Criticisms of Relational Frame Theory: implications for a behavior analytic account of derived stimulus relations.

When human subjects learn to select some stimulus B in the presence of another stimulus A, they often readily select stimulus A in the presence of stimulus B. In this performance, stimulus B appears to exert conditional stimulus control over the selection of A; however, subjects do so without a history of conditional discrimination training for this particular symmetrical response. Further, given a history of reinforcement for selecting B in the presence of A, and C in the presence of B, subjects will readily pick C given A and A given C. The phenomenon has been called stimulus equivalence among behavior analysts, and it has generated increasing attention and excitement in recent years among researchers.

The excitement comes in large part from the implications of this basic finding. Stimulus equivalence has been argued to be important in understanding a wide range of complex human behavior including language acquisition (Sidman, 1971), categorization (Adams, Fields, & Verhave, 1993), syntax (Green, Stromer, & Mackay, 1993), emotional reactions (Dougher, Augustson, Markham, Greenway, & Wulfert, 1994; Leslie, Tierney, Robinson, Keenan, Watt, & Barnes, 1991; Plaud, 1995), and social stereotyping and prejudice (Kohlenberg, Hayes, & Hayes, 1991; Watt, Keenan, Barnes, & Cairns, 1991).

After more than 20 years of behavioral research into stimulus equivalence and similar derived stimulus relations, these phenomena are only recently being examined theoretically, not just procedurally and definitionally. Relational Frame Theory (RFT) is one such account (Barnes & Holmes, 1991; Hayes, 1991; Hayes & Hayes, 1989, 1992; Hayes & Wilson, 1993; Barnes, 1994; Watt et al., 1991). Two recent publications (Boelens, 1994; Sidman, 1994) examine the weaknesses of RFT. This paper responds to those criticisms.

The Basic RFT Account

The RFT account is based on two traditional ideas in behavioral psychology. First, it relies on the idea of a functional behavioral class that cannot be defined topographically. A rat may press a lever with its forepaw, nose, tail, or even by forceful breathing if the bar is sensitive enough. All these responses may become members of the same functional class. Class membership is defined by the functional relation between responding and its antecedents and consequences, and it may take on an infinite variety of forms.

The idea of response classes with an infinite variety of forms is built right into the concept of the operant, but often topographical and functional classes of behavior-environment interactions overlap greatly and the two are confused. Sometimes, their independence is more obvious. For example, having trained a generalized imitative repertoire, a virtually unlimited variety of response topographies can be substituted for the topographies used in the initial training (e.g., Baer, Peterson, & Sherman, 1967; Gewirtz & Stengle, 1968).

Although this idea is a simple extension of the three-term contingency as an analytic unit, qualifiers are usually added when classes are not readily topographically defined (i.e., the class is said to be "generalized," "overarching," or "higher order"). These qualifiers are not technical terms. No additional step or mediational process leads to the formation of operants of this kind. Instead, these qualifiers remind readers that a particular functional class cannot be defined by its response forms - something that is true in principle of functional classes more generally. Boelens analysis of equivalence relies on this idea of a functionally defined, generalized operant as well, but Sidman explicitly rejects it.

The second component of RFT is a simple extension of the fact that organisms can respond to relations among events. This has long been recognized in instances in which the relations are based upon formal properties (see Reese, 1968). For instance, a rat can be trained to run down the least brightly lit alley when given several options. RFT is an extension of the idea that such relational responding can be brought under the contextual control of aspects of the situation other than simply the formal properties of the related events.

For instance, one might be taught, using nonarbitrary examples, the relational response "greater than." We can imagine a child being taught to respond to such questions as "Which bag has the greater number of apples?" or "Which glass has the greater amount of milk?" If a relational response can come under the control of situational features other than actual relative quantity, it might be arbitrarily applied to other events even when the formal properties of the related events do not occasion the relational response, for example, "x is greater than y." Here, the relational response may be controlled by cues such as the words "greater than" rather than by the relative physical proportions of the letters.

RFT was originally used to analyze equivalence-type responding, but from the beginning it was also clear that if equivalence can be viewed as a relational operant, so could many other relations, such as "greater than." This argument was made in the earliest presentations of RFT (e.g., Hayes & Hayes, 1989), and several recent studies have in fact shown how a variety of relations can emerge in traditional matching-to-sample studies with proper relational pretraining (e.g., Steele & Hayes, 1991; Lipkens, 1992; Dymond & Barnes, in press).

RFT has a separate nomenclature because the language used among equivalence researchers is too narrow when applied to other derived stimulus relations. Symmetry, for example, applies to relations such as sameness, difference, and opposition. However, if A is greater than B, we cannot say that B is therefore greater than A, as would be implied by the term symmetry. RFT provides a technical language to describe the psychological properties of relational responding that is sufficiently general to allow for discussion of any number of arbitrarily applicable relations.

Arbitrarily applicable relational responding involves the following properties:

1. Mutual Entailment: In a given context, if A is related to B, then, in that context, a relation between B and A is entailed. We formulate mutual entailment this way:

[C.sub.rel] {A [r.sub.1] B III B [r.sub.2] A}

where [C.sub.rel] represents a contextual event that brings to bear a history of relational responding, and where [r.sub.1] represents the particular type of relation between two events X and Y, then a second relation [r.sub.2] is necessarily entailed (III) between Y and X. If the relation were one of equivalence, [r.sub.1] and [r.sub.2] would be identical; however, this need not be so. For instance, if A were larger ([r.sub.1]) than B, a smaller-than ([r.sub.2]) relation would be entailed between B and A.

