history> anaximander

Organicism or mechanicalism? From ancient times there has been a to and fro between the two views of reality. Here is an account of the history of the debate that runs from the organicism of the first true philosopher, Anaximander of Miletus, through Greek atomism, Aristotle's complex causality, and then finally the triumph of atomism in the mechanics of Galileo and Newton.

There are three pages to this section - Anaximander, Atomism and Newton.

the dawn of thought

Greek philosophy began some two centuries before Athens in the scattered city states and colonies of Ionia, now the coast of Turkey. Ionia was the birthplace of rational thinking for many reasons.

The great civilisations of Mesopotamia, Egypt and the Indus had been agriculture-based, inward-looking, feudal and bureaucratic. The Ionian cities survived on fishing and trading. They were ruled by laws rather than kings. They had a wealthy merchant class who travelled widely. And by this time – around the 7th century BC – there was writing to record people’s ideas.

These first thinkers also had the advantage that they could come at the problem of existence with an utterly fresh eye. To use a memorable phrase, they saw: "the world lit by a kind of six-o'clock-in-the-morning light and the dew imperishably on the grass."

ionia There were many famous Ionians - Thales, Pythagoras, Heraclitus, Parmenides, Zeno, Empedocles and Democritus are just some of them. Thales is conventionally considered the very first philosopher. But I would rather accord that honour to Anaximander of Miletus. He was arguably the first real metaphysician. More importantly, he was an organicist. And so organicism can be said to be older than mechanicalism in Western thought. Of course precedence doesn’t really matter. But it does matter that the history of Greek philosophy is usually told by the winners and hence the ideas of even major figures, like Plato and Aristotle, are reported in distorted fashion. And key figures like Anaximander are left out of the story almost entirely.

But back to the question of why the Greeks dichotomised? The primitive way of thinking about reality is animistic. Things happen because the world is full of mind. The winds, the seas, the sun and stars – everything has a will, a purpose, a reason. There are a host of animating gods and they come across as a somewhat dysfunctional soap opera family perhaps.

In pre-classical times, the poet Hesiod told how the Greek gods were born out of an initial shapeless state of chaos. The first gods were the most general ones such as the earth and the sky, love and the underworld. These elemental gods then coupled in various ways to produce a succession of steadily more human-like gods such as Zeus and Venus. Divinity became increasingly constrained in its form as the gods gave birth to a host of demi-gods then eventually mortal humans.

The purpose of myths and religions are not really to explain the world, though they may claim to do so. They are the ideas that control a culture. And they are judged by their success in doing that. So gods provide the authority. They promise the rewards that follow the actions. They teach the moral lessons.

It was quite a thing for the Ionians to start to break away from this machinery of social control. To think about reality in an objective way (though as we can see, rational philosophy eventually became valued as an instrument of even greater social and technological control).

Anyway, philosophy began once there were individuals with the freedom of thought to see that humans and their ways were highly particular. The deeper truths of reality were probably more general, simpler, less contingent.

Again this is probably a distortion of what mattered most to these ancient thinkers, but as we normally tell the history of philosophy, the burning question was what was everything made of? What was the fundamental principle or essence of being? The arche or the ousia?

Behind everything there must be one common stuff. A substance that was neither created nor destroyed but merely changed its form or got mixed in new ways. In the everyday world, there were abundant examples of things changing, and yet stuff persisting. Ice melted to water, water boiled to steam. Larva cooled to rock. Wood burnt to make heat and smoke. But what was elemental? The clay or the metal that could be shaped into any chosen form?

Three Miletians offered answers. Thales said all was water. Anaximenes said all was air. Anaximander who came between these two said all was apeiron – whatever the heck that was.

As the tale is normally told, the Greeks got hooked on this idea of identifying something primal and essential. They soon realised that substance was only one possible dimension of this equation. Heraclitus said all was flux. Parmenides that all was stasis. Plato that all was form. In modern eyes, the atomists got in most right in saying all was again substance. Or rather little lumps of substance in a void. The lumps had shapes and motions thus a set of properties. You could have both change and stasis as the atoms rearranged without ever getting used up. You could also have form both in the shape of the atoms themselves and the shapes they made.

Greek metaphysics gets a little confusing as there seems to be so much zig-zagging. As soon as one philosopher says everything is all one kind of thing, some other philosopher pops up to say no, it is all its opposite.

