in its organisation or its stable existence.

To be vague is to be everything and nothing. Anything could be happening and yet nothing has clearly happened. Once things become crisp, there is no doubt. Something exists. And “somethings” are usually organised.

Vague~crisp is definitely an ur-dichotomy for organic logic. Things start in the unbroken symmetry of vagueness, become developed by a process of dichotomisation, and then result in the crisp order of a hierarchy – the crisp asymmetry of a local~global division with a scalefree middle. The crisp final state has stable existence, or rather persistence, because while things still must change (the dichotomy is still separating~mixing) the change no longer makes a visible change.

So vague~crisp as a dichotomy quite neatly sums up the essence of the organic causal story. To say fuzzy~definite, hazy~clear or potential~actual is really saying exactly the same thing using a different choice of words. I prefer vague~crisp mainly because there is a reasonable philosophical history to the use of the term vagueness. And crisp seems to refer more to some final organised state, the idea of an organised hierarchical structure, than do more “structureless” words such as definite, clear or actual. 

Becoming~being is another way of talking about the potential developing into the actual. However as a dichotomy it has its own particular history of philosophical usage that could be confusing.

Development~equilbrium is not a standard dichotomy like the rest but it neatly summarises the actions or dynamics of the vague~crisp ur-dichotomy. Vagueness is development and crispness is the eventual steady persistence of equilibrium change.

Open~closed is then another way of saying the same thing. An open system is developing, still dissipating its degrees of freedom, while a closed one has reached equilibrium, or soon will be.

Diachronic~synchronic can also be mapped like this. Diachronic is the view of a system that sees its whole (open and developmental) history while synchronic is the instantaneous snapshot view. It cuts across the system at some moment in time and so sees (by choice) a closed, static, developed, view.

Finally symmetric~asymmetric gives us a more mathematical description of the vague~crisp ur-dichotomy. We can model vagueness as a state of extreme symmetry, while crispness can equally be modelled as extreme asymmetry, a fully dichotomised state of hierarchical order. So saying organic logic is the causal trajectory from the vague to the crisp is exactly the same as saying it leads from unbroken symmetry to totally dichotomised asymmetry.

local~global as the developed dichotomy

local~global
locale~ambience
microscopic~macroscopic
particular~general
specific~universal
part~whole
partial~complete
atom~void

Local~global is our second ur-dichotomy. It is the one that cuts across the cone of development at right angles. It is the closed view, the equilibrium view.

Why does local~global seem the most general pairing in this little group? It helps that the words, local and global, are fairly neutral – already abstract and generalised. If they have any concrete reference, it is of course to the idea of space and time. To be local is to exist at some point within a spacetime context. To be global is to be everywhere (and everywhen) possible in a smooth and even way – to be the context.

So local~global has a useful neutrality. It does not smack of particular entities or properties that might be local or global, like perhaps minds, or atoms, or substances. However local~global does clearly refer to some of the axiomatic qualities of organic logic such as scale and asymmetry. Local~global is quite simply the most naked description of two contrasting extremes of scale. And there are some good implications in the way that local sounds isolated. To be localised is to be cut off. And equally to be global is to be cohesively a whole.

So local~global is much more than being small and large, or even microscopic~macroscopic. This is merely to be different in size. Local~global implies the emergence of differences in causal relationships. The local is isolated and therefore would become the atoms from which constructions could arise. The global is by contrast about wholeness, about an ambience or context that weighs down evenly everywhere in equilibrium fashion to constrain.

Locale~ambience is obviously a synonym of local~global. Ambience suggests a global scale that is a bathing, all-pervading, realm that bears down on any locale. And locale is more clearly about some particular small spot, not just the general concept of locality. The asymmetry between an ambience and a locale is pretty clear.

Particular~general and specific~universal can also be mapped directly to local~global. In ordinary usage, they refer more to the realm of human ideas than the physical realm of space and time. So it is our minds that pick out particular and specific things (highly localised impressions) and then generalise from such experiences to develop universals or global abstract truths.

However these boil down to differences in scale. To be somewhere in particular or something specific is the same as being located (within some context). And to be completely general or a universal truth is to be that global constraining context. It is to prevail everywhere and everywhen.

This leaves us part~whole, partial~complete and atom~void.

Part~whole is the classic dichotomy of holism. You have a bunch of specific local components. Then they are arranged (usually hierarchically and with downward or cybernetic causation) into some cohesive global whole.

