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The philosophy of modeling and futures research
TECHNOLOGICAL
FORECASTING
AND SOCIAL CHANGE 21, 267-280
(1982)
The Philosophy of Modeling and Futures Research A Guide to Different Models IAN I. MITROFF
ABSTRACT The concept of inquiry systems as originally formulated by Churchman is an exceedingly powerful one. Each inquiry system can be construed as an archetypal or generic kind of model structure that applies generally throughout all of the sciences. Recent developments in the logic of argumentation and symbolic logic show how, paradoxically enough, the model structure of each inquiry system can itself be modeled in terms of the first-order predicate calculus. The result is a “model of models.” More important and more fundamental still, the effort shows the tremendous assumptions that must be bought if one is to warrant belief in any particular inquiry model.
Introduction In 1973, Murray Turoff and I wrote a paper [4] for this journal that described some basic philosophical systems and their importance for technological forecasting and futures research. Since that time the technical sophistication of various approaches and models in the field has increased enormously. However, from a philosophical perspective, the soundness of these models has not changed or improved accordingly. The models of the field are only as good as the underlying premises on which they rest. And in fact, the more the technical sophistication of the models has improved, the more critical it has become to examine the premises that underlie them. In short, the danger is even greater that we will mistake technical sophistication for philosophical soundness. This paper revisits the philosophical systems described earlier and shows how each of the systems can be operationalized mathematically. In the intervening years since the Mitroff and Turoff paper was written, some powerful tools have been developed that allow one to build prototypical models of each of the systems. These models are themselves so general that they allow us to show the general premises that must be posited and accepted if one is to authorize a particular model or approach. It is important to appreciate the significance of the preceding comments. By operationalizing the systems, philosophy thereby becomes of direct interest and relevance to the model builder. It becomes a powerful tool for exposing the general assumptions upon which all models and approaches must of necessity rest. If the assumptions underlying a particular model or approach are judged inadequate or unwarranted, then the use of the model or type of approach is not warranted. IAN I. MITROFF is the Harold Quinton Distinguished Southern California. 0 1982 by Elsevier Science Publishing
Co., Inc.
Professor on Business Policy at the University 0040-1625/82/040267-14$02.75
of
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1.1. MITROFF
The Structure of Arguments The philosopher Stephen Toulmin has developed a qualitative framework that in the opinion of the author is so general and so powerful that it provides the basis for capturing the structure and dynamics of all models [6). Originally developed by Toulmin to capture the structure of complex arguments, the framework can be applied to the field of modeling. In effect, a model can be viewed as a series of propositions or logical statements (arguments) designed to convince the model builder or user (often it is the builder more than the user) of the reasonableness or plausibility of the output of the model, if not of the entire model itself. In Toulmin’s language, every argument terminates in a claim (i.e., an assertion designed to convince an interested party such as a citizen. decision maker, and the like) of the reasonableness or truthfulness of a purported state of affairs or a proposed set of actions (i.e., a policy). Every claim thus terminates in one of two ways: I) it asserts that the facts describing the state of a certain system or of the world are of a certain nature; for example, company X in industry Z will make or has made a 25% profit during the last quarter; 2) based on the “facts,” company X ought to take a certain series of actions (policy Y) if it wants to increase its profits. Thus in the first case the assertion is either a forecast (“will”) or a statement of facts (“has”). In the second case, the assertion is either a technical hypothetical (“if you want to get to goal G, then you ‘ought’ to do Y”) or a moral imperative (“you ‘ought’ to do G because it is good, desirable, and so forth”). In order to reach or justify the claim, every argument appeals to a certain body of evidence, which represents the prior data, facts, and so forth available to us on which to base our argument. In logic, the evidence stands for the minor premise of an argument. The warrant is that part of an argument that allows us to go from the evidence to the claim. It authorizes, as it were, the mental leap or transition from evidence to claim. The warrant thus takes the logical and semantic form “If the evidence is E, then the claim C follows because “; that is, all warrants are of the same or fundamental logical form “if E, then C,” or in symbols, E + C, where the arrow may be taken in the usual sense of logical implication [3]. All warrants, however, are not of the same semantic form for the obvious reason that warrants differ significantly in their reasons for justifying the logical form E -+ C. For example, some arguments justify E -+ C “because C is causally connected to E.” Others justify E -+ C “because of analogy”; that is, C follows or has followed in the past from a series of Es. The E in this particular case is judged to be similar to past Es; therefore, by analogy, E -+ C holds. Note that the author is not necessarily justifying this kind of argument, merely noting one of the prevalent forms of argumentation. Whether a particular form is warranted in a particular case is precisely the topic motivating this paper. The reader is directed to Mason and Mitroff [2] for an extensive review of other forms of argumentation, especially in the field of policy analysis. Thus far the Toulmin framework has the same structure as that of the classic syllogism. The claim represents the conclusion we seek to establish or to justify. The evidence represents the minor premise; the warrant, the major premise. It is the other two terms that give the Toulmin framework its uniqueness and power. The backing represents the deeper, background parts of an argument. These are rarely brought up to the surface. However, if the warrant or the evidence is not accepted on its face validity, then the backing comes into play. It attempts to justify the relevance of a particular set of evidence to the establishment of the claim. The backing does not establish the technical reliability, validity, or objectivity of the evidence. That must be done by
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other means (i.e., through another argument structure pertaining to the methodology under which the evidence was collected, assessed, and so on). The backing also attempts to justify the “because” part of the warrant (i.e., why it applies or holds in the case under consideration). From the standpoint of modeling, forecasting, and futures research, the last term, the rebuttal, may be the most critical of all. The rebuttal stands for any or all of the challenges to any part of the main argument structure-claim, evidence, warrant, and backing. Thus, for instance, one can challenge the E, or evidence, by asserting that some other evidence set -E (read “not E”) is more applicable, relevant, reasonable, and the like. Similarly one challenges the warrant E -+ C by asserting that some other warrant, say, -E + C, is more applicable. In this case, one asserts that, as before, C follows, but that it results from -E and not from E. In a similar fashion, by means of the first-order predicate calculus, one can tabulate the simple kinds of arguments and their corresponding possible rebuttals. (See Mason and Mitroff [2] for a systematic treatment.) The first-order predicate calculus is indispensable in this effort because almost from logical considerations alone it can be shown that there are only so many forms of rebuttals to any argument [2]. The first-order predicate calculus is indispensable in another but related way. All models attempt to establish the existence of a logical structure holding between a set of variables. Given that this is the case, it makes sense to employ some concept of formal logic to represent this logical structure. Finally, there is another reason as well. The number of formal relationships in a model often quickly exhausts our ability to see all the implications that follow from the model. The use of the first-order calculus can aid our ability to examine all of the complex implications that would otherwise escape us if we restricted ourselves to a merely qualitative examination of models. Thus we will employ the first-order calculus in this paper even though the representations of the models we will examine are simple enough that they could all be stated in words. The importance of the Toulmin framework should be apparent by now. It allows us to lay out in a systematic and logical fashion the structure of complex arguments. In the sequel, we will attempt to show the different kinds of evidence, warrants, backing, and rebuttals that different systems use in seeking to establish and to challenge different kinds of claims (i.e., the outcome of different models viewed as arguments). By expressing each part of the argument as much as is possible in the first-order predicate calculus, we will also attempt to show how the Toulmin framework originally developed as a purely qualitative tool can be extended to give a more precise quantitative rendering of the structure of models. We need two other pieces of machinery before we can proceed. The presence of R (the rebuttal) in an argument structure introduces some serious logical difficulties; it also introduces some novel opportunities as well. Consider, for instance, a simple argument consisting of evidence E and warrant, E -+ C. Suppose also that we have an R of the form E + -C; that is, there is a counterargument to the main argument that -C, and not C, follows from E. For instance, E could be a series of data on the current state of the American automobile industry and C a prediction as to the fate of the industry relative to imports in 1990. Then -C would be a counterprediction based on the very same evidence but different underlying reasons (i.e., backing). If we consider the entire set of assertions as a total system of propositions, then a logical contradiction results; that is, from E and E --$ C, one is entitled to conclude E & C by means of traditional logic [3, 51. If E is