But let us start again and see the development of Greek philosophy as a systematic process of dichotomising.

anaximander

Anaximander, born around 610 BC, was the first philosopher in history. At least he was the first to develop a metaphysical system from totally abstract principles. So let us spend a little extra time on him.

Hardly anything is actually known about Anaximander apart from the fact he was respected enough to have led an expedition to set up a trading colony at Apollonia in the Black Sea. He drew the first known map of the world. It seems probable that like most early Greek philosophers, his speculations grew as a sideline to his day job as a man of practical action.

Anaximander did write a book, On Nature, but only a single sentence survives. So his philosophy has mostly had to be reconstructed from the secondhand accounts of later Greek scholars. The thirdhand retelling by modern scholars then almost entirely miss his organic turn of mind. Today he is mostly judge by his failures to be sufficiently mechanical and atomistic, not celebrated for the crystal clarity of his dichotomising logic.

the apeiron This is Anaximander’s creation tale. In the beginning was the apeiron - a term that has been variously translated as the boundless, the infinite, the indefinite, the indeterminate. Anaximander said the apeiron was a state of simple potential, a formless block of pure existence that spread without limit. A vagueness in other words. Being eternal and ungenerated, the apeiron could be considered divine. But as said, not in the Christian sense of a God that is a unique and individual creating intelligence. The apeiron was just a stuff which had an infinite generality. It was both everything and nothing.

Then something happened. The apeiron began to "separate out". There is a lot of debate about the exact translation of this term – apokrisis. Obviously Anaximander had to adopt standard everyday words to express some very technical ideas. Some say his separating out means to squirt or eject. Others that it is a process like shaking and sifting which separates the wheat from the chaff.

Anyway, in one small region of the limitless apeiron there was a symmetry-breaking and the hot and the cold started to split apart. To Anaximander, heat and coolness seemed about the most basic possible qualities of reality and so it made sense they should be the first division to appear. And indeed this seems an inspired choice given modern cosmology which sees the Universe beginning as a hot point and expanding to become a cold void. The Universe really is defined by its approach towards two boundary conditions – the maximum heat represented by the Planck energy density and the maximum coldness represented by the vacuum, a flat, empty, spacetime.

So there was a vagueness and its first coherent impulse was to begin to divide into the cool and the hot. Any increase in heat in one location of course would suck it out of the surrounding apeiron, making it consequently colder. The potential contained an automatic dichotomy. Now the cold part of what was separating out was naturally also the heavier, thus it contracted to form a central dank, vaporous mass. Meanwhile the hot part grew into an expanding shell of warm air that became increasingly fiery and rarefied as it dried itself out. One symmetry-breaking led smoothly to the next. Properties became exposed in succession and led to further reorganisations or separations of the original potential.

Anaximander felt this primordial Universe then developed in disc-like fashion – perhaps because he imagined it separating itself in a natural way with a gathering vortex-like motion. Spin murky water in a bowl and the heavy sediment gathers in the centre while the light stuff drifts to the side. Anyway, the cold mist at the centre congealed to form an earth shaped like a squat cylinder, or drum. The Greek world lay at the centre of one face. On the other was an unknown, probably unreachable, continent - the antipodes.

anaximander's cosmos At the same time the outward-swirling layers of warm air grew hotter until they became the celestial fire of the sun, moon and stars. Anaximander's explanation for how these cosmological objects could look like burning balls, yet follow fixed tracks through the -sky, sounds a little odd but was quite rational in its way. He said first circular bands of fire formed around the rim of the earth like rings of bark around a tree. Each band of fire had to be fed by an encircling mass of air as fire was made by a separating out of any remaining heat and dryness in the air. This now cooling and condensing air mass made an opaque fog that shrouded the fire so it only showed at "breathing holes". What we see as the sun or the stars are actually small vents in a series of great wheels of fire rotating around the earth.

As the hot and the cold moved ever further apart, there were more symmetry-breakings, a more definite division of the world into parts. The light became increasingly separated from the heavy, the dry from the damp. The dank vaporous mass that first formed the earth was gradually dried by the sun to become mostly hard rock. The separated off water became the seas and the clouds. The heat of the sun also reached down to stir up the air, causing winds. Clouds banged together, releasing rain. Interactions between the extreme realms of the hot and the cold created rhythms and processes in the space in-between.

Finally as wet earth became drying mud, life emerged from this flesh-like material. The first creatures were simple animals like sea urchins or shellfish that had moist interiors and thick clay crusts. Later their dry coating split to release the wriggling fish and squirming amphibians which had developed – by a further internal separating out of structure – within them. Humans eventually arose inside the wombs of the largest fish. And with this, the development of the world was complete.

