The System Dynamics Concepts of Model
Manuel Liz
Margarita Vazquez
University of La Laguna, Fac. of Philosophy,
Dept. of Hist. & Phil. of Science, Education & Language,
La Laguna, Canary Islands, Spain
ABSTRACT
When modeling and simulation in System Dynamics, we
can find many different uses of the term "model". Although
these uses are very interrelated among them, and with other
uses this term has in science, technology and philosophy,
they serve to very specific and diverse goals and purposes.
This paper tries to sketch a general framework in order to
analize that wide variety of uses the term "model" has in
System Dynamics. Sometimes, the differences among some of
these uses will be so important that more than different
uses of a term associated with a single concept, we could
speak of different and mutually irreductible concepts.
Nevertheless, whether these uses of the term "model" are
associated with a single underlying concept or with
different concepts, all of them are perfectly integrated in
System Dynamics. Our point is that this is one of the main
sources of its great success for making clear our ideas and
for managing our actions trought complexity.
1- Introduction: terms, concepts, and uses
First of all, we think necessary to say a few words on
the differences, from the point of view of the philosophy of
language, among terms, concepts and uses. Terms belong to
the grammar of a language, concepts belong to its semantics
and uses to its pragmatics. The grammar of a language is
composed by its alphabet, its vocabulary, and its sintaxis.
Grammar is the right place where types and tokens of terms
are identified. By definition, primitive terms of an
alphabet cannot be but gramatically correct. All other terms
can be gramatically correct or incorrect and more or less
complex. Semantics only appears through the interpretation
of a language. Roughly, concepts are the meanings of the
terms of a language. Philosophers, psychologists,
linguistics and computer scientists discuse whether meanings
fix the reference of these terms by means of necessary and
sufficient conditions, or by means of prototypes with
similarity conditions associated, or by means of any other
procedure. As an example of this, we can see Rosenberg &
Travis (1987) and Schiffer (1987). It is also disputed which
is the ontological place of meanings: are they social,
psychological or platonic objects?. See Block (1980), Lycan
(1990) and Haugeland (1985) for recent and interesting
reviews of these issues. In any case, if we understand
concepts as meanings, they are not linguistic entities of
the same sort terms are. Concepts are not used either. What
are used are the languages or, more properly, certain of the
terms of some languages. Really, concepts and uses are
related, but this relation is not direct. On the one hand,
uses of the terms of a language are actions, and these
actions can be very different depending on the goals and
purposes. This topic has constituted one of the most
interesting branches of recent linguistics and philosophy of
language. See, for instance, Austin (1962) and Searle
(1969). Only the declarative uses of the terms of a Janguage
are directly linked with the meanings these terms%can have
and, therefore, with the concepts these terms can express.
On the other hand, especially in the case of our natural
languages, concepts are selected by the way in which terms
are used with declarative purposes. We identify these
concepts by interpreting the language in relation to how it
is used. When we face a language in use, the determination
of the involved concepts always needs a hard work of
interpretation and rational reconstruction. That
interpretation and rational reconstruction must do justice
to the intended declarative use of the terms of the
language, but it must also permit to criticize some of these
uses as incorrect ones. This strategy, known as "reflective
equilibrium" in the ambit of analytical philosophy, is well
expoused and defended by Goodman (1973), Rawls (1971), and
Sosa (1991).
These distintions that we have just made are relevant to
our topic. When in System Dynamics we say that we have a
model, that we want to build a model, that a model is used
in some way, and so on,.we are applying to something certain
term, the term "model", and we use this term to express some
intended concept.
2- The uses and concepts associated with the term "model" in
everyday, scientific, technological, and philosophical
languages
The term "model", including here all its derivates,
appears very often in our everyday, scientifical,
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technological, and philosophical languages. To begin with,
let us consider three of the most prominent uses of the term
"model" in everyday language:
@)
(2)
(3)
its
"Model" can be used referred to an object of
representation or copy.’ So, we can say “to copy a
model", or "to pose as a model for an artist", etc.
"Model" can also be used referred to a representation,
design, project, mold, plan, etc., of something. So, we
can say "to model an object", or "to make a model of
something", or "to create new political or economical
models", or "theoretic models", etc.
