Scope Statements: Imperatives for Evaluating Theory STOR Henry A. Walker; Bernard P. Cohen

American Sociological Review, Vol. 50, No. 3 (Jun., 1985), 288-301.

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SCOPE STATEMENTS: IMPERATIVES FOR EVALUATING THEORY*

HENRY A. WALKER BERNARD P. COHEN Stanford University

Sociology faces a peculiar paradox: Every general sociological proposition is both true and false. On the one hand, one can easily find exceptions to most of the

propositions which are advanced as general sociological principles. Yet, there are many instances in which general sociological principles are supported by empirical findings. As a consequence, it is not clear when some sociological principle is to be counted as false. This paper argues that a proper assessment of the state of sociological knowledge and the possibility of cumulative growth in sociology depends on resolving the true-false paradox. We argue that the paradox can be resolved if sociologists make the scope

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mon observation: There is evidence that con-tradicts every set of propositions advanced as a general sociological theory.

When the relative frequency with which sociological theories are faced with negative evidence is considered, it is surprising that so few of them are ever abandoned. 1 In the for-

. mative years of the discipline, sociologists as-sumed (as did scientists in other fields) that the worth of a theory was determined by the mass of evidence that could be mounted in support of it, i.e., its verifiability. Over the years, the importance of verifiability as a criterion of sci-entific status has declined and its former posi-tion has been assumed by the criterion of fal-sifiability (Popper, 1959; Hempel, 1965). The view that theories must be falsifiable in order to be scientific has received wide, but by no means universal, acceptance in sociology and other scientific disciplines. 2 If the logic offal-sification is accepted, it might be expected that sociologists would proclaim their theories false when they find data that are inconsistent with them. However, very few sociologists are willing to reject a theory on the basis of one set of negative findings.

The relative frequency with which sociologi-cal theories are confronted with negative evi-dence raises an important question. When should an investigator count negative evidence as justification for rejecting a theory? The question is one of the central methodological concerns of sociological theorists and re-searchers. Indeed, Kuhn (1970) has pointed out that it is a knotty problem for science in gen-eral.

There is evidence that supports most sociological arguments and that evidence is often applied to social policy concerns. In many cases, practitioners have continued to

1 Consider the recent findings of research that tests the functional theory of stratification. Betz et al. (1978) found that a scarcity of public school teachers did not result in higher incomes for teachers. Similarly, Wanner and Lewis (1978) failed to find a significant relation of functional importance, measured as an occupation's relative representation in the labor force, to either changes in skill require-ments or rewards. Finally, even though Broom and Cushing (1977) found a positive association between company assets (a measure of executive responsibil-ity or functional importance) and executive compen-sation, their overall findings fail to support the theory. None of these findings support the functional theory of stratification, but we are left with the im-pression that the theory, which has survived for four decades, will not be relegated to the theoretical scrap heap.

2 Halfpenny (1982) has suggested that this in-terpretation of positivism is the sociological view of the positivist position.

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use social interventions despite the fact that the theories on which they are based have been tested and found wanting, However, the con-tradiction associated with treating false theories as if they were true serves as an im-portant deterrent to the application of such theories to new or previously unsolved social problems. We contend that the question of when to count negative findings against a theory results from the failure to resolve a paradox that is faced by any sociologist who proposes general theoretical formulations: Every proposition that is advanced as a general sociological principle is both true and false.

Sociological theories are proposed as expla-nations of empirical phenomena, i.e., social behavior. Hence, the very nature of theory construction dictates the existence of data that are consistent with the "truth" of the theoreti-cal principles. This happy circumstance is tempered by the fact that there are data that are inconsistent with every general, i.e., strictly universal, proposition (Hempel, 1965). This true-false paradox poses a dilemma for the development of cumulative knowledge. How can theoretical progress occur or knowledge develop in a cumulative fashion if every theory or theoretical formulation is, strictly speaking, false? .

Our central thesis is that the cumulative de-velopment of sociological knowledge depends on satisfactorily resolving the true-false paradox. In tum, resolution of the paradox de-pends on the development and adoption of a set of methodological principles that clearly define when "false" theories are to be counted as true, i.e., not false. We offer a strategy for constructing and testing theoretical formula-tions that avoids the true-false paradox. The strategy we propose requires investigators to develop and test conditional theories. We argue that falsifying theories which have been made conditional through explicit specification of their scope can be a progressive rather than degenerative process (Lakatos, 1970). There are several methodological implications of the theory-driven strategy we propose. One of the most important implications is that the falsifi-. cation of theories is made meaningful to the practicing sociologist while the explanatory and practical utility of theoretical formulations which have encountered negative findings is preserved.

We begin our analysis with a brief discussion of theory and theory testing in sociology. Next we present a formal conception of the scope of theories, discuss the methodological implica-tions of the formulation and the manner in which it resolves the true-false paradox. Finally, we illustrate the differences between the strategy we propose and other procedures

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which purport to make theoretical arguments .conditional.

