logic> dichotomies > axioms

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.

1) dichotomies have vague beginnings

Dichotomies have vague beginnings - We are talking here about the formalisation of a logic. And a logical tale has a beginning, a middle, and an end. There is a start point, some kind of change, and then the coming to a halt that allows us to say something has now happened.

For mechanical logic, the initiating conditions are axiomatically crisp. Something must always definitely exist to set the ball rolling. There must first be a concrete set of ingredients or processes, then there can be some kind of consequent action.

Of course this view of causality has its well-known paradoxes. How does anything ever begin for the first time if there must always be some step that came before? How can a universe leap into being without some prime mover to act as the causal ground? It seems impossible – or at least illogical – that a something could come from a nothing.

crisp beginningsThe idea that all beginnings are crisp creates other familiar difficulties. It implies that the fate of any world or system is determined from its first instant. Change is somewhat an illusion as the parts are fixed, their properties conserved, and all that happens is a mechanical shuffling about of static components into new arrangements. Chance or creativity appear to be ruled out. A world unwinds like clockwork.

vague beginningsOrganic logic begins with a different view of initiating conditions. It takes the opposing (or rather dichotomous) position that beginnings are axiomatically vague. That is, the more definite always develops from something rather less definite.

What exactly do we mean by vagueness? Let us give a few examples and then attempt a more formal definition.

An embryo is a vaguer or less specified entity than an adult. An embryo has an abundance of potential destinies but not yet any actual destiny. An adult by contrast is the crisp expression of some now definite fate. And dichotomously – a point rarely made – the adult also stands for all the possible paths crisply not taken.

So a seed represents a vague variety of possible futures. The grown tree can be tall or gnarled, branched this way or that. And if it turns out tall and straight, it is crisply not wizened or twisted or anything else. All these alternatives fates are now definitely absent from the world (whereas before they were only vaguely absent because they were still potential fates).

Another example that gives something of the flavour of vagueness is the white noise static of an untuned TV screen. We can imagine how potentially every program that ever existed, or ever could exist, is flickering in the pixellated blur. Just a little re-organisation and a whole lost episode of Kojak might appear. Or maybe one of the trillions of possible South Park storylines never actually written. Every kind of crisp actual program is present vaguely as a potential in the random activity.

Of course, an embryo or seed is itself a crisp object. A TV screen crackling with static is still displaying some definite pattern of light. But we can begin to see how vagueness is a step back in definiteness. It is a loosening that is the result of things not yet having happened – and also, not yet definitely having failed to happen either.

Now how do we pin down the idea of vagueness more formally? How do we generalise these sorts of particular examples to reach some properly universal notion of vagueness – a vagueness that is complete and fundamental. There are two approaches I will use.

The first relies on dichotomies. If all things are dichotomous, then vagueness must be the opposite of whatever it is that crispness is. And if crispness is the asymmetrically developed end state (a hierarchy in other words) then vagueness must be a state of total undifferentiated symmetry. Vagueness must be a realm that looks the same in every direction and so lacks any particular direction, any particular scale or dimensionality.

So we ought to be able to model vagueness as an infinite symmetry – what I call elsewhere an infinoverse.

The second way to know vagueness is via the precursor argument. It seems a logical thing to say that anything which comes out of a vagueness must have once been in this vagueness as a potential. So we may come to understand vagueness by what it emits.

Here of course, we are stating axiomatically that dichotomies come out of vagueness. Not just individual things or a plenitude of things but precisely dichotomous pairs of things.

If the world has both chance and necessity, or both substance and form, then these contrasting poles of being were both once present together in the undifferentiated oneness that is vagueness.

So to be clear, vagueness as a concept is not strictly tied to dichotomies. Organicism of any stamp could claim that beginnings are vague. But here we are claiming that only dichotomies can come from vagueness. And this fact then also allows us to make some more precise statements about vagueness itself using the asymmetry and precursor arguments.

2) dichotomies are dynamic

Dichotomies are dynamically developing not passively existent - Our first axiom is that all dichotomous developments start from vague beginnings. Before there is crisply two, there was the vaguely one – the less-developed potential.

Of course implied in this is our second axiom, that dichotomies are dynamically developing and not just passively existent. A dichotomy is an open and continuing self-actualising process, not a closed static realm of being. An organic world is always being made and so it comes to have persistence rather than existence. Like a whorl in a stream, constant action is needed to shape what seems to be an enduring feature.

How does this differ from mechanicalism? The mechanical view allows for change as well as stasis. It could hardly do otherwise when we know that the world moves and develops. However the mechanical presumption is that the world begins with statically existent stuff and that change is then somehow superficial.

So we start with a world created of some concrete set of materials. Or in an attempt to get round the paradox of a creation event, the mechanically-minded might instead claim that the necessary materials have existed for all eternity. But either way, the materials are passively existent in the sense that no further action is needed to underwrite their continuing presence in a world. The materials are simply there. And once there, they freely begin to act and react according to their various inherent properties.

mechanical causality This mechanicalism allows for the change, but it becomes a secondary play. In a logical sense, nothing new happens. Nothing further gets created. The universe is a clock born fully wound with a set of atoms, laws, voids and energy gradients. It then runs down in a deterministic fashion. Atoms may get shuffled into new arrangements, but the first law of thermodynamics rules. The total quantity of mass and energy is conserved. Change is explicitly relegated to the second law of thermodynamics which says stuff may end up messily spread about as a generalised heat, however it remains essentially the same stuff. Substance is free to find new forms, but substance itself is neither created nor destroyed.