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regarded as true, and if the warrant “if E. then C” is also true, then E and C are true. But from E & C and E -+ -C, E & C & -C results. That is, if E is true, and if “E implies -C” is also true, then E and -C is true. However, C & -C is a logical contradiction. According to traditional logical reasoning, C and -C cannot both be true at the same time 13, 51. The point is that the presence of R introduces deep logical contradictions into the structure of an argument considered as a total system of propositions. Now one can always preserve logical consistency by throwing out those parts of the argument that conflict, but this seriously begs the questions: Which parts should one throw out? How does one insure oneself (i.e., know) that one is throwing out the “right” parts? What does “right” mean? Is it possible to proceed without throwing out any of the parts of an argument‘? Notice the critical nature of these questions. If every argument has Rs, if no argument is ever so airtight that it is free from all challenges (no matter how weak they may appear), then this situation is completely general. All decision makers face it all the time whether consciously aware of it or not. Indeed, if they are not consciously aware of this situation, it means they unconsciously throw out parts of an argument structure. If so, we need some nonarbitrary basis for handling those parts of an argument that conflict with one another and for raising this up to consciousness for explicit examination. Although developed for other means, the concept of maximally consistent subset (mcs) invented by the logician Nicholas Rescher [5] can be profitably applied [2] in this case. A mcs is the largest subset of propositions that can be formally conjoined (i.e., linked together through the logical operator “and”) such that the subset is logically consistent. Thus in the case E and W = (E -+ C), and R = (E --+ -C), there are two me’s: mcs, = {E, W} and mcsz = {E, R} because from mcs,, E & W = E & C and from mcs?, E & R = E & -C, each of which is internally consistent. The concept of a mcs thus allows one to preserve all the information contained in the entire original set of propositions. To handle contradictions, we merely form all the possible mcs’s. Each mcs represents a different logically consistent conclusion that can be formed from the original set. The concept of mcs allows us to examine many more potential conclusions lurking within a formal system than if we were only to focus on the parts we naturally prefer. This feature once again shows the power of employing some concept of formal logic to express the components of a model. This is only half a Rescher’s contribution. Once we have the full set of mcs’s, we would like some way of ranking them in order of preference. This is where Rescher Plausibility is tantalizingly close to subjective introduces the concept of “plausibility.” probability in many ways but is noticeably different nonetheless. Probability refers to the likelihood of occurrence of an event; plausibility refers to the credibility, the believability of an assertion within the context of a total argument or a streaam of other propositions. As such, plausibility follows a different axiomatic structure, one that is better suited to judging the modality of a proposition representing various grades of possibility and/or believability. Thus, for instance, a proposition could be highly plausible in that logically it makes a great deal of internal sense or it is uttered by someone in whom one has a great deal of faith. At the same time, the proposition could be highly improbable in that the events contained in the propositions may have a low probability of occurrence. Without going deeply into the detailed axiomatic structure of plausibility, plausibility is an important concept for forecasting and futures research, for the field not only has a need to judge, say, the cross-impact probabilities of various events on one another, but it has no less a
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need to judge the credibility of various arguments and scenarios, both independently and dependently of their probabilities. For our purpose, one feature of the axiomatic structure of plausibility is especially important. Consider modus ponens, one of the traditionally accepted and most deeply regarded valid forms of logical reasoning (i.e., if E is regarded as true, and if E -+ C is also regarded as true, then C follows or is also regarded as true, that is, a justified conclusion). If plausibility is measured on a scale where 0 or a small number represents a logical truth or the highest degree of plausibility and if N >> 0 represents the lowest degree of plausibility, then pi(C) = max[pl(E), pl(E -+ C)]. In words, the plausibility of the consequent C of an argument will in general be no stronger than the weakest of its antecedents. Other rules can be formulated, but we will not pursue them here [5]. Models As Arguments:
The Role of Judgment
CONSENSUAL
SYSTEMS
INDUCTIVE
in Model Building
At least five basic or archetypal kinds of model structures can be identified [ 1, 41. These archetypal structures can themselves be combined in almost endless ways. In addition, countless variations and varieties exist within each structure. In order to illustrate therefore the spirit of an almost bewildering variety of structures, Tables 1 through 5 present what the author believes is a core example from each approach. Table 1 portrays the structure of a consensual inductive model system. This system corresponds most closely to what Churchman has termed a Lockean inquiring system [ 1). The model is inductive because it infers, or attempts to infer, a universal pattern from the observation of n occurrences of a series of events. That is, if an event a has occurred n times, then the next if not all subsequent occurrences will also be a. This kind of structure underlies a great variety of models and processes in science. In particular, the early Delphis, with their extreme emphasis on consensus and the wide variety of trend extrapolation models with their emphasis on continuity, are prime examples of this kind of model structure. The model starts with the observation that the same event a has repeatedly occurred n times in succession. The warrant then tries to infer that not only will the next observation result in the same observation a but that all successive observations will result in a. In actuality, the warrant may be more complicated than this. With each increase in the number of previous us that has been observed, presumably the higher the plausibility of = u)],k f i,k>i, the complex assertion (a, = a & *..&a,, = a)--+[(~, = a)-+(~, i 2 n becomes. Note the considerable complexity of this warrant. It is an inference ((a, = a & *mm & 1) of an inference [(a, = a) + (an = a)]. Notice also that the warrant a” = a)-+[ may assume a wide variety of different characteristic shapes. Instead of the mere number of same occurrences of a basic or atomic event u, the variance between the n u, may be used to infer the next in a sequence of events or observations. Presumably the tighter the variance, the higher the plausibility of the inference. Another prevalent form is the prediction of the frequency of two basic kinds of atomic events a and b, because the indefinite occurrence of II exactly similar events a is highly limiting. For another, the warrant may be thought of as a continuity principle instead of as a prediction or inference license. Finally, a critical part of every warrant in this model, no matter how it is expressed, is the assertion or postulation that the continuity of the
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sequence eventually terminates in the attainment of some desired goal or end state q,,,,. As can be seen in Table 1, qrr,, is typically the tightness among the estimates of a panel of Delphilike experts on some important topic of prediction or a series of empirical observations. In the extreme, qu,, is taken to be the truth or correctly predicted end state of some system. Thus in a Delphi, presumably the tighter the agreement between the predictions of an independent set of experts, the more that the mean or some function of the expert’s predictions will converge toward the “truth.” In effect, the claim expresses the sentiments of the preceding paragraph and conveys that belief in the general principle [(a, = a) + (al. = a)] is warranted or supported by argument (i.e., the structure of the model), and that as a result, q,,,, is obtained. The backing is rarely if ever expressed in such systems. It constitutes one of the core beliefs of all empiricist systems. This is the strong belief that the act of observation alone does not presuppose any prior theory in order for the act of observation to occur. That is, observations are theory-free. Although people may disagree on the meaning of the “facts,” presumably all can agree on the same basic “facts” (i.e., that something has at least occurred). The rebuttal challenges all of this. First, it denies that observations are theory-free (i.e., it asserts that a, = a,(7’,). It asserts that some theory (not necessarily unique, hence 7”) underlies the taking of all observations in science. There must be some prior principles of selection and categorization operating in order to single out some features of a complex system as foreground as distinguished from background, whether the observer is consciously aware of this or not [ 1). The second element of the rebuttal denies or challenges that a finite set of observations is ever sufficient to establish a general inductive principle of the form [(a, = a)-+(~, = a)]. Indeed, the plausibility of this part of the rebuttal may even reach maximum if even one counterinstance of an a not occurring is observed (i.e., if a, = -u). Finally, a more sophisticated challenge to the backing, R statement number (3), is the Kantian point that the observation of n occurrences of a phenomenon does not necessarily warrant belief in an inference; rather, it is the other way around. Belief in some fundamental principle of continuity, order, and/or categorization is necessary if the act of observation is to be possible by anything resembling a cognizing agent. i.e., an entity, human or not, capable of having experience. The ability even to have experience implies an agent capable of, first of all, distinguishing some “things” from “others” and, second, of ordering them into some framework [ 11. All of this is implied in R statement number (3) in Table 1. Notice that not all of these rebuttals are equally damaging to the claim. The claim can live with all of them except the strict denial that the observation of tz occurrences necessarily implies a universal inference. If the judged plausibility pl of this part of the rebuttal is greater than the judged pl of the corresponding part of the warrant, then the claim does not follow (i.e., is not warranted). The author and his colleagues [2] have found that one of the great benefits of this whole approach is that it lays out clearly what one is required to give fundamental assent to (to believe) if one is to justify the output (claim) of a particular model. Often just laying out the propositions in such stark form is helpful. For instance, it becomes painfully obvious just how big a leap the warrant entails. One has to warrant the inference of an inference. It becomes painfully obvious that the inference required to warrant the inference is often no more certain or justified than the inference ((a, = u+(u, = LI)) one is trying to establish! If the warrant itself cannot be established or if it must be presumed
KEY:
= a)]}
= a & ... & a, = a)
= a)-t(ar
Backing:
a, = a($)
(2) [(a, = a)-(ar
= a)J +
9,,1,
k = i, k > i, i 2 n
[(a, = a)-(~,
= a)]
(I) a, = a
(n) a,, = a
(2) al = a,
There exists a series of observations such that the same event is repeatedly observed to occur.