:fORMULATING AND TESTING SOCIOLOGICAL THEORY Sociological opinion about the nature of theory is so diverse that it is virtually impossible to provide a summary of the various positions that is both reasonable and concise. There are sociologists who use the term "theory" to refer to category schemes that are assumed to de-scribe a wide variety of social activity, e.g., the AGIL scheme (Parsons, 1951). The term is also used with reference to general arguments or conceptlial frameworks that purport to explain the majority of social behaviors (Parsons, 1964; Homans, 1974), while others seem to mean by theory quite specific and detailed explanations

1 .of unique events (Blumer, 1969; Garfinkel, 1967). In turn, there are those who use the term to refer to the application of general arguments to a limited set of phenomena. Such theories include Davis and Moore's (1945) theory of social stratification, Becker's (1963) theory of deviance, Lipset's (1963) theory of the legiti-mation. of nation-states and Dornbusch and Scott's (1975) theory of formal authority.

Throughout this paper, we will use the term "theory" to refer to a set of logically intttrre-lated propositions or "arguments" that make assertions about the nature of relationships between theoretical constructs.3 There is con-siderable variation in the degree to which theories are -formalized, e.g., compare Becker's (1963) theory of deviance and Emer-son's (1972a, b) theory of power and depen-dence. They, do, however, share some com-mon features. First, statements about the re-lationships that are to be explained can be de-ri\;"ed (with .the application of appropriate log-ical qperations and rules of correspondence)

3 Willer and Webster (1970) make the important distinction between constructs and observables. In their conception, observables are concepts that are susceptible to direct sensory experience while con-structs are not generally observable. Explanations that consist of statements about relationships be-tween observables are fundamentally different from those that consist of statements about relationships between constructs. By almost any criterion of theoretical development, e.g., the number of empiri-cal implications (Stinchcombe, 1968), confirmation status, or degree of falsifiability (Popper, 1959), ex-planations that assert relations between constructs are more highly developed. More importantly, how-ever, we agree with Willer and Webster that theoretical progress and the cumulative development of knowledge is more likely to occur when explana-tions employ constructs (see also Willer and Ander-son, 198i).

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from the core theoretical propositions. Ob-servable phenomena-or, more correctly, statements about observable phenomena-that stand in such a relation to theories are said to be explained. Second, assertions made by theoretical statements can be refuted by obser-vations in the empirical world-they are falsifi-able.

There are two problems associated with using the logic of falsification to evaluate the relation between theory and evidence. The first problem concerns the nature of theoretical statements:. Theoretical statements are univer-sal statements the truth of which is indepen-dent of time, place or historical circumstance.

_ They can be contrasted with slngular state-ments that refer to particular times.and places. For example: "Power varies with control of resources" is a universal statement; whereas, "In the United States fa 1985, men have more power than women" is a singular statement. It is generally recognized that the truth of strictly universal statements cannot be verified (Hem-pel, 1965). It is always possible to uncover observations (if they do not exist at present) that contradict such statements. Hence, no matter how much empirical evidence is amas-sed in support of them, general principles are never more than conditionally true. This log-ical difficulty is realized as a practical problem for the sociological researcher.

Theories are proposed as explanations for systematic patterns of empirical phenomena. As a result, there are data that are consistent with every serious theoretical formulation. At some point, however, every 'theory will be confronted with negative evidence.4 The sociological researcher must decide at what point negative evidence justifies rejecting a theory.

There are several criteria which any pro-posal to solve these difficulties must satisfy. First, a solution must preserve the universal character of theoretical propositions. That is, general theoretical statements cannot refer to particular times or places. Second, an adequate solution should permit the falsification of theoretical statements. Third, any proposed solution should specify when negative evi-dence is to be regarded as justification for re-jecting a theoretical formulation. Finally, a

4 These assertions assume that theoretical formu-lations are offered 'as serious attempts to explain phenomena. Hence, in the not too distant past there was considerable evidence in support of the phlogiston theory of combustion and, more recently, the phrenological "theory" of criminal deviance. However, both theories were eventually counted as falsified, i.e., they encountered negative evidence and were given up.

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solution should permit the investigator to take advantage of the "empirical content" of the formulation. That is, the explanatory utility of the formulation under consideration should be preserved. Satisfaction of this last criterion would permit sociologists to continue to use the empirical content of a theory which has been falsified to solve practical problems.

In the next section of this paper we offer a formulation which satisfies these four criteria. We argue that sociologists should test and re-formulate conditional rather than strictly uni-versal theories. Theoretical arguments which have been made conditional by explicitly stat-ing their scope of applicability are fully testable and retain their universal character. In addi-tion, the proper use of scope limitations pro-vides guidelines ~or determining when negative evidence should be counted against a theory. Finally; the strategy proposed here permits the falsification_of conditional propositions with-out affecting the empirical content of less gen-eral propositions, i.e., those with more restric-tive scope limitations.

THE SCOPE OF FORMAL THEORIES The general conception of the scope of theories appears to have been introduced by Toulmin (1953). The conception recognizes the inherent fallibility of any system of uncon-strained propositions. However, despite the intuitive appeal of the idea, it has not been used extensively and its importance for apply-ing the logic of falsification to the relation be-tween theory and evidence has not been fully explicated.

