To comprehend and cope with our environment we develop mental patterns or concepts of meaning. The
purpose of this paper is to sketch out how we destroy and create these patterns to permit us to both shape and
be shaped by a changing environment. In this sense, the discussion also literally shows why we cannot avoid this
kind of activity if we intend to survive on our own terms. The activity is dialectic in nature generating both
disorder and order that emerges as a changing and expanding universe of mental concepts matched to a
changing and expanding universe of observed reality.
GOAL
Studies of human behavior reveal that the actions we undertake as individuals are closely related to survival,
more importantly, survival on our own terms. Naturally, such a notion implies that we should be able to act
relatively free or independent of any debilitating external influences — otherwise that very survival might be in
jeopardy. In viewing the instinct for survival in this manner we imply that a basic aim or goal, as individuals, is
to improve our capacity for independent action. The degree to which we cooperate, or compete, with others is
driven by the need to satisfy this basic goal. If we believe that it is not possible to satisfy it alone, without help
from others, history shows us that we will agree to constraints upon our independent action — in order to
collectively pool skills and talents in the form of nations, corporations, labor unions, mafias, etc — so that
obstacles standing in the way of the basic goal can either be removed or overcome. On the other hand, if the
group cannot or does not attempt to overcome obstacles deemed important to many (or possibly any) of its
individual members, the group must risk losing these alienated members. Under these circumstances, the
alienated members may dissolve their relationship and remain independent, form a group of their own, or join
another collective body in order to improve their capacity for independent action.
ENVIRONMENT
In a real world of limited resources and skills, individuals and groups form, dissolve and reform their cooperative
or competitive postures in a continuous struggle to remove or overcome physical and social environmental
obstacles (11, 13) In a cooperative sense, where skills and talents are pooled, the removal or overcoming of
obstacles represents an improved capacity for independent action for all concerned. In a competitive sense,
where individuals and groups compete for scarce resources and skills, an improved capacity for independent
action achieved by some individuals or groups constrains that capacity for other individuals or groups. Naturally,
such a combination of real world scarcity and goal striving to overcome this scarcity intensifies the struggle of
individuals and groups to cope with both their physical and social environments (11, 13).
NEED FOR DECISIONS
Against such a background, actions and decisions become critically important. Actions must be taken over and
over again and in many different ways. Decisions must be rendered to monitor and determine the precise nature
of the actions needed that will be compatible with the goal. To make these timely decisions implies that we must
be able to form mental concepts of observed reality, as we perceive it, and be able to change these concepts as
reality itself appears to change. The concepts can then be used as decision-models for improving our capacity for
independent action. Such a demand for decisions that literally impact our survival causes one to wonder: How do
we generate or create the mental concepts to support this decision-making activity?
CREATING CONCEPTS
There are two ways in which we can develop and manipulate mental concepts to represent observed reality: We
can start from a comprehensive whole and break it down to its particulars or we can start with the particulars
and build towards a comprehensive whole. (28 / 24) Saying it another way, but in a related sense, we can go
from the general - to - specific or from the specific - to - general. A little reflection here reveals that deduction is
related to proceeding from the general - to - specific while induction is related to proceeding from the
specific - to - general. In following this line of thought can we think of other activities that are related to these two
opposing ideas? Is not analysis related to proceeding from the general-to-specific? Is not synthesis, the opposite
of analysis related to proceeding from the specific - to - general? Putting all this together: Can we not say that
general-to-specific is related to both deduction and analysis, while specific - to - general is related to induction and
synthesis? Now, can we think of some examples to fit with these two opposing ideas? We need not look far. The
differential calculus proceeds from the general - to - specific — from a function to its derivative. Hence is not the use
or application of the differential Calculus related to deduction and analysis? The integral calculus, on the other
hand, proceeds in the opposite direction — from a derivative to a general function. Hence, is not the use or
application of the integral calculus related to induction and synthesis? Summing up, we can see that: general - to - specific is related to deduction, analysis, and differentiation, while, specific - to - general is related to induction,
synthesis, and integration.
Now keeping these two opposing idea chains in mind let us move on a somewhat different tack. Imagine, if you
will, a domain (a comprehensive whole) and its constituent elements or parts. Now, imagine another domain and
its constituent parts. Once again, imagine even another domain and its constituent parts. Repeating this idea
over and over again we can imagine any number of domains and the parts corresponding to each. Naturally, as
we go through life we develop concepts of meaning (with included constituents) to represent observed reality.
Can we not liken these concepts and their related constituents to the domains and constituents that we have
formed in our imagination? Naturally, we can. Keeping this relationship in mind, suppose we shatter the
correspondence of each domain or concept with its constituent elements. In other words, we imagine the
existence of the parts but pretend that the domains or concepts they were previously associated with do not
exist. Result: We have many constituents, or particulars, swimming around in a sea of anarchy. We have
uncertainty and disorder in place of meaning and order. Further, we can see that such an unstructuring or
destruction of many domains — to break the correspondence of each with its respective constituents — is related to
deduction, analysis, and differentiation. We call this kind of unstructuring a destructive deduction.
