General Systems Theory
David S. Walonick, Ph.D.
General systems theory was originally proposed by
biologist Ludwig von Bertalanffy in 1928. Since
Descartes, the "scientific method" had
progressed under two related assumptions. A system could
be broken down into its individual components so that
each component could be analyzed as an independent
entity, and the components could be added in a linear
fashion to describe the totality of the system. Von
Bertalanffy proposed that both assumptions were wrong. On
the contrary, a system is characterized by the
interactions of its components and the nonlinearity of
those interactions. In 1951, von Bertalanffy extended
systems theory to include biological systems and three
years later, it was popularized by Lotfi Zadeh, an
electrical engineer at Columbia University. (McNeill and
One common element of all systems is described by
Kuhn. Knowing one part of a system enables us to know
something about another part. The information content
of a "piece of information" is proportional to
the amount of information that can be inferred from the
information (A. Kuhn., 1974).
Systems can be either controlled (cybernetic) or
uncontrolled. In controlled systems information is
sensed, and changes are effected in response to the
information. Kuhn refers to this as the detector, selector,
and effector functions of the system. The detector
is concerned with the communication of information
between systems. The selector is defined by the rules
that the system uses to make decisions, and the effector
is the means by which transactions are made between
systems. Communication and transaction are
the only intersystem interactions. Communication is the
exchange of information, while transaction involves the
exchange of matter-energy. All organizational and social
interactions involve communication and/or transaction.
Kuhn's model stresses that the role of decision
is to move a system towards equilibrium. Communication
and transaction provide the vehicle for a system to
achieve equilibrium. "Culture is
communicated, learned patterns... and society is a
collectively of people having a common body and process
of culture." (p. 154, 156) A subculture can
be defined only relative to the current focus of
attention. When society is viewed as a system, culture is
seen as a pattern in the system. Social analysis is the
study of "communicated, learned patterns common to
relatively large groups (of people)." (p. 157)
The study of systems can follow two general
approaches. A cross-sectional approach deals with
the interaction between two system, while a developmental
approach deals with the changes in a system over time.
There are three general approaches for evaluating
subsystems. A holist approach is to examine the
system as a complete functioning unit. A reductionist
approach looks downward and examines the subsystems
within the system. The functionalist approach
looks upward from the system to examine the role it plays
in the larger system. All three approaches recognize the
existence of subsystems operating within a larger system.
Descartes and Locke both believed that words were
composed of smaller building blocks. Both thought that
one could strip away all terms of ambiguity and be left
with the clarity of comprehension. Kuhn argues for clear
definitions in science. The criteria that Kuhn (1974)
uses to evaluate system terminology is that it provides
"analytic usefulness and consistency with other
Kuhn's terminology is interlocking and mutually
consistent. The following table summarizes his basic
element any identifiable entity
pattern any relationship of two
or more elements
object a pattern as it exists at
a given moment in time
event a change in a pattern over
system any pattern whose
elements are related in a sufficiently regular way to
acting system a pattern where
two or more elements interact
component any interacting
element in an acting system
interaction a situation where a
change in one component induces a change in another
mutual interaction a situation
where a change in one component induces a change in
another component, which then induces a change in the
pattern system is a pattern
where two or more elements are interdependent
interdependent a situation where
a change in an element induces a change in another
Systems can be identified by their structure. A real
system is any system of matter and/or energy. An abstract
or analytic system is a pattern system whose elements
consist of signs and/or concepts. Unlike the real system,
which can only exchange information, abstract systems are
information. A nonsystem is one or more elements
that show no pattern of change. Since change is measured
relative to a reference, something can be viewed as both
a system and a nonsystem depending on the researcher's
A system variable is any element in an acting
system that can take on at least two different states.
Some system variables are dichotomous, and can be one of
two values--the rat lives, or the rat dies. System
variables can also be continuous. The condition of a
variable in a system is known as the system state.
The boundaries of a system are defined by the set
of its interacting components. Kuhn recognizes that it is
the investigator, not nature, that bounds the particular
system being investigated. (A. Kuhn., 1974)
A controlled (cybernetic) system maintains at
least one system variable within some specified range, or
if the variable goes outside the range, the system moves
to bring the variable back into the range. This control
is internal to the system. The field of cybernetics
is the discipline of maintaining order in systems.