Theoretical propositions are universally quantified statements of the form,

(X) (Y), xRy,

which can be interpreted as, "For all X and Y, X stands in relation R to Y." 5 A theory's scope, or domain of applicability (Bonin, ,, 1965), is a set of conditions such that, ifll},e conditions are satisfied the theory will not/be found false. The scope of a theory can be de-scribed by a set of statements which we refer

5 We have chosen to represent theoretical state-ments in this form for several reasons. First, general principles are compound statements and unlike some other representations, e.g., X ~ Y, representing them in this manner does not invite decomposition into their component statements. Second, general principles are statements of relationshipi; among variables. Such statements typically employ two-place predicaters, which can be more parsimoniously represented in the form we have chosen or, alterna-tively, as R(X,Y), where X and Y are free variables.

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to as scope statements. Scope statements share the property of universality with state-ments of general principles. That is, they are comprised of constructs that do not refer to particular times a,nd places. Unlike theoretical principles, however, scope statements do not make assertions about relations between theoretical constructs. In the sense that they specify something about general theoretical principles, scope statements are metatheoreti-cal. However, scope statements are not part of the general theoretical principles. They con-strain the applicability of general principles and modify them as follows,

[(X) (Y): SC], xRv,

where the bracketed phrase is read, "for all X and Y if the scope limitation, SC, is satisfied." Note that what is predicated for X and Y, that is, R, is unaffected by adding the scope state-ment;-only the class of individuals (in the log-ical sense) about which R is predicated has been restricted.

General principles say nothing about par-ticular times and places and are not empirical until they are instantiated. Instantiation of a general principle requires linking it to an ob-servation statement, and this is accomplished by means of statements of initial conditions. Neither the set of observation statements nor the set of initial conditions is part of the general principle. However, both observation state-ments and statements of initial conditions are required to complete a deductive chain which permits using observation statements to make inferences about the truth or falsity of general theoretical principles. Many alternative sets of observation statements and sets of initial con-ditions can be associated with a given theory.

Scope statemel)ts also require instantiation through statements of initial conditions. Ob-servations which instantiate scope limitations both augment and constrain the instantiation of general theoretical arguments. The set of aug-mented principles, i.e., those which include the instantiated scope statements, specifies when observation statements which have been prop-erly deduced from the basic theorietical princi-ples can be treated as confirming or discon~ firming evidence.6 The methodological impli-

Scope restrictions are not variables in the strict sense. A scope restriction which specifies that per-sons must differ on only one social rank is either satisfied or not in any empirical situation. On the other hand, social rank is a variable which may take any number of values. To be sure, what is an empiri-cal instance of the abstract scope restriction may vary from one test situation to another. For example, a situation which includes a black female college professor and a black female office worker satisfies

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cations of these ideas can be illustrated by a few simple arguments.

If a theory, or set of theoretical statements, is represented as an unconstrained statement of the form xRv, then it implies the observation statement aRb. When an investigator finds negative evidence (the observation statement is not true of some empirical instance) the theoretical statement is falsified. The argu-ments can be represented in symbollc form as follows:

1.1 xRv 1.2 xRv - aRb 1.3 -(aRb) 1.4 -(xRv)

Argument 1 is our representation of the in-vestigative process. A set of theoretical state-ments (1.1) is proposed as an explanation for some empirical phenomenon. That is, a set of theoretical propositions is assumed to imply a set of observations (1.2). 7 An investigation is conducted and the data are inconsistent with the theoretical argument (1.3). Statement 1.4, which can be derived from statements 1.2 and 1.3, indicates that the set of theoretical state-ments is falsified by the negative findings.

However, the logic of our arguments does not permit us to falsify the set of unconstrained propositions (1.1) (see Lakatos, 1970: 133). 8 In-stead, evidence is brought to bear on condi-tional propositions of the form,

the scope restriction, whereas a situation Which in-cludes a white female college professor and a black male college professor does not. Each observation must tie justified as an instance of the abstractly stated scope restriction. Compared to the ability to introduce qualifications on an ad hoc basis, our pro-posal is quite restrictive.

7 Strictly speaking, statement 1.2 should be inter-preted to mean that a set of observation statements is formally deduced from a set of theoretical statements and statements of initial conditions. Since theoretical statements can not employ singular terms, state-ments of initial conditions are required to instantiate the constructs in the theoretical statements.

8 The methodological position which holds that a theory can be falsified by one instance of negative evidence has been called dogmatic falsificationism (Lakatos, 1970), which is distinguished from naive and sophisticated falsificationism. Space limitations preclude a full exegesis of these positions. Put sim-ply, naive falsificationists require negative findings to be corroborated, i.e., they must. be replicated, while sophisticated falsificationists require corrob-oration of negative evidence and a new or replace-ment theory prior to counting the old theory as fal-sified.

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which can be interpreted, "If a set of condi-tions, SC, is satisfied, then for all X and Y, X stands in relation R to Y." When a statement which has been made conditional in this man-ner is confronted with negative evidence, only the conditional principle is in danger of falsifi-cation.9 This assertion is demonstrated by argument 2.

2.1 SC - xRv 2.2 SC - (xRv - aRb) 2.3 SC 2.4 xRv - aRb 2.5 -(aRb) 2.6 -(xRv) 2.7 -(SC - xRv) Argument 2 represents the empirical test of a

theoretical formulation which has been made conditional by specifying its scope (2.1). As before, the formulation implies a set of obser-vations (2.2). Wben the scope restrictions as-sociated with a formal theory are satisfied (2.3), the observation of negative evidence (2.5) permits the inference that the conditional principle (2.1) is false (2.7). Statement 2. 7 is the case if and only if the scope restrictions are satisfied and a "true" theoretical statement en-counters negative evidence.