The problem with part~whole, the reason why it is less general than local~global, is that it seems to be talking about concrete local parts rather than something more abstract such as a locale or a local constructive degree of freedom – a dimension or an inertia. It conjures up a rather more mechanical image of a system. However part~whole suggests all the key organic ingredients such as scale and asymmetry and complex causal interactions, so it is a close synonym of local~global.

Partial~complete is a somewhat looser version of part~whole and I mention it here mainly to show just how many dichotomies come close to expressing the ur-dichotomy of local~global. The pairing definitely alludes to something about broken scale and the causal wholeness of a system. It even has overtones of mindfulness – someone has to know that things are partial and not yet complete. However it is nowhere near as metaphysically crisp an idea as local~global or even part~whole.

Finally atom~void is an interesting one because it is of course the ur-dichotomy of mechanical logic. It refers to scale and asymmetry. It sharply dichotomises the world into what is, and what is not – localised substances within the global form, the empty frame, of space and time.

Yet atom~void lacks essential features of the organic approach such as an inherent dynamism, a world formed by the interactions between the players and the stage, the local and the global scale. Instead, atom~void suggests local substances that simply exist. These then may act (construct) in a global void, but this void is a-causal. It is a blank slate and does not interfere with (constrain) the local doings of the atoms. The larger world is blind to the behaviour of its parts.

Of course this mechanical version of the local~global dichotomy creates its paradoxes. Where do the crisp atoms come from. And if there are universal laws of physic regulating their behaviour, then where (except the global level) do these constraining causes reside? The mind of God?

Anyway, this is a good start. We have two candidate ur-dichotomies – the vague~crisp and the local~global. We have found a number of other dichotomies that mean much the same thing while have somewhat different nuances. Our ur-dichotomies seem capable of folding all these other meanings into themselves and becoming strengthened as a result (nothing in the other dichotomies has so far contradicted or weakened them). So let’s press on and see how other dichotomies might particularise~generalise our understanding of the two ur-dichotomies.

figure~ground and symmetry-breaking

figure~ground
focus~fringe
impression~idea
attention~habit
event~context
information~meaning
mark~interpretation
what~where
object~world
proximate~distal
action~reaction
thesis~antithesis

We now come to a group of dichotomies that lay stress on the act of symmetry-breaking. To varying degrees they may also have connotations of scale, mindfulness and dynamism (or indeed lack them, and so be more mechanical as dichotomies).

Figure~ground comes from Gestalt psychology where the symmetry of a flat perceptual field gets crisply broken into a “what-is” and a “what-is-not”. Take a sheet of paper and scratch a mark on it. Even the tiniest blemish breaks the symmetry (the vagueness) into some figure on some ground. A local particular something within a global space that is then the everything the something is not.

The relationship between figure and ground is dynamic and mutual. When the eye makes sense of some baffling scene, as in the classic example of a Dalmatian dog wandering in dappled sunlight, it is the ground of forest scene as well as the figure of the dog that forms up into some more definite perceptual experience. The global sense of organisation emerges simultaneously with the localised marks, each making the other meaningful.

So figure~ground is nicely descriptive of organic causality. The way the specific figures become crisply separated from a generalised ground through mutual dichotomising interaction implies a kind of mindful and dynamic process.

Focus~fringe, impression~idea and attend~ignore work out in a similar way though they are perhaps even more clearly semiotic dichotomies – divisions of the world that a mind makes.

So consciousness is characterised by having a focus of attention surrounded by a fringe of more habitual, or actively disregarded, awareness. What some call the subconcious, preconscious or even unconscious. There is the part to which we attend, the figure, and the background which we (find ways to) ignore.

However local~global scale is global is not just about small~large but also short~long. It involves a scale breaking in both space and time. So we need to bring this to our descriptions of how minds work. And we can see that focus~fringe, or attend~ignore, have shortcomings in that they are dichotomies with just a single scale of moment – the moment inhabited by some mind right now.

This is why impression~idea and attention~habit are more principled as dichotomisations. They embrace a scale-breaking across both space and time. They are properly local~global.

An impression is local and particular. It is an event happening at some a specific moment. While an idea is global and long-lived. An idea is a context, a ground to perceiving, remembering and anticipating. Ideas act downwards to constrain our impressions. And we can also see how a number of impressions will become generalised to construct an idea.