The details seem quaint - creatures born of mud, wheels of fire, a drum-shaped earth. However Anaximander's cosmology was a stunning intellectual achievement. To the Greeks, commonsense said the earth had to be supported by something - probably it floated on a vast ocean like a boat. The sun and stars likewise must be attached to a vault overhead - perhaps held up by giant pillars at the four corners of the earth like the roof of a temple. But Anaximander saw that the earth could simply hang in space, all its stuff having fallen as far towards a centre as it could go. Similarly, the sun and stars were rings of fire that stayed aloft having risen as far as they could rise.

Anaximander made further startling predictions about the place of humans in the cosmos. He argued that because the apeiron is infinite, existing everywhere and for all time, it must support an unlimited number of other solar systems, all presumably inhabited. So the earth was not a special act of creation – something which even most other Greek philosophers found too bold an idea to accept.

However the real value of Anaximander's scheme was that it attempted to explain the whole of Reality in terms of a single arche or causal principle - the separating out of a ground of pure potential.
 
To Anaximander, it seemed perfectly natural to begin with a state of unlimited everythingness, the apeiron, rather than an emptiness or a void. This everythingness then became a something through an organic process of self-constraint. After an initial seam had been opened up, a nested hierarchy of other divisions could follow, each building on the foundation of the last. First the hot and the cold began to move apart. This then started a process of drying and condensing that, in turn, led to the forming of light and heavy materials. Importantly, the stuff of the world remained essentially continuous. Nothing was being added or lost during this separating out. And nothing was actually being broken.

The apeiron was like a puddle of grey paint in which all the blackness began moving in one direction and all the whiteness in another. We could say that all the blackness expanded as much as possible, for example, and all the whiteness contracted. So a symmetry in the fact that half the initial grey wants to get darker and the other half lighter, but also an asymmetry in that the kinds of change are of opposing types. As each half develops towards its extreme, we would see the emergence of a jet black ground, a void, studded with a set of bright white points of light. So the potential for light and dark in the grey can be exploited to create a world of stark black and white contrast. Yet this puddle of activity – the apeiron – remains one fundamental stuff. The points of white and the backdrop of black are always ready to bleed back into each other, returning the puddle to featureless grey. 

Thus Anaximander had an intensely dynamic vision of what it means to exist. Reality is not made of static substances. It is the result of a continuous, never-ceasing, act of creation. The structure of the world arises out of a ground of potential due to divisions that produce further divisions. Each new separation opens up fresh possibilities for further development. Soon there is a range of basic building materials such as fire, air, water and earth.

To ordinary folk, these stuffs look to be fixed substances. It seems that the difficult part is to create them, but once made they should last forever. However Anaximander says this is an illusion. The fundamental stuffs merely represent the limits of a separating out process. If you were to ease the internal web of pressures - slacken the effort that keeps the blackness and whiteness moving apart - then the structure of the world would collapse. This complex hierarchy of development would subside like a punctured balloon. Fire, earth, air and water would all dissolve back into their ground state of formless potential again.

Or to talk about it in more modern terms such as mass, energy, time, space, particles and forces, all these would melt away. The Universe is not something you can simply fabricate and then step back to admire. A God could not decide to rest on the seventh day. Creation has to keep running or else it dies.
  
This is why we talk of Anaximander's causal picture as being organic rather than mechanical. There is both growth and decay. That which comes to exist may seem substantial enough, yet it arises out of a process, and can be lost with the relaxing of that process.

anaximander's logic

Think again about the various unusual features of Anaximander’s world scheme – least ways unfamiliar to modern cosmological theorising. The ground of all things, its initial “cause”, is not anything definite but just a potential, an unformed vagueness. The vagueness of the apeiron is so radical that it is neither a nothing nor even an everything. It is only the potential to generate every kind of thing that is later found to have crisply particular existence. Vagueness is neither organised nor disorganised, neither a whole nor a set of parts. It is not even a ground or a state or a realm. It is beyond all such tangible thingness.

This idea of absolutely naked potential is a difficult one to grasp. It certainly does not fit with the way of thinking in the Western tradition. For us it is simple black and white, yes or no – the law of logic known as the excluded middle. Something either is or it isn’t. There are no shades of grey. Or even if there are, then the greyness can be measured to whatever degree of precision is required.