If scope limitations define a theory's range of applicability, conditional formulations .should not be in danger of falsification if a particular research setting fails to satisfy the scope limi-tations. Argument 3 demonstrates how the use of scope statements preserves the integrity of a theoretical formulation when the scope re-strictions are not met and an investigation un-covers negative evidence.

3.1 SC - xRv 3.2 SC - (xRv - aRb)

9 In response to an earlier version of this paper which did not employ the symbolism we use here, an

anonymous reviewer pointed out that the symbolic .representation of our use of scope statements, i.e., SC - (X - Y), is logically equivalent to the schema "(SC & X) - Y." While that argument is technically correct, such a representation requires a unique bracketing of the elements that comprise the com-pound statement, e.g., employing the representation above rather than "SC & (X- Y)," which, while not logically equivalent to our formulation, is an equally plausible rendering. Most importantly, however, the interpretation requires decomposing the theoretical statement "X - Y" into X and Y, its components, and treating them separately. Our representation permits us to avoid the complicated and potentially confusing use of symbolic logic which has plagued others (cf. Maris, 1970) and allows us to maintain the integrity of the theoretical statements which the symbols represent.

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3.3 -SC 3.4 xRv --+ aRb 3.5 -(xRv--+ aRiJ 3.6 -(aRb) 3.7 -(xRv) 3.8 (xRv)

When scope restrictions are not satisfied (3.3), either statement 3.4 or 3.5 is consistent with the truth of statement 3 .2. If an investiga-tion turns up negative evidence (3.6), the theoretical statement must be false (3.7) in order for statement 3.4 to hold; but the theoretical statement must be true (3.8) in order for statement 3.5 to be true. The irrele-vancy of data under such conditions is illus-trated by noting that the truth of either 3.7 or 3.8 is consistent with the truth of the condi- ' tional proposition (3.1). That statement cannot be falsified when the scope limitations are not satisfied.

There is another advantage to specifying the scope of theoretical formulations. The scope of a theory represents a specification of the class of phenomena within which the theory will not be found false. If the unconditional form of propositions is exempt from falsification, the repeated observation of data which are incon-sistent with conditional propositions signals the limitations of a theoretical formulation. That is, it is an indicator that the scope of the formulation is not sufficiently restrictive: A conditional theory is not false within its scope. Argument 4 demonstrates the logic of this argument.

4.1 SC --+ (xRv --+ aRb) 4.2 xRv 4.3 -(a.Rb) 4.4 xRv --+ aRb 4.5 SC --+ (xRv--+ aRb) 4.6 -SC

Argument 4 assumes that the basic theoreti-cal proposition, the unconstrained form, is true (4.2). If the observations are inconsistent with the argument (4.3), statement 4.4 must be false, i.e., statement 4.5 is the case. Statement 4.6 follows from statements 4.1 and 4.4. That, is, for statement 4.1 to be true when the basic proposition is true and the observations incon-sistent with it, the scope limitations must fail to be satisfied. This result corresponds to our intuition that "true" theories cannot generate negative evidence within their scope.

The arguments we have presented generally define our conception of scope restrictions as statements .that specify the set of instances in which a theoretical formulation is expected to be true: (1) If scope limitations are satisfied, inconsistent evidence falsifies the conditional

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formulation; (2) if scope limitatfons are not satisfied, all observation statements are con-sistent with either the truth or falsity of the formulation and hence, are irrelevant to it; and (3) if a formulation is true, negative evidence implies that some scope limitation is unsatis-fied. This last point suggests a research strat-egy that permits the retention of a theory in the face of negative evidence. There are empirical situations in which scope limitations may fail to be satisfied; hence, the explicit formulation of scope limitations permits them to be investi-gated when inconsistent evidence is encoun-tered. Furthermore, if a theory is not false out-side its scope, an investigator can pursue a program of research in which the scope limi-tations of a formulation are progressively re-laxed. The systematic observation of negative evidence will serve as an indicator that the formulation has been pushed "beyond its limits," i.e., beyond its scope. 10

THE SOCIOLOGICAL IMPORTANCE OF SCOPE LIMITATIONS The true-false paradox is demonstrated by a recent dispute in the sociological literature. The dispute concerns Chiricos and Waldo's (1975) test of arguments advanced by Chambliss (Chambliss, 1969; Chambliss and Seidman, 1971). Proposition 1 is central to the Chiricos and Waldo paper.

Pl: When sanctions are imposed, the most severe sanctions will be imposed on persons in the lowest social class. Chiricos and Waldo test this proposition by

examining the length of prison sentences given prisoners in three southern states, but they fail to find a significant relation between social class, as measured by socioeconomic status (SES), and severity of sanction, as measured by length of prison sentence. If the data are taken at face value, they are inconsistent with Chambliss and Seidman's theoretical argu-ment. Yet the results generate a dispute which

10 Our formulation differs in important respects with the recent formulation of Freese ( 1980). Freese distinguishes the "scope extent"" ofa theory from its "scope refinement.'' His notion of the scope extent of a theory, i.e., the range of successful predictions a theory is expected to be capable of making, can be easily reconciled with the present formulation. However, his concept of scope refinement makes the precision of a theory part of its scope. While we agree with Freese that refinements in precision are important to both theoretical growth and testability (cf. Popper, 1959), the issue is not one of scope. Precision is a characteristic of predicates and, in our view, scope restrictions operate on statements in their entirety and in no way affect predication.