When children first see a cat, they may experience it as some generalised animal. They might call it “bow-wow” – standing for the idea of a four-legged furry critter much like the family dog. But with enough particular experiences of cats, the pointy ears, the flat faces, and other features will begin to form the idea, the mental schema, of some idealised feline.

Attention~habit cuts up conscious experience in a slightly different way. One of the difficulties of talking about the mind is that habits seem to be faster than attentive processing. We can react automatically (unconsciously, or rather preconsciously) to something like a flashing stop light in around a fifth of a second. But to perceive it consciously and start having thoughts about it takes more like a half a second.

So habit appears to be the local response and attention the global response. But actually habits take a long time to develop. They may cause actions to be emitted in a short-circuit way – as when we hit the brakes on the car even before we have really taken in the stop light. But the construction of a habit happens over a long time – days and years.

So which is local, which global? If we generalise the idea of habits to cover both motor reactions and learnt perceptual routines, then we can see that habits are really the more general aspect of a conscious mind. They are indeed just another word for the ideas. And it is no trouble that they are both quicker and slower than the attentional states they frame. Habits are both the before and the after to every localised attentional act, every moment of sharply distinctive impressions.

We have strayed a little from a discussion about ur-dichotomies mainly because dichotomies like attention~habit have been a big concern of mine in the past. Being able to map then in a principled way to some ur-dichotomy is a big step forward for any theoretical account of minds (and mindfulness). But now let’s whiz through the others.

Event~context, information~meaning and mark~interpretation are all similar in being fairly abstract dichotomies yet with a mindful connotation. Events are localised happenings that take place within a global context. A lot of events will eventually shape a context – reconstruct it. But the context is always acting down in prevailing fashion to constrain the kinds of events that can actually happen. Event~context is a pretty good dichotomy, one very close to the ur-dichotomy of local~global, as it has all the essential connotations we are seeking in an organic relationship.

Information~meaning and mark~interpretation are also quite good. Except it is much less clear that there is an asymmetry based on scale-breaking.

The mechanical view of an information bit or a memory mark is that it is a binary or symmetric affair. You have the 1 or 0 of a simple presence or absence (with no acknowledgement of the void, a greater global space, that makes it possible for a crisp mark, or its crisp absence, to actually exist).

This is of course why here I have chosen to talk about information~meaning rather than the more usual dichotomies of information~entropy or signal~noise. I am deliberately drawing attention to the fact that marks and bits are local actions that draw their meaning from some global context in which they are seen to “make sense”. Or indeed a global mindfulness that can supply the meaningful interpretation of the message – what is called semiosis.

Information~noise or marked~unmarked would be good dichotomies if you are a mechanical thinker because they have all the right connotations. They embody the logic of the atom~void ur-dichotomy. But they are bad dichotomies for an organicist. They would mislead our thinking.

Information~meaning or mark~interpretation allows us instead to talk about atomistic information bits and memory marks while bearing in mind that there must also be, dichotomistically, a global interpretative context.

Indeed, such dichotomies would then tell us something about the “how” of real-life systems. We would understand that a system would become organised by producing a sharp distinction between information – the symbolic marks, genetic codes, languages, or whatever – and the meaning-making, the global or pansemiotic act of interpretance. When looking at a cell or society, we would know not just to expect a dichotomisation in such a fashion. We would be able to predict something about how the dichotomy would be instantiated as a physical mechanism or a processing structure. Dichotomistic principles would dictate systems architecture.

What about what~where, object~world, proximate~distal, action~reaction, thesis~antithesis? All these also seem to refer to a symmetry-breaking via a figure~ground or event~context division, while being a little vague on the issues of scale, mindfulness, dynamism and causality in general.

What~where (or what~when) is useful because it describes a major physical division in the processing architecture of the brain (as do of course, attention~habit and focus~fringe). One part of the higher brain, the temporal lobe, becomes increasingly focused on extracting a sense of whatness from a perceptual scene. Is that a cat or a dog? A Dalmatian or a heap of leaves? The other path, the where processing stream of the parietal lobe, extracts a complementary sense of where and when-ness. One lobe focuses on the localised identity, on entification, while the other focuses on an overall, global, sense of how all these entities relate in space and time.

Object~world is the same kind of entity~context dichotomy. Proximate~distal is mostly getting at the idea that there are always nearby specific causes and then far-off or generalised global causes. One kind constructs an action (triggering it) while the other usually exerts an ambient constraint-type effect on what happens.