Faced with such disorder or chaos, how can we reconstruct order and meaning? Going back to the idea chain of
specific - to - general, induction, synthesis, and integration the thought occurs that a new domain or concept can
be formed if we can find some common qualities, attributes, or operations among some or many of these
constituents swimming in this sea of anarchy. Through such connecting threads (that produce meaning) we
synthesize constituents from, hence across, the domains we have just shattered. (24) Linking particulars together
in this manner we can form a new domain or concept — providing, of course, we do not inadvertently use only
those "bits and pieces" in the same arrangement that we associated with one of the domains purged from our
imagination. Clearly, such a synthesis would indicate we have generated something new and different from what
previously existed. Going back to our idea chain, it follows that creativity is related to induction, synthesis, and
integration since we proceeded from unstructured bits and pieces to a new general pattern or concept. We call
such action a creative or constructive induction. It is important to note that the crucial or key step that permits
this creative induction is the separation of the particulars from their previous domains by the destructive
deduction. Without this unstructuring the creation of a new structure cannot proceed — since the bits and pieces
are still tied together as meaning within unchallenged domains or concepts.
Recalling that we use concepts or mental patterns to represent reality, it follows that the unstructuring and
restructuring just shown reveals a way of changing our perception of reality. (28) Naturally, such a notion implies
that the emerging pattern of ideas and interactions must be internally consistent and match-up with reality. (14, 25) To check or verify internal consistency we try to see if we can trace our way back to the original constituents
that were used in the creative or constructive induction. If we cannot reverse directions, the ideas and
interactions do not go together in this way without contradiction. Hence, they are not internally consistent.
However, this does not necessarily mean we reject and throw away the entire structure. Instead, we should
attempt to identify those ideas (particulars) and interactions that seem to hold together in a coherent pattern of
activity as distinguished from those ideas that do not seem to fit in. In performing this task we check for
reversibility as well as check to see which ideas and interactions match-up with our observations of reality. (27, 14, 15). Using those ideas and interactions that pass this test together with any new ideas (from new destructive deductions) or other promising ideas that popped out of the original destructive deduction we again
attempt to find some common qualities, attributes or operations to re-create the concept — or create a new
concept. Also, once again, we perform the check for reversibility and match-up with reality. Over and over again
this cycle of Destruction and Creation is repeated until we demonstrate internal consistency and match-up with
reality. (19, 14, 15)
SUSPICION
When this orderly (and pleasant) state is reached the concept becomes a coherent pattern of ideas and
interactions that can be used to describe some aspect of observed reality. As a consequence, there is little, or
no, further appeal to alternative ideas and interactions in an effort to either expand, complete, or modify the
concept. (19) Instead, the effort is turned inward towards fine tuning the ideas and interactions in order to
improve generality and produce a more precise match of the conceptual pattern with reality. (19) Toward this
end, the concept — and its internal workings — is tested and compared against observed phenomena over and over
again in many different and subtle ways. (19) Such a repeated and inward-oriented effort to explain increasingly
more subtle aspects of reality suggests the disturbing idea that perhaps, at some point, ambiguities,
uncertainties, anomalies, or apparent inconsistencies may emerge to stifle a more general and precise match-up
of concept with observed reality. (19) Why do we suspect this?
On one hand, we realize that facts, perceptions, ideas, impressions, interactions, etc. separated from previous
observations and thought patterns have been linked together to create a new conceptual pattern. On the other
hand, we suspect that refined observations now underway will eventually exhibit either more or a different kind
of precision and subtlety than the previous observations and thought patterns. Clearly, any anticipated
difference, or differences, suggests we should expect a mismatch between the new observations and the
anticipated concept description of these observations. To assume otherwise would be tantamount to admitting
that previous constituents and interactions would produce the same synthesis as any newer constituents and
interactions that exhibit either more or a different kind of precision and subtlety. This would be like admitting
one equals two. To avoid such a discomforting position implies that we should anticipate a mismatch between
phenomena observation and concept description of that observation. Such a notion is not new and is indicated
by the discoveries of Kurt Gödel and Werner Heisenberg.
INCOMPLETENESS AND CONSISTENCY
In 1931 Kurt Gödel created a stir in the World of Mathematics and Logic when he revealed that it was impossible
to embrace mathematics within a single system of logic. (12, 23) He accomplished this by proving, first, that any
consistent system that includes the arithmetic of whole numbers is incomplete. In other words, there are true
statements or concepts within the system that cannot be deduced from the postulates that make-up the system.
