Brain hierarchy and the logic operatorsPosted in MindBrain Yahoo group by Chris ( email@example.com )
Hi all, some comments on tools of logic being 'hard wired'.
Through analysis of the manner in which our brains deal with paradox, using XOR to extract objects from complex patterns (the AND realm), as well as analysis of how, out of the neurology, we can elicit the qualities of number types used in Mathematics, so all of the formal logic operators are usable in the reflection of the development and maintenance of mental states.
I have emphasised before the notion of the IDM "Dimension of Precision" that reflects the general characteristics of information processing 'in here', with increasing precision in categorisation, and we can map onto that dimension all of the core logic operators showing a movement from the vague/integrated to the crisp/differentiated. Thus, the dimension of general-to-particular is mapped right-to-left and we overlay the operators:
particular ............ general
IMP ... XOR ... AND ... IOR
(missing are COIN, NOT, NAND, and NOR - all not necessary to make the point)
In paradox processing the more 'obvious' of these is the AND-to-XOR dynamic where we see a pattern in a complex line drawing and 'extract' that pattern to find it is 'paradoxical' in what we SEE is two forms trying to share the one space (e.g. Necker Cube). NO matter how much bandwidth we add, we cannot resolve the issue and so fall back onto the complement of bandwidth, time. So we experience 'oscillations' in the images as the stimulus/response elements of the brain tries to resolve things one step at a time!
The XOR operator reflects the ability to extract parts from a whole, to clearly differentiate those parts and as such reflects the development of a set of elements that make-up the whole. It can have 'issues' when it sees in something more than what is there such that that 'something' is interpretable as 'non-reducing'.
The AND operator applies to the integration of many into a 'whole' without the application of a label - the application takes that implicit whole and makes it explicit in the form of a represention - the label. IOW we differentiate WHOLES by labelling them and so REPRESENTING them in our XOR-realm but not accomodating them in that realm.
The mapping of general to particular introduces a focus on mapping from the symmetric to the asymmetric, and the IMP (Implies) operator is the only operator that is asymmetric in form. The IMP operator reflects an in-built trait of using implication to derive information. Its asymmetry is in the consequences of its actions. For example, lets look at the cartesian coordinate system we use in Mathematics etc.
If I assert a dimension (+/-, and so a dichotomy) and label it as the X axis, and assert it to be fixed, so I have set down an initial context. If I then assert another dimension, 'orthogonal' to the X axis and call it Y, GIVEN Y I can imply X - but given X I cannot imply Y.
As we add dimensions so each new dimension IMPLIES all that is 'before/below' it. As such, using X,Y,Z dimensions (or, here abstracted into the notion of SETS with all points on the dimension being elements of the set - the set relations fall into the concept of subsets etc) we can assert:
Z <= Y <= X, and in its purest form we have Z = Y = X. I can work backwards in deriving implications but I cannot work forwards. There are QUALITATIVE differences here, even if, using the quantitative, Z = Y = X, there is still present a hierarchic format such that I can NEVER imply Z given X, nor Y given X, but I will ALWAYS be able to imply Y from Z and X from Y.
For a more practical example, imagine walking down the street and picking up a piece of paper that has written on it:
"...Z axis was 5". From this snippet of information we can infer the definite presence of the Y axis and the X axis. If, on the other hand the piece of paper said ".. X axis was 6", I cannot definitely infer the presence of any dimensions other than X.
Another example is more 'set theory' oriented where, given the set of pencils, X, and the set of writing tools, Y, so X < Y (is a subset of Y). But also not the PRECISION issue, X is more 'particular' in its focus, Y more general. At best and I can make X the set of writing tools and so X = Y but X can never 'transcend' Y. (and so the sum of parts cannot transcend the whole)
This perspective can move us into issues regarding 'completeness', where the truely complete is in the IOR state - the problem being that this state is more unconscious, more implicit than explicit, more immediate than partial, such that 'completeness' is sensed intuitively at best and so requires something Science has issues with - a leap of faith. To avoid that leap we maintain the concept of incompleteness/uncertainty and focus on IMP and the use of probabilities reasoning (this probabilities reasoning in fact appears to be hard-coded into the brain reflecting the asymmetry)
In our brains, so our more conscious, mediations dominating, states are closer to the IMP/XOR realm than they are to the AND/IOR realm. BUT, integration DOES exist in the realm of the differentiating but is focused WITHIN what has been differentiated; through continuous differentiating, so the AND/IOR elements become manifest not as senses of 'semantics' but into a more concentrated, and so intense, focus on what we label as "syntax" - the focus of integrating is on one's position in the hierarchy of 'parts' that make-up the 'whole', such that all that can matter, all that is 'meaningful', is focused on position.
This focus on POSITION applies to the "dimension of precision" itself in that, as covered in past comments, each point on that dimension can serve as a ground out of which to interpret reality - thus some individuals/collectives can be more "IMP" oriented, others more "XOR", others more "AND". IOW position affects perspective (implied in this is that the position of IMP contains the root of, is the ground for, imagination).
Note that all of the above operators are from ANALYTICAL logic and as such lack the notion of thermodynamic time - time is at best mechanised, but more often removed from perspectives - the analytical will focus on idealisation, the static, the universal. What is needed is the copying of the analytical terms and then their association with time to give us formal representations of the DIALECTICAL processes to aid in 'completing' logic as best we can.
Thus, the IMP operator represents "IF X THEN Y". However, the serial format is not tied to time elements, the focus is purely structural.
Thus in 'full spectrum' logic we would have: "IF X, SO Y" to reflect the presence of structure Y given X and then re-define "IF,,THEN" to be a purely temporal format where "IF X, THEN Y" means that given X Y will follow AFTER it (X = grey clouds, Y = rain) This latter format reflects the rigid sequence of events that in analytical logic is focused more on hierarchy, be it explicit (X < Y) or implicit (X = Y - they are the same 'quantitatively'). As such, in analytical logic any reference to time is in the content of the variables, not in the overall form, not explicitly represented as a universal itself.
The UNIVERSALS of analytical logic, being universals, lack meaning until used in a context (we can play around with the 'pure' forms WITHIN the realm of that universal, but their use is in mapping to local contexts). The lack of temporal references in a world dominated by the arrow of time is an issue - IOW the implicit relationship here is of time being 'secondary', a LOCAL concept to which we can apply the universals; but nature appears to show othwerwise, thermodynamics is no local illusion, it applies universally.