A system's input is defined as the movement of
information or matter-energy from the environment into
the system. Output is the movement of information
or matter-energy from the system to the environment. Both
input and output involve crossing the boundaries that
define the system.
When all forces in a system are balanced to the point
where no change is occurring, the system is said to be in
a state of static equilibrium. Dynamic
(steady state) equilibrium exists when the system
components are in a state of change, but at least one
variable stays within a specified range. Homeostasis
is the condition of dynamic equilibrium between at least
two system variables. Kuhn (1974) states that all systems
tend toward equilibrium, and that a prerequisite for the
continuance of a system is its ability to maintain a
steady state or steadily oscillating state.
Negative equilibrating feedback operates within
a system to restore a variable to an initial value. It is
also known as deviation-correcting feedback. Positive
equilibrating feedback operates within a system to
drive a variable future from its initial value. It is
also known as deviation-amplifying feedback.
Equilibrium in a system can be achieved either through
negative or positive feedback. In negative feedback, the
system operates to maintain its present state. In
positive feedback, equilibrium is achieved when the
variable being amplified reaches a maximum asymtoptic
limit. Systems operate through differentiation and
coordination among its components. "Characteristic
of organization, whether of a living organism or a
society, are notions like those of wholeness, growth,
differentiation, hierarchical order, dominance, control,
and competition." (von Bertalanffy, 1968)
A closed system is one where interactions occur
only among the system components and not with the
environment. An open system is one that receives
input from the environment and/or releases output to the
environment. The basic characteristics of an open system
is the dynamic interaction of its components, while the
basis of a cybernetic model is the feedback cycle. Open
systems can tend toward higher levels of organization
(negative entropy), while closed systems can only
maintain or decrease in organization.
A system parameter is any trait of a system
that is relevant to an investigation, but that does not
change during the duration of study. An environmental
parameter is any trait of a system's environment that
is relevant to an investigation, but that does not change
during the duration of study.
Systems theory provides an internally consistent
framework for classifying and evaluating the world. There
are clearly many useful definitions and concepts in
systems theory. In many situations it provides a
scholarly method of evaluating a situation. An even more
important characteristic, however, is that it provides a
universal approach to all sciences. As von Bertalanffy
(1968, p. 33) points out, "there are many instances
where identical principles were discovered several times
because the workers in one field were unaware that the
theoretical structure required was already well developed
in some other field. General systems theory will go a
long way towards avoiding such unnecessary duplication of
Organizational development makes extensive use of
general systems theory. Originally, organizational theory
stressed the technical requirements of the work
activities going on in the organizations. In the 1970's,
the rise of systems theory forced scientists to view
organizations as open systems that interacted with their
environment. Although there is now a consensus on the
importance of the environment, there is still much
disagreement about which features of the environment are
Meyer and Scott (1983) identified three dominant
models for analyzing the relationship between
organizations and the environment. The organization-set
model (often called resource-dependency theory) focuses
on the resource needs and dependencies of an
organization. The organizational population model
looks at the collection of organizations that make
similar demands from the environment and it stresses the
competition created by limited environmental resources.
The interorganizational field model looks at the
relations of organizations to other organizations,
usually within a localized geographic area.
Five major themes of organizational change were
examined by Goodman. (1982)
1) Intervention methods represent
alternative approaches to organizational change at
the individual, group, and organizational levels.
Most studies attempt to ascertain the effectiveness
of these approaches by using survey feedback. Some
utilize long-term longitudinal approaches to examine
the impact of intervention methods. The cataloging of
intervention methods is still the dominant way of
thinking about planned change.