Organicism wants to see reality quite differently. It cherishes dynamism, openness and creativity. So it begins with a vagueness, a realm like a bubbling sea of impulses or a quantum foam where anything can potentially happen. An infinity of directions or tendencies are possible because vagueness is unconstrained. It has the potential for change and stasis, motion and location, in equal measure.

But while vagueness is free to go in all possible directions, many of these directions will turn out to be mutually cancelling or otherwise self-contradictory. Only naturally balanced or otherwise synergistic actions will have the chance to develop and grow. Jumping ahead of the argument somewhat, only dichotomies will offer vagueness the path of least action, the path of maximum dissipation. Complementary actions will do the most work and thus grow so rapidly that they overwhelm all other possible routes out of vagueness.

So again, any brand of organicism would tend to assume the world to be essentially dynamic, persisting rather than existing. But we are saying axiomatically that dichotomisation is the process by which organic realities form and therefore it is specifically dichotomies that are dynamic.

And once more this kind of absolute statement has its further consequences. In the organic view, stasis must become the secondary feature of reality – something of an illusion. For anything to seem still, at rest, passively existent, it must be the result of things having changed until continued change was creating no more effective change. There can be no actual stasis, but systems can arrive at an equilibrium balance which gives the appearance of a state of rest.

equilibrium across a membrane Think of the way molecules pass across a membrane. The molecules can move freely in either direction and so the concentrations either side of the membrane will fall into some equilibrium balance without the molecules ever ceasing to move.

As Heraclitus so famously said, for the organicist, all is flux. Even a world apparently at rest is merely a world where ceaseless change has ceased to make a detectable difference.

3) dichotomies are asymmetric

Dichotomies develop in asymmetric fashion - Our third axiom is that organic dichotomies are asymmetric. A symmetry is where you can make a change that isn’t really a change. For instance, you can rotate a sphere or reverse a straight-line motion – go two steps left then two steps right – and end up exactly where you started. There may have been a change but it is in some way unremarkable. The world is not left marked by the occurrence of the event.

In physics, symmetries are important because they are always connected to a conservation principle, an inertia. And this is logical. A change which does not really make any difference in the larger view can happen freely and without cost to the universe that is observing it.

Symmetry-based inertias pop up all over the place in. We have the various Newtonian inertias of spin, momentum and even existence. A mass can spin forever, or travel in a straightline at a constant speed forever, so long as there are no other forces acting on it such as the pull of gravity or drag of friction.

A mass also enjoys a symmetry in time. Mass and energy are conserved during any interactions according to the first law of thermodynamics. Everything going into an event like a collision also comes out of it. And so under Newtonian modelling, going forward in time looks exactly the same as going backwards in time. An interaction is time-symmetric. And because every symmetry delivers an inertia, this gives masses and energies a basic freedom to exist. They can persist from moment to moment in an uncaused way – or so says the mechanical view of reality.

Quantum mechanics of course creates a little uncertainty about this kind of moment to moment persistence principle. The observing world has to stand in a certain relationship to the observed for it to appear stabily existing rather than wildly fluctuating. But even quantum mechanics derives powerful results from its own versions of symmetries. For example, it allows the fleeting creation of a something from a nothing. If you have a void, a nothingness, then on the Planck-scale it must seethe with virtual particle pairs. The symmetry of nothingness can be broken to produce matching matter and anti-matter particles like electrons and positrons. A zero-point vacuum energy is created “for free” – inertially.

Symmetries are fundamental to all branches of mechanically-minded science. Particle physics and string theory now create whole particle families from elegant symmetries. Goldstone’s theorem states that for every kind of physical symmetry there must exist a resonance and thus a particle. The exceptional Lie algebras give a clue to how the whole of reality might spring from the harmonies of mathematical symmetries.

So this is why physicists and cosmologists are always saying symmetry is beauty. Any change that is not really a change but instead a self-mapping symmetry becomes a freedom for something to exist or happen in the mechanical scheme of things. It is the great simplifying principle from which even whole universes might freely, inertially, leap into concrete existence.

Asymmetry, by contrast, is deemed ugly. It is the marked world. A world sullied by a history that cannot be easily reversed. Asymmetry is the world dirtied up and robbed of its pristine Platonic splendour.

ugliness of asymmetry If mechanicalism detests the asymmetric, the uneven, then the organicist must love it! Everything must be switched about so that symmetry is the superficial view, asymmetry the deep. So instead of inertias and conservations being primary, it must be accelerations and dissipations. The organicist enjoys the fact of actual changes that create an irreversible history. The mechanist dreams of a memoryless world where all change is fundamentally symmetric and thus self-erasing The organicist sees change as taking place within a developing context and so every world will have both an idea of where it came from and also where it must be going. The marked world will have the teleological power of anticipation. It will have an arrow of time pointing in some particular direction.

Organic logic still has a place for a realm of perfect, memoryless, symmetry. But as we have seen, it is called vagueness – a place where every direction is the same and so any movement is not really a movement. The self is left with no way to move apart from the self. Except for the one kind of movement that is an asymmetric dichotomy.

Anyway, our rationale here is that symmetry is so fundamental to the mechanist’s position that its opposite must turn out to be fundamental for the organicist. And then we are developing a more particular organic logic here – one based on the 1, 2, 3 of vagueness, dichotomies and hierarchies. So asymmetry has to be slotted into this wider story. Our answer is that crisp asymmetries are what emerge.

So by the precursor argument, every nascent asymmetry will have been lurking as a potential symmetry breaking in the general confusion of symmetries that is vagueness. Just as for the organicist, stasis is a concealed state of dynamism, so the apparent symmetry of vagueness is a concealed state of potential asymmetries. Then by dichotomisation, these asymmetries can become crisply expressed. They will separate themselves from their initial confusion by moving apart.