Another thing that marks Anaximander as an organicist is his holistic approach to causality. Holism or systems thinking is the idea that while the parts make the whole, the whole also makes its parts. Causality in an organised system acts top-down from the global to the local level as well as bottom-up from the local to the global.

The ordinary mechanical view of a hierarchical system is of something constructed from the bottom. You take a set of fundamental parts then build them into something larger. A bunch of bricks makes a house, a bunch of houses a city. A bunch of cells form an organism, a bunch of organisms an ecosystem.
   
Causality moves in a single direction and it works by discrete steps. New qualities or properties pop out with each new level of structure. Indeed it is the emergence of such novelty that helps define the levels of a hierarchy.

The classic example is the step from an H2O molecule to water.water molecule There is nothing liquid or wet about a single isolated H2O molecule. But put a whole bunch together – a sufficient quantity – and you get the sudden emergence of a new quality. The lower level of single molecules provides the cause, all of the cause, while the next level of molecular chemistry provides the effect, all of the effect. And of course this sharp distinction fits nicely with the general logical prohibition against vagueness. A property like liquidity is either present or not present. In a single molecule it clearly is not present. Yet this crisp division of cause and effect also sets up our familiar paradox of appearing to be getting a something out of a nothing. First, no wateriness of any kind, then hey presto, its instantaneous emergence in a collection of H2O molecules.
   
Anaximander was imagining quite a different route to complex hierarchical structure. In his tale of the evolution of the apeiron, both the whole and the parts developed to definite crisp order together. The local did not have to come before the global, the totality of causes assembled before the appearance of the totality of the effect. Instead the whole and the parts grew in a process of continuous negotiation. Yes, there was difference between the bottom-up and the top-down causal story. While the parts might construct, the whole did its work by constraining. It set limits, boundaries. And the downward pressure exerted by crisp constraints was what helped the parts develop their increasingly focused existence. 

Let’s run through the story again. In the beginning was the apeiron – pure vagueness – a place with neither wholes nor parts, which was neither organised, nor disorganised. Then a first gentle, almost imperceptible, tendency to separate into the warmer and the cooler manifested itself. This was not a thunder and lightening production like the Big Bang – symmetry-breaking as a deafening shattering of a void. Instead it was an organic swell which, once started, grew of its own accord.

And once a first tendency had become established, a series of others could follow. The heat began to dry its part of the world. It split off into gradations with the driest heat rising to become bright fire, the damper remaining as the air. To the other side, the wet and heavy cold was separating into water and earth. All the while there was interaction between the emerging levels of structure. The increasing fire in the sky drove the increasing evaporation of the heavy earth, baking much of it to hard rock. Water was rising to make clouds that then got banged together by the winds to make rain. The wheels of fire became shrouded by obscuring layers of air, creating definite rhythms of day and night as sun, moon and stars appeared to roll around the sky. From vague potential arose a world of increasingly sharp order, with crisp parts interlocked into a crisp whole by a coherent, self-stable, web of causal interactions.
   
The mechanical view is that a pile of structure rises up on fixed foundations. The organic view is that a separating tendency feels out its natural limits and this finding of global boundaries in turn sets up strong constraining pressures on what is still happening within. So the growth of hierarchical order becomes involutional – the rise of crisp detail inside the boundaries of a wholeness – rather than a pile of happenstance blindly building its way ever higher in a space which is in fact a nothingness, a place of no context, a place where all outcomes are thus accidents. Think about the way whorls of turbulence arise to pack a stream when its flow is constricted by its banks. As the boundary constraints tighten, local features erupt on all scales. Whorls, large and small, froth into being.
   
It is the circular, or rather interactive, nature of this causality – the balance of top-down constraint and bottom-up construction – that ends up making the emergent system robust. Quite naturally we don't like the idea of building things on foundations that are not solid. Bricks, cells, atoms – as any mechanically-minded person will argue, the stability of our materials seems to offer our only real guarantee for the stability of any structures constructed from them.  But in an organic view of causality, it is the wholeness - the developing cohesion of the system - that fixes the identity of the parts. So the stability of things does not exist at a particular level. All levels of a hierarchically-organised world grow in stability as a result of the interlocking web of interactions between levels. 
   