Evidence:
a($)
= an assertion to the effect that the occurrence
of event a is not dependent on the prior presumption
of a theory T,
9,,,, = some end state prediction as to the state of a system and/or a series of actions (policy) that ought to be undertaken to improve on the state of the system.
= a)]+(a,
= a & ... & a,, = a)+[(a,
(3) [(a, = a)-+(ar
(2) -{a,
warrant: (I) (a, = a & ... & a,, = a) +
(I) a, = a(T,)
i2 n
Rebuttals:
k = i, k > i,
a,,,
I = a& I@,= 0)+ (4 = 41 & 9.1,
Claim:
TABLE 1 The Model Structure of Consensual Inductive Systems
1.1. MITROFF
274
by means that are themselves outside the model [ 1, 21, or if the pl of the rebuttal is judged to be gt’eater than the pl of the warrant [2], then this model or approach is itself not warranted. ANALYTIC
DEDUCTIVE
SYSTEMS
Table 2 represents a very different kind of model structure from the first system. It corresponds most closely to what Churchman [l] has termed a Leibnitzian inquiring system. It claims that starting from a unique, intuitively known, if not “self-evident,“’ proposition or set of primitive notions, p,, one can by means of a network’ of other propositions that follow from p, but are themselves presumably less certain than p, finally deduce q,,,r. The warrant also says that q ,,,, does not follow any other series of propositions r,. This system is the archetype of formal, analytic, deductive models; “formal” because the concepts are typically expressed in formal mathematical terms; “analytic” because concepts are typically taken as “self-evident” or “given”; “deductive” because the claim follows with whatever deductive force the system can muster (i.e., the system functions as one huge syllogism). The backing for such systems is typically a statement of the “primitive,” “fundamental,” “ laws” of logic. That is, a proposition p, and its negation -pi cannot both be certain or true at the same time; hence -@, and -p,). Notice that the backing in this case is much broader. It reads that an intuitively certain proposition p, and any of its competitors p, cannot both be true or highly pl at the same time. Alternately, p, or p, is true, but not both of them. Without commenting in detail, the rebuttal challenges every part of the structure of the main argument. For instance, it denies that p, is unique (R number (l)), that there is no other way to reach y,,,, (R number (3)), that p, and p, cannot both exist at the same time (R number (2)). An even stronger form of challenge is that there is only one form or kind of TABLE 2 The Model Structure of Analytic Deductive Systems Claim: p, & y ,,,, Rebuttals:
Warran,:
(I) There exists another
(1)
proposition p, such that its plausibilityplfpj) is high & PKPA >> PKp,) j is not unique
PI -
4,,/,
YI
tn +
(I)’
P, -
rl
(2)’
(2)
1) Y,,+I -L 9,,,,
(n + I)’ -(r,,+,
i
q,,,,)
There exists a p, such that its plausibility p/(p,) is high & Pl(P,) >>
PRP,)
or
Backing: (1) -c/7, & p,) -
(2) P, &P,
(3) rr,+I +
E~kknw.
c-p,
(2) p, or p, = -c-p,
or -p,)
Pl(P,) + Pl(P,) = N for all ”j; i unique
& -p,‘,)
KEY: See Table I for the meaning of Y,,,,. Note that the warrant consists of two argument chains. One chain says that q,,,, follows from a series of propositions q$. The other chain says that y, does not follow from any other series r,.
‘This is expressed in the evidence as pl(p,) = 0 or that the plausibility recalling that large pl numbers stand for low plausibilitiea and vice versa. ‘That is, the warrant: ~1,-
y,, and so on
of,‘, is high &
p/b,) >3>p&p,).
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q,,,, (i.e., set of criteria by which successful problem-solving performance is judged. That is, there are a whole series of other q{,,,,. Again, it should be apparent that this approach underlies a wide variety of applications in science. The first two approaches outlined briefly in Tables 1 and 2 often exist side by side without significant interaction. Data or observations are often collected without the conscious or explicit presumption of theory and then are fed into a formal model consisting of a very explicit, formal theory. Typically, the data input to the model are downgraded in importance, the formal model being considered of prime importance in establishing q,,,,. However, considered as a total system, this means that other arguments are lurking beneath the surface (i.e., in the backing), namely, that the formal part of the system takes precedence over the informal or data parts of it. If this part of the argument is challenged, then it moves us to the next archetypal class of systems. SYNTHETIC
MULTIMODEL
SYSTEMS
This system comes closest to what Churchman [1] has termed a Kantian inquiring system. The basic idea is that all phenomena, physical as well as social, are too complex to think that there is one and only one model that is correct, achieves the “truth,” or comes closest to qu,,, whatever q,,,, may be. Instead, this approach believes’ that no one single model is ever sufficient to capture the “reality” underlying any phenomenon. Indeed, every model self-selects a basic set of variables or notions that it takes to be fundamental over all others (i.e., intuitively obvious, self-evident, certain, and so on). Extending this a bit, different disciplines give fundamentally different explanations of phenomena. Thus a sociologist emphasizes institutional and social factors; a psychologist, individual factors; an architect, spatial factors. One of these is not necessarily right; all others wrong. Instead, each picks up a partial slice of an exceedingly complex “whole” of reality. The fundamental presumption of this approach is that the ultimate user of a model will gain more of an understanding of this complex, holistic reality by being exposed to the interplay of several models M, rather than being presented with just one. Hence this approach starts with a fundamental entity called the executive. The executive is that component of a system that decides which of the several models of which it is aware to present to a particular decision maker to model his or her problem. In Table 3 this is represented by s, (i.e., there exists a basic notion s, such that s, + UM,,where U stands for the union. That is, S, generates a series of separate models, each of which has a model structure as represented in Tables 1 and 2. Each M, represents an integrated inductive, consensual, and an analytic deductive system. There is a theoretical ordering principle in the model somewhere, q,,,, which directs the model to collect a kind of data D that is compatible with the notions underlying the model. A data structure D is made of two components: the observation of n as in a phenomenon and an inductive principle (a, = a) + (a, = a)-if a, is a, then the next uk will also be a. The backing is the presumption that the intersection, represented by the symbol n , of the models does not lead to nothing (i.e., the null model does not result). This is a psychological condition more than it may be a logical one. It assumes that the user learns something significant (and hence not @ or nothing) from the flMj. It is also assumed that nM, do not lead to a logical contradiction (LC). It is also assumed contrary to the assertion of each of the individual models that no single M, leads to q(,,,.
‘We are not necessarily
arguing for it. but rather presenting
the reasoning that underlies it
+
& (a, = a) --j (a,, = 4
M’)
-(M + 4.1,)
-(nM,
-{q:X:
(3) There exists a model M, such that
(3)
+
does
y,,,,); none of the initial models by itself is sufficient to achieve q,,,,.
not lead to a lo@cal contradiction.
LC): the intersection
of the M, does not result in the null model.
# @: the intersection
-(M, +
(2) -(nM
( I ) nM,
Buching.
q,,,,
The intersection of the initial models M, gives rise to a new model M’ that then achieves q.,,.
LC
= @
(2) nM, *
M’ +
(I) nM,
nM, +
Wurrunt:
s, & nM, & M’ & q ,,,,
Rebuttals:
Claim:
TABLE 3 The Model Structure of Synthetic Multimode1 Systems
4,,I,
[Jlas & (0, = (I) -
Y,,,+
(/w & D -
(I,?
