logic> dichotomies
Why does something – anything – happen?
This is a wonderful question and it is amazing how little we discuss
such things.
It is also a modelling question. We cannot of course know the world and
its reasons directly. But we can suppose. We can develop ideas that
seem to explain, or at least predict.
The normal way of thinking about causality is what I call mechanical
logic. Or to stress the fact that it is an interlocking package of
beliefs, I also call it RAMML – standing for its key
components of reductionism, atomism, mechanicalism, monadism and
locality.
But here I am setting out an alternative organic logic. A view of why
things happen that depends on asymmetric dichotomisation.
In the mechanical world, collections of parts combine according to
their properties to construct outcomes. A cause produces an
effect in machine-like, step-by-step, fashion.
However in the organic view, parts and wholes swim into
existence
together as aspects of a single holistic system. The causality is
bootstrapping or self-organising. And every development begins in some
vaguer state. Formed structure arises out of a pool of potential. You
don’t need concrete materials – already existent
atoms or components – to get the ball rolling.
Holism is a reasonably familiar idea. Vagueness much less so. But the
real heart of the story here is the dichotomous nature of the
developmental process. Things happen first by separation and then by a
mixing of the separated. And the dichotomisation is asymmetric. The
only possible way to divide a vague state of potential is to separate
in two complementary ways. Every move creates a counter-move; every
action, a reaction. To make a figure, you must also make a ground.
Other terms for this central process of asymmetric dichotomisation
might be a symmetry-breaking or phase transition. Or we could talk
about dialectics, antimonies, synergies, yin-yang or paticca samuppada
(dependent co-arising). There are many discourses that recognise there
is something different about organic causality.
But I prefer to use dichotomy as this is the most ancient and general
term. And then asymmetry stresses the fact that the initial symmetry of
vagueness is not just broken, but broken in distinctive fashion.
what is a dichotomy in simple terms?
Dichotomy is Greek for cut
in two. But split an apple in two
and you simply have two halves of one thing. This is a symmetrical
division. Greek philosophy developed by breaking something like an
apple into two quite different seeming things.
So
Plato and Aristotle would ask what
is the essence of an apple? Is it a particular kind of stuff? A
lump of some substance? A collection of atoms? Or does its essence lie
in its form? Is appleness all about the way some stuff is
arranged? Does the essence of being an apple reside in a
particular set of qualities that
must be possessed, such as being juicy, crunchy and round?
The Greeks came up with many enduring metaphysical dichotomies.
Substance~form was a
biggie. Other still familiar ones are atom~void, stasis~change,
chance~necessity, being~becoming, particular~universal, part~whole,
discrete~continuous, quantity~quality, body~mind...the list goes on.
And today we could add many more. Such as local~global,
integrate~differentiate, information~entropy,
figure~ground. Even mechanical~organic.
You can see from this list that it is not much of a dichotomy to say x
and not-x.
Like fat and not-fat, or fast and not-fast. Or even fat~thin,
fast~slow. A dichotomy strikes a chord
when the two extremes seem both complementary and different –
asymmetric. The two are opposite in some deep qualitative way, not
merely in a quantitative fashion. Yet even being so different, they are
necessary to make a complete, integrated, whole.
So the local is pretty much defined by the fact it
is not globally spread. The stationary is pretty much defined
by the fact it is not moving, Substance would be pretty
much defined by the fact it is a stuff without yet the imprint
of
a particular form. By the same token, the global has nothing that seems
tied to some local happenstance. The changing is defined by the fact it
is managing to leave something standing behind. Pure form is that which
is so
insubstantial as to appear almost as a wish or an idea - a latent
desire of nature.
In each case, one is defined as the complete absence of the
other. And yet it is hard to imagine any real thing which does not have
both combined. An apple must be composed of both substance and form.
For an apple to be moving, there must be a world that is standing still
(rather than moving with it and so leaving the apple looking as though
it stands relativistically at rest). For an apple to be located as a
particular instance of an apple, there must be a global context that is
all the other places that the apple is not (yet where it could
have been as a crisp
possibility).
Once you start looking for them, dichotomies are everywhere. You might
think that this is merely evidence of a particular metaphysical
affliction - dichotomania! We humans like dividing nature by simple
numbers. There are the three dimensions of
space,the four corners of the earth,the five powers
of Taoist wu-hsing (wood, fire, earth, metal and
water), the seven deadly sins - you name it.
But I hope to show that only dichotomies are fundamental. All other
divisions into a this and a that and then some number of others are
superficial and unstable. The larger sets
will always reduce to a more fundamental dichotomistic
description. Space for example becomes the dichotomy of space~time - or
the located and the changing. The five (or however many) elements
reduce to the larger dichotomy of substance~form - all the many kinds
of stuff and then also all the many kinds of possible organisation.
Mathematicians might note that this is exactly the
conclusion of category theory. Every kind of mathematical construct
reduces to an object and process, or object~process.