2) Large-scale multiple system intervention
methods have been gaining in popularity since the
late seventies. The interest in the quality of
working life (QWL) is primarily responsible for this
popularity. This approach places strong emphasis on
designing innovative techniques that serve as a
catalyst for change. It's most important application
is that is stresses the relationships between the
individual, company, community, state, national, and
3) Assessment of change is a major theme
that has emerged as a result of the large-scale
multiple system intervention methods. These include
models of assessment, instruments for measuring
organizational change, the development of time-series
models, and an overall increase in the use of
multivariate analysis for the testing and evaluation
4) The examination of failures provides us
with valuable information about organizational
change. It forces us to focus on the theoretical
constructs of change. By comparing successful and
unsuccessful attempts at implementing change, we can
evaluate the effectiveness of various techniques.
5) The level of theorizing about
organizational change has seen significant
improvements in recent years. Of particular
importance is broad-systems orientation. These
theories propose a model of organizational change
that examines inputs, transformational processes, and
outputs. Inputs refer to the environmental resources.
Transformation refers to the tasks, and the formal
and informal system (organizational) components.
Outputs include changes in both the individual and
organization. The advantage of this approach is that
it forces us to look at the broad spectrum of
variables that need to be incorporated into the
Organizational and social systems must change in order
to remain healthy. Both are open systems, and are
sensitive to environmental changes. A change in the
environment can have a profound impact on an open system.
The overall health of and organization is strongly linked
with its ability to anticipate and adapt to environmental
change. Furthermore, the health of the environment is
related to the matter-energy transactions taking place in
the social and organizational systems. A bilateral
relationship exists between the environment and the
components of all subsystems operating within the
Planned organizational or social change is an attempt
to solve a problem or to catalyze a vision. A change is
introduced into an organization or social system with the
specific intent of affecting other system variables.
Knowledge of the nonlinear relationships between
variables gives planners the potential to effect large
changes in a desired variable with relatively small
changes in another. Systems theory forces planners to
broaden their perspective, and to consider how their
decisions will affect the other components of the system
and the environment.
Chaos is the science of the global nature of systems.
In a 1980 lecture, cosmologist Stephen Hawking pointed
out that we already know the physical laws that govern
our everyday experience. (Gleick, 1987) That being the
case, we must now extend systems theory to include the
phenomena that lies outside of our normal perceptual
limits of experience.
Traditional predictive mathematical models have
incorporated error into the model to explain seemingly
random fluctuations. Chaos theory is an attempt to
explain and model the seemingly random components of a
system. It recognizes that systems are sensitive to
initial conditions, so that seemingly small changes can
produce large changes in the system.
Meteorologist Edward Lorenz (1963) used a
microcomputer to simulate weather patterns in 1960. While
inputting initial starting conditions to the computer, he
inadvertently rounded one the numbers to three, instead
of six decimal places. The small difference .506 (instead
of .506127) produced rapidly divergent simulations of
weather patterns. Small differences in initial conditions
produced widely different results. Some meteorologists
believed that Lorenz's discovery meant that weather
control was just around the corner. Small nonnatural
changes could be used to manipulate large weather
patterns. Lorenz, however, believed that this was the
reason for the failure of long term forecasts. Any
uncontrolled system variable could thwart efforts to
control the overall state of the system.
Chaotic systems depend on the nonlinear nature of its
components. Differential equations are used to describe
the changes in a system over time. Chaotic systems can
have both stable and unstable components.
Mathematician Stephen Smale (1980) began his work with
dynamic systems in the mid 1950's. Originally Smale
proposed that stable chaos could not exist, but soon
changed his theory. He proposed the concept of phase
space, where if the system changed, a trajectory
could be drawn on paper to represent the changing state
of the system. Phase space contains the complete
knowledge of a system. Each point in phase space
represents the state of a dynamic system at an instant in
The problem with phase space is that it requires a
dimension for each variable being studied. Modern
computer graphing techniques do a good job of graphing
three variables and representing them in two dimensions
(on paper). However, even our greatest minds have
difficulty conceptualizing phase space for four or five
dimensions. It is interesting to note that computers have
no difficulty performing calculations for any number of
dimensions. The problem is in our ability to visually
represent this space, not our ability to compute its
Three dimensional plots of chaotic behavior can be
very complex and difficult to interpret. The Poincaré
map was developed as a way of understanding three
dimensional systems by taking a series of two dimensional
"slices" relative to a line through the origin
(Gleick, 1987, p. 143). The slices are overlaid on top of
each other to create the final map. Distinct patterns can
emerge by combining the Poincaré sections.