Yes, this contradicts what we said about the threat of Reality subsiding like a busted balloon. However there was a crucial “if” in that assertion. The organic view says that a system is robust because its cohesive global order is locking its local structure in place. We can even say that the global order becomes the running memory for what the system should be. If ever released from this global or top-down constraint , the parts would indeed begin to disintegrate. They might even turn what we earlier called quantum haywire.

Try to isolate a physical location by taking a Planck-scale measurement of what exists at that spot and we in fact find that the physical values of the location – like its mass, its speed, its energy – go crazy, uncontrolled. This is the case even if we are measuring a scrap of empty vacuum. But in a mature system, with a developed causality, all the scales of organisation have become locked into each other through their shared history. The system would have a memory that can’t simply evaporate. So the system can decay or senesce perhaps – unwind slowly to a death, becoming more forgetful with old age. However only an instantaneous and complete amnesia would leave the parts unsupported and so see them fall out of crisply developed being.
   
turbulent streamAgain think of a stream. Take away the stream banks and the whorls of turbulence would immediately disappear. But stream banks can’t be removed just like that. In nature they change their shape only relatively slowly. And so patterns of turbulence tend to persist, a fragile creation, but enduring nonetheless.

This brings us neatly to the third quirky feature of Anaximander’s metaphysics. As well as suggesting vagueness as an extra dimension to Reality, and taking a holistic view of causality, his scheme depended on the continuous consumption of the apeiron. Both heavenly fire and earthly matter were being used up in the business of existing. So like a stream needs a continuous flow of water through it to produce its turbulent whorls, the world would have to keep separating out more apeiron to keep the whole production going. Fortunately, said Anaximander, the supply of this vague potential was infinite. Or rather boundless, which is a subtle difference. But anyway, there was always enough apeiron about to generate an unlimited number of worlds.
   
To modern minds, this kind of cosmological thinking flies in the face of reason. One of the greatest heresies of recent times was the steady state theory of the Universe put forward by the British astronomer, Sir Fred Hoyle, among others. First proposed in 1948 to explain the discovery that the Universe was expanding at the speed of light, it was argued that new material must be being continually fed into the Universe to prevent it diluting away to nothingness. Indeed, it was the “negative energy” of the expansion of space – the yawning of a void – which drew forth an exactly matching amount of positive mass in the form of a quantum roil sufficiently energetic to generate new hydrogen atoms. This extra gas eventually condensed into new stars and new galaxies, plugging the gaps and leaving the Universe looking eternally much the same, even if it was always growing larger.
   
In physics-speak, Hoyle was claiming that the Universe was an open system. A dissipative structure. It drew energy – or at least whatever material from which it was actually constructed – from outside itself. So like a stream, it existed by feeding off a flow.
   
However fundamental physics likes to deal only in closed systems, ones in which all the materials are accounted for from within, sealed as if in an air-tight flask at the moment of creation, and so closed to any further outside influence. This fits with a mechanical view of things. How can a causal explanation be considered complete unless all the causes are captured in the one scientific snapshot of the system? Everything that happens in the subsequent history of the system must be seen to follow from stuff that is already present, not supplied from some mysterious outside – as if by a whimsical hand of God!

So open system theories are the left to the more provincial kinds of physics, those that deal with thermodynamics or chemical processes. Certainly there is a place for open system modelling in the scientific repertoire, but not where physicist or cosmologist are getting down to the brass tack fundamentals of existence.
   
It was for this reason that there was great sigh of relief when the Big Bang theory happened along as an alternative. It was a simple closed system story. Everything that existed got made at one single instant. All the complexity that followed was simply a straight-forward consequence – an unfolding of possibilities already present.
   
Well, of course, as it has transpired, Big Bang theory is not so straight-forward as first envisaged. A quantum fluctuation out of nothing has become the localised collapse of an inflaton field. The Big Bang – a derisive term coined by Hoyle to laugh off this upstart theory – has come to need some kind of larger context, an outside. However it is still largely a closed system story, especially if theorists manage to make the Big Bang the start of time as well as space. Atoms and void, mass and gravity, were manufactured at an instant in balancing quantities. Everything since has been the unwinding of a system already constructed.

So, the Big Bang version of events was precisely the kind of theory which physicists were primed to accept as fundamental. Very quickly the steady state theory came to be seen as an obvious mistake and those who continued to fight for it, like Hoyle, became marginalised as cranks. Steady state theory with its open flow of material to keep the Universe in equilibrium simply had the wrong kind of logic for the creation problem.
   