Next, he proved even though such a system is consistent, its consistency cannot be demonstrated within the
system.
Such a result does not imply that it is impossible to prove the consistency of a system. It only means that such a
proof cannot be accomplished inside the system. As a matter of fact since Gödel, Gerhard Gentzen and others
have shown that a consistency proof of arithmetic can be found by appealing to systems outside that arithmetic.
Thus, Gödel's Proof indirectly shows that in order to determine the consistency of any new system we must
construct or uncover another system beyond it (29, 27). Over and over this cycle must be repeated to determine
the consistency of more and more elaborate systems. (29, 27)
Keeping this process in mind, let us see how Gödel's results impact the effort to improve the match-up of
concept with observed reality. To do this we will consider two kinds of consistency: The consistency of the
concept and the consistency of the match-up between observed reality and concept description of reality. In this
sense, if we assume — as a result of previous destructive deduction and creative induction efforts — that we have a
consistent concept and consistent match - up, we should see no differences between observation and concept
description. Yet, as we have seen, on one hand, we use observations to shape or formulate a concept; while on
the other hand, we use a concept to shape the nature of future inquiries or observations of reality. Back and
forth, over and over again, we use observations to sharpen a concept and a concept to sharpen observations.
Under these circumstances, a concept must be incomplete since we depend upon an ever-changing array of
observations to shape or formulate it. Likewise, our observations of reality must be incomplete since we depend
upon a changing concept to shape or formulate the nature of new inquiries and observations. Therefore, when
we probe back and forth with more precision and subtlety, we must admit that we can have differences between
observation and concept description; hence, we cannot determine the consistency of the system — in terms of its
concept, and match - up with observed reality — within itself.
Furthermore, the consistency cannot be determined even when the precision and subtlety of observed
phenomena approaches the precision and subtlety of the observer — who is employing the ideas and interactions
that play together in the conceptual pattern. This aspect of consistency is accounted for not only by Gödel 's
Proof but also by the Heisenberg Uncertainty or Indeterminacy Principle.
INDETERMINACY AND UNCERTAINTY
The Indeterminacy Principle uncovered by Werner Heisenberg in 1927 showed that one could not simultaneously
fix or determine precisely the velocity and position of a particle or body. (14, 9) Specifically he showed, due to the
presence and influence of an observer, that the product of the velocity and position uncertainties is equal to or
greater than a small number (Planck's Constant) divided by the mass of the particle or body being investigated.
In other words,
| |
 |
Where |
|
|
is velocity uncertainty |
|
is position uncertainty and |
|
is Planck's constant (h) divided by observed mass (m). |
Examination of Heisenberg's Principle reveals that as mass becomes exceedingly small the uncertainty or
indeterminacy, becomes exceedingly large. Now — in accordance with this relation — when the precision, or mass,
of phenomena being observed is little, or no different than the precision, or mass, of the observing phenomena
the uncertainty values become as large as, or larger than, the velocity and size frame-of-reference associated
with the bodies being observed. (9) In other words, when the intended distinction between observer and
observed begins to disappear (3), the uncertainty values hide or mask phenomena behavior; or put another way,
the observer perceives uncertain or erratic behavior that bounces all over in accordance with the indeterminacy
relation. Under these circumstances, the uncertainty values represent the inability to determine the character or
nature (consistency) of a system within itself. On the other hand, if the precision and subtlety of the observed
phenomena is much less than the precision and subtlety of the observing phenomena, the uncertainty values
become much smaller than the velocity and size values of the bodies being observed. (9) Under these
circumstances, the character or nature of a system can be determined — although not exactly — since the
uncertainty values do not hide or mask observed phenomena behavior nor indicate significant erratic behavior.
Keeping in mind that the Heisenberg Principle implicitly depends upon the indeterminate presence and influence
of an observer, (14) we can now see — as revealed by the two examples just cited — that the magnitude of the
uncertainty values represent the degree of intrusion by the observer upon the observed. When intrusion is total
(that is, when the intended distinction between observer and observed essentially disappears, (3) the uncertainty
values indicate erratic behavior. When intrusion is low the uncertainty values do not hide or mask observed
phenomena behavior, nor indicate significant erratic behavior. In other words, the uncertainty values not only
represent the degree of intrusion by the observer upon the observed but also the degree of confusion and
disorder perceived by that observer.