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takes several forms. 11 One position suggests that the data are simply inqonsistent with the proposition and, consequently, the proposition is "false" (Chiricos and Waldo, 1975, 1977). A second position contends that the data are ac-tually consistent with the proposition and, hence, the proposition is not false (Greenberg, 1977; Hop~ins, 197/). A third position argues that the concepts of the argument are not prop-erly operationalized and, therefore, the inves-tigation does not constitute a test of the argu-ment (Hopkins, 1977; Reasons, 1977).

The sociological literature is replete with examples like the one we have provided. A new or existing sociological theory is subjected to empirical investigation; the findings are in-consistent with the theoretical argument, but the theory is not counted as false. It is no wonder that some critics have argued that the decision to retain or reject a theory is purely subjective and that sociology is not capable of producing explanations in the natural science paradigm. It is not necessary, however, that a researcher's methodological position depend on whether he or she agrees with the substance of a .theoretical statement. The strategy we propose provides criteria for deciding when to count negative evidence as justification for fal-sifying a theory. Furthermore, these crit~ria are independent of any particular theoretical position (although they are not independent of one's philosophy of science). In the next sec-tion of this paper we demonstrate how the ex-plicit use of scope limitations can be used to make sociological propositions conditional while maiiltaining their universal character.

MAKING SOCIOLOGICAL THEORIES CONDITIONAL In addition to making general principles test-able, scope statements provide clear guidelines for choosing the appropriate empirical situa-tion in which to evaluate a theory. Theorists who make the scope of theoretical statements explicit are making a commitment to a class of situations in which the general principles will not be falsified. This fact can be used to help resolve many of the current disputes about the relevance of evidence to a theoretical claim. We return to our example.

Both Greenberg and ,Hopkins argue that

11 There are. many issues in this controversy that are not germane to the present paper. One of the most important of these is the question of whether the propositional inventory offered by Chambliss and Seidman constitutes a theory in the sense used here. Our use of this exampl~ should not imply any position on our part with respect to that or any other issue which their work raises.

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Chiricos and Waldo should have looked at the full range of (qualitative) sanctions rather than

simply examining (quantitative) differences in the severity of one type of sanction. Yet neither the naked proposition nor the theory offers any guidelines for believing that the ef-fects of social class should not be distributed across categorie.s of sanctions, e.g., supervi-sion by the courts or incarceration, if those categories can be ranked in terms of severity or within sanctioning categories when differences in severity exist, e.g., length of probation, length of sentence or actual time served. Scope limitations can be used to specify the instances in which negative evidence is to be counted toward falsification.

Consider the following statements: SCI: For all classes of offenses for which offenders are randomly distributed among social classes (Chambliss and Seidman, 1971:475). SC2: For all classes of offenses for which in every social class there is a nonzero proba-bility ?f committing that offense. The first statement, SC 1, could be construed

as a scope limitation on the Chambliss-Seidman theory, and we offer SC2 as a less restrictive limitation. set is not satisfied in Chiricos and Waldo's investigation. Their data were collected in three southern states, and it is generally recognized that there is a relation between the incidence of criminal behavior and social class in contemporary American society.

. While their findings might be interpreted to suggest that the theory has been tested beyond its limits, the inconsistent evidence neither fal-sifies nor supports the theory according to the formulation of scope restrictions presented here. It is simply irrelevant to the theory's truth or falsity. If the statement we are calling SCI were a scope restriction on the theory, investigators would immediately recognize that only an examination of sanctions applied to particular classes of offenses-those for which offenders are randomly distributed across so-cial classes-would serve as a test of the theoretical argument. In addition, evidence re-garding the relation of social class to severity of sanctions for violations which satisfy the scope restriction cannot be "generalized" to other classes of crimes, unless those other of-fenses satisfy the same scope limitations.

As the term is used in much of the sociologi-cal literature, generalization refers to using data from some limited instance (one study, one sample, etc.) to make inferences about some larger set of instances (a set of similar studies, the population from which the sample was drawn or some universal proposition). The formulation used here provides a conception of

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generalization that is free of the "inductivist fallacy." That is, the conception of generaliza-tion does not rest on the untenable notion that one can make logically valid Uiferences from a specific case (or cases) to a more general set of cases. Under the present strategy, generaliza-tion is a theoretical activity.

A theory is generalized by relaxing its scope,. Relaxing a scope limitation, by eliminating it entirely or by substituting a less restrictive form, highlights an important implication of testing conditional formulations. Asserting a scope restriction entails the claim that if the conditions it specifies are met, the theory will not be false and nothing is assumed about the, truth-value of the theory if the conditions are not met. A theory is not false outside its scope. Indeed, since comprehensiveness is a goal of theory construction, one always expects that there are additional but unknown circum- stances to which a theory applies. Relaxing scope, then, is extending (generalizing) the theory to additional situations to which it may be applicable. Examples of this approach to generalization are found in the recent work of Willer and associates (cf. Willer and Ander-son, I98I:106; Willer and Brennan, I981).