(/,I +
(2) M,: p, -+ q,,
(q = u,]
(I) There exists a concept s, such that 5, + UM, i>2 or .\,generates a series of models. where a model is defined as
EGdewr:
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AND FUTURES RESEARCH
The warrant assumes that the fM4, leads to a new understanding on the part of the user, a synthesis, a new model M’, and that M’ leads to qu,, more than any other M,. There is no guarantee that the M, lead to a significant M’ in every case or that M’ in every case or that M’ leads to qr,,,, a fact reflected in the rebuttals. Also, there is no guarantee that the M', if it exists, can be formalized to the same degree that the M, are initially. This point in itself is not necessarily a rebuttal. Rather, the important point is that the synthesis need not be formal in order for significant understanding to be said to exist for the user, the party perhaps above all for whom this system exists, and not the model builder as in the previous two systems. In many ways the most critical feature of this system is the executive. Because so much depends on it, how do we know that it is any better than the analytic deductive system considered previously? In many respects we do not know, except insofar that one of the aspects of qu,, is self-reflection. One of the basic goals of going through the process represented in Table 3 is to learn more about which models should be included in the executive (i.e., whether it should be expanded or broadened. How this can be done is beyond the scope of a short paper. A methodology for designing an executive is described in [2] and its application to a variety of real world cases is illustrated. SYNTHETIC
DIALECTIC
SYSTEMS
In a number of ways this system is similar to the previous one, with one critical, principal difference: the role that an explicit logical contradiction (LC) plays within it. This system deliberately goes out of its way to construct or to seek at least two submodels that are in the strongest possible conflict with one another. The presumption of this system is that the strongest possible conflict between submodels, not the agreement or consistency between them, will allow the user 1) to become maximally aware of the assumptions underlying any proposed model of the phenomenon under scrutiny, and 2) to construct a new model M' that represents a synthesis uniquely tailored to the interest of the user [2]. This system, shown in Table 4, is thus in maximal philosophical opposition to that described in Table 1. Notice that the evidence contains a neutral submodel M,, whose function is to generate a data structure D used by the competing submodels to derive contrary implications. Here D represents the point of agreement between the submodels (i.e., that which is
TABLE 4 The Model Structure of Synthetic Dialectic Systems Claim:
s, & c, & -c,
warrant: c,
& --cl
& M’ & q ,,,,
+
M’ -+ a<,
The explicit presence of a LC (i.e., c, & -c,) forces the construction of a new model M’ from which q,,,, can be derived. Backing:
(I) LC +
(M’ or @)
(2) -_(LT + M’)
There exists a concept s, such that s, implies the existence of at least two models, MO and M,. Evidence:
In symbols: s, +
U(M,,, M,) ie2
M,,: q ,,,, +
D. a data structure
qr,,&D+c, qn2 & D +
-c,
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1.1.MITROFF
not in conflict between them) and is a critical feature of the system. It shows explicitly how, starting from the same data base, the two or more competing submodels reach opposing interpretations of the relevant data. The system emphasizes that data alone are never information; only their interpretation is. And in fact, this system reveals a point that applies to all the systems we have encountered. This is that each system is the systemic sum of all its parts: evidence, warrant, backing, and rebuttal. Contrary to the typical interpretation of models, the essence of a model is not contained solely in the warrant or in any one part but in the interaction between a!1 of them. The backing shows that a synthesis does not always or inevitably result from a LC. A LC may lead to the production of a new model capable of resolving, containing, or going beyond the contradiction. It may, however, also result in a null state Q, (i.e., a breakdown or confusion of inquiry due to the presence of a LC). It is still assumed that if a synthesis is possible, it results from a LC, not a LT. This is expressed in the second part of the backing -(LT -+ M’), or in words, it is not the case that a LT leads to M’. MULTIINQUIRY TRANSDISCIPLINARY
SYSTEMS
Table 5 represents in effect what Churchman [l] labels a Singerian inquiring system. The essence of the system is the notion that each of the known sciences depends on and contributes a fundamental concept to each of the other sciences. Thus science, has at least two different concepts, ck and c,),. Furthermore, science, has a contribution to make to science,. Thus, for example, each of the sciences in its desire to reason logically presupposes some concept or theory of logic. Hence logic is a part or aspect of every science. But the same can be asserted [I] for each of the sciences. For instance, every science is carried on in an institutional setting or has an important institutional aspect; hence some concept of social organization-in the .broader context, sociology-is presupposed by every other science, whether it is consciously aware of it or not [ I]. This system attempts to spell out explicitly the mutual interaction and interdependency of all the sciences. And indeed, the core of the warrant is the notion that a world view (WV) consists of the particular interaction between the concepts of a series of sciences. The WV in turn is responsible for generating an executive that in turn generates a series of submodels. The range of sciences to which one gives recognition is at the heart of a view of the world. A particular WV in turn gives rise to a particular kind of executive, as discussed in Table 3. The WV is even more general in that the submodels of this system can be the previous systems described in Tables 1 through 4. Hence in its most general terms, this system is a model of the previous systems. The rebuttal to this system is a central tenet of positivism. That is, R number (1) says that there is at least one significant concept in the social sciences derived from or dependent on one significant concept from the physical sciences. However, R number (2) says that it is not the case that there is a significant concept in the physical sciences that is dependent on or derived from the social sciences. The Singerian system in effect rebuts or denies this set of rebuttals. For instance, as much as the science of social psychology presupposes the science of logic in order for social psychology to order its concepts logically, social psychology contributes to logic by revealing that different persons have different patterns of reasoning. These patterns can be used as a basis, if one so desires, to construct different logics. Whereas this may not be important to traditional logic, it is to the designer of management information systems, especially if the designers want to persuade as many different kinds of people to use the system 121.
TABLE 5
(2) _
c,( social sciences,)
~
c,( physical sciences,) I q.,,
+
&
+
c,(science,))
c,(science,)
c,(science,) +
q’.,,,
q.,+.
Systems
The union U of q,,,,, leads to the recognition of the significance of a new concept from science,. This in turn leads to the recognition of a new q.,,, (i.e., a previously unrecognized aim).
(1) uqu,,, +
Backing:
Each particular executive leads to a particular M, and as a result a particular
(2) WV + executive, executive, + M, 3
c,(science,)
(1) WV = { c,(science,)
cd social sciences,)
(1) c,( physical sciences,)
~
Warrant:
Uq“,,,& c,(science,) & qfvI,,
Rebuttals:
Claim:
The Model Structure of Multiinquiry Tramdisciplinary
(4) c,(science,)
(3) c,(science,)
(2) ck(science,)
(1) r,(science,)
Each of the known sciences supplies us with various distinct concepts:
Evidence:
280
I .I. MITROFF
Concluding Remarks This paper constitutes in effect a Kantian inquiring system treatment of models or inquiring systems. We have presupposed a prior framework (a mode1 of the structure of arguments) due to Toulmin to explicate the structure of some archetypal models. Originally formulated as a purely qualitative device, we have shown how to extend it by means of the first-order predicate calculus to rate the plausibility of the components of models. In that all models attempt to formulate a set of formal relationships holding between a set of variables, we have argued that the first-order predicate calculus is one way to capture the set of logical relationships underlying any model. The treatment described here allows model builders and users to judge the appropriateness of the components of a particular model structure for their problem. Given the importance of such decisions, we believe it is of vita1 concern to develop even further our ability to choose between models. We need more than ever a “model of models.” We hope that this paper represents a step in this direction.
References I. Churchman,
C. West, The Design cflnquiring Systems. Basic Books. New York, 1971. 2. Mason, Richard O., and Mitroff, Ian I.. Challenging Strarqic Planning A.\sumptions. Wiley, New York, 1981. 3. Michalos, Alex. Principlrs @Logic. Prentice-Hall, Englewood Cliffs, N.J.. 1969. Forecasting and Assessment: Science and/or Mythol4. Mitroff, Ian I.. and Turoff. Murray, “Technological ogy,” Joumaul of Technological Forecasting and Social Change 5: I l.i- 134 (1973). 5. Rescher, Nicholas, and Manor, Ruth, “On Inference from Inconsistent Premises,” Theo? und Decision 1:179-217 (1970). 6. Toulmin, Stephen. The Uses ofArRumrnf, Cambridge University Press, Cambridge. England, 1958. Rewired
25 January
1982
FORECASTING
AND SOCIAL CHANGE 21, 267-280
(1982)
The Philosophy of Modeling and Futures Research A Guide to Different Models IAN I. MITROFF
ABSTRACT The concept of inquiry systems as originally formulated by Churchman is an exceedingly powerful one. Each inquiry system can be construed as an archetypal or generic kind of model structure that applies generally throughout all of the sciences. Recent developments in the logic of argumentation and symbolic logic show how, paradoxically enough, the model structure of each inquiry system can itself be modeled in terms of the first-order predicate calculus. The result is a “model of models.” More important and more fundamental still, the effort shows the tremendous assumptions that must be bought if one is to warrant belief in any particular inquiry model.