"Model" can be used referred to an special example or
pattern of imitation in matters of knowledge or
practical behavior. So, we could speak of “serving as
a model", "taking someone as a model of virtue", even
“being a top model".
In the scientific languages, the term "model", and all
derivates, appears and it is used in three main
contexts: in the context of the presentation and use of any
scientifical knowledge, in the empirical context of the
cognitive science, and in the formal context of the logical
and mathematical model-theory. In the first general context,
it is possible to distinguish the following uses:
(4)
(5)
(6)
(7)
"Model" can be used referred to particular selected
examples of a general set of rules or theory. So, we
can talk about the solar system, about the pendulous,
about the tides, etc., as particular "models" of
classical mechanics, or about a particular system of
human relations as a particular "model" of some theory
of social choice, etc. Examples of this use can be
round in Suppes (1960), Sneed (1971) and Stegmuller
(1979).
"Model" can be used referred to pieces of relevant
scientific knowledge or to sets of algorithms or rules
that, having not properly the status of theories,
because they are something less than theories, are very
useful in order to articulate, systematize and make
operative the scientific work. Examples of this use can
also be found in Suppes (1960).
"Model" can be used as a term synonimous of "theory",
as it happens very often in the social sciences.
"Model" can be used referred to a set of interelated
theories or, including practiques too, that is
institutional and ideological affairs and so on,
referred to what has been called a "paradigm". This is
usual in the works of historians of sciences.
In the empirical context of cognitive science, the term
model appears as a theoretical term of a set of theories
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that oppose their concept of "mental model" to the concepts
of "schema" "script", "frame", etc., developed by Minsky
(1975), Schank and Abelson (1977), Rumerlhart (1980) and
others, which have been extremely influential in cognitive
psychology and artificial intelligence. The main references
to mental models in this context are Johnson-Laird (1983),
Schank (1982) and Holland J. et al. (1989). Brehmer (1989)
makes some references to this concept of mental model from
System Dynamics. Nowadays, these theories are not
rigourously defined, but they are one of the most prominent
alternatives in the recent cognitive science. We can
summarize the use of term "model" in this context as
follows:
(8) "Model" can be used referred to the sort of dynamical
and ruled-based internal representations that a
psychological subject is able to make from parts of its
environment and of itself as integrated in its
environment. "
In the formal context we have indicated, the term
"model" also appears as a theoretical term of a concret
theory. In this case, the term is introduced more precisely
and defined because the theory is not empirical but formal:
this is the mathematical and logical "model-theory". This
theory was initiated by Alfred Tarski and others in the
1950s and constitutes one of the main branches of the actual
Mathematical logic. See, Tarski (1953) and, for a more
recent presentation, Chang, C. & H. Keister (1973).
(9) "Model" in the context of model-theory is used referred
to a domain of objects which made true (according to
some explicited and precises stipulations make by that
model~theory) a set of statements of a formal language
always with respect to an interpretation of this
language in that domain of objects.
Scientific uses of the term "model" in these contexts
are related with our everyday ones in the following way:
uses 4 and 9 express a concept similar to the concept
expressed by 1, and uses 5, 6, 7, 8 and 9 express a concept
similar to the concept expressed by 2.
In technological languages, we have more ambiguity. The
Main uses of the term "model" in technology are:
(10) "Model" can be used referred to certain material
objects made with the purpose to offer a concret
perspective of a design or project, perhaps not
completely understood, or described only from a
theoretical point of view. The term "model" and its
derivates can be replaced here for the terms
"prototype", "map", etc.
f
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(
(11) "Model" can be used referred to pieces of relevant
knowledge, scientific or not, or to sets of algoritms,
rules, computer programs, and so on, known or supposed
as interesting and useful with respect to some topic.
(12) "Model" can be used referred to any specification or
description of an object or system. Some formal
theories about the processes of modeling and simulation
in technology try to analyse that use. Zeigler (1976,
1984a and 1984b) is one of the more interesting ones.