The Poincaré map is a dimensional compression
technique whereby three dimensions are displayed in two
dimensional space. Unlike a photograph, which implies the
third dimension through perspective, the Poincaré map
involves the third dimension in its creation. It is
interesting to speculate on the nature of the patterns
revealed by Poincaré maps. The map itself is created by
using a line drawn through the origin as a reference for
defining the y-axis of the map. Different maps are
produced for each of the infinite selections of lines
through the origin. Patterns appear and disappear
depending on the selection of the reference line. One
interpretation might be that our concept of
"order" is incorrect. We generally perceive of
"order" as an absolute (i.e., the quest for the
"true" nature of things). Poincaré maps imply
that order is not an absolute, but rather, something that
can only be understood relative to an observer. An
observer using one reference line might see order, while
another observer using a different reference line might
see chaos, or a completely different pattern. In other
words, the nature of a system is a matter of perception
At the same time that Lorenz was experimenting with
weather forecasting models, ecologists were beginning to
model population growth using a logistical difference
equation. For many initial starting parameters, the
equation shows the traditional growth model--a population
grows, exceeds its optimal steady state level, and then
experiences oscillations of diminishing magnitude as the
system approaches equilibrium. Some starting values
however, produce oscillations that do not diminish over
time. At first, scientists did not recognize the stable
chaos they were observing. They assumed that the
fluctuations were just oscillations around an
equilibrium. The equilibrium was the important point.
Mathematician, James Yorke, believes that physicists had
"learned not to see chaos...through the process of
learning to solve differential equations, most scientists
have lost sight of the fact that most differential
equations cannot be solved". (Gleick, 1987, p.67).
Biologist Robert May (1976) at Princeton studied the
simple logistical difference equation. He noticed that as
the growth factor increased beyond the value of three,
equilibrium would never be reached. The system would
enter a chaotic state. Furthermore, if a system displays
a regular cycle of three, then the system will also
display regular cycles of all other lengths.
The author wrote the following simple BASIC program to
verify May's findings:
INPUT "Enter the growth factor: "; R
INPUT "Enter the initial population size:
XNEXT = R * X * (1-X) 'Logistic differential formula
ITERATIONS = ITERATIONS + 1
IF XNEXT = LASTX THEN GOTO FINISH
PRINT "Iterations to achieve stability =
Running this program clearly demonstrates May's
findings. When a value less than three is entered for the
growth factor, the program achieves convergence. However,
when a value of three of more is entered, the program
never achieves stability. The computed value for the
variable enters a state of stable chaos where it
alternates between two or more values with periods of
While examining line noise in IBM communication
systems, Benoit Mandelbrot (1977) discovered that the
apparent random noise bursts were actually following a
regular cycle (the Cantor mathematical set). By examining
the noise using various time periods, Mandelbrot was able
to model the noise. German mathematician Georg Cantor
(1845-1918) had discovered these sets nearly one hundred
years before, while demonstrating that there are many
different infinities. Cantor demonstrated a one-to-one
correspondence between the space defined by a cube and
the space of the universe. Both contained an infinite
number of points (McNeill and Freiberger, 1993).
Mandelbrot also hypothesized the Noah and Joseph
Effects. The Noah Effect states that change happens in
discrete jumps. The Joseph effect states that some things
tend to persist. These two effects push the world in
different directions (Gleick, 1987, p. 92-94)
Mandelbrot has pointed out the chaos theory models a
rough, pitted world. Mountains are not seen as cones and
lightning doesn't travel in a straight line. In
Mandelbrot's most famous experiment, he asks the question
"how long is a coast line?". Common sense would
dictate that the distance is a real number, however, it
turns out that it depends on the observers measuring
technique. As the observer uses a smaller and smaller
measurement tool, the estimate of the coastline becomes
increasingly large. In fact, Mandelbrot argues that the
actual length is infinite (at least until the measuring
tool is at the atomic level). Furthermore, Mandelbrot
proposed that the concept of dimension itself can only be
stated relative to an observer. He proposed the word fractal
as a way of visualizing infinity on the dimension of
roughness. Fractal implies a quality of self-similarity.