ENTROPY AND THE SECOND LAW OF THERMODYNAMICS
Confusion and disorder are also related to the notion of entropy and the Second Law of Thermodynamics (11, 20)
Entropy is a concept that represents the potential for doing work, the capacity for taking action, or the degree of
confusion and disorder associated with any physical or information activity. High entropy implies a low potential
for doing work, a low capacity for taking action or a high degree of confusion an disorder. Low entropy implies
just the opposite. Viewed in this context, the Second Law of Thermodynamics states that all observed natural
processes generate entropy. (20) From this law it follows that entropy must increase in any closed system — or,
for that matter, in any system that cannot communicate in an ordered fashion with other systems or
environments external to itself. (20) Accordingly, whenever we attempt to do work or take action inside such a
system — a concept and its match - up with reality — we should anticipate an increase in entropy hence an increase
in confusion and disorder. Naturally, this means we cannot determine the character or nature (consistency) of
such a system within itself, since the system is moving irreversibly toward a higher, yet unknown, state of
confusion and disorder.
DESTRUCTION AND CREATION
What an interesting outcome! According to Gödel we cannot — in general — determine the consistency, hence the
character or nature, of an abstract system within itself. According to Heisenberg and the Second Law of
Thermodynamics any attempt to do so in the real world will expose uncertainty and generate disorder. Taken
together, these three notions support the idea that any inward-oriented and continued effort to improve the
match - up of concept with observed reality will only increase the degree of mismatch. Naturally, in this
environment, uncertainty and disorder will increase as previously indicated by the Heisenberg Indeterminacy
Principle and the Second Law of Thermodynamics, respectively. Put another way, we can expect unexplained and
disturbing ambiguities, uncertainties, anomalies, or apparent inconsistencies to emerge more and more often.
Furthermore, unless some kind of relief is available, we can expect confusion to increase until disorder
approaches chaos — death.
Fortunately, there is a way out. Remember, as previously shown, we can forge a new concept by applying the
destructive deduction and creative induction mental operations. Also, remember, in order to perform these
dialectic mental operations we must first shatter the rigid conceptual pattern, or patterns, firmly established in
our mind. (This should not be too difficult since the rising confusion and disorder is already helping us to
undermine any patterns). Next, we must find some common qualities, attributes, or operations to link isolated
facts, perceptions, ideas, impressions, interactions, observations, etc. together as possible concepts to represent
the real world. Finally, we must repeat this unstructuring and restructuring until we develop a concept that
begins to match - up with reality. By doing this — in accordance with Gödel, Heisenberg and the Second Law of
Thermodynamics — we find that the uncertainty and disorder generated by an inward - oriented system talking to
itself can be offset by going outside and creating a new system. Simply stated, uncertainty and related disorder
can be diminished by the direct artifice of creating a higher and broader more general concept to represent
reality.
However, once again, when we begin to turn inward and use the new concept — within its own pattern of ideas
and interactions — to produce a finer grain match with observed reality we note that the new concept and its
match - up with observed reality begins to self-destruct just as before. Accordingly, the dialectic cycle of
destruction and creation begins to repeat itself once again. In other words, as suggested by Gödel's Proof of
Incompleteness, we imply that the process of Structure, Unstructure, Restructure, Unstructure, Restructure is
repeated endlessly in moving to higher and broader levels of elaboration. In this unfolding drama, the alternating
cycle of entropy increase toward more and more disorder and the entropy decrease toward more and more order
appears to be one part of a control mechanism that literally seems to drive and regulate this alternating cycle of
destruction and creation toward higher and broader levels of elaboration. Now, in relating this
deductive/inductive activity to the basic goal discussed in the beginning, I believe we have uncovered a Dialectic
Engine that permits the construction of decision models needed by individuals and societies for determining and
monitoring actions in an effort to improve their capacity for independent action.
Furthermore, since this engine is directed toward satisfying this basic aim or goal, it follows that the goal seeking
effort itself appears to be the other side of a control mechanism that seems also to drive and regulate the
alternating cycle of destruction and creation toward higher and broader levels of elaboration. In this context,
when acting within a rigid or essentially a closed system, the goal seeking effort of individuals and societies to
improve their capacity for independent action tends to produce disorder towards randomness and death. On the
other hand, as already shown, the increasing disorder generated by the increasing mismatch of the system
concept with observed reality opens or unstructures the system. As the unstructuring or, as we'll call it, the
destructive deduction unfolds it shifts toward a creative induction to stop the trend toward disorder and chaos to
satisfy a goal-oriented need for increased order.
Paradoxically, then, an entropy increase permits both the destruction or unstructuring of a closed system and
the creation of a new system to nullify the march toward randomness and death. Taken together, the entropy
notion associated with the Second Law of Thermodynamics and the basic goal of individuals and societies seem
to work in dialectic harmony driving and regulating the destructive / creative, or deductive / inductive, action — that
we have described herein as a dialectic engine. The result is a changing and expanding universe of mental
concepts matched to a changing and expanding universe of observed reality. (28, 27) As indicated earlier, these
mental concepts are employed as decision models by individuals and societies for determining and monitoring
actions needed to cope with their environment — or to improve their capacity for independent action.
Return to Beginning of Article
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