Eventually the original potential will become as dichotomised as possible, the extremes of asymmetry will have been achieved, and the result will be the threeness of a hierarchy – a moving apart in two directions which then also has the thirdness of an emergent equilibrium to fill the middle ground. Separation is accompanied by mixing. There is a differentiation but also the backwash of an integration of what has been differentiated.

However this is getting on to the full story of organic logic. For the moment we just want to state the explicit axiom that dichotomies emerge from the symmetry of vagueness by a process of development towards contrasting extremes. Dichotomies are asymmetric.

4) dichotomies depend on scale

Dichotomies thus depend on scale - Following on from this, we can argue that dichotomies depend on a separation of scale.

symmetrical change If you have symmetrical change, it is really no change at all as the resulting this and that, the flip and the flop, leave things looking the same. A spinning mass goes around and ends up back where it started. Two virtual particles wink into being and then mutually annihilate to leave the vacuum once more unmarked. So somehow dichotomisation has to deliver asymmetric change, some actual difference. And change based on scale breaking is the only possible way of producing robustly persistent asymmetry. Or at least that is the axiomatic principle I will now argue.

asymmetric development Let’s start by asking how the same could become different, how the unblemished symmetry of vagueness could become something more definitely marked by a dichotomous act of separation? Clearly the two developing poles of being must seem to become as unlike as possible. Each must become “washed clean” of the presence of the other. As long as they can still see some trace of their opposing pole in themselves, they will have to keep moving apart until that otherness finally disappears from sight. A few classic dichotomies will help illustrate the point.

Are positive and negative or left and right good dichotomies? No. They are just simple symmetries that can be mapped on to each other. They are unstable symmetry breakings as there is nothing within themselves that can keep them apart. They freely happen yet they are just as freely reversed. Two halves of one apple are always just two halves of one apple. Nothing essential has changed. Unlike some actual process of development such as the change from a pollinated ovum to a ripe fruit.

A much better example of a dichotomy is chance~necessity. If something is a random accident, then it is completely undetermined. And if something is determined, then there is absolutely no role for chance in the outcome.

Of course, chance and necessity are a little problematic as metaphysical concepts. The decimal expansion of pi is a completely random sequence. Given 999 decimal places we have no way of predicting the next number in the sequence. Well, not unless we know the formula for calculating pi. Then the next digit becomes completely determined. So predictable or unpredictable? It all depends on what you know.

Discrete~continuous is another good candidate dichotomy. If something is broken and isolated, like a point, then it is not continuous with its surroundings. And vice versa. To be continuous is not to have any kind of break.

But again there are difficulties. A line is a continuous geometric object. However convention also has it that a line is made up of an infinity of discrete points, none of them touching, yet none of them leaving any empty space in-between either.

Well chance~necessity and discrete~continuous are a little baffling as dichotomies. But this is because they are scale-less dichotomies. And also lack a developmental dimension. Defects we can correct of course once we bring in scale and development as part of an organic logic. So let’s talk about scale dichotomies.

Local and global are a dichotomisation of spatiotemporal scale – and it is vital here to include time in our mental picture. Something that is local is maximally located to a spot in both space and time. Thus it would be called an event or an occasion.

An atom as a smallest particle may be local in space, but atoms are also meant to last forever. They are meant to exist freely in time. So their extent is potentially infinitely large in this dimension. The truly local has to be as small as possible in all its directions, which in physics means that it is an event or occasion on the Planck-scale.

Of course there are other ways of defining locality in physics. We might define locality as the smallest possible scrap of meaning. A single bit of information. Or the least amount of mass and energy. Or the least amount of motion, or temperature, or other visible signs of action. A good definition of local is in fact interestingly difficult.

The global is then the other end of the spectrum. It is the largest and longest scale that can count as an event or occasion – some super-sized moment such as the total lifecycle of a universe.

To be local is to be somewhere in particular. To be global is to be precisely nowhere in particular – and thus everywhere in general. A particular spot in space and time can be defined by some specific set of properties. The global view is then the prevailing ambient conditions. It is defined by long-running average properties that are the same for everywhere and everywhen, such as some overall temperature, pressure, curvature, density, expansion rate, or whatever other qualities seem most relevant.

Local~global (like particular~general) makes a good dichotomy because it is “same but different”. The two poles are alike, being made out of essentially the same stuff. Yet asymmetrically different in that each pole is defined by the way it is washed clean of any visible trace of the other.

small and large moments The smallest possible event, moment or occasion will be the one that looks not the slightest bit large, or extended, or enduring. It will be the flash of existence that is so fleeting it lies at the very limit of what we can know to be there. The global on the other hand is the largest and most enduring, or unchanging, scale of existence. It is the big canvas that appears quite unmarked by anything small, or particular, or local.

So we can imagine zooming in closer and closer until we reach some faintest point-like event, contracting existence until it is on the very brink of disappearing. And then stepping back and back until the stepping back makes no further difference as a whole world fills our view. It would be as if we had pulled back into an opaque fog – a maximally general ambience – so that any further motion would leave our view unchanging.

An asymmetry of scale makes a good dichotomy as the same becomes different by growing out of sight of itself. The local gets shrunk until it can no longer see the global – it hovers on the edge of not actually being. Being on the global stage, that is. And likewise, the global is an expansion of the view that becomes so large that anything local or particular has been averaged away to a continuous, blank, smoothness.

Local~global is a good candidate for our ur-dichotomy. A breaking of physical scale seems the simplest way of creating asymmetry from symmetry. However there is another good dichotomy to be found in substance~form.