Introduction In 1973, Murray Turoff and I wrote a paper [4] for this journal that described some basic philosophical systems and their importance for technological forecasting and futures research. Since that time the technical sophistication of various approaches and models in the field has increased enormously. However, from a philosophical perspective, the soundness of these models has not changed or improved accordingly. The models of the field are only as good as the underlying premises on which they rest. And in fact, the more the technical sophistication of the models has improved, the more critical it has become to examine the premises that underlie them. In short, the danger is even greater that we will mistake technical sophistication for philosophical soundness. This paper revisits the philosophical systems described earlier and shows how each of the systems can be operationalized mathematically. In the intervening years since the Mitroff and Turoff paper was written, some powerful tools have been developed that allow one to build prototypical models of each of the systems. These models are themselves so general that they allow us to show the general premises that must be posited and accepted if one is to authorize a particular model or approach. It is important to appreciate the significance of the preceding comments. By operationalizing the systems, philosophy thereby becomes of direct interest and relevance to the model builder. It becomes a powerful tool for exposing the general assumptions upon which all models and approaches must of necessity rest. If the assumptions underlying a particular model or approach are judged inadequate or unwarranted, then the use of the model or type of approach is not warranted. IAN I. MITROFF is the Harold Quinton Distinguished Southern California. 0 1982 by Elsevier Science Publishing
Co., Inc.
Professor on Business Policy at the University 0040-1625/82/040267-14$02.75
of
268
1.1. MITROFF
The Structure of Arguments The philosopher Stephen Toulmin has developed a qualitative framework that in the opinion of the author is so general and so powerful that it provides the basis for capturing the structure and dynamics of all models [6). Originally developed by Toulmin to capture the structure of complex arguments, the framework can be applied to the field of modeling. In effect, a model can be viewed as a series of propositions or logical statements (arguments) designed to convince the model builder or user (often it is the builder more than the user) of the reasonableness or plausibility of the output of the model, if not of the entire model itself. In Toulmin’s language, every argument terminates in a claim (i.e., an assertion designed to convince an interested party such as a citizen. decision maker, and the like) of the reasonableness or truthfulness of a purported state of affairs or a proposed set of actions (i.e., a policy). Every claim thus terminates in one of two ways: I) it asserts that the facts describing the state of a certain system or of the world are of a certain nature; for example, company X in industry Z will make or has made a 25% profit during the last quarter; 2) based on the “facts,” company X ought to take a certain series of actions (policy Y) if it wants to increase its profits. Thus in the first case the assertion is either a forecast (“will”) or a statement of facts (“has”). In the second case, the assertion is either a technical hypothetical (“if you want to get to goal G, then you ‘ought’ to do Y”) or a moral imperative (“you ‘ought’ to do G because it is good, desirable, and so forth”). In order to reach or justify the claim, every argument appeals to a certain body of evidence, which represents the prior data, facts, and so forth available to us on which to base our argument. In logic, the evidence stands for the minor premise of an argument. The warrant is that part of an argument that allows us to go from the evidence to the claim. It authorizes, as it were, the mental leap or transition from evidence to claim. The warrant thus takes the logical and semantic form “If the evidence is E, then the claim C follows because “; that is, all warrants are of the same or fundamental logical form “if E, then C,” or in symbols, E + C, where the arrow may be taken in the usual sense of logical implication [3]. All warrants, however, are not of the same semantic form for the obvious reason that warrants differ significantly in their reasons for justifying the logical form E -+ C. For example, some arguments justify E -+ C “because C is causally connected to E.” Others justify E -+ C “because of analogy”; that is, C follows or has followed in the past from a series of Es. The E in this particular case is judged to be similar to past Es; therefore, by analogy, E -+ C holds. Note that the author is not necessarily justifying this kind of argument, merely noting one of the prevalent forms of argumentation. Whether a particular form is warranted in a particular case is precisely the topic motivating this paper. The reader is directed to Mason and Mitroff [2] for an extensive review of other forms of argumentation, especially in the field of policy analysis. Thus far the Toulmin framework has the same structure as that of the classic syllogism. The claim represents the conclusion we seek to establish or to justify. The evidence represents the minor premise; the warrant, the major premise. It is the other two terms that give the Toulmin framework its uniqueness and power. The backing represents the deeper, background parts of an argument. These are rarely brought up to the surface. However, if the warrant or the evidence is not accepted on its face validity, then the backing comes into play. It attempts to justify the relevance of a particular set of evidence to the establishment of the claim. The backing does not establish the technical reliability, validity, or objectivity of the evidence. That must be done by
MODELING
AND FUTURES RESEARCH
269
other means (i.e., through another argument structure pertaining to the methodology under which the evidence was collected, assessed, and so on). The backing also attempts to justify the “because” part of the warrant (i.e., why it applies or holds in the case under consideration). From the standpoint of modeling, forecasting, and futures research, the last term, the rebuttal, may be the most critical of all. The rebuttal stands for any or all of the challenges to any part of the main argument structure-claim, evidence, warrant, and backing. Thus, for instance, one can challenge the E, or evidence, by asserting that some other evidence set -E (read “not E”) is more applicable, relevant, reasonable, and the like. Similarly one challenges the warrant E -+ C by asserting that some other warrant, say, -E + C, is more applicable. In this case, one asserts that, as before, C follows, but that it results from -E and not from E. In a similar fashion, by means of the first-order predicate calculus, one can tabulate the simple kinds of arguments and their corresponding possible rebuttals. (See Mason and Mitroff [2] for a systematic treatment.) The first-order predicate calculus is indispensable in this effort because almost from logical considerations alone it can be shown that there are only so many forms of rebuttals to any argument [2]. The first-order predicate calculus is indispensable in another but related way. All models attempt to establish the existence of a logical structure holding between a set of variables. Given that this is the case, it makes sense to employ some concept of formal logic to represent this logical structure. Finally, there is another reason as well. The number of formal relationships in a model often quickly exhausts our ability to see all the implications that follow from the model. The use of the first-order calculus can aid our ability to examine all of the complex implications that would otherwise escape us if we restricted ourselves to a merely qualitative examination of models. Thus we will employ the first-order calculus in this paper even though the representations of the models we will examine are simple enough that they could all be stated in words. The importance of the Toulmin framework should be apparent by now. It allows us to lay out in a systematic and logical fashion the structure of complex arguments. In the sequel, we will attempt to show the different kinds of evidence, warrants, backing, and rebuttals that different systems use in seeking to establish and to challenge different kinds of claims (i.e., the outcome of different models viewed as arguments). By expressing each part of the argument as much as is possible in the first-order predicate calculus, we will also attempt to show how the Toulmin framework originally developed as a purely qualitative tool can be extended to give a more precise quantitative rendering of the structure of models. We need two other pieces of machinery before we can proceed. The presence of R (the rebuttal) in an argument structure introduces some serious logical difficulties; it also introduces some novel opportunities as well. Consider, for instance, a simple argument consisting of evidence E and warrant, E -+ C. Suppose also that we have an R of the form E + -C; that is, there is a counterargument to the main argument that -C, and not C, follows from E. For instance, E could be a series of data on the current state of the American automobile industry and C a prediction as to the fate of the industry relative to imports in 1990. Then -C would be a counterprediction based on the very same evidence but different underlying reasons (i.e., backing). If we consider the entire set of assertions as a total system of propositions, then a logical contradiction results; that is, from E and E --$ C, one is entitled to conclude E & C by means of traditional logic [3, 51. If E is
270
1.1.MITROFF