Columbia University geologist Christopher Scholz
(1982) began to apply Mandelbrot's findings to the study
of earthquakes. Fractal geometry provided a new way of
viewing the fissures and bumpiness of the Earth's
surface. At the same time, biologists began to realize
that fractal type geometry was operating throughout the
body. Some argue that fractal scaling is universal to
Turbulence has been a problem in the application of
fluid dynamics. Sometimes turbulence is desirable. For
example, a jet engine depends on the turbulence of
burning fuel for its propulsion. Other times, turbulence
can have disastrous effects, such as the loss of lift
created by turbulent air-flow over the wing of an
airplane. Turbulence is chaos on all scales. It is
dissipative (i.e., it drains energy) and unstable.
Closer examination of turbulence, however, reveals
that energy is not dissipated evenly through out the
system. Areas of calm remain regardless of the observer's
scale. While studying turbulence, physicist David Ruelle
(1971, 1980), coined the term strange attractor to
describe the tendency of systems to move toward a fixed
point, or to oscillate in a limited repeating cycle. A
pendulum is a good example of a fixed point attractor. It
moves closer to its steady state over time, as it gives
up energy to air friction. Strange attractors imply that
nature is constrained. The shape of chaos unfolds
relative to the properties of the attractor. An
interesting property of the strange attractor is that
initial conditions make little difference. As long as the
starting points lie somewhere near the attractor, the
system will rapidly converge upon the strange attractor.
Cornell physicist Mitchell Feigenbaum (1978, 1979,
1981) examined simple nonlinear systems and described how
these systems could often exist in two stable states. Intransitive
systems have two stable states. After one of the
states is achieved, the system will remain in that state
until given a "kick" from the environment. A
pendulum clock is an example, where it has two steady
states--the swinging state and the at rest state. In the
swinging state, energy is continually added to the system
through the wind-up springs, and the clock keeps ticking.
If, however, we momentarily stop the pendulum from
swinging, it will continue to remain at rest when we
release it. In the almost intransitive system, the
system can change stable states without a push from the
environment. At the present time, there are no
explanations for almost intransitive systems. The study
of fractal basin boundaries is an attempt to
understand why a system chooses one steady state over
One of the most important discoveries from chaos
theory is that a relatively small, but well-timed or
well-placed jolt to a system can throw the entire system
into a state of chaos. One group of scientists (Guevara,
Glass, and Schrier, 1981) have experimented with
cardiofibrillation and how the heart displays the same
chaotic characteristics of other nonlinear systems. Some
physiologists are now looking at diseases at breakdowns
in the normal oscillator cycles of the body. Physicist
James Lovelock (1979) proposed the Gaia hypothesis, where
life itself creates the conditions for life, and is
maintained by a self-sustaining process of dynamic
feedback. Von Bertalanffy (1968) believes that life can
exist only in an open system, and that feedback is the
mechanism that provides an explanation for a wide range
of physiological and biological processes. Erwin
Schrodinger, one of the major pioneers of quantum
physics, believed that life operates as an aperiodic
crystal (different than the periodic crystals of the
elements). Physicist Joesph Ford said that
"evolution is chaos with feedback." (Gleick,
1987, p. 314)
Seventeenth century Dutch physicist Christian Huygens
was the first to discover entrainment or
mode-locking (Gleick, 1987, p. 292-293). He noticed that
several pendulum clocks in his laboratory were all
operating in unison. Knowing that the timing of the
clocks could not be that precise, he correctly
hypothesized that the clocks became synchronized with
each other through minute vibrations in the building.
Examples of frequency locking abound in both the physical
and biological sciences. Planetary systems, electronics,
and the human body all show examples of entrainment.
Simple systems can behave in complex ways.