Action~reaction is the classical Newtonian dichotomy that is framed as a mechanical symmetry (for every action, an equal and opposite reaction), yet in fact conceals an asymmetric dichotomy. It is a clever accounting trick really. To endow some located body with a “force”, Newton then created the fiction of a “reaction force” in which the world, as a whole, pushes back in exactly symmetrical fashion. As a model it works beautifully. But as a causal image, it can be dreadfully misleading.

Thesis~antithesis is then basis of dialectics, the formal method of dichotomistic argument that goes back to Socrates and before. Kant resurrected the method with his antinomies, then Hegel artfully turned it into a spiralling, hierarchical or triadic, system with his thesis/antithesis/synthesis.

The idea the dialectic is that you first say one thing – make a crisp statement – then turn round and consider the truth of its contradiction. If Heraclitus said all is flux, then Parmenides could turn round and say all was stasis. So thesis~antithesis works by a figure~ground symmetry-breaking. Making some distinct foreground move (such as stating all as flux) then serves to draw attention to the ground that does not seem shifted by that bold act.

Of course, dialectics leads nowhere if the two poles of being ended up treated as symmetric – if the essential dimension of scale is lost from the discussion. The argument becomes dualistically one of either/or rather than being organically the story of how both are fundamentally the same, just different because they have been moved apart in scale.

some things change, others stay the same

stasis~change
stable~plastic
static~dynamic
passive~active
location~motion
position~momentum
space~time
matter~energy
inertia~acceleration

This next set of dichotomies seem to be about the physical world and how it can be divided into the things that change and the things that stay the same.

First we have stasis~change, stable~plastic and static~dynamic which are obviously three nearly identical ways of saying the same thing. Reality dichotomises into that which appears to stay the same (it does not move, it does not alter) and that which changes (it ages, it roams, it evolves). The static is the located and therefore the small scale. The plastic or the dynamic inhabits the larger space of all the possible developmental trajectories – a phase space in other words.

Imagine we could see a single particle, or even better, the brief flash of some event like a flare of light. It would have existence at some place and some instant. Then if we waited we would see its actions define a larger world. Its wanderings as a particle, or spreading as a wave of energy release, would mark out the presence of a global stage, a context.

The same is true of passive~active. To be passive is to be unchanging, and indeed not making a change, not creating a difference. It effectively defines the smallest scale of being – what it is like simply to have existence at some location. To be active is then to explore the global space of possibilities. It is the motions and changes that turns the large scale into something actual.

Location~motion and position~momentum are again about the locatedness of what stays the same, passively at rest, versus the global stage that is betrayed (or indeed constructed) by actions such as moving and developing.

Space~time is a classical mechanical dichotomy and so somewhat a “bad” dichotomy in having a few too many mechanical connotations. It is scaleless and symmetric. Space and time are not intrinsically large or small. They are simply directions that can be crisply marked off in measured intervals. And being scaleless-ly symmetric, it seems that any action can be easily reversed. A motion left can be erased by a motion right. A move forward in time can be erased by a move backwards.

Yet still, space~time does dichotomise the world in a believable fashion. Space is about locations, places where things can be found. Time measures the capacity for change, development and interaction.

And it is worth noting that in modern physics, space and time – in our universe at least – have certain definite limits. You cannot get more located and motionless than the Planck-scale. Or zero degrees Kelvin. Likewise you cannot spread or communicate faster than lightspeed. Or exceed the hot kinetic jitter of the Planck energy density.

So the scaleless void of Newton has in fact been replaced by a vacuum strictly scaled – bounded to either side – by quantum and relativistic limits. Local and global, location and motion, stasis and change, have strict physical meaning. The universe is actually confined within the asymptotic limits of motion of restmass~lightspeed. Or absolute zero~Planck heat as the smallest and largest kinetic energies.

Matter~energy is another mechanical dichotomy that we would want to reinterpret in a more organic light. The original Newtonian dichotomy was of course matter~force. The separation of located substance from its global propensity for dynamic action. Within the discourse of physics, force eventually became energy – modelled as a substance and so now subject to conservation principles based on an explicit time symmetry. As a substance, energy cannot be destroyed or created, just “rearranged”. Finally with E=MC2, Einstein reunited matter and energy as complementary faces of the same substance.

But still we can see that matter and energy map to local~global as the stuff that has the crisp location (particles of mass) and the stuff which represents the global potential for change (the spreading rays of light and other “messenger particles”).