regarded as true, and if the warrant “if E. then C” is also true, then E and C are true. But from E & C and E -+ -C, E & C & -C results. That is, if E is true, and if “E implies -C” is also true, then E and -C is true. However, C & -C is a logical contradiction. According to traditional logical reasoning, C and -C cannot both be true at the same time 13, 51. The point is that the presence of R introduces deep logical contradictions into the structure of an argument considered as a total system of propositions. Now one can always preserve logical consistency by throwing out those parts of the argument that conflict, but this seriously begs the questions: Which parts should one throw out? How does one insure oneself (i.e., know) that one is throwing out the “right” parts? What does “right” mean? Is it possible to proceed without throwing out any of the parts of an argument‘? Notice the critical nature of these questions. If every argument has Rs, if no argument is ever so airtight that it is free from all challenges (no matter how weak they may appear), then this situation is completely general. All decision makers face it all the time whether consciously aware of it or not. Indeed, if they are not consciously aware of this situation, it means they unconsciously throw out parts of an argument structure. If so, we need some nonarbitrary basis for handling those parts of an argument that conflict with one another and for raising this up to consciousness for explicit examination. Although developed for other means, the concept of maximally consistent subset (mcs) invented by the logician Nicholas Rescher [5] can be profitably applied [2] in this case. A mcs is the largest subset of propositions that can be formally conjoined (i.e., linked together through the logical operator “and”) such that the subset is logically consistent. Thus in the case E and W = (E -+ C), and R = (E --+ -C), there are two me’s: mcs, = {E, W} and mcsz = {E, R} because from mcs,, E & W = E & C and from mcs?, E & R = E & -C, each of which is internally consistent. The concept of a mcs thus allows one to preserve all the information contained in the entire original set of propositions. To handle contradictions, we merely form all the possible mcs’s. Each mcs represents a different logically consistent conclusion that can be formed from the original set. The concept of mcs allows us to examine many more potential conclusions lurking within a formal system than if we were only to focus on the parts we naturally prefer. This feature once again shows the power of employing some concept of formal logic to express the components of a model. This is only half a Rescher’s contribution. Once we have the full set of mcs’s, we would like some way of ranking them in order of preference. This is where Rescher Plausibility is tantalizingly close to subjective introduces the concept of “plausibility.” probability in many ways but is noticeably different nonetheless. Probability refers to the likelihood of occurrence of an event; plausibility refers to the credibility, the believability of an assertion within the context of a total argument or a streaam of other propositions. As such, plausibility follows a different axiomatic structure, one that is better suited to judging the modality of a proposition representing various grades of possibility and/or believability. Thus, for instance, a proposition could be highly plausible in that logically it makes a great deal of internal sense or it is uttered by someone in whom one has a great deal of faith. At the same time, the proposition could be highly improbable in that the events contained in the propositions may have a low probability of occurrence. Without going deeply into the detailed axiomatic structure of plausibility, plausibility is an important concept for forecasting and futures research, for the field not only has a need to judge, say, the cross-impact probabilities of various events on one another, but it has no less a
MODELING
271
AND FUTURES RESEARCH
need to judge the credibility of various arguments and scenarios, both independently and dependently of their probabilities. For our purpose, one feature of the axiomatic structure of plausibility is especially important. Consider modus ponens, one of the traditionally accepted and most deeply regarded valid forms of logical reasoning (i.e., if E is regarded as true, and if E -+ C is also regarded as true, then C follows or is also regarded as true, that is, a justified conclusion). If plausibility is measured on a scale where 0 or a small number represents a logical truth or the highest degree of plausibility and if N >> 0 represents the lowest degree of plausibility, then pi(C) = max[pl(E), pl(E -+ C)]. In words, the plausibility of the consequent C of an argument will in general be no stronger than the weakest of its antecedents. Other rules can be formulated, but we will not pursue them here [5]. Models As Arguments:
The Role of Judgment
CONSENSUAL
SYSTEMS
INDUCTIVE
in Model Building
At least five basic or archetypal kinds of model structures can be identified [ 1, 41. These archetypal structures can themselves be combined in almost endless ways. In addition, countless variations and varieties exist within each structure. In order to illustrate therefore the spirit of an almost bewildering variety of structures, Tables 1 through 5 present what the author believes is a core example from each approach. Table 1 portrays the structure of a consensual inductive model system. This system corresponds most closely to what Churchman has termed a Lockean inquiring system [ 1). The model is inductive because it infers, or attempts to infer, a universal pattern from the observation of n occurrences of a series of events. That is, if an event a has occurred n times, then the next if not all subsequent occurrences will also be a. This kind of structure underlies a great variety of models and processes in science. In particular, the early Delphis, with their extreme emphasis on consensus and the wide variety of trend extrapolation models with their emphasis on continuity, are prime examples of this kind of model structure. The model starts with the observation that the same event a has repeatedly occurred n times in succession. The warrant then tries to infer that not only will the next observation result in the same observation a but that all successive observations will result in a. In actuality, the warrant may be more complicated than this. With each increase in the number of previous us that has been observed, presumably the higher the plausibility of = u)],k f i,k>i, the complex assertion (a, = a & *..&a,, = a)--+[(~, = a)-+(~, i 2 n becomes. Note the considerable complexity of this warrant. It is an inference ((a, = a & *mm & 1) of an inference [(a, = a) + (an = a)]. Notice also that the warrant a” = a)-+[ may assume a wide variety of different characteristic shapes. Instead of the mere number of same occurrences of a basic or atomic event u, the variance between the n u, may be used to infer the next in a sequence of events or observations. Presumably the tighter the variance, the higher the plausibility of the inference. Another prevalent form is the prediction of the frequency of two basic kinds of atomic events a and b, because the indefinite occurrence of II exactly similar events a is highly limiting. For another, the warrant may be thought of as a continuity principle instead of as a prediction or inference license. Finally, a critical part of every warrant in this model, no matter how it is expressed, is the assertion or postulation that the continuity of the
272
1.1. MITROFF
sequence eventually terminates in the attainment of some desired goal or end state q,,,,. As can be seen in Table 1, qrr,, is typically the tightness among the estimates of a panel of Delphilike experts on some important topic of prediction or a series of empirical observations. In the extreme, qu,, is taken to be the truth or correctly predicted end state of some system. Thus in a Delphi, presumably the tighter the agreement between the predictions of an independent set of experts, the more that the mean or some function of the expert’s predictions will converge toward the “truth.” In effect, the claim expresses the sentiments of the preceding paragraph and conveys that belief in the general principle [(a, = a) + (al. = a)] is warranted or supported by argument (i.e., the structure of the model), and that as a result, q,,,, is obtained. The backing is rarely if ever expressed in such systems. It constitutes one of the core beliefs of all empiricist systems. This is the strong belief that the act of observation alone does not presuppose any prior theory in order for the act of observation to occur. That is, observations are theory-free. Although people may disagree on the meaning of the “facts,” presumably all can agree on the same basic “facts” (i.e., that something has at least occurred). The rebuttal challenges all of this. First, it denies that observations are theory-free (i.e., it asserts that a, = a,(7’,). It asserts that some theory (not necessarily unique, hence 7”) underlies the taking of all observations in science. There must be some prior principles of selection and categorization operating in order to single out some features of a complex system as foreground as distinguished from background, whether the observer is consciously aware of this or not [ 1). The second element of the rebuttal denies or challenges that a finite set of observations is ever sufficient to establish a general inductive principle of the form [(a, = a)-+(~, = a)]. Indeed, the plausibility of this part of the rebuttal may even reach maximum if even one counterinstance of an a not occurring is observed (i.e., if a, = -u). Finally, a more sophisticated challenge to the backing, R statement number (3), is the Kantian point that the observation of n occurrences of a phenomenon does not necessarily warrant belief in an inference; rather, it is the other way around. Belief in some fundamental principle of continuity, order, and/or categorization is necessary if the act of observation is to be possible by anything resembling a cognizing agent. i.e., an entity, human or not, capable of having experience. The ability even to have experience implies an agent capable of, first of all, distinguishing some “things” from “others” and, second, of ordering them into some framework [ 11. All of this is implied in R statement number (3) in Table 1. Notice that not all of these rebuttals are equally damaging to the claim. The claim can live with all of them except the strict denial that the observation of tz occurrences necessarily implies a universal inference. If the judged plausibility pl of this part of the rebuttal is greater than the judged pl of the corresponding part of the warrant, then the claim does not follow (i.e., is not warranted). The author and his colleagues [2] have found that one of the great benefits of this whole approach is that it lays out clearly what one is required to give fundamental assent to (to believe) if one is to justify the output (claim) of a particular model. Often just laying out the propositions in such stark form is helpful. For instance, it becomes painfully obvious just how big a leap the warrant entails. One has to warrant the inference of an inference. It becomes painfully obvious that the inference required to warrant the inference is often no more certain or justified than the inference ((a, = u+(u, = LI)) one is trying to establish! If the warrant itself cannot be established or if it must be presumed
KEY:
= a)]}
= a & ... & a, = a)
= a)-t(ar
Backing:
a, = a($)
(2) [(a, = a)-(ar
= a)J +
9,,1,
k = i, k > i, i 2 n
[(a, = a)-(~,
= a)]
(I) a, = a
(n) a,, = a
(2) al = a,
There exists a series of observations such that the same event is repeatedly observed to occur.