So as a way of modelling the world, chopping it up in ways that make it
comprehensible, the dichotomy is fundamental. Two-ness rules
for a sound reason. We can claim further proof of this from
information theory. Binary choices are the most efficient possible way
of dissipating uncertainty - this is the famous 20
questions principle.
However the big claim here is that a
dichotomy is not just a division
imposed on nature by a modelling mind – a useful
generalisation we create to make the world seem a simpler place. It is
a causality, a model of why things happen. Dichotomisation is the
actual process by which a world makes itself.
So the reason we find
ourselves dichotomising is not because we have made some free choice.
If thinking is a process, then dichotomising is going to have to be the
most effective and natural way of our thoughts forming. And indeed that
is essentially the story when it comes to accounting for the evolution
of human brains and human minds.
It is dichotomies everywhere you look.
The left and right brain as figure and ground style hemispheric
processing. The what~where division and the sensori~motor division. The
split of speech into syntax~semantics and words~rules. The overall
divide of cognition into attention~habit and ideas~impressions. The
nature~nurture or biology~sociocultural dichotomies. All mental
distinctions and abilities arise through the dichotomisation of less
well-formed potentials. So we don't impose dichotomies on nature.
Instead by dichotomising we are going along with the flow of nature.
Finally I will argue that the many dichotomies – and the list
is vast – all reduce back to a single ur-dichotomy. Well
really it is a pair of dichotomies at right angles to each other
– asymmetrically arranged!
The really important dichotomies are substance~form, local~global,
matter~mind, atom~void, figure~ground and discrete~continuous. As we
will see when we get
to scale hierarchies and semiotics, all of
these are really different ways of saying much the same thing.
And
local~global emerges as the ur-dichotomy because naked scale is the
most basic measure of all existent things.
But if there is an ur-dichotomy that is the fundamental description of
the way things are,
there must also be an
orthogonal axis of description to track their development.
As Aristotle argued, the world is composed of both being and becoming.
The synchronic and the diachronic view. So we have to have
a second
ur-dichotomy that describes the developmental trajectory. And this is
the vague~crisp.
The
ur-dichotomy is dichotomised to give us local~global, the view of the
instant, and vague~crisp, the view of the journey. And in terms of the
1,2,3 story, local~global is the scale-breaking, the triadic
hierarchy, the crisply developed end-state of any process of
development. Vagueness is the monadic oneness that
lies before the dichotomisation, before any development has
got
going. Think of this as a cone. Two ur-axes are needed to describe it.
And there is a progression from simplicity to complexity. As a system,
it is all perfectly logical and beautifully complete.
notation
Before setting down the axioms of organic logic, first a quick comment
about notation. The tilde or squiggle here
“~” was suggested to me by Scott Kelso.
I have adopted it to stand specifically for an organic
dichtomy where a potential has become separated, however not actually
broken. As we can see, there are then just three
other possible ways of viewing
a
dichotomous division. And we would want a different notation to mark
each.
To start with, there would be two forms of a broken or
mechanical dichotomy – one
monadic, the other dualistic. The monadic view says that reality has to
be one thing or another. This
is a binary choice and it can be marked with a Sheffer stroke
– “|”. So if we write substance|form,
then we are saying that an apple must be fundamentally one thing or the
other. Either its essence is a substance, a set of molecules or some
such stuff, or its essence is its
particular qualities, the result of some special state of organisation.
But we can also take a dualistic stance and say that reality is
fundamentally both. We would mark this dualistic position with a slash
– “/”. So when we say mind/body, we are
following Descartes in saying that reality breaks into both categories
of existence. They are both equally fundamental. Even if this claim
then
raises some causal paradoxes, like how are the two realms
then connected?
For the sake of completeness, we may as well throw in a fourth symbol,
the hyphen, to mark the most general case where we are not really
making any strong claim about the nature of the relationship between
the two poles of a dichotomy. So substance-form and mind-body would
just say
that reality seems to be broken in this kind of way but we are
not yet saying
anything definite about how the division works.
the twelve axioms of organic logic
Now we are at the heart of the whole site. These are the
twelve axioms of organic logic that I wish to
defend.
1) Dichotomies have vague beginnings.
2) Dichotomies are dynamically developing not passively existent.
3) Dichotomies develop in asymmetric fashion.
4) Dichotomies thus depend on scale.
5) Dichotomies always develop in both their directions at the same time.
6) Dichotomies are separations not breakings.
7) Dichotomies involve separation but also the mixing of the separated.
8) The middles of dichotomies have scale symmetry.
9) Dichotomies have only two poles because three or more is unstable.
10) Organic causality is hierarchical or holistic.
11) Organic logic is dichotomous with mechanical logic.
12) Organicism is only modelling.
Continue to the axioms
of organic logic and then the search for the
ur-dichotomy.