Finally we have inertia~acceleration which is again a mechanical dichotomy that is better read as a story of local~global scale asymmetry. An inertia is a degree of freedom, an action (or lack of action) that does not make a difference (to the larger system). So a mass can exist at a point, rotate round that point, and even travel in a constant speed in a straightline, all inertially. These actions are symmetric and hence free to happen.

An acceleration is by contrast a difference that makes a difference. It is a contextual story in which the global scale becomes involved. The action is no longer free but constrained. In Newtonian mechanics, an acceleration is simply the result of some extra force from “outside”. But with relativity, the involvement of the global scale becomes explicit. Spacetime itself is warped by accelerations.

So inertia~acceleration maps very nicely to the idea of local~global scale and other organic notions such as the opposition of bottom-up (from the local level) construction and top-down (from the global contextual level) constraint. We even have symmetry and asymmetry built into these physical concepts.

locally broken and globally unbroken

discrete~continuous
abrupt~gradual
rough~smooth
digital~analog
hyperbolic~hyperspheric
algebra~geometry
finite~infinite
particle~wave

Now we come to another set of very familiar dichotomies that all have something to do with the idea of the broken~unbroken. Or isolated locales versus global coherence.

Discrete~continuous is an ancient and important distinction. A line for example can be treated as an infinite set of points or one continuous trajectory. A mechanical interpretation of the dichotomy as actually broken (a dualism) of course gave rise to Zeno’s famous paradoxes.

The organic interpretation of course is that discreteness and continuity are both ideal limits –local and global boundaries which a process of asymmetric separation can approach, yet never actually reach. Any actual thing begins in a state of vagueness. Then it can be broken into isolated parts. Or it can be appreciated in terms of it global form, its global organisation or cohesion, its local goals.

So we can talk about a line as embodying a geometric “desire”. If we ask what the line is made of, we can approach the idea of it being constructed of infinitesimal points. And if we ask about its global organisation, we would think of it being one coherent trajectory. In this view, there is no Zeno-ian paradox. A line can never be completely deconstructed into points and so there is therefore no problem concerning its construction from points. Likewise it never becomes simply a global whole, so there is no paradox that it can be constrained in ways that appear to produce a series of infinitesimally small and located points.

Abrupt~gradual and rough~smooth are a couple more ways of talking about the discrete~continuous. The world seems to offer two extremes. You can either break it up into bitty smallness, sudden events, or stretch it out into an elastic largeness, an unfolding history.

Digital~analog is yet another synonym for the crisply broken and the smoothly continuous.

Hyperbolic~hyperspheric is a more general geometric version of broken~unbroken or discrete~continuous. Hyperbolic means open curvature, where all “straight lines” diverge. Hyperspheric is a closed curvature, where they all converge. It is not a standard dichotomy, but I mention it here because it seems to offer a good way to unify quantum theory and relativity – the two extremes of being.

We can say that the world of the very small is broken up into discrete bits, a quantum foam, by its hyperbolic curvature. On this scale, every point of space is fluctuating over all curvatures and so one point would move away from the next in hyperbolic fashion. Modelled as a random walk (or chaotic Levy flight) spacetime would diverge.

Then the realm of the very large, the global scale would have the opposite tendency. Being a smooth relativistic manifold, a hypersphere, all paths would eventually cross. This would be a dichotomy just like discrete~continuous, but defined in a higher dimensionality than flat Euclidean space.

Maths of course also depends on its dichotomies. Algebra~geometry dichotomises mathematics into the realms of discrete patterns and continuous patterns. Finite~infinite is all about the broken and the unbroken, the discrete and the continuous.

Finally we have particle~wave – Bohr’s famous quantum complementary pair. A particle is located, discrete, isolated. The wave is continuous, whole and global in its extent. Any observed event can be dichotomised into particle and wave. Though because these limits lie in opposite directions, as an observer you can not approach both limits during the same act of observation.

substance~form as nearly an ur-dichotomy

substance~form
structure~process
quantity~quality
entity~property

If local~global is the ur-dichotomy for the developed, then substance~form would run it a close second. Indeed, substance~form has some of its own advantages such as being more clearly asymmetric. 

So local and global seem to be about different degrees of the same thing – physical scale. Of course what starts as essentially the same becomes different in causal terms. A dichotomisation of scale produces eventually a local realm that constructs and a global realm that constrains; a local realm that acts blindly and inertially and a global realm that acts knowingly and acceleratively. But substance and form seem more clearly to be asymmetric as notions – orthogonal in that each seems so completely not to be anything of the other.