Aristotle and Plato were certainly right to focus on substance~form as a candidate ultimate dichotomy. It seems logical that for anything to exist – either for the shortest moment or the longest time – it must be made of some stuff, something substantial that can be moulded. But also it must find some form, some actual shape or arrangement, whether this be a matter of careful design or comes about in quite accidental fashion.

Aristotle is often portrayed as believing that substance was fundamental, with forms arising because of potentials inherent in the various kinds of elemental stuff. Plato was supposed to have taken the opposing view that organisation was king. There exists some eternal realm of perfect forms that creates our actual world like an imperfect shadow cast upon a wall. In the Platonic realm there would be the perfect conception of a cat or table. And then our actual world would be full of pale imitations of this ideal cat or table.

substance~form But it is only modern mechanical thinking that requires this to be framed as an either/or debate. It is what we think they should have been arguing about back then. In fact both Plato and Aristotle were fairly dichotomistic in their positions. Aristotle clearly saw substance and form as equally fundamental in his discussions of hylomorphic form. And Plato accepted there needed to be a realm of chora, a formless stuff, to take the imprint of his forms. The two philosophers drove the opposing ideas of substance and form as far apart as they could logically go. But they still ended up with both poles of the dichotomy as necessary for an actual world.

So substance~form does seem a very basic dichotomisation of reality. The question is then whether it is also a scale dichotomy? Does the same become different by becoming disconnected in the size of its moments in some sense?

Substance is traditionally defined by the stuff that is left over once any particular form has been washed away. Likewise, forms are the patterns or arrangements that “exist” as at least logically coherent ideas – structural attractors or cogent concepts – even if there are no actual substantive incarnations. So each is defined asymmetrically by the complete absence (or at least visible presence!) of the other.

What does this have to do with local~global? Well if we zero in on a location within some object,  or structure, or system, we lose all sight of the global context, the larger arrangement that is its shape, or organisation, or purpose. We can only see its substance – the atoms, events, information, or other localised entities from which it is constructed. Likewise if we pull back to the most global view, now we see just its form, its overall shape and purpose. So substance~form is a dichotomy that depends on observational scale – on semiosis.

We can see this is getting a bit complex. Substance~form is somewhat less general than local~global because it is more interested in what is actually there in a world. Local~global takes another step back to talk about the place in which things exist. Yet both depend on scale for the creation of asymmetry.

According to our axiom, all good dichotomies should turn out to be scale dichotomies on closer inspection. So let’s go back to chance~necessity and discrete~continuous to see if that is true.

Chance and necessity are normally asking the question of why some particular located event took place. The question thus assumes a global context that either fixes an event to happen, or couldn’t care less and so allows it to happen freely or randomly. So flip a coin. There is a global process – you flicking the coin in the air – that is highly determined in its way. You are constraining matters so that the coin toss has to happen. But you have also decided you will not control whether the coin falls heads or tails. If you had wanted, you could have placed the coin on the ground with care and constrained that aspect of its existence as well.

Chance~necessity does indeed conceal issues of scale. Discrete~continuous also makes more sense once we grant it a scale dimension. As might be guessed by now, the discrete as one pole maps neatly to the idea of the local, the substantial, while the continuous maps with equal ease to the global view, the idea of an overall cohesive form.

So for example when we consider the universe, it seems discretely constructed on its finest grain. It breaks up into a foam of Planck-scale events or quantum gravity loops – the tiniest possible fragments of coherent existence. Yet when we step back, the universe becomes a continuous geometry, a flowing relativistically seamless whole, presided over by universal laws.

Anyway, our fourth axiom is that dichotomisation depends on the development of an asymmetry. The same must find a way to become visibly different. Dichotomies thus depend on scale. It is only via a breaking into different sized moments – different effective scales of interaction – that smallness and largeness can come to have a different causal character. As we shall see when we get into the dichotomy of construction~constraint.

5) dichotomies develop both ways

Dichotomies always develop in both their directions at the same time - This has just been pretty much argued. But it is worth now stating explicitly. Dichotomies have to go in both of their directions at the same “time” with a matching vigour.

The mechanical view of causality is of course chicken and egg. One thing must lead to another. First the cause, then the effect. First the substrate, then the development.

which comes first? If we are asking one of those big scientific questions – such as which came first in the evolution of Homo sapiens: the ability to speak or the ability to think of something to say? – then even though it is clear that the two are part of the same evolutionary shift, and that they are linked in some kind of circular causal feedback loop, there is still the “logical” demand that one or other has to be the prime mover in the story. So thought or language? You must take a side and say which came first, thus paving the way for the other.

Organic logic completely changes the notion of what would be a good scientific theory here – what would count as a rational tale. A dichotomy is an asymmetric separation of some vaguer state. And the separation goes in both of its directions at once. Figure and ground, parts and whole, substance and form – these are all developing at the same time together.

There is no priority required. In fact it is expressly forbidden. It would be quite ridiculous to think of one direction of change being the first to occur and the other asymmetrically-opposed direction following as a consequence. As Newton said – though it is not widely recognised as an assertion of dichotomistic logic – for every action there must be a reaction. A reaction equally immediate and equally powerful.

Of course, because all dichotomies are really scale dichotomies, we have to be a little careful here. In the complex world we are now modelling, even our notion of time must become (complexly) scaled. So what we are really saying is that dichotomisations go in both of their directions simultaneously at their own rates – and with things going ever faster in one direction, ever more slowly in the other.

This is how we get the appearance of localised changes against a fixed global backdrop. The universe as a whole seems to stand relatively steady because the pace of its expansion (and cooling) looks so slow relative to the hot and fast actions that may be taking place locally. The moment for one – the pace at which its interactions can achieve local equilibrium – may be measured in milliseconds. The moment for the other may be measured in eons.