Complex behavior implies complex causes. Different
systems behave differently. In Thriving on Chaos (HarperPerennial,
1987), Tom Petersarpelld main hypothesis is that all
institutions are operating in a chaotic environment, and
that "no firm can take anything in its market for
granted." (p.13) Because of the interactions of many
economic forces and the rapidity of change, institutions
must constantly reassess their vision and adapt to abrupt
changes in the environment.
Organizations and social systems operating within a
chaotic environment are being continually challenged to
maintain their purpose and structure. The paradox,
however, is that larger and more established structures
are usually less able to change. The inertia resulting
from their size (e.g., number of people) makes it
difficult to introduce planned organizational or social
change. Large institutions generally encompass
well-established patterns. The stability of these
structures makes them less able to adapt to environmental
and internal system changes. All other things being
equal, small structures can adapt to change more
efficiently than larger ones.
Chaos theory is beginning to teach us much about the
nature of change in our organizations and social
institutions. Nonlinear relationships among system
components is a pathway to the introduction of
institutional change. The challenge comes in the
discovery of those relationships and the understanding of
the dynamics of these systems. The planning of change
involves the application of this knowledge.
At the heart of fuzzy logic is the question of how we
categorize things. Cantor (1845-1918) examined the way
that we categorize things into sets. He called the entire
set, the universe of discourse. Of course, the
definition of the universe depends on what is being
studied--its definition is relative. For example, if we
study a dog, the universe of discourse might be all dogs,
all mammals, or all living creatures. The important point
is that the universe contains variability. The complement
of a set is all that does not belong to the set. Cantor's
studies of the relationships of sets led to precise
definitions for intersections and unions.
The problem with Cantor's set theory had to do with the
difficulty in defining the boundaries of a set. These
boundaries were often vague, lacking in precision.
American philosopher Charles Peirce (1934, 1935)
disagreed with Cantor's method of classifying everything
as either in the set or not in the set. He believed that
all things existed on a continuum. Whether an object
belonged to a set or not depended on where it fell on the
continuum. At some points on the continuum, it is clearly
part of the set. At other points, a vagueness exists
making it difficult to determine membership. Bertund
Russel (1945) proposed that this vagueness was a function
of language, not reality.
In 1920, Polish mathematician Jan Lukasiewicz proposed
the idea that the simple dichotomy of true or false
might also contain a third logical value of possible.
Once that assumption was made, Lukasiewicz (1970)
asserted that any number of middle values were equally
possible. Instead of simply true or false, a numerical
value could be used to represent the degree of
Cornell mathematician Max Black (1937) proposed that
vagueness is a matter of probability based on the
distribution of human belief. If, for example, 60% of the
population believe that something is true, then it is
true to a .6 extent. The degree of truthfulness is .6.
Berkeley electrical engineer Lofti Zadeh (1969) built on
Black's work and proposed the idea that set membership
could be graded. Some items could belong completely to a
set, while others could be expressed as a partial
membership. The key to "fuzzy" membership is
that judgment and context are used to assign values to
membership. Zadeh points out that people have a
remarkable ability to quantify set membership. People can
easily assign a number between zero and one to represent
the truthfulness of a statement. In spite of this, some
logicians do not believe in the concept of a partial
truth. They state that "truth" is an absolute,
without the degrees implied by fuzzy logic.
One counter-intuitive assertion proposed by Zadeh is
that "as complexity rises, precise statements lose
meaning and meaningful statements lose precision".
(McNeill and Freiberger, 1993, p. 43) The so called
"Law of Incompatibility" places limits on our
ability to perform analysis of complex systems.
Zadeh was the recipient of much criticism over his
fuzzy logic theories. The most prominent argument was
that set membership was subjective. There was no way to
objectively determine membership values, and therefore,
fuzzy logic could not be counted on to yield accurate
results. Others argued that fuzzy logic was a
manifestation of unprecedented permissiveness in society.
Rudolph Kalman, a former student of Zadeh's, argued that
things appeared fuzzy only until we understood them.
William Kahan pointed out that fuzzification leads one to
entertain illogical thoughts, that are not verifiable
through logic. He called it the "cocaine of
science". (McNeill and Freiberger, 1993, p. 46-48)
One of the problems accepting fuzzy logic lies in its
name. The word "fuzzy" implies a negative
uncertainty that is mutually exclusive with the word
logic. Fuzzy became equated with sloppy, and American
industry ignored it. Since the early Greek cultures, we
have assumed that things fall into dichotomous classes.