He considers a model as a possible specification of a
system. Specifications could be made through systems of
diferential equations, automata, etc. He proposes a
general hierarchy of specifications. They beging with
low levels of specification, as those of "black boxes",
and goes up to rise specifications in the form of
multicompoused systems. The bottom-up, top-down, and
horizontal studies of those jerarquies show very
interesting points about modeling, simulation, and the
relationships between structures and behaviours. See
Vazquez & Liz (1989).
(13) "Model" can be used to refer to certain material or
conceptual objects with which help it is possible to
solve certain problems of calculus and, in the end,
certain practical problems. This use is very common in
technology. For instance, in the field of artificial
intelligence, Minsky (1968) wrote "We use the term
"model" in the following sense: To an observer B, an
object A* is a model of an object A to the extent that
B can use A* to answer questions that interest him
about A."
The technological uses of the term "model" overlap both
the everyday uses and the scientific ones. Of course, up to
a certain extent, the same could be said of the everyday and
scientific uses, but the situation is not exactly the same.
With respect to the concret term "model", technological uses
are more parasitic from the everyday and scientific ones
than the seconds are from the formers. Technological use 10
is conceptually related with scientific uses 4 and 9, and
with everyday use 1. Technological uses 11 and 12 are
related with scientific uses 5, 6, 7 and 8, and with
everyday use 2. Finally, technological use 13 is in some
indirect way related with scientific use 5, but it is
strongly connected with everyday use 3. Uses 10, 12 and 13
are typically technological. We should note the following.
First, in 10 we have something like the converse concept
that is expresed by scientific uses 4, 9 and by everyday use
1. In 4, 9 and 1 the objects are given, in 10 the objects
are built. Second, in 12 but not in scientific uses 5, 6, 7
and 8, the strict scientific descriptive components are not
necessarilly present. 12 is closer to 2 than to strict
scientific uses of "model". Third, technological use 13
involves the need to solve practical problems with the help
of material or conceptual objects which are called "models".
This use of "model" is not present in science and go
directly to everyday use 3.
Finally, in philosophical languages the term "model",
and its derivates, is mainly used in a methatheoretic sense.
It is used in order to make clear what can be its proper
meaning, especially in the fields of science and technology.
In other words, it is used to describe and legislate its
correct uses. From the seminal work of Suppes (1960) and
through all the philosophy of science dedicated to the
rigorous formalization of scientifical theories, see for
instance Sneed (1971), there is a constant tendency to
asimilate and reduce all the uses of "model" to the precisse
use that this term has in the model-theory. According to
this perspective, there is only a concept that all uses of
"model" intend or must intend to express, the, concept
referred by our use 9. This use is pretty close ‘to use 4
and, in certain sense, to use 10, and the same concept is
intuitivelly referred also by everyday use 1. Other uses
must be reconstructed with relation to that basic one. And
all differences of meaning must lie in the situations of
uses of the term "model", not in the very concept expressed
by the term itself. For instance, use 6 will be superfluous
if actually there is a theory, and if there is not such a
theory, use 6 must be analogous to uses 5 or 7. This was the
radical explicit thesis maintained by Suppes (1960). What
happen with uses like 5, 7, 8, 11, 12, linked to everyday
use 2?. A possible direct answer can be found in Mosterin
(1984). According to him, "system A serves as a model of
system B for subject h if and only if 1) A is simpler or
more known for h than B, 2) h developes (or could do it) a
theory T from A, and A is a model of T in the sense of the
model-theory, and 3) B is also a model of T in the sense of
the model-theory".
The sort of objects that can be models in the sense of
the model theory is so wide that there is no problem in
considering both a real system and a numerical or linguistic
description of it as models of certain theory T. But, in
spite of this, the problem is that even if we accept all
that sort of sugestions and reconstructions for uses 2, 4,
5, 6, 7, 8, 10, 11, and 12, it is very odd to try to do the
same with uses 3 and 13. These uses have and irreductible
practical component. The main point is that the conceptual
or material objects that are called here "models" have an
unavoidable reference to the actions a subject is able to
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oN
perform with their help. Going back to 13 and seeing again
the characterization that Minsky (1968) gives of these
models, to find out that sometimes, uses 5, 8 and 10 have
also important practical components.