Yet substance and form map easily to local~global because when we ask about the substance from which a system or entity is constructed, we have to zero in on what exists at some location. We are seeking out its atoms, its particles, its elements. Then to see the form we have to draw back to appreciate its global organisation, the coherence or cohesion that holistically makes something whatever it is.

Substance~form is nearly the ur-dichotomy. In Greek philosophy, it was the ur-dichotomy. But I think it can be shown that while local~global is general enough to incorporate all the meaning of substance~form, substance~form does not really talk about spacetime. It is not a causal model based directly on dimensionality – the most basic possible level of description. This is what leads to problems such as the whereabouts of Plato’s realm of forms (with local~global, we know exactly where form is to be found). And creates the mistaken impression that the local scale is best defined by enduring stuff rather than fleeting events.

Then we have structure~process, quality~quantity and entity~property which all seem to be versions of substance~form as a dichotomy.

A structure is made of some stuff, then the process is its form – how it (per)forms! Quantity is again about certain amounts of located substance while quality is the global, emergent, cohesive, form. Then an entity is some localised stuff. Its properties are the sum of all its potential interactions with the wider world. The forms it can create if given sufficient time.

mind~matter as a mechanical story

mind~matter
subjective~objective
knower~known
model~modelled
self~other
internal~external
organism~environment

This set of dichotomies refer to various kinds of located and autonomous being within a wider, more global, world. And they bring us a new kind of problem because they seem to reverse the usual dichotomous order in which mindfulness is associated with largeness and global constraint.

To be a mind, a self, an individual, an organism, a knower or a model is normally to be something quite small within a much bigger world or environment. And a subjective or internal realm would also seem to have to be smaller than whatever objective or external realm lay outside of it. So what is going on here? Well close attention is needed at this point because the logic gets complex – literally.

Organic logic says that all things follow the 1,2,3 path by starting in vagueness and then proceeding by dichotomisation to a state of emergent hierarchical order. So the final equilibrium outcome, the hierarchy, is a fundamental three-ness. You have a local and global boundary sandwiching a flat scalefree middle. Inbetween the smallest and largest scales is now the further realm of the mesoscale.

Already we can see the start of an answer. Mind, selves and other forms of autonomous being could actually be mesoscale phenomena. But let’s get more detailed.

Organic development forms a world with a flat middle ground. For example, it would create an expanding Universe out of a Big Bang. In the beginning, this universe would have been small and hot. Indeed still vaguely differentiated because atom and void would been entangled. But expansion allowed cooling and the appearance of a definite separation between solid particles and empty vacuum.

Once this universe had cooled and expanded enough to be pretty stable – to be in equilibrium as a hierarchical system – it could begin to develop a new kind of hierarchical order. Except now instead of the development being organic, it became mechanical. An evolution or indeed involution. In the familiar way that traditional science describes it, a stable ground of physical structure could become in turn the platform for the growth of complex structure. Physics could give rise to chemistry, biology and neurology in turn.

We thus have two kinds of causality – organicism and mechanicalism. And they result in two kinds of hierarchical development. Stan Salthe calls them the scalar and the specification hierarchies. But I will call them the organic and the mechanical hierarchies. The organic hierarchy develops a stable world – a realm of flat scalefree simplicity. The mechanical hierarchy then finds way to evolve complexity from this ground.

The hierarchy pages explain this in detail. But we can briefly say that the mechanical hierarchy is about the use of memory mechanisms like genes, neurons, membranes and words to take local control over the world and create more complex structure.

This complexity is meso-scale. It arises in the middle of the world. If we think of a human mind for example, it forms halfway between the small scale substance – the neural tissue that makes a brain – and the large scale form, the sociocultural environment that shapes and constrains the individual mind. We have a hierarchical involution that we can describe as [neurology [psychology] sociology]. Or [neurons [person] culture].

This in turn can be nested within the more general hierarchy that defines biology. So if life is [cells [organism] ecosystem] then mind is [cells [neurons [person] culture] ecosystem].

Stepping back another level would bring in chemistry. So we have [metabolism [cells [neurons [person] culture] ecosystem] geosphere]. Every level of organisation would be more complex, more evolved or involuted. And it would be bounded both by the smaller and the larger scale. It would be constructed of some set of material substances and constrained by some broader global ambience.

So when we talk about mind~matter, we are really talking about [atom [mind] void]. Minds arise in the middle and so are smaller (constrained by) a wider environment, but also larger than (and so constructed by) particular materials.