Aristotle believed math provided that ultimate approach
to logic. The classic problem with dichotomous thinking
is evoked by the question "How many grains of sand
constitute a heap?" If we keep adding more and more
grains of sand to create a pile, at some point we'll call
it a heap. If we remove a grain, is it still a heap? The
boundaries of the word "heap" are fuzzy (i.e.,
not well defined).
Aristotle originally proposed the first rules of
logic. The Law of Contradiction states that A
cannot be both B and not-B. The same thing cannot belong
to a set and the complement of the set--opposites do not
overlap. The Law of Bivalence states that A must
be either B or not-B. In other words, something must be
either true or not true. Both laws were accepted and
became the foundation of logic for the next two thousand
years. The great philosophers such as Descartes and Locke
embraced the idea that every proposition was either true
or false. This paradigm fostered our current way of
Fuzzification and probability are very similar to each
other, however, probabilities change with increasing
information, where fuzziness remains the same.
Fuzzification attempts to deal in truths, where
probability has to do with the likelihood of something.
The problem with the acceptance of fuzzy logic is that
it feels natural for us to round things off (into
categories). Rounding creates clear delineations between
classes. It enables us to categorize things more easily.
Berkeley linguist George Lakoff (1987), worked with
Zadeh to describe hedges. These are words that we
use to modify (fuzzy) sets. The terms fall into various
categories, such as:
All purpose modifiers (very, quite, extremely)
Truth-values (quite true, mostly false)
Probabilities (likely, not very likely)
Quantifiers (most, several, few)
Possibilities (nearly impossible, quite
Some words (e.g., more or less) perform
dilation and expand the set. Others (e.g., very)
perform concentration and narrow the set. Hedges are
vague, since they have no exact definition, but they do
reflect human thought. Multiple experiments (Simpson,
1944; Hakel, 1968; Hoyt, 1972) have confirmed that people
order these words the same. Words like always, very
often, almost never and never, have shared
(but not exact) meaning.
Psychologist Eleanor Rosch (1975) also examined how
words were related to the fuzzy logic concepts. She found
that certain words (prototypes) were better
examples of a class than other words, and that the
ranking of these words matched our intuitive
understanding. Her research led to a three-tier
classification of categories as superordinate (abstract
categories), basic (concrete images), and subordinate
(subcategories). Rosch has proposed that classes exist
"to provide maximum information with the least
cognitive effort". (McNeill and Freiberger, 1993,
The Whorfian hypothesis states that linguistic
patterns determine how an individual perceives and thinks
about the world. This relativistic view is consistent
with general systems theory. Our culture and experience
define our understanding of all systems. The fact that
systems theory recognizes the relativity of perception,
may in itself, serve to expand our understanding of our
role in the universe. It provides a framework for us to
examine and understand our environment.
A systems approach provides a common method for the
study of societal and organizational patterns. It offers
a well-defined vocabulary to maximize communication
across disciplines. Rather than being an end in itself,
systems theory is a way of looking at things. It is a
internally consistent method of scholarly inquiry that
can be applied to all areas of social science.
Thomas Kuhn, in The Structure of Scientific
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scientific knowledge. He challenged the historical notion
that scientific truths were accumulated gradually over
time. Kuhn maintained that knowledge increases to the
limits of the current paradigm, and then gets replaced by
a new paradigm. The paradigm shift that occurs
reshapes scientific thinking until replaced by another
new paradigm. Examples of paradigm shifts are abundant in
history, but the most prominent feature is the enormous
resistance that the scientific community to entertain new
ideas. Scientists who have proposed new paradigms have
been the subject of intense professional criticism.
Physicist Max Planck summed up the scientific communities
resistance when he said, "A new scientific truth
does not triumph by convincing its opponents and making
them see the light, but rather because it opponents
eventually die, and a new generation grows up that is
familiar with it" (McNeill and Freiberger, 1993, p.
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