The idea of generalizing a theory by in-creasing its scope of applicability has another important featm:e. By appending more general, i.e., more inclusive, less restrictive, .scope statements to a theory, the sociological inves-tigator makes the theory more vulnerable to falsification. The arguments are exposed to -more, potentially falsifying situations. Hence; if one theory is more general in scope than another., it is, in some sense, more testable. Although it is not cited by Chambliss and Seidman, SC2 can be formulated by making SCI less restrictive. Now if SC2 is more gen-eral than SCI, SC2 is satisfied (true) when SCI is satisfied but not vice versa. Since SCI can-not be true and SC2 false, there are only three cases of interest: (1) Both SCI and SC2 are true; (2) both statements are false; or (3) SCI is

false while SC2 is true. However, if both SCI and SC2 are true or if both are false, the arguments are equivalent to the arguments for one scope restriction which we have presented above. When both scope limitations are satis-fied, negative evidence falsifies the conditional theory no matter which scope limitation is ap-pended to it. When both are false, negative evidence is irrelevant to both condjtional for-mulations. The instance in which SC2 is be-lieved to be true and SC l is believed to be false can be analyzed by slightly modifying our ear-lier arguments and examining them simulta-neously.

As before, let xRy be a theoretical statement and let aRb be an observation of the presence or

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absence of a particular relation (R) between an indicator of X and an indicator of Y. Finally, let C1 be an indicator of a scope restriction, SC1. Argument 5 represents the instance in which SC2 is satisfied, and argument 6 repre-sents the case in which SCI is not. satisfied. 12

5.I [(SC1 - xRv) - (C1 - aRb)] 5.2 C2 5.3 -(aRb) 5.4 -(C2 -. aRb) 5.5 -(SC2 - xRv) 5.6 SC2 & -(xRv) We assume that statement 5.I, the basic

principle of falsifiability, is true. The inves-tigator observes C2 and assumes that SC2 is satisfied (5.2) but finds negative evidence (5.3). Statement 5 .4 can be deduced from statements 5.I, 5.2 and 5.3, and statement 5.5 can be de" duced from statements 5.I and 5.4. Statement 5 .5 suggests that the conditional proposition is false, and statement 5.6 is the only instance which satisfies the truth of statement 5 .5 under the given conditions. The investigator must conclude that the theoretical formulation is false.

6.I [(SC1 - xRv) - (C1 - aRb)] 6.2 -Ci 6.3 -(aRb) 6.4 C1 - aRb 6.5 [(SC1 - xRv) v -(SC1 - xRv)] 6.6 [(SC1 & xRv) v (SC1 & - xRv)

v (-SC1 & xRy) v (- SC1 & -xRy)] Argument 6 establishes 6.2 as an initial con-

dition, i.e., SCI is not satisfied. Statement 6.4 can be derived from statements 6.I, 6.2 and 6.3. That is, the truth of 6.4 is consistent with the failure of the situation to satisfy the scope limitation and a finding of negative evidence. If, however, statement 6.4 is true, and state-ment 6. I is true (by assumption), then state-ment 6.5 is also consistent with the argument. That statement can be rewritten as 6.6, and it can be readily observed that it represents an instance of complete indeterminacy.

This feature of conditional theories is im-portant to a strategy of theory testing and de-velopment. If a sociological theory is sup-ported by evidence when SC I is satisfied, the investigator can move on to test the theory under the less restrictive conditions specified by SC2. If the evidence is still supportive, the researcher can attempt to "push .. the theory, e.g., test it under the even more general condi-

12 We use the symbols"& .. and "v .. to represent the logical operators "and .. and "or .. which are used for conjunction and disjunction respectively.

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tions specified by SC3. On the other hand, if the evidence from a test under conditions specified by SC2 is negative (and other reasons for negative evidence have been ruled out), it can be concluded that the theory has been pushed to its limit, at least in the specified direction. Under such circumstances, further attempts to test the theory are unwarranted.

Because it is more general, SC3 is satisfied when SC2 is true and evidence which falsifies a formulation made conditional by SC2 also fal-sifies the formulation with SC3 and any other more general scope limitation.

Our central point is that the use of condi-tional formulations in the manner we have pro-posed provides a strategy for assessing the re-lation of data to theory. The procedure permits a unique resolution of the problem of theory assessment given "negative findings." What follows is a demonstration of how our concep-tion differs from other proposals that purport to make theories conditional.

SCOPE STATEMENTS AND OTHER CONDITIONAL STATEMENTS Many sociologists are aware of the conditional truth of general principles. Although this is a salutary development, we should note that for the most part sociological theorists and re-searchers do not employ the kind of condi-tional statements which concern us. It is im-portant to examine the differences.