For the organicist however, open system thinking is just as natural as closed. A living system is closed in some senses. Skin, shell and membrane wall off an internal world against an outside world. But an organism also needs a flow of energy and materials through it to maintain its shape. The closed order needs to be fed. So perhaps biological theories that combine the open and the closed might have something to say to the cosmologist? Maybe the Universe forms itself something like a living entity to survive as a localised spot of order in a wild realm of inflaton energies, a dimensional structure within some type of dimensional roil?
   
Certainly vagueness again comes to the rescue of the organicist. If openness and closedness now exist as crisp facets of our Reality, then they must also both have existed as potentials in whatever vagueness we originally sprang from. Yet because this vagueness is the ultimately murky state, there would have been no detectable difference between the two choices. A tendency in one direction would have looked much the same as a tendency in the other.
   
This sounds like so much word play. But it is being said quite seriously. As we shall see, the mechanical approach to explaining Reality always stumbles into chicken and egg paradoxes because causation is seen as one thing leading to another. There must always be something already in crisp existence to allow the first crisp developmental step. But organicism with its extra dimension of the vague allows both chicken and egg to arise together. All that is demanded is that they are exactly symmetrical – or rather asymmetrical – kinds of fate.

For vagueness to become developed, it must grow in balancing directions like Anaximander’s hot and cold, dry and moist, fire and earth. So open and closed systems – if found to be asymmetrical partners – would be a natural kind that could thus begin to arise from vagueness without one needing to exist prior to the other. Instead they would come to exist crisply as opposing destinies, rival poles of Reality, by a long process of separating out.

modern misunderstandings

We have to be careful not to read too much into Anaximander’s philosophising about the world. After all, only a single fragment of what he supposedly wrote survives, a poetic passage that seems to describe how all things arise from the apeiron in balancing quantity, and must also eventually decay back to this primal vagueness – “Whence things have their origin, thence also their destruction happens; as is the order of things, giving justice and reparation to one another for their injustice, in conformity with the ordinance of time.” Well, it probably loses a lot in the translation.
   
But equally, Anaximander’s thinking is usually interpreted from the standpoint of the modern mechanical approach to Reality and so mostly what strikes scholars are its failures to fit with this tradition in logic. Anaximander is remembered in undergraduate textbooks as merely one anaximander of three famous Miletian philosophers who tried to identify the fundamental substance of the world. Thales said everything formed itself from water. Anaximenes said it was air that was the basic substance. Anaximander came along with this odd-bod notion that everything was made from some boundless stuff known only as the apeiron. Serious metaphysics did not get going until the Athenian philosophers, Plato and Aristotle, realised that form was just as important as substance in the making of worlds.
   
Yet even Aristotle’s legacy is badly misrepresented by modern attempts to see just how mechanical he managed to be. It could be argued that Aristotle ought to be considered as Anaximander’s most direct heir, someone who was trying to negotiate between the rival organicist and mechanical threads in the growing cacophony of Greek thought.

Aristotle’s many famous mistakes – such as his teleological approach to causality in which ends could create the means – may in fact be successes of organic insight. And in celebrating his greatest contributions – like the law of the excluded middle so central to modern logic – we may be overlooking the counterpoints he also made, such as that middles actually need to be excluded first. A binary state of either/or is only true for certain crisply established situations.
   
For example, asked Aristotle, what is the case with statements such as there will be a sea-battle tomorrow? Is this true or false? The law of the excluded middle suggests it must be one or the other. But Aristotle says that even if we can see the fleets lined up, such things count only as a vague potential until they either actually happen or don’t happen. As some commentators recognise, Aristotle was arguing for a triadic logic in which the vague was another dimension to Reality, another direction against which the existence of things can be measured!

We could go on about exactly who said what in ancient Greek philosophy. And it indeed matters as Greek thought is the conscious bedrock of Western rationality, the crucible of our scientific imagination. But all we need to see here is that quite a different idea of what was logical seemed obvious to at least one thinker at the very dawn of recorded thought. So we can ask why do we now say Anaximander? Who?
   
As it happens, Anaximander’s organicism was not that extraordinary for his time. In his talk of a seed of order erupting in the midst of a formless sea, he echoes the creation myths of other cultures such as Hinduism and Taoism. This is hardly surprising given that early civilisations lived by agriculture and husbandry. Plants were seen to sprout, animals to be born and develop, seasons to ebb and flow in cycles of heat and cold, damp and dry. Growth was both natural and fundamental.
   