Where it gets really messy is that we also want to be able to talk about mindfulness as a general potential of reality. So we have individual conscious humans as a very intense and specific form of mindfulness. But then we also can trace a gradient of mindfulness that becomes increasingly more generalised through aware animals, cognitive lifeforms, dissipative structures, and organised universes. In this sense, mind can be identified with the global level of scale, the level that looks down holistically and constrains.

So a universe can be said – pansemiotically – to have something like a mind in the most general possible sense of the world. And this mindfulness can be identified with the upper bound. But then we have mind in the specific sense of a conscious human, and this then is a mesoscale thing. Human minds arise smack in the middle of material reality.

Anyway, enough has been said to show that we have to make a distinction between organic and mechanical hierarchies. Both are the result of dichotomies that lead to trichotomies. But organic development leads to a flat and scalefree middle. So the dichotomy labels the boundaries to this process of development. Mechanical hierarchies by contrast develop by involution from this flat, scalefree, middle ground. So the dichotomy instead labels the simple ground and then the figure that arises from it.

We have matter and then the evolution of minds. Or the objective world and the subjective view into it. Or the known and the knower that arises at intermediate scale. Or the modelled world and the modeller who dwells in the midst of it.

Self~other, organism~environment and internal~external are more ambiguous. But selfhood, an organism, and the internal realm would usually all be thought of as existing within a world. And that world would be both smaller and larger in scale.

It makes sense once you understand the differences between organic and mechanical hierarchies. Words like mind and matter can shift their meaning as we switch from one idea of development to the other. But it is important to see how they can indeed be legitimate aspects of both hierarchy theories.

descriptions of causal interactions

separation~mixing
differentiation~integration
growth~involution
antagonistic~synergistic
competition~co-operation
bottom-up~top-down
construction~constraint
discriminate~assimilate

With this group of dichotomies we are now back to the simplicities of the organic view and focusing on descriptions of the essential causal interactions. The ur-dichotomies of vague~crisp and local~global are the limit states. This lot are descriptions of the kinds of interaction that take place inbetween.

Separation~mixing and differentiation~integration talk about the dividing that makes a dichotomy and then the interaction of the divided that makes for a middle. This is a complex notion of causality. You have two directions of action happening at once, each mutually supporting the other. The separation makes the stuff to be mixed and the mixing keeps the stuff continuously expanding and separating by filling out the middle.

But which of the two ur-axes are they aligned with - the open developmental axis of the vague~crisp or the closed and developed axis of local~global polarised scale? Clearly they describe the causal interactions of the developmental axis. It is separation that develops smallness and largeness, localities within the global ambience. Mixing then leads to the emergence of a scalefree middle ground between the limits.

Growth~involution would also be a developmental dichotomy. Growth creates organic scale, both the local and global, while involution is the filling in of the mesoscale middle with a mechanical hierarchy.

Antagonistic~synergistic would be another synonym capturing the idea of a simultaneous moving apart that also then works together.

Competition~co-operation is a little more ambiguous but can be taken as the striving to dominate that results in the same becoming increasing unlike, while co-operation is about the integration that actually fills the middle with a balance of togetherness.

Then we have a couple of dichotomies which seem aligned with the final developed realm. Once there is a local~global organisation we can see that the complementary limits also produce their own distinctive, yet also complementary, causalities. So we have a bottom-up construction from the locales. Small and discrete substances or atoms can begin to build. And then we have a top-down constraint being exerted by the global ambience. The large scale order or form marshals all the parts to make a functioning whole.

Finally discriminate~assimilate is a way of describing the local~global interaction that makes a mind – the process of forming impressions and ideas. To discriminate is to break experience into its component bits. To assimilate is wash away the details and extract the generalities that makes for some over-arching notion.

chance and necessity are a puzzle

chance~necessity
chaos~order
noise~signal
random~determined
arbitrary~purposeful

This is certainly a familiar group of dichotomies. But how do they fit in? Are they aligned with the vague~crisp or local~global? In fact these are all classic mechanical dichotomies. They say that events are either caused or not caused. And of course, for things to happen without a cause – as in some random act - is paradoxical. So it takes a bit of unpacking to show how they in fact make sense from the organic point of view.

Let us start by considering a classic example of a chance event – a coin toss. It seems that so long as we spin the coin high and fast enough, the outcome will be random, arbitrary, a noisy or chaotic affair. There will be no particular cause for it to land heads rather than tails.