So the organic view is the same as the mechanical view in this regard. There does seem to be a void largely at rest and then an atomistic play of events that are the figures marking the ground, the local marking the global, the changes marking the stasis.

However mechanicalism assumes the atoms and the void to exist – and so stasis (the local and global persistence of things) is a fundamental. Organicism by contrast presumes dynamism to be fundamental. And so local and global are always growing away from each other, continuing to separate. And they are doing this “simultaneously” with neither having causal priority.

chicken~egg arising from vagueness Thus when we are faced with chicken and egg questions like which comes first, we have a new logical answer. What comes “first” is always some vaguer potential. Then both directions of any dichotomisation start to form “at once”.

Of course, while this may be generally true, there are also examples of dichotomisations that appear to proceed so rapidly in both their directions as to be happening within the same physical moment – at a single shared instant. So we have phase transitions where suddenly there is a swift change and some local property becomes globally organised. Water cools steadily (globally) and suddenly at freezing point there is a phase change as local bonds overcome the free jiggling of the H2O molecules to lock them into a regular crystalline lattice.

But we will find that these kinds of dichotomisations mask a deeper story. For a start, the local bonds that glue the H2O molecules together pre-exist the moment of dichotomisation, and so they are also “global” in that regard. As we shall see, a phase transition is a kind of quasi-dichotomisation in that it relies on a pent-up change – a shift is delayed so it then must happen more abruptly. And then the system is thermodynamically “boxed”, so the change can swiftly go to completion.

It is important to understand the way that dichotomisations can be manipulated, even controlled. However what is axiomatic here is that in the wider picture, dichotomies are always busily going in both their directions, even if it might look as though there is a global context that is unchanging, unmoved.

three scales of moments In fact, both the local and the global moments can appear come to appear static to the meso-scale observer – someone looking at things from a viewpoint in-between. If we look upwards to the largest scale moments – such as the billions of lightyears which make up the expanse of the visible universe – things will be changing so slowly as to seem like a frozen, fixed, backdrop. An eternal order. But equally, looking down to the smallness of the Planck scale, events – such as the knotting and unknotting of the fabric of spacetime – will occur at such a frantic pace as to fuse into a solid blur. The smallest scale, made of an infinity of discrete points, will come to seem a static, or steadily enduring, realm as well.

But again, axiomatically, dichotomies are always dynamic and so if they are a separation, they will always be separating in both of their directions with equal vigour. It may not immediately look that way, but that is another matter.

6) dichotomies are not broken

Dichotomies are separations not breakings - This is a prime principle – or at least one of the first that got me going with a formal definition of organic logic.

In the mechanical view, reality is crisp. It is always definitely something or other. Any vagueness can only be semantic. It is a failure in the exactness of our description. Even a fog could be described precisely if we had the instruments to place each H2O molecule.

dualism breaks apart So when the mechanically-mind are faced with a dichotomy like substance~form, mind~body or random~determined, the assumption is that these are mutually exclusive alternatives. They involve a crisp division of reality in which the middle ground – any inbetween-ness – is 100% excluded.

This creates the familiar causal paradoxes. Causation implies a shared history of development. But if two things like mind and body, or chance and necessity, appear to have no current connection, then how can they have had some past connection? If there is only black and white, no shades of grey, then how can black and white be also “the same thing”?

dichotomies separate towards limits The organic view (as it must) takes the opposite tack. It says that all things indeed do start out as a grey one-ness – a vagueness. Then this one-ness gets teased apart. The potential becomes developed towards two mutually exclusive extremes. But the separation is an active process. Like Sisyphus rolling the stone up hill, a dichotomisation cannot rest without sliding backwards. So nothing ever gets actually broken apart, just moved away as far as it can go.

As we have said, things keep changing until further change seems to be making no difference. The dichotomistic separation becomes a game of diminishing returns. Like the asymptotic approach towards the x-axis by a parabolic curve, the effort can be continued to infinity without ever hitting the crisp limit that marks the boundary, the final equilibrium point. The limits of a dichotomy are precisely the places that can never be reached, the goals that can never be quite grasped. Reality can become 99.9999% separated towards black and white, mind and matter, chance and necessity, but never actually broken in two.

Once again, where mechanical logic talks of entities that exist, organicism talks of processes that persist.

7) dichotomies also mix

Dichotomies involve separation but also the mixing of the separated - So far we have been speaking of an organic process of separation. We start with a vague potential. It divides towards opposing extremes of scale. There is a separating, but nothing actually gets broken apart. Next we need to consider what occupies the space created in-between. What now fills the middle ground?

We can start by saying that it seems logical there is indeed some middle ground. In fact because a dichotomy is a separation rather than a breaking, there really only ever exists a middle! The process of separation may strive towards its contrasting limits, but because it can never reach them, they remain ontologically unreal – never actually realised. Only the middle ground, the stuff sandwiched in-between, thus has concrete existence.

Following on from this, we can say that a separating realm must continue to be in intimate communication with itself. And being in communication, it is reasonable to suppose that it is free to mix. Whatever distinctions are being created in the move towards the extremes must then also set up intermediate eddies of interaction. And out of this mixing of extremes can come a complex world.

separate and integrate So vagueness is just a potential with nothing distinct happening. A dichotomy creates complementary distinctions and then also a world of interactions between the distinctions. This is as it should be under organic logic. The process of dichotomisation is itself dichotomised!

Mechanical logic would think that causality ought only ever go in a single direction. So even when a feedback model is employed, there is still a psychological difficulty about having two things happening at once. One direction must happen first, so usually the input is followed a little later by the response.

