logic - an introduction
Logic is about the way things happen. Indeed the way things must happen. But as
they teach in Epistemology 101, we don't know the world
directly.
We only model it. So logic is just our model
of causality. And there can be different models for different
purposes.
In these logic pages, I do three things. Mainly, of course, I want to
outline a
model of organic logic.
That is something new (even if its roots are ancient). But I also need
to put organicism in context by talking about its
competition – ordinary mechanical
logic. Or what I call
RAMML.
That is,
reductionism, atomism, mechanicalism, monadism and locality. Yes, good
old cause and
effect logic may seem a simple causal model. But only because
it is so everyday familiar. Mechanicalism is in
fact based on its own rather intricate set of assumptions about
the world.
Then I devote some space to the philosophical principles
of modelling as
well – because plenty of people have
never
done
Epistemology 101 and so are unclear about why it could be OK to have
more
than one
"true" model of causality. But first let's get stuck into the
story of organic logic.
organicism as one, two, three....
Organic logic breaks neatly into
three components because, when anything happens, there
must of course be the “1, 2, 3” of a
beginning, a middle, and an end. Some kind of initial conditions, a
process that is the change, and then the outcome which is when
things finally seem to have settled and so stopped happening.
Here is a quick
introduction to the 1, 2, 3 tale of vagueness,
dichotomies and hierarchies that are the three essential components of
any
organic sequence of development.
In fact organic logic is
more intricate. As the diagram suggests the three stages are themselves
divided in varying degrees, so that they have a oneness or monadicity,
a duality, and then a triality. Scholars of Peircean semiotics will
recognise this as Peirce's interpretive system of firstness,
secondness
and thirdness. But everyone else only needs to notice the nesting
of threeness here. You have the beginning, middle and end
needed to
tell a causal tale. But then there is also a change in the
structure of things
during this progression so that there is a singleness at the beginning,
a duality as things happen, and then a triadic state of balance marking
the final outcome.
As we shall see, mechanical logic instead assumes the story to be one
of a sequence of events rather than a progression or development. The
starting position is monadic, and so is the end state.
There is no increase in the essential complexity.
Instead change becomes almost no change because it is merely a
meaningless rearrangement of the simple. Though that said, the
inadequacies of the mechanical view (when
describing complex systems such as minds and universes) often does lead
to
the twoness of a dualistic split. A kind of proto-dichotomy.
This is then a first distinguishing mark. Organic logic is
irreducibly
monadic, dyadic and
triadic.
All three ontological alternatives work
together to make the system. Next let's sketch a quick picture
of these three before, during and after phases.
1) Vagueness
- for the
organicist, all happenings originate from the one
kind of stuff. But it is
not the usual idea of a stuff that we
would normally
think of as a suitable departure point for development – one
that
is substantial or crisply
existent. Instead it is some kind of vague stuff, a
nothingness that is also an
everythingness. In other words, a state of pure potential.
Anaximander, the first proper philosopher, called it the apeiron. The
boundless, the
unlimited. Plato talked about the chora.
Aristotle
talked about potential, and about being and becoming. Peirce
seems to have been the first to call it vagueness. In modern
philosophy there is a lot of discussion of semantic vagueness, using
the familiar example of the
sorites
paradox. But the vagueness we mean here is ontic
vagueness – an actual vague state of reality.
Vagueness is a beautiful idea. Mechanical thinking always demands crisp
beginnings.
The origins of something like a universe or a mind must lie in
something already definite. Something with concrete existence
itself. This leads to an ugly choice
between things like minds and universes either having to have existed
forever - to be eternal and uncreated - or to have
winked into being out of nothingness. Out of a void. And for
no particular
reason. But vagueness is like a state of everythingness. It is a raw
potential that is poised equally between existence and non-existence.
It is doing everything and nothing. And yet it must eventually become a
something.
So with vagueness as the starting point, reality can swim into
crisper being with a gentle ease. Abruptness is done away with. Well,
abruptness in the logic. The actual event of taking shape may be swift,
as it is with a phase transition or other forms of symmetry breaking.
Vagueness is a subtle as well as beautiful concept. It
is easy to misunderstand on first meeting, but
eventually it is sure to grow on you.
2)
Dichotomies - if
vagueness is the ground from which things spring, the
dichotomy is the twoness that
results from splitting this ground. It is the phase transition or
symmetry breaking step.
The idea of asymmetric dichotomisation is the
real focus of
this site. I am arguing that when you boil down organicism to its
causal core, it is all about the
driving force of a dichotomy. The dichotomy makes the separation that
then also
results in an integration, a mixing of what just got moved far enough
apart to become semiotically (that is, meaningfully)
different.
3) Hierarchies -
the third
component of organicism is the triadic structure of the hierarchy. As
Stan Salthe argues, a hierarchy is formed from the minimal structure of
two limits of contrasting scale and the interactions that take place
between these two limits. Salthe calls this model the
basic
triadic system (BTS).
Like a sandwich, you have
a top and bottom plus a jammy filling. The top level is the global
scale, which is also the realm of the large, the continuous, the
causally constraining. The bottom level is the local scale; the realm
of the small, the discrete, the causally constructing. The middle
ground is the filling in of all the possible scales in-between. In an
ideal world - one that has had the time to go to the heat death of
thermal equilibrium - this middle ground will be flat. Geometrically
empty. A void in other words.
If vagueness is the starting point for any organic development, the
hierarchy is the natural destination. It is the way all things must
end. And if vagueness is a kind of ultimately disorganised
everythingness, then the hierarchy is a kind of completely organised
nothingness. It would be for example an infinitely large universe with
nothing much left in it apart from some ultracold blackbox
photons, a faint residue of Beckenstein radiation.
So now jump to DICHOTOMIES, VAGUENESS or HIERARCHIES. Or if you feel really confused, perhaps start with a little HISTORY.