Anaximander could also draw on ancient Greece’s own creation myths. In pre-classical times, the poet Hesiod told how the Greek gods were born out of an initial shapeless state of chaos. The first gods were the most general ones such as the earth and the sky, love and the underworld. These elemental gods then coupled in various ways to produce a succession of steadily more human-like gods such as Zeus and Venus. Divinity became increasingly constrained in its form as the gods gave birth to a host of demi-gods then eventually mortal humans. Anaximander’s scheme had the same kind of logic. He just was more scientific in replacing gods with abstract entities such as the formative apeiron and the process of separating out.
   
Even the detail of Anaximander’s vision of development can be found in other great intellectual cultures. The Buddhist theory of paticca samuppada – dependent co-arising – talks about just the same kind of mutual causality where complementary tendencies emerge together, each driving the growth of the other in an upward spiral.
    
However what we want to pursue here is not who should get credit for being first with an idea but to ask what now counts as the best approach to making sense of the puzzling fact of existence?  So does organicism have anything at all to offer the hard-nosed mechanists of science today?

dichotomies become dualities

With the idea of a separating out, a dichotomisation of a vagueness, Anaximander had struck on a powerful mental image of reality. His weakness in the eyes of those that followed was perhaps that he was still thinking in terms of simple physical dichotomies. Or as we might say, in terms of substances.

Later philosophers looked for still more generalised and abstract principles. Out of this effort came the host of contrasts that have become the familiar furniture of Western rational thought. Chance and necessity, continuous and discrete, change and stasis, integration and segregation, parts and wholes, passive and active, structure and process, construction and constraint, specific and general, mind and matter, substance and form – a lengthy list of dichotomies that describe the logical limits of what might be the case concerning Reality.

Some of these pairings seem more basic than others. What makes a good dichotomy is that it is not just symmetric – a balancing pair of directions – but asymmetric. The two poles appear as opposite as it is possible to be in their nature. Go towards one end and you can see you are in a different place – so different as to seem no longer to have any connection with the destination lying off away to the other side.

For instance, with the dichotomy of chance and necessity, the fate of some event is being described as either completely caused or completely uncaused. Or to be more accurate – stepping back to take the system-level view – either completely constrained or completely unconstrained.

If the localised event is a coin toss, then this can be carried out in a maximally chance or uncontrolled fashion. We can flick it high and fast. Alternatively we could take the same coin and place it heads up with great deliberate care. So there is a spectrum of possible control linking the random to the determined. A dimension that can be travelled in either direction. But as we reach the extremes, we seem to arrive at places that are as different in their character as can be. So different that chance and necessity look to be not just opposites but disconnected, unrelated.

symmetry of yin yang The more usual mirror image notion of symmetry is a boring way of being opposite. A static reflection. There is no development into different kinds of things after the two halves are separated. It takes an asymmetric divergence to produce two directions that are interestingly rich with new causal possibilities – two halves with opposing emergent qualities.

Consider another classic example, the dichotomy of parts and wholes. Or as we might also put it, the local and the global. A simple symmetrical move in space is just bidirectional. If we move up and down, or to and fro, nothing much really changes. The world still looks the same kind of place. As Heraclitus argued, going up a hill is much the same as coming back down that hill. A world composed of only this kind of mirror image activity would be a meaningless flux. Moving along a line is moving in some kind of dimension to be sure, but it is a thin dimensionality. A dichotomy of hierarchical scale, such as parts and wholes, the local and the global, offers a thick dimensionality.

Travelling between the extremes involves qualitative change. To be maximally local on a scale of existence is to become absolutely located in one spot and crisply not present at any other available spot. To move in the other direction and become maximally global is to grow to be everywhere at once – and thus nowhere in particular. So the local and global are certainly symmetric in the sense of lying in opposite developmental directions. But as with chance and necessity, the different poles are asymmetric in their nature. They each sharpen their own identity by constraining the feature that distinguishes the other. The locales are as little global in their extent, their connectedness, as they can manage to be, while the global level returns the favour by avoiding all hint of locatedness. So as destinations they become as little alike as possible.

The continuous and the discrete was another key asymmetry in Greek thought. We can see that the continuous~discrete is another way of looking at the local~global distinction. To be continuous is to be seamless with some greater whole. To be discrete is to be an isolate part. So what is being emphasised is whether the relationship between the local and the global should be considered broken or unbroken.