We could of course chose simply to place the coin on the ground, heads up or down, and so completely determine its fate. And noting this should draw attention to the fact that there is in fact a higher level cause for the behaviour of the coin. There is a process (a person tossing coins) who is generating the events. And this process can be carried out with various degrees of control. The coin tosser can strive for a lack of control over the outcome with a high spinning throw, or for tight control by placing the coin with deliberate care.

So we can see there is a local~global distinction that hinges on the existence of an event generating process, a constraining context, which creates events with varying degrees of knowledge or control. In the ordinary philosophy of causality, we would call this the difference between proximate and distal causes. Anyway, we can now see that coin tossing should creates no big mystery. The randomness is in the mind of a thrower who does not seek to control the fall of the coin. The coin of course has already been made with two faces, so it must land on one or other.

However the mechanical view of reality cannot be satisfied with the idea that there is any chance – any lack of specific causes – in the affairs of the universe. So the presumption is that down at the microscale, determinism indeed rules. If we could measure all the forces acting on the coin at the time of the toss with complete accuracy, then we ought to be able to predict its every rotation and tell which way it must fall.

The same mechanical presumption lies behind chaos theory and even the hidden variable interpretation of quantum mechanics. If only we could measures every last flap of a butterfly’s wing, we could predict the course of the weather. If we knew the hidden variables that trigger a quantum collapse, we could see the reason why an atom decayed or emitted at some particular moment. Everything would actually happen for a reason. Chance and fluke would be an illusion born purely of macroscale ignorance.

Now let’s see all this from the organic view. Organicism says all developments start in vagueness. And then there is a dichotomous separation towards limits. So there is now no determinism built into the smallest level of being. Instead, crisp determinism can only emerge out of the spontaneity, the open potential, of vagueness. Any determinism at the microscale would have to be shaped by the constraint of a global context. And finally absolute determinism (or indeed, absolute randomness) could only be approached as limit states.

So it we were talking about the decay of an atom, there must always be a world that acts as the context that constrains the event by, for example, providing the necessary absorbers of the decay products. And then as the quantum Zeno effect suggests (a watched atom never decays) the context will have variable effect. It can only approach the ideal of creating either a determined or random decay event.

This is considered more carefully elsewhere. But we can see that chance~necessity and its various synonyms are rather entangled with both organic ur-dichotomies rather than being tightly aligned with one or the other.

The mechanical view wants causality to be founded monadically on the small and the crisp. Causes are atomised. So any kind of randomness, uncertainty, spontaneity or material creativity is a problem. However organicism loosens up our thinking in two ways – in both of the directions provided by our ur-dichotomies.

It is partly a developmental story as all things start in vagueness. So the quantum realm would be naturally vague at base. And then wholes shape up their parts, so a determinism is imposed to varying degrees. It reflects a top-down constraint on vague possibility, turning it into something more locally definite and constructive.

A last question is which way round should we order these dichotomous pairings? Should it be chance~necessity or necessity~chance. It would seem that chance and randomness lie nearer the vague end of the spectrum. They are less constrained. While the global realm is all about definite organisation and purpose. So it is the deterministic pole. Thus chance~necessity appears the right way round.

finally the epistemological dichotomies

mechanical~organic
reductionism~holism
analysis~synthesis
simple~complex
control~truth

The final gaggle of dichotomies are epistemological – about how we model the world. And so they would be aligned with the local~global axis as modelling always aims to be crisply developed, never vague or open-ended.

Mechanical~organic and reductionism~holism are pretty obviously the local and the global views of how systems are created and organised. And we could say one style concentrates on analysis, the other on synthesis. One is the simple approach, the other complex. One is tuned to creating control over the world, the other for representing the truth of it.

So now we have considered some 76 dichotomies, sorting them into groups and sifting them for patterns. The vague~crisp and the local~global stand up as the most general possible descriptions of our two ur-dichotomies. Though the other dichotomies can clearly be useful for supplying extra nuances.

We have also perhaps found a pair of ur-dichotomies for mechanicalism. If there is a mechanical hierarchy, then atom~void seems to define its crisp foundations. And the duality of matter~mind describes its mysterious axis of complex hierarchical development.

So we really end up with a complete tale. The organic and the mechanical realm are like distorted, or rather asymmetric, reflections of each other in the mirror. Two hierarchies, each developing from two ur-dichotomies.

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