The concern for making general principles conditional typically takes the following form: For a particular relation, under what empirical conditions does the relation occur? For exam-ple, a sociologist might ask, "Under what con-

. ditions will I find an inverse relation between the socioeconomic status of criminal defend-ants and the severity of punishments they re-ceive?" There are several possible answers to such a question and indeed several reasons for asking it. However, it seems to us that the answer rarely concerns the scope of a theory. Rather, the answer is one which adds state-ments of initial conditions to a set of observa-tion statements or adds additional variables to theoretical propositions in order to formulate alternative general principles. 13

-If the answer to the question is the addition of initial conditions, several factors that are specific to those empirical situations in which observations have been consistent with a for-mulation are appended to the observation

13 We argue that adding variables results in the construction of alternative propositions. That is, in-stead of being made conditional, statements like xRv are modified to create new statements, e.g., (x & z) Rv, (x V Zl Rv, (xRv & zRv).

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statements. Hence, an investigator may con-clude that the relationship holds if the judge is a member of the majority racial group or of upper-class background or presides in a politi-cally conservative jurisdiction (cf. the previ-ously cited commentary on Chiricos and Waldo). The statements of initial conditions then qualify observations about the relation between the social class of offenders and the severity of sanctions. What is qualified is an . empirical finding not a theoretical proposition, and the qualifiers are concrete, specific fea-tures of the particular historical situation in which the data have been collected.

The question of"underwhat conditions" can be a theoretical concern. However, scope re-strictions are often treated as if they were ad-ditional theoretical variables, either in mul-tivariate propositions or in statements of inde-pendent bivariate relations. Examples are (1) "as the relation between social class and the likelihood of engaging in criminal behavior in-creases, and the social class of defendants de-creases, the severity of sanctions increases"; or (2) "either as the relation between social class and the likelihood of engaging in criminal be-havior increases or as the social class of de-fendants decreases, the severity of' sanctions increases." Rather than making the theoretical argument conditional, these strategies result in the creation of new and different theoretical arguments (see note 13).

Our alternative view of what is meant by "conditional theories" has important practical implications for researchers who must make decisions about the relevance of data to theory. Research findings that are uninterpretable or ambiguous under current formulations of con-ditionality are easily interpreted when our for-mulation is applied. We will illustrate the use of the various strategies for making theoretical formulations conditional with hypothetical data.

THEORY, EVIDENCE AND SCOPE LIMITATIONS Consider the following situation: A sociologist decides to reanalyze the Chiricos and Waldo data in order to test the proposition that there is an inverse relation between the social class of criminal defendants and the severity of judi-cial sanctions. The .data are organized in sub-files by criminal jurisdiction, i.e., three south-ern states which we will refer to as A, B, and C. Social class and judicial punishment are measured as before by socioeconomic status and length of prison sentences. The basic data are displayed in Table 1. A preliminary analysis of those data indicates that there is no relation between the two variables of interest.

SCOPE STATEMENTS

Table 1. Relation of Defendant's Social Class to Se-verity of Sanctions8

Defendant's Social Class (X) Low High x2 = 0.00, p, n.s.

Severity of Sanctions (Y)

Low High 75 75 75 75

a N =; 300 (hypothetical data).

The data in Table 1 are clearly inconsistent with the theory under test. However, the in-vestigator is aware that all theories are only conditionally true, and ,a colleague suggests that the theoretical formulation might be "con-ditioned" by the relation between social class and the incidence of criminal activity. But how is conditionalization accomplished? The in-vestigator might ask one or both of the follow-ing questions: First, isn't the use of scope lim-itations equivalent to adding additional inde-pendent variables to the theoretical proposition and to its operationalization? In oither words, isn't conditionalization accomplished by add-ing one (or more) independent variables to a multiple correlation or multiple regression analysis?

Second, the researcher might ask, isn't the statement, "xRv given that SC is met,'' equiv alent to the. statement, "xRv controlling for the variable of which SC is one value?" That is, aren't partial correlation and contingency-table analysis appropriate techniques for operationalizing the qualifications represented by scope restrictions? The crucial issue for both questions is the distinction among con-stants, variables and the value of a variable. An example will demonstrate the implications of our-formulation and the differences between it and the other methods of making theories con-ditional.

It is important to recall that X and Y stand for constructs which are linked by R. For example R might stand for, "two constructs are inversely related." In the Chiricos and Waldo study, X could be "defendant's social class,'' and Y could stand for "severity of judicial sanctions." The predicate, R, binds X and Y together in a unique way. Statements that specify the scope of a theory are bound to theoretical statements in a different manner, as indicated by,the statement we employ: "SC~ xRy." Now suppose that the variable Z repre-sents the relation between social class and the likelihood of engaging in criminal behavior. For simplicity, we will assume that Z can take on only three values (A, B, C). The three categories of Z take the meanings, "no relation between social class and the incidence of

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criminal behavior," "an inverse relation be-tween the two constructs," and "a direct relation between the two constructs." Our theoretical variable, Z, could be opera-tionalized in a number of ways. We could choose three different crimes that represent "A," "B" and "C,'' or three southern states where for all crimes, "A" is true for the first, "B" for the second and "C" for the third. 14 Then we could write a scope statement such that SC is satisfied when Z takes the value A. The conditional theoretical statement would be written "(Z = A)~ xRv.'' As we have empha-sized above, we take no stand on whether the theory is true when the scope restriction is not satisfied, i.e., when Z = B or C. Furthermore, we are not concerned with specifying a law-like relation between Z and either X or Y. It may be. that particular values of Z are associated with particular values of X or Y, but that is not the concern of the theory .1s