It is no accident that the continuous~discrete became the most important dichotomy to the next generation of Ionian philosophers after Anaximander – thinkers like Parmenides, Zeno and Democritus. By focusing on the broken~unbroken question, it was the point where Greek philosophy turned decidedly mechanical in its flavour. It was decided that Reality had to be fundamentally broken or unbroken – there were two possibilities and only one of them could now be true.

This was a very different story to Anaximander’s organicism. For the organicist, the question does not arise as Reality springs from vagueness and so is neither broken nor unbroken in its essence. The alternatives of seamless continuity and isolated discreteness are simply states to which Reality can aspire. This means that both limiting conditions remain equally “fundamental”. And furthermore, the limits of a dichotomy are defined as the very places that a development can’t reach. But some hundred years after Anaximander, others were reading dichotomies to stand for concrete alternatives that afforded no middle ground.

Let’s pause to get a grip on this. As it is a crucial difference between the organic and the mechanical.

For the organicist, crisp Reality arises by a process of development. It may begin by striking out in many directions. Its impulses to separate are unoriented. But then it strikes a fruitful seam, some hidden degree of freedom, and the vague’s creative ardour can dissipate itself in neatly counter-balancing directions. The poles of the resulting dichotomy are then the emergence of an upper and lower boundary to growth. The counter-tendencies go as far from each other as possible.

But this is a game of diminishing returns. As the local becomes cleansed of the global, or chance of necessity, or the objective of subjectivity, there is less and less to fight against. A pressure of constraint inflates the dichotomy, but it can only stretch so far before the driving force thins out. The question then becomes does this bubble of activity have a membrane? Is the boundary that appears to mark the limit itself something real? Is it included? Or does it by definition always lie just beyond the grasp of the real – and so counts as something unreal, something strictly in the imagination of the modeller?

We can illustrate the two approaches to limits with a few examples from mathematics – examples which also happen to show why the continuous~discrete remains the most problematic dichotomy in mathematical thought.

Take the simple matter of defining a number. The mechanical view of a number is that it just exists. It is a discrete point on the continuous number line. Its value never changes. Look away and it won’t fall apart. It is an eternal part waiting to be woven into some larger mathematical construction.

But an organic view of number says a particular value can only be constrained towards an existence at a point. It takes an active process of development to keep a number pinned down. For example, the number one is a little fuzzy around its edges. Yes, we can say it is about halfway between zero and two. But to locate it more closely, we have to start adding noughts after the decimal point. To avoid confusion with other possible numbers like 0.999999 or 1.000001, we would have to identify it as 1.000000, the place again halfway in-between. Yet that still leaves a degree of uncertainty. An infinity of noughts would be needed to eradicate any lingering vagueness. So one-ness is the limit of a journey in which we find that the number we seek cannot be anywhere else. We never actually grasp the number, just home in on the only place left.

The same existence versus approach dichotomy applies to the idea of the infinite. The mechanical view takes the “not-finite” to be a discrete mathematical object. Infinity simply exists as a passive fact. But the organic sees it instead as referring to a mathematical operation that is without definite limit. Start counting and you can imagine keeping going continuously forever – whatever forever might mean. So the goal can certainly be imagined, but it would be unreal to think that any actual physical system could pursue it ad infinitum. A computer set ticking of digits to the end of time would still not complete its journey. For the mechanist and the organicist, terms like infinity and the infinitesimal – or even the Infinoverse – mean different things.

asymptotic curve The organic view of limits is intensely irritating. We can feel the frustration of only being able to look but not touch. The harder we push, the closer we can get. But it is also a game of diminishing returns. To use another mathematical illustration, it is like an asymptotic curve that descends through the space marked by a y-axis, yearning desperately to intersect the x-axis at some discrete point. But the curve flattens exponentially as it approaches. It can spend infinity getting infinitely closer to the crisp perfection of the x-axis limit, yet will never actually grasp it.

As an aside, we should note that the x and y axes are themselves an example of a dichotomy. As directions in space, they are special because the x dimension shows no trace of y-ness within it. Any y-ness has been so constrained that it can only appear as a discrete point of intersection. From within the realm of x-ness, the freedom to move that defines y-ness can no longer be seen. And of course, the same applies the other way round. As an orthogonal dimension, set at precisely right angles, the y-axis stands purified of x-ness. As the other pole of a dichotomy, it is as little like a state of x-ness as it can manage to be. Of course space comes with three dimensions – there is the z-axis to consider as well. So a trichotomy rather than a dichotomy?

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