Evidence:
a($)
= an assertion to the effect that the occurrence
of event a is not dependent on the prior presumption
of a theory T,
9,,,, = some end state prediction as to the state of a system and/or a series of actions (policy) that ought to be undertaken to improve on the state of the system.
= a)]+(a,
= a & ... & a,, = a)+[(a,
(3) [(a, = a)-+(ar
(2) -{a,
warrant: (I) (a, = a & ... & a,, = a) +
(I) a, = a(T,)
i2 n
Rebuttals:
k = i, k > i,
a,,,
I = a& I@,= 0)+ (4 = 41 & 9.1,
Claim:
TABLE 1 The Model Structure of Consensual Inductive Systems
1.1. MITROFF
274
by means that are themselves outside the model [ 1, 21, or if the pl of the rebuttal is judged to be gt’eater than the pl of the warrant [2], then this model or approach is itself not warranted. ANALYTIC
DEDUCTIVE
SYSTEMS
Table 2 represents a very different kind of model structure from the first system. It corresponds most closely to what Churchman [l] has termed a Leibnitzian inquiring system. It claims that starting from a unique, intuitively known, if not “self-evident,“’ proposition or set of primitive notions, p,, one can by means of a network’ of other propositions that follow from p, but are themselves presumably less certain than p, finally deduce q,,,r. The warrant also says that q ,,,, does not follow any other series of propositions r,. This system is the archetype of formal, analytic, deductive models; “formal” because the concepts are typically expressed in formal mathematical terms; “analytic” because concepts are typically taken as “self-evident” or “given”; “deductive” because the claim follows with whatever deductive force the system can muster (i.e., the system functions as one huge syllogism). The backing for such systems is typically a statement of the “primitive,” “fundamental,” “ laws” of logic. That is, a proposition p, and its negation -pi cannot both be certain or true at the same time; hence -@, and -p,). Notice that the backing in this case is much broader. It reads that an intuitively certain proposition p, and any of its competitors p, cannot both be true or highly pl at the same time. Alternately, p, or p, is true, but not both of them. Without commenting in detail, the rebuttal challenges every part of the structure of the main argument. For instance, it denies that p, is unique (R number (l)), that there is no other way to reach y,,,, (R number (3)), that p, and p, cannot both exist at the same time (R number (2)). An even stronger form of challenge is that there is only one form or kind of TABLE 2 The Model Structure of Analytic Deductive Systems Claim: p, & y ,,,, Rebuttals:
Warran,:
(I) There exists another
(1)
proposition p, such that its plausibilityplfpj) is high & PKPA >> PKp,) j is not unique
PI -
4,,/,
YI
tn +
(I)’
P, -
rl
(2)’
(2)
1) Y,,+I -L 9,,,,
(n + I)’ -(r,,+,
i
q,,,,)
There exists a p, such that its plausibility p/(p,) is high & Pl(P,) >>
PRP,)
or
Backing: (1) -c/7, & p,) -
(2) P, &P,
(3) rr,+I +
E~kknw.
c-p,
(2) p, or p, = -c-p,
or -p,)
Pl(P,) + Pl(P,) = N for all ”j; i unique
& -p,‘,)
KEY: See Table I for the meaning of Y,,,,. Note that the warrant consists of two argument chains. One chain says that q,,,, follows from a series of propositions q$. The other chain says that y, does not follow from any other series r,.
‘This is expressed in the evidence as pl(p,) = 0 or that the plausibility recalling that large pl numbers stand for low plausibilitiea and vice versa. ‘That is, the warrant: ~1,-
y,, and so on
of,‘, is high &
p/b,) >3>p&p,).
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AND FUTURES RESEARCH
q,,,, (i.e., set of criteria by which successful problem-solving performance is judged. That is, there are a whole series of other q{,,,,. Again, it should be apparent that this approach underlies a wide variety of applications in science. The first two approaches outlined briefly in Tables 1 and 2 often exist side by side without significant interaction. Data or observations are often collected without the conscious or explicit presumption of theory and then are fed into a formal model consisting of a very explicit, formal theory. Typically, the data input to the model are downgraded in importance, the formal model being considered of prime importance in establishing q,,,,. However, considered as a total system, this means that other arguments are lurking beneath the surface (i.e., in the backing), namely, that the formal part of the system takes precedence over the informal or data parts of it. If this part of the argument is challenged, then it moves us to the next archetypal class of systems. SYNTHETIC
MULTIMODEL
SYSTEMS
This system comes closest to what Churchman [1] has termed a Kantian inquiring system. The basic idea is that all phenomena, physical as well as social, are too complex to think that there is one and only one model that is correct, achieves the “truth,” or comes closest to qu,,, whatever q,,,, may be. Instead, this approach believes’ that no one single model is ever sufficient to capture the “reality” underlying any phenomenon. Indeed, every model self-selects a basic set of variables or notions that it takes to be fundamental over all others (i.e., intuitively obvious, self-evident, certain, and so on). Extending this a bit, different disciplines give fundamentally different explanations of phenomena. Thus a sociologist emphasizes institutional and social factors; a psychologist, individual factors; an architect, spatial factors. One of these is not necessarily right; all others wrong. Instead, each picks up a partial slice of an exceedingly complex “whole” of reality. The fundamental presumption of this approach is that the ultimate user of a model will gain more of an understanding of this complex, holistic reality by being exposed to the interplay of several models M, rather than being presented with just one. Hence this approach starts with a fundamental entity called the executive. The executive is that component of a system that decides which of the several models of which it is aware to present to a particular decision maker to model his or her problem. In Table 3 this is represented by s, (i.e., there exists a basic notion s, such that s, + UM,,where U stands for the union. That is, S, generates a series of separate models, each of which has a model structure as represented in Tables 1 and 2. Each M, represents an integrated inductive, consensual, and an analytic deductive system. There is a theoretical ordering principle in the model somewhere, q,,,, which directs the model to collect a kind of data D that is compatible with the notions underlying the model. A data structure D is made of two components: the observation of n as in a phenomenon and an inductive principle (a, = a) + (a, = a)-if a, is a, then the next uk will also be a. The backing is the presumption that the intersection, represented by the symbol n , of the models does not lead to nothing (i.e., the null model does not result). This is a psychological condition more than it may be a logical one. It assumes that the user learns something significant (and hence not @ or nothing) from the flMj. It is also assumed that nM, do not lead to a logical contradiction (LC). It is also assumed contrary to the assertion of each of the individual models that no single M, leads to q(,,,.
‘We are not necessarily
arguing for it. but rather presenting
the reasoning that underlies it
+
& (a, = a) --j (a,, = 4
M’)
-(M + 4.1,)
-(nM,
-{q:X:
(3) There exists a model M, such that
(3)
+
does
y,,,,); none of the initial models by itself is sufficient to achieve q,,,,.
not lead to a lo@cal contradiction.
LC): the intersection
of the M, does not result in the null model.
# @: the intersection
-(M, +
(2) -(nM
( I ) nM,
Buching.
q,,,,
The intersection of the initial models M, gives rise to a new model M’ that then achieves q.,,.
LC
= @
(2) nM, *
M’ +
(I) nM,
nM, +
Wurrunt:
s, & nM, & M’ & q ,,,,
Rebuttals:
Claim:
TABLE 3 The Model Structure of Synthetic Multimode1 Systems
4,,I,
[Jlas & (0, = (I) -
Y,,,+
(/w & D -
(I,?