But a dichotomy must always have two directions. And go in both those directions at the same time with equal vigour. So an outwards separation will naturally be matched by an inwards mixing. Or a process of differentiation by a process of integration. Or a downwards acting constraint by an upwards building construction. The moving apart makes possible also a coming together.

8) middles have scale symmetry

The middles of dichotomies have scale symmetry - So middles are produced by mixing. And this mixing can be given a precise mathematical characterisation.

In the ordinary view, any kind of mixing will eventually lead to an equilibrium state. Things will mix until further mixing makes no apparent difference. So in standard thermodynamics, a bunch of gas particles trapped in box will spread themselves out randomly until the box is filled with an even temperature, pressure and density. The box will have just a single scale of organisation! A single measurement will describe the typical strength of any particle interaction. Though of course if we look closer at the individual particles, they will show random variations around this mean. There will be a gaussian distribution – a bell curve – for the strengths of interaction events.

This is obviously the mechanical idea of an equilibrium system. It assumes a static global boundary – the walls of the box are fixed and rigid. The particles are also static in the sense that they endure without effort. They have inertial existence. It is only their collisions that are fleeting events. In this static world, all the energy of the particles is being reflected back into the system. Particles bounce back off the walls and so it is no surprise that their fates become homogenised around a single mean, the one scale of organisation.

But organicism is based on dynamism and so a very different kind of equilibrium model must be considered as canonical. If we have a box of particles, it must be dynamic either because it is energetically open or because its walls expand freely along with the contents. And such a system will then display scalefree behaviour. Or more properly, it will have scale symmetry. It will display a typical organisation over all possible scales of existence.

fractal sphere There are many familiar mathematical notions that incorporate an axis of scale symmetry. Fractals, 1/f noise, scalefree networks, percolation, renormalisation theory, holograms, criticality, the edge of chaos, opalescence – anything that is powerlaw, dissipative, open, or otherwise freely expanding and equilibrating.

For example, there is the turbulence of any fluid system. If we force water through a narrow channel it will erupt with events such as whorls or bubbles over all scales. If we feed sand onto a sandpile, there will be avalanches with a fractal distribution.

Note that we are focusing here on the scale of events. The size of whorls or avalanches. The Boltzmann model based on particles trapped in a box takes its small and large – the individual gas molecules and the container – as fixed. This set-up then creates a gaussian distribution of events. When a measurement is taken of the temperature or some other emergent system property, it has a single averaged scale. But with the more complex systems we are talking about now, such as a heated pan or a compressed flow, measurement will find the events to occur over all possible scales.

Driving a system like a box of particles with an energy gradient – sandwiching it between a heat source and a heat sink – is one way of creating a middle ground with scale symmetry. It will erupt with a dissipative, or energy shedding, structure over all scales. But the same kind of powerlaw or “long-tail” distribution of structure can be achieved by expanding the box itself – letting its walls spread along with the contents so that they are no longer reflecting energy back into the system and thus imposing an averaging effect on the scale of its events.

If we imagine our particles dashing about randomly in this smoothly expanding box – or indeed existing unboxed and free to spread out in some infinite space – then the distribution will become fractally patchy. The resulting system will not have one typical scale of density, or pressure, or temperature. Probe the system and we might find areas that are quite empty of particles while others in which by accident they have gathered in high concentration.

So organicism has its own version of thermodynamics. One that now takes dynamism as fundamental. Boxes of particles are assumed to be energetically driven or freely expanding unless there is some further step to regulate the system and hold it static.

And note yet another neat dichotomy that applies here. The process of dichotomisation involves both separation and mixing. The separation results in a scale asymmetry. It breaks scale apart to make the distinctly largest and smallest. But the mixing creates the very opposite. It produces a realm characterised by an axis of scale symmetry. Spanning the space inbetween the “third thing” of a middle ground where the two extremes always look mixed to a steady equilibrium balance.

Remember that symmetry is where a change makes no visible difference. So what we are saying is that in the middle ground, we can move up or down in scale and the world about us will continue to look the same.

fractal blood vessels This is clearly true with a fractal structure, a scalefree network, or a system at criticality. If we look closely we will always find that some deep dichotomy is at work creating the events that make the system. For example, with a dissipatively branching network like the body’s blood vessels, there is a critically poised balance between the tendencies to integrate and differentiate. If we then begin to measure the frequency of branching, we will find that it is the same whether we are looking at large arteries or fine capillaries. Changing the scale of our observations makes no visible difference and hence there is a symmetry of scale. The event which we call branching occurs evenly – it has an equilibrium mixing of the two tendencies, integrate~differentiate – over all possible scales.

So to sum up here, where there is separation, there is also a mixing. The mixing will go to some sort of equilibrium. In a dynamic world, one that is always still changing because it is either energetically open or freely expanding, the equilibrium cannot fall to some single value gaussian distribution. Instead the balance point now becomes a powerlaw distribution in which some characteristic event, or structure, or process, occurs over all possible scales. Middles must have scale symmetry – even if this then implies that an organic system is naturally either an open dissipative structure, or a closed but smoothly expanding one!

9) more than two poles are unstable

Dichotomies have only two poles because three or more is unstable - One of the things that put me off dichotomies for a long time was that they seemed a lazy over-simplification of a complex reality. To say the world always breaks down into a choice between two opposing things – a this and a that, an either/or – seemed to suggest a failure of the imagination. Surely reality was richer in possibilities than this?

Indeed any kind of metaphysical numerology appeared suspect. It would be just as bad to talk about a fundamental threeness, or fourness or fiveness. There seemed no logical reason why reality should divide itself into some fixed number of fundamental categories, let alone as few as just two.

