I think it is safe to say that the notion in the field of logic of the "excluded middle"
stems from our sensory systems and in particular the visual system.
Neurocognitively, if I present one part of our brains with a complex line drawing, that is exactly what is perceived.
When I present the same drawing to another part, a part concerned with 'dot' precision and so concerned with extracting
details from a 'field', the attempts to identify particulars can become 'confused' when the complex line drawing
is made-up of lines such that it creates a perception of TWO objects occupying the same space; for example the
Necker Cube diagram.
Since the diagram 'breaks' the rule of the excluded middle, where A and ~A (aka B etc) are summed to equal zero
(and so EITHER/OR concepts, no sharing of the same space by opposites), the brain compensates by taking the static
diagram and making it dynamic by oscillating between the two images and so retaining the excluded middle 'rule'.
This of course creates an 'illusion' where the oscillation is NOT representive of reality but an attempt to interpret
reality within the bounds set by the nature of our species. This 'approximation' reflects a transition from an
analytic, dot, approach to a more dialectic, field approach (timing is used to resolve the issue and so a sense
of history).
This same sort of compensation is present when I introduce a complex sound, where the 'dot' biased brain will interpret
the sound as a sequence of consonent sounds, jumping from one to the other (the jump emphasing the 'dot' nature,
the discreteness of that part of the brain doing the analysis)
When we introduce the concept of trancendence as a property of the neurology, we introduce the allowance for the
emergence of mind from brain. Elsewhere I have speculated on this emergence as being a property of synchronisation
processes in the brain as different from the more dendrite-located 'filterings' of data by habits 'encoded' into
the dendrite tree (in the spines of the dendrites).
This emerged mind recruits the neural networks of the brain but functions at a more abstract level, focusing on
'out there' as well as 'in here' in a very intellectual manner as it too attempts to map reality but more so from
a universal context.
The recruitment process means that day-to-day, concrete, brain processes are abstracted to the level of mind and
as an example we can identify the exclusion principle identified above, a property of brain sourcable to sensory
systems, being expressed as a property of complex interpretations of reality, in particular the Pauli Exclusion
Principle which basically 'says' no two 'dots' (in this context - electrons and other 'fermions') can share the
same 'space'.
Another example of the concrete being recruited to describe the abstract is where we mediate between stimulus(A)/response(~A)
and in doing so oscillate between stimulus/response as we attempt to modify and/or derive a representation of the
whole stimulus/response process.
In this realm of mediation the brain creates a habit/symbol of the event, all very 'concrete' stuff but when abstracted
to the level of MIND some interesting notions emerge. In particular is the notion of wave/particle duality in that,
at the concrete level, the combination of an oscillation across A/~A together with a degree of indeterminacy
on perception, will introduce distortions such that the pattern that emerges from the process reflects 'wave interference'
patterns rather than without indeterminacy where we get normal distribution curves.
This brain-level process has been recruited by mind to describe 'out there'. In fact the structure of the experiments
performed 'out there' are identical to the brain processes described above, where we take A/~A and oscillate -
e.g. left slit/right slit combined with a lack in observational precision - we do not look directly at the slits
but rather an impression device some distance away.
The indeterminacy reflects the transition from a unit approach (the 'dot', the single electron, photon etc) to
a statistical approach. In a statistical approach, being statistical, the basic unit of measurement is the
PAIR and as such we cannot identify 'sequence' order within the pair, only between pairs. This perspective
is similar to the one of the complex line drawing where as we shift from a focus on a dot to a field focus, dots,
so there are perceptual changes and resulting 'distortions' if we still try to perceive from a 'dot' perspective.
It is this indeterminacy, the distortion, that allows for the emergence of wave interference patterns, In other
words the method of the brain used to mediate/represent A/~A processes has been recruited by the mind without acknowledgement
of that fact, and is presented as if a direct reflection of 'out there' rather than an abstract representation
of how 'in here' processes A/~A distinctions combined with indeterminacy.
All maps of reality, no matter how abstract and seemingly 'objective', stem from the functions of mind that has
recruited and generalised the more concrete functions of brain; and so the patterns of the brain are recruited
by the mind and re-labelled in the process of abstraction. This sharing of the same space, mind and brain entangled
'in here', will lead to perceptions that, without validation, can lead to illusions/delusions regarding reality
and our place in it.
That said, the trancendence factor, a factor that allows for multiple personalities in the one brain, can also
serve as a source for mental expressions not directly locatable in the brain and these in turn can become
the 'concrete' elements of mind. However, as we find with computers, the expression of the software is still dependent
on the precision of the hardware and the use of binary representations, the A and NOT A as well as the dynamics
of the 'middle'.
These dependencies are identifiable in the brain where we see the workings of both analytical approaches (dot biases,
mechanistic, reversables, time is 'eternal') as well as dialectical approaches (field biases, theromodynamic, irreversibles,
time is 'begin-end'). The implications are that the dot perspective has emerged from the field perspectives as
a result of seeking precise details on sensations and in doing so has developed a world of its own besides allowing
us to 'refine' the field - this 'dot' process, besides being a source of transcendence, contains illusions/delusions
and we need to identify these to enable the continued development of the species and in particular we need to focus
on dialectical processes/logics to understand/enable further trancendences as well as transformations.
The following is very rough but it may aid in focusing on the qualitative elements we deal with re meaning in
that the IC is a set of ordered qualities we use to relate to 'out there'. Moving from 'yes' or 'no' to 'maybe'
(as reflected in changing lines in a hexagram) shifts focus from two valued to a perception of three valued logic
(this will change later as we get into the cyclic negations etc - see below) [in 'truth' we are dealing with fours
BUT the dynamics of the situation raises the issue of static and dynamic relationships sharing the same space and
to some degree representing threes when dealing with ACTUAL EXPRESSION and fours when dealing with POTENTIAL EXPRESSION]
To move to n-valued logic we move first from twos to threes.
In two valued logic the operations are:
~A : negation (NOT)
A V B : disjunction (inc OR)
A ^ B : conjunction (AND)
A -> B : A implies B
A eq B : A equivalent to B
In three valued we have T (true), F (false), and I (indeterminate)
In three valued logic we have the operations:
complete negation
cyclical negation
diametrical negation
conjunction
disjunction
quasi implication
standard implication
alternative implication
standard equivalence
alternative equivalence
What is noticable in the truth tables for three-values is that the truth values work using cyclic negation where
a value is shifted to the next lower one until you get to the lowest and then you shift to the highest. This reflects
the passage through the binary sequence of trigrams where the lowest (yin) loops around to become the highest (yang).
As such ~A is now interpreted as next-A rather than NOT-A.
Diametrical negation reverses T and F, leaving I unchanged. The negation is -A, minus-A.
The complete negation 'shifts a truth value to the higher one of the other two' and we read this as _A, non-A.
Negation Table form (from Reichenbach, H., (1998[1944]) "Philosophical Foundations of Quantum Mechanics"
Dover):
|
A |
~A |
-A |
_A |
|
T |
I |
F |
I |
|
I |
F |
I |
T |
|
F |
T |
T |
T |