(/,I +
(2) M,: p, -+ q,,
(q = u,]
(I) There exists a concept s, such that 5, + UM, i>2 or .\,generates a series of models. where a model is defined as
EGdewr:
MODELING
27-l
AND FUTURES RESEARCH
The warrant assumes that the fM4, leads to a new understanding on the part of the user, a synthesis, a new model M’, and that M’ leads to qu,, more than any other M,. There is no guarantee that the M, lead to a significant M’ in every case or that M’ in every case or that M’ leads to qr,,,, a fact reflected in the rebuttals. Also, there is no guarantee that the M', if it exists, can be formalized to the same degree that the M, are initially. This point in itself is not necessarily a rebuttal. Rather, the important point is that the synthesis need not be formal in order for significant understanding to be said to exist for the user, the party perhaps above all for whom this system exists, and not the model builder as in the previous two systems. In many ways the most critical feature of this system is the executive. Because so much depends on it, how do we know that it is any better than the analytic deductive system considered previously? In many respects we do not know, except insofar that one of the aspects of qu,, is self-reflection. One of the basic goals of going through the process represented in Table 3 is to learn more about which models should be included in the executive (i.e., whether it should be expanded or broadened. How this can be done is beyond the scope of a short paper. A methodology for designing an executive is described in [2] and its application to a variety of real world cases is illustrated. SYNTHETIC
DIALECTIC
SYSTEMS
In a number of ways this system is similar to the previous one, with one critical, principal difference: the role that an explicit logical contradiction (LC) plays within it. This system deliberately goes out of its way to construct or to seek at least two submodels that are in the strongest possible conflict with one another. The presumption of this system is that the strongest possible conflict between submodels, not the agreement or consistency between them, will allow the user 1) to become maximally aware of the assumptions underlying any proposed model of the phenomenon under scrutiny, and 2) to construct a new model M' that represents a synthesis uniquely tailored to the interest of the user [2]. This system, shown in Table 4, is thus in maximal philosophical opposition to that described in Table 1. Notice that the evidence contains a neutral submodel M,, whose function is to generate a data structure D used by the competing submodels to derive contrary implications. Here D represents the point of agreement between the submodels (i.e., that which is
TABLE 4 The Model Structure of Synthetic Dialectic Systems Claim:
s, & c, & -c,
warrant: c,
& --cl
& M’ & q ,,,,
+
M’ -+ a<,
The explicit presence of a LC (i.e., c, & -c,) forces the construction of a new model M’ from which q,,,, can be derived. Backing:
(I) LC +
(M’ or @)
(2) -_(LT + M’)
There exists a concept s, such that s, implies the existence of at least two models, MO and M,. Evidence:
In symbols: s, +
U(M,,, M,) ie2
M,,: q ,,,, +
D. a data structure
qr,,&D+c, qn2 & D +
-c,
278
1.1.MITROFF
not in conflict between them) and is a critical feature of the system. It shows explicitly how, starting from the same data base, the two or more competing submodels reach opposing interpretations of the relevant data. The system emphasizes that data alone are never information; only their interpretation is. And in fact, this system reveals a point that applies to all the systems we have encountered. This is that each system is the systemic sum of all its parts: evidence, warrant, backing, and rebuttal. Contrary to the typical interpretation of models, the essence of a model is not contained solely in the warrant or in any one part but in the interaction between a!1 of them. The backing shows that a synthesis does not always or inevitably result from a LC. A LC may lead to the production of a new model capable of resolving, containing, or going beyond the contradiction. It may, however, also result in a null state Q, (i.e., a breakdown or confusion of inquiry due to the presence of a LC). It is still assumed that if a synthesis is possible, it results from a LC, not a LT. This is expressed in the second part of the backing -(LT -+ M’), or in words, it is not the case that a LT leads to M’. MULTIINQUIRY TRANSDISCIPLINARY
SYSTEMS
Table 5 represents in effect what Churchman [l] labels a Singerian inquiring system. The essence of the system is the notion that each of the known sciences depends on and contributes a fundamental concept to each of the other sciences. Thus science, has at least two different concepts, ck and c,),. Furthermore, science, has a contribution to make to science,. Thus, for example, each of the sciences in its desire to reason logically presupposes some concept or theory of logic. Hence logic is a part or aspect of every science. But the same can be asserted [I] for each of the sciences. For instance, every science is carried on in an institutional setting or has an important institutional aspect; hence some concept of social organization-in the .broader context, sociology-is presupposed by every other science, whether it is consciously aware of it or not [ I]. This system attempts to spell out explicitly the mutual interaction and interdependency of all the sciences. And indeed, the core of the warrant is the notion that a world view (WV) consists of the particular interaction between the concepts of a series of sciences. The WV in turn is responsible for generating an executive that in turn generates a series of submodels. The range of sciences to which one gives recognition is at the heart of a view of the world. A particular WV in turn gives rise to a particular kind of executive, as discussed in Table 3. The WV is even more general in that the submodels of this system can be the previous systems described in Tables 1 through 4. Hence in its most general terms, this system is a model of the previous systems. The rebuttal to this system is a central tenet of positivism. That is, R number (1) says that there is at least one significant concept in the social sciences derived from or dependent on one significant concept from the physical sciences. However, R number (2) says that it is not the case that there is a significant concept in the physical sciences that is dependent on or derived from the social sciences. The Singerian system in effect rebuts or denies this set of rebuttals. For instance, as much as the science of social psychology presupposes the science of logic in order for social psychology to order its concepts logically, social psychology contributes to logic by revealing that different persons have different patterns of reasoning. These patterns can be used as a basis, if one so desires, to construct different logics. Whereas this may not be important to traditional logic, it is to the designer of management information systems, especially if the designers want to persuade as many different kinds of people to use the system 121.
TABLE 5
(2) _
c,( social sciences,)
~
c,( physical sciences,) I q.,,
+
&
+
c,(science,))
c,(science,)
c,(science,) +
q’.,,,
q.,+.
Systems
The union U of q,,,,, leads to the recognition of the significance of a new concept from science,. This in turn leads to the recognition of a new q.,,, (i.e., a previously unrecognized aim).
(1) uqu,,, +
Backing:
Each particular executive leads to a particular M, and as a result a particular
(2) WV + executive, executive, + M, 3
c,(science,)
(1) WV = { c,(science,)
cd social sciences,)
(1) c,( physical sciences,)
~
Warrant:
Uq“,,,& c,(science,) & qfvI,,
Rebuttals:
Claim:
The Model Structure of Multiinquiry Tramdisciplinary
(4) c,(science,)
(3) c,(science,)
(2) ck(science,)
(1) r,(science,)
Each of the known sciences supplies us with various distinct concepts:
Evidence:
280
I .I. MITROFF
Concluding Remarks This paper constitutes in effect a Kantian inquiring system treatment of models or inquiring systems. We have presupposed a prior framework (a mode1 of the structure of arguments) due to Toulmin to explicate the structure of some archetypal models. Originally formulated as a purely qualitative device, we have shown how to extend it by means of the first-order predicate calculus to rate the plausibility of the components of models. In that all models attempt to formulate a set of formal relationships holding between a set of variables, we have argued that the first-order predicate calculus is one way to capture the set of logical relationships underlying any model. The treatment described here allows model builders and users to judge the appropriateness of the components of a particular model structure for their problem. Given the importance of such decisions, we believe it is of vita1 concern to develop even further our ability to choose between models. We need more than ever a “model of models.” We hope that this paper represents a step in this direction.
References I. Churchman,
C. West, The Design cflnquiring Systems. Basic Books. New York, 1971. 2. Mason, Richard O., and Mitroff, Ian I.. Challenging Strarqic Planning A.\sumptions. Wiley, New York, 1981. 3. Michalos, Alex. Principlrs @Logic. Prentice-Hall, Englewood Cliffs, N.J.. 1969. Forecasting and Assessment: Science and/or Mythol4. Mitroff, Ian I.. and Turoff. Murray, “Technological ogy,” Joumaul of Technological Forecasting and Social Change 5: I l.i- 134 (1973). 5. Rescher, Nicholas, and Manor, Ruth, “On Inference from Inconsistent Premises,” Theo? und Decision 1:179-217 (1970). 6. Toulmin, Stephen. The Uses ofArRumrnf, Cambridge University Press, Cambridge. England, 1958. Rewired
25 January
1982