It did not help that Socratic dialogues, Taoist mutualism, Cartesian dualism and Marxian dialectics were the familiar face of dichotomous thinking. None of these get a great press in scientific circles. So it was easy to take the view that dichotomies were just a sloppy first-cut habit of metaphysical thought – the result of saying “on the one hand”, and then immediately realising that this created a balancing need to think about “on the other”.

Now of course I am completely sold on the naturalness of dichotomistic two-ness. And indeed this two-ness can be taken as axiomatic on the grounds that any separation in more than a pair of directions would be unstable, so would end up reducing back to two anyway.

There are a number of familiar results from mathematics that are suggestive here. There is information theory and its proof that binary choices dissipate ignorance the fastest – the old 20 questions game. There is the three body problem and the fact that only two body interactions can be calculated.

more than three links reduces There is network theory and its proof that all networks with more than three links per node can be reduced to networks with just three. And then it is easy to see that this three-ness is really a two-ness as it is the simplest possible representation of an input~output asymmetry. A network with just two links or edges connecting each node is just a chain or a ring. It can carry a signal perhaps but it is too symmetric to process information. However two inputs and one output sets up an asymmetry – a figure~ground dichotomy – where the inputs can act as a constraining context and the output as a constructing event.

So the general argument here is that vagueness is free to break in as many different directions as it likes. It is after all a raw unbounded potential. However only the twoness of a dichotomy will prove to be a self-stablising, mutually enabling, move. Remember that in dichotomisation, the extremes must not only move apart, they must also be able to mix. And it would seem that any early tendency to split into three or more directions would sooner or later collapse into precisely two, exactly complementary, directions. Only by moving orthogonally, going in exactly asymmetric directions, could a pair of tendencies be sure of diverging without ever later meeting up again.

10) organic causality is holistic

Organic causality is hierarchical or holistic - Our causal story is growing increasingly detailed as we state the various axioms of organic logic. Now we are about near the end. We have just about all the elements in place to describe the final outcome of a process of dichotomisation. And that is the development of a hierarchically ordered system. Or one with a holistic causality.

whole is more than the sum of its parts Holism, which comes from the Greek for entire or total, is often described as the idea that the whole is greater that the sum of its parts – a definition that goes right back to Aristotle’s Metaphysics. It is easy enough to get what is being said here. A complex system like a society, a body, or a mind has an identity that does not seem reducible to the properties of its components. The whole appears to have capacities that are emergent – they pop out at the top level and it is not at all clear how they could have been (mechanically) caused. So the whole, perhaps as a system of relationships, seems more than the heap of elements or components that form it. Form is greater than substance.

 Of course, to say the whole is greater than the parts in this way is not the dichotomistic view. Dichotomies start in vagueness and both the parts and the whole emerge together. Their need for each other is mutual, their relationship synergistic. So holism for us is parts~whole, or local~global, or substance~form, or event~context, or matter~mind. Both poles of any dichotomy are equally fundamental. Neither is the greater.

However the idea that holism obviously does capture is the fact that parts alone are not enough. There is also the large-scale order to match the small-scale materials. And the large-scale or global has some kind of causal role. It organises the parts in some way.

So our definition of holism here can be that it depends on a two-way causal interaction. The parts make the whole and the whole also makes the parts. Or more accurately, the parts construct the whole while the whole constrains the parts. Holism is based on the asymmetric causal dichotomy of construction~constraint.

Construction is of course a mechanical view of a causal process. We start with an atomistic collection of parts. These parts possess properties. As the parts react according to their properties they begin to construct some larger outcome. It is a mindless, additive process. The parts act with no apparent goal. And they are free to move about within an unresisting void. It is all very accidental yet also deterministic. The small is fundamental and the large emerges from the accumulation of a lot of discrete events.

Constraint is quite a different conception of causality. Constraint is about preventing things from happening. It is about looking down from on high and placing a set of restrictions on what is able to take place at some location. It is about context and history. It is even about goals and knowing or semiosis. To stop something happening, the world must be somehow mindful of it. You cannot stop prisoners escaping if you don’t watch them. You can’t keep particles in a box unless the walls are ready to interact with them (neutrinos, for example, will stream through most boxes with ease).

The corollary to this is that what cannot be constrained – prevented from happening – is then necessarily free to happen. In a dynamic world, infested by restless potential, things are always wanting to happen. And if nothing exists as a constraining context to prevent it, then they will.

So in paradoxical fashion, constraints breed freedoms. Indeed, in our organic description of the world, they even shape up the parts – the features or ingredients – that make up a system.

What exists at any location can be taken to be rather vague or general. We see this in quantum theory – anything might be happening down there. Except we also know from quantum theory that the world then frames eventhood with a prevailing context, a global ambience. It decoheres. So a global context focuses a potential. It constrains a location in certain ways, making it crisply not some kinds of thing. And then what it cannot constrain is left unfettered as a localised freedom – an inertia that can be exploited in unconstrained fashion. Indeed, an inertia that will blindly begin to construct!

falaco solitons in a swimming poolIt is a causality like we find with the solitons, phonons or other excitations of condensed matter physics. Particle-like entities are created by a constraining environment. These quasi-particles are then have various inertial freedoms just real particles. They have the freedom to persist, to move, to interact. So in holistic fashion, the wider world shapes the identity of the parts. It does not so much make them what they are, but makes it definite what else they are not. Then having been pinned down this way, the parts have their now equally crisply delineated freedoms – the various persisting properties that make them “a part”. And as a part, they can freely and mindlessly start to construct.

So we have reached a stage where causality is dichotomised into two basic types, one associated with the downward action from the global scale, the other with the upwards thrust from the local scale. And of course each kind of causality is serving to shape and define the other.