There is, in consequence, enough reasons to think that,
even if uses 1, 2, 4, 5, 6, 7, 8, 9, 10, 11 and 12 of the
term "model" express a single concept, a concept make
precise by model-theoretic use 9, uses 3 and 13, and
sometimes uses 5, 8 and 10 too, express a different concept,
a concept in which the actions performed with the help of
the so called "models" become fundamental. Let us call this
concept the operational concept of model. And, there is also
reasons to distinguish among uses in which a theory is or
could be clearly involved from uses in which this is not so.
This last distintion goes across 1, 2, 4, 5, 6, 7, 8, 9, 10,
11 and 12, and allows us to speak of two other concepts
associated. Let us call them, respectively, the model-
theoretical concept. of model and the purelly
representational concept of model.
Now, we dispose of some conceptual framework in order
to analyse the uses and concepts associated with the term
"model" in SD.
3- The uses and concepts associated with the term "model" in
SD.
In SD there are theoretical developments and practical
aplications related with everyday, scientific and
technological knowledge. See Forrester (1986) and Vazquez,
Liz & Aracil (1990). The term "model" is present everywhere
in SD. In relation to some of the most complex expressions
term "model" that appear in SD, we could distinguish, at
least, the following uses: a)'mentalmodels"; b) "verbal or
linguistic models"; c) "models expressed in causal
diagrams"; d) "models expressed in Forrester’s diagrams"; e)
"models in a DYNAMO (or STELLA, or any other more basic,
sofisticated or extended software) format"; f) "simple
mathematical models", "models expressed by means of systems
of equations", etc, and g) "cualitative models" or "more
completed mathematical models".
The standard process of modelling and simulation goes
from a) to g), perhaps omiting some of the steps or going
through feed-back movements. The important point here is
that generally we have no explicit and concrete theories
with respect to which all these so called "models" can be
models in relation to a model-theoretical concept of model.
i BBL
Usually, we build models in SD just because we have not such
theories. From this point of view, in all the uses of the
term "model" in SD, we cannot mean but a _ purely
representational concept of model. This is specially obvious
if we realize that, at the end, the whole process of
modelling and simulation in SD lays on mental models, the
intuitive and fuzzy knowledgé experts, or people in general,
have about the systems that are modelled and simulated. See
Forrester (1986), Meadows (1980), Randers (1980) and
Vazquez, Liz & Aracil (1990).
But, we have another important point of view in SD. Our
models are tools with which help we improve, manage and
control our action. The conceptual or material objects
mentioned in b), c), da), e), f) and g) interact with the so
called "mental models". Mental models change with the
experience and the discussion, and they also change through
SD’modelling and simulation process. All the useS of the
term "model" in SD are related with an operational concept:
of model.
Mental models ocuppy an important place in our
analysis. If they were superfluous, we could have models in
the sense of a model-theoretical concept of model, but we
could not have models in the sense of an operational concept
of model. Because mental models are not certainly
superfluous in SD, our models are something less than models
in the first sense, they are only purely representational
models, and they are models in the second sense, they are
models in the sense of an operational concept of model.
Actually, the term "mental model" in SD has all the
ambiguity that this term has in everyday language. And this
language makes impossible any attempt to impose definite
meanings. We use "mental models" in all the everyday senses
indicated in 1, 2 and 3. This has a lot of danger, but it
is also one of the main sources of the value that the SD
formal reconceptualizations have as tools for making clear
our ideas and for managing successfully our actions trought
complexity. Of course, futures developments in the cognitive
sciences on models could make our mental models models of
some psychological theory, in the sense of a model-
theoretical concept of model, and therefore the three
different concepts of model we have distinguish could be
unified. But this would be to speak of the future, not of
our real models.
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4- Conclusions : :
In this paper we have distinguished three different
concepts of the term "model": 1) a model-theoretical
concept, 2) a purely representational concept, and 3) an
operational concept. In SD, the term "model", and its
derivates, should be associated with the second and the
third of these concepts. The main reasons for this make
reference to the special and unavoidable role played by
mental models in SD.
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