The proper use of scope restrictions pro-vides a method of analyzing data without get-ting tangled up in all possible relationships among variables that are not central theoretical concerns. In order to. answer the questions posed by our hypothetical sociologist, we con-trast the research strategy that uses operational forms of SC 1 and SC2 with formulations that treat statements of scope as equivalent to add-ing theoretical variables or as values of vari-ables in contingency-table analysis. 16 We rep-

14 We spell this argliment out in ordeno empha-size two important points. There is a distinction be- tween using indicators that represent instances of theoretical variables and using indicators on an ad hoc basis .. Second, there is a difference between using spatio-temporal restrictions that are instances of general theoretical constructs and spafio-temporal restrictions that are not linked to theoretical con-structs or only li1;1ked to them after the fact. It is true, as one revi.ewer pointed out, that spatio-temporal quantities are proxies for general sociological fac-tors. The problem is that they can be proxies for a great many constructs simultaneously. Hence, as our example illustrates, if spatio-temporal boundaries are not explicitly linked to scope restrictions, the researcher is given no guidance in selecting circum-stances in which to test a theory.

15 It may be the case that a researcher would want to treat the relationship between class and the inci-dence of criminal activity as a theoretical variable rather than as a scope limitation. We take no stand on that substantive issue here. We are primarily con-cerned with illustrating the different consequences of treating scope limitations as variables rather than constants.

16 One referee of an earlier version of this paper suggested that the logic of this analysis is equivalent to the logic of contingency-table analysis. The con-clusion was based on a unique interpretation of the symbolic representation we used in that paper (see note 9). The referee's comments have stimulated' us

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Table 2. Relationship Between Defendant's Social Class and Severity of Sanctions by Relationship Between Social Class and Incidence of Criminality8

Severity of Class and Incidence Defendant's Sanctions (Y) of Criminality (Z)b Social Class (X) Low High x2 p A Low 20 30

.A High 30 20 4.00

SCOPE STATEMENTS 299 Table 3. Tests of Fit of Relationship Between Defendant's Social Class and Severity of Sanctions by

Strategy of Analysis

Severity of Class and Incidence Defendant's Sanctions (Y)

Strategy of Criminality (Z)a Social Class (X) Low High x2 P Strategy 2 A Low 20 30

A High 30' 20 B+C Low 55 45 B+C High 45 55 6.00 n.s.

Strategy 3A A Low+ High 50 50 B+C Low+ High 100 100 0.00 n.s.

Strategy 3B A+B+C Low 75 75 A+B+C High 75 75 0.00 n.s.

Strategy 4A A Low 20 30 A High 30 20 4.00

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yields a different theory for every empirical situation and that is equivalent to no theory at all.

SUMMARY This article addresses a paradox that confronts every sociologist who sets out to test general theoretical formulations. Every proposition which is advanced as a general sociological principle is both true and false. The paradox creates a dilemma for the sociologist who finds data that are inconsistent with the theory under test: Under what conditions should negative findings be counted as justification for giving the theory up, i.e.; should such findings be treated as falsifying instances? If all negative findings were treated as falsifying instances there would be few, if any, sociological theories to study~ On the other hand, the re-tention of "false" theories appears to con-tradict the very notion of theories as general explanations for phenomena. The problem is all the more critical for practitioners who must decide if, and how, they can use falsified theories as if they were true.

We argue that the true-false paradox can be resolved if sociologists test theories that have been made conditional through explicit specif-ication of their scope. We offer a formulation of scope restrictions under which such condi-tional theories retain their universal character and are fully testable, i.e., falsifiable. We dem-onstrate that theoretical formulations thal have been made conditional by specifying their scope are different than theories that have been made conditional by adding new theoretical variables to them. Furthermore, falsification of a particular conditional theory results in the falsification of any, more general formulation from' which it can be derived. However, the falsification of conditional theories in no way affects the truth-value of less general, i.e., more restrictive, formulations. These two properties of conditional theories have both theoretical and practical significance.

The method we propose suggests a strategy for determining both the limits and possibilities of theoretical growth. Conditional formulations that have not been falsified can be generalized by relaxing their scope. That is, the scope lim-itations can be made less restrictive. The more general a formulation is, the more susceptible it is to falsification, i.e., the greater the number of potentially falsifying instances (cf. Popper, 1959). As a consequence, the failure to find

' evidence against a conditional formulation suggests one direction in which the theory might grow-its scope might be relaxed. On the other hand, the repeated observation of negative evidence suggests that, in terms of its

AMERICAN SOCIOLOGICAL REVIEW

scope, a theory might have reached its growth limit.

The theoretical implications also have prac-tical importarn;:e. First, they suggest guidelines for the researcher who encounters negative evidence. A conditional formulation that con-sistently runs up against negative evidence should be given up. That is one of the functions of scope restrictions: They force the sociologist to make a commitment to count a theory as false if it encounters negative evi-dence under the given conditions. Second, however, the proper use of scope restrictions permits the sociologist to retain and use less general formulations of the same theoretical arguments if those less general formulations have not been falsified. This implication of the strategy we propose permits practitioners to continue to use theories even though more general formulations have been tested and found wanting. The proper use of scope re-strictions permits sociologists to preserve the falsifiability of our theoretical claims without making them universally false.

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SCOPE STATEMENTS

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