Downward constraint focuses whatever it is that is crisply to be found populating the most local level – the atoms, or substances, that are the building blocks. But to make the whole system work, the building blocks must then be of the right nature to construct the global ambience that is making them. For the parts to have some sort of stable, persisting identity, they have to manufacture the right kind of long-lived prevailing context. The story is mutual in the deepest sense. Each must make the other and so neither has priority in out story.

Then on top of all this, the thirdness of a middle ground emerges because the forces of construction and constraint are interacting and going to equilibrium over all possible intervening scales of being. What we end up with is a triadic system, a hierarchy. We started with vagueness, developed it with dichotomies, and now finally arrive at a hierarchical outcome with a holistic causal order.

The whole system is still dynamic – still moving apart and also growing together. Separating and mixing. But because we are in fact observers with a limited view of the scale of the system we inhabit – a universe with limits some 30 orders of magnitude distant in either direction – we can feel that some kind of final static order has been arrived at. We exist. A universe has been created and we now live in it. All around us, the world seems pretty much at equilibrium. If there is further change, it is resulting in no real apparent change. We can take the sun, moon and stars as eternal, taking stasis rather than dynamism, existence rather than persistence, to be our fundamental.

11) mechanical logic is complementary

Organic logic is dichotomous with mechanical logic - We can now turn to the formal relationship between organic logic and mechanical logic. No surprises here – they are of course dichotomistic. The organic and the mechanical are asymmetrically related. Each needs the other for completeness and neither enjoys epistemic priority. Any total model of causality will have to incorporate both within the same (holistic!) framework.

We can suggest something even more extraordinary. Being opposites, whatever one forbids, the other will have to mandate. If one says things can only be this way, then the other must say they can only be that. And following from this, we can argue that any paradoxes produced by one logic are guaranteed to be exactly cancelled by the other.

For example, it is widely held that it is paradoxical matter can produce mind. So organic logic would have to say it would be paradoxical for matter to be mindless. Which would be the pansemiotic view of reality.

Or to give another example, if the mechanical view is that the universe sprang into being out of nothing, then the organic view must be that it sprang into being out of everything. The everythingness of vagueness in fact.

organic~mechanical dichotomyLeaving such wider claims aside for the moment, the point is that organicism as defined here contains within it both the mechanical and the organic approach to logic. The mechanical model of causality is certainly opposed to the organic – exactly opposed in every respect – but that is also precisely what the dichotomistic view must demand. And indeed by now we can see just how neatly mechanical causation maps to the local pole of the local~global spectrum. It is all about atomistic construction, blind upward thrusting, inertial freedoms and material creativity. And equally, the traditional view of the organic – as the larger whole, the ecological or systems level view, the realm of constraining forms and knowing purposes – maps just as neatly to the global scale of being.

So local = mechanical and global = organic. And yet organicism still manages to be the larger causal view at the end of the day (yes it wins!) because it is the dichotomistic approach and so is the one that formally demands just such a mutual pairing of asymmetric, apparently antagonistic, alternatives. Mechanicalism has instead the expectation that it is must be a case of either/or. And so mechanicalism loses at the higher level of meta-theory. We can say that ultimately it is the logic of organicism that incorporates the logic of mechanicalism rather than the other way round.

12) organicism is only modelling

Organicism is only modelling - Our final axiom is really the reminder that in the end, organicism like mechanicalism is only modelling. It is the truth only in the sense a model can be true.

A lot of intellectual energy can be wasted worrying about truth. Which is really right here – organicism or mechanicalism? Or something else still? However this is to misunderstand the modelling relation – the basis of the relationship between a knower and the known.

the modelling relation We can only model reality. We never know it directly. We merely develop ideas that shape our impressions. These impressions can seem to be correct, which validates the ideas. But we remain epistemically always “trapped in the bag”.

The fact that we are only modelling what we believe to be out there is hardly controversial of course. But we need to consider the modelling relation rather more carefully for a number of reasons.

The difficulty is that the modelling of reality is generally taken to have only a single purpose – the pursuit of truth. However it is no surprise to find that dig deeper and purpose can be dichotomised. There is modelling for truth, but also the modelling for control. And there is a functional asymmetry characterising the difference. One kind of modelling involves a maximisation of information about the world. The other aims for a minimisation of what needs to be known, remembered and measured. 

So for example, to claim to know the truth of a light switch, we would need to represent all the possible information about it, from the physics of electric circuits and tungsten filaments to council building codes and the optics of the human visual system. Yet to control that same switch, we only need to know how to flick it off and on. A plankton or a photocouple could know as much.

Any kind of causal modelling involves some sort of reduction of information. This is because models are formed by the reduction of many real-life particulars to some more universal principle. The idea of a cat is the assimilation of a great many real-life experiences of cats into the one generalised notion of cat-ness. Then from this condensed model of cat-ness we can generate as many particular cat-like experiences – perceptions, memories, anticipations – as we wish.

So all models are reductive in this fashion. Local particulars are washed away to leave global generalities (that can then be employed to regenerate particulars). But there is still a distinct difference in modelling styles that follows from having the different purposes of truth and control. And it will be then no surprise to say next that our two logics, mechanicalism and organicism, appear optimised for opposing purposes. One makes the best sort of generalising tool for science as technology. The other for science as philosophy. One is for acting on the world. The other is better for understanding it.

This final point matters as it admits that organicism probably fails to match mechanicalism as a method for controlling the world. If the history of Western intellectualism has favoured the mechanical approach, it is no accident. Our story has been one of technological advance – of located actions.

But on the other hand, organicism is efficient at offering the largest view. It may be the more passive view – where we have to stand back to see how all the parts fit together – yet it gives us the hope of understanding reality’s global nature.

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