2. Combinatorial Entailment: If A has some relation to B, and B has some relation to C, then a relation is entailed between A and C, and C has some relation to A. We formulate combinatorial entailment in this way:

[C.sub.rel] {A [r.sub.1] B and B [r.sub.2] C III A [r.sub.3] C and C [r.sub.4] A}

where [C.sub.rel] represents a contextual event that brings to bear a history of relational responding, and where [r.sub.1] represents the particular type of relation specified between two events A and B, and where [r.sub.2] represents the particular type of relation specified between two events B and C, then a third relation ([r.sub.3]) is necessarily entailed (III) between A and C, along with a fourth relation ([r.sub.4]) between C and A. With mutual entailment, the specificity if not the direction of the relation is the same between A and B and between B and A. Combinatorial entailment may involve relations with differing degrees of specificity. For instance, if A were one unit larger than B, and B were one unit larger than C, then a relation such that A is two units larger than C would be entailed. Lesser degrees of specificity might be seen depending on the relation. Thus, if A were different from B, and B were different from C, we could say little about the relation between A and C.

3. Transformation of Stimulus Function: If stimulus A is in some relation to stimulus B, and stimulus A is given, some psychological function, then the stimulus functions of stimulus B will be transformed in accord with the specified relation. Which functions are transformed must also be under contextual control. Consider the example of an equivalence relation. If all the stimulus functions of A were transferred to B, A and B would no longer be distinct stimuli in a psychological sense. Given mutual entailment and combinatorial mutual entailment between A, B, and C, the final formulation would then take the form:

[C.sub.func] [[C.sub.rel] {A[f.sub.1]r III B[f.sub.2]r and C[f.sub.3]r}].

In the presence of contextual cues ("[C.sub.func]") that select particular psychologically relevant stimulus functions that are present with respect to event A ("[f.sub.1]"), events B and C will show functional transformations in terms of the derived relations between these events and event A ("B[f.sub.2]r and C[f.sub.3]r").

The usual language used in the stimulus equivalence literature is the transfer of stimulus function. RFT replaces the term transfer with transform, because apart from equivalence relations, "transfer" is frequently misleading. Consider for example the relation of oppositeness. If a training history established A as the opposite of B, and A is given a punishing function, we might expect B to have a reinforcing function. In this example, it would be misleading to say that the stimulus functions of B transferred from A to B because the trained and derived function is different. Rather, the stimulus functions of B are transformed based on its relation to A (see Dymond & Barnes, 1995, for an empirical demonstration of this process).

Relational frames defined. The term "relational frame" is used to specify a pattern of arbitrarily applicable relational responding involving mutual entailment, combinatorial entailment, and the transformation of stimulus function. Consider the relations of sameness, oppositeness, and difference. In Steele and Hayes' (1991) experiments subjects' responses to three nonarbitrary stimulus relations (sameness, oppositeness, or difference) were first brought under contextual control. For example, given a contextual cue (an arbitrary visual figure) for "same," a subject shown a short line as a sample earned points for picking a short line from a set of comparisons. Given a contextual cue for "opposite" and the same sample, picking a long line was reinforced. Given the "different" context, selecting any comparison other than one identical to the sample was reinforced. Later in the experiment, these same contextual cues were used in an arbitrary matching to sample procedure and the expected derived relations occurred.

In the beginning of this experiment, the relations were arbitrarily applicable in the sense that any one of the three relations could be applied to a given matching-to sample problem. However, during this early phase, the relations were not arbitrarily applied, because the formal properties of the stimuli occasioned the relational response. In the latter part of the experiment, by contrast, the relations were not only arbitrarily applicable, but were also arbitrarily applied, because the relations were brought to bear on stimuli that did not have any formal characteristics supporting the relational responses.

RFT holds that this pattern of responding is established by a history of differential reinforcement for producing particular relational response patterns in the presence of relevant contextual cues. Although the term relational frame is a noun, it always refers to the situated act of an organism. That is, the organism does not respond to a relational frame. It responds to historically established contextual cues. The response is to frame relationally. Although "framing relationally" may be preferred from a technical perspective, the noun form is less cumbersome and is frequently used (cf., Hayes & Hayes, 1992, and Malott, 1991).

Reply to Boelens' Account

In "A Traditional Account of Stimulus Equivalence," Boelens (1994) offers an operant analysis of stimulus equivalence. According to Boelens,

Novel conditional relations found in studies of stimulus equivalence are instances of generalized performances. The generalized performances are generalized in the sense that they are shown for a variety of sample and comparison stimuli. It is assumed that the generalized performances are produced by reinforcement histories in the usual (extra-experimental) environments of humans. (p. 589)

Consider the example of symmetry. According to Boelens' account, we could give an organism a history of reinforcement both for selecting B in the presence of A, and for selecting A in the presence of B. We could repeat this process with many stimulus pairs (e.g., X[right arrow]Y, O[right arrow]P, etc.). With a sufficiently extensive history, subjects presented with a new stimulus pair L[right arrow]M might be expected to select L in the presence of M, though they had only been directly reinforced for selecting M in the presence of L. (A very similar history is outlined in Hayes & Hayes, 1989, p. 167.) Boelens suggests that a similar history of direct reinforcement with multiple exemplars produces transitivity and equivalence. Boelens (1994) analyzes such performances as "generalized symmetric responding," "generalized transitive responding," and "generalized equivalences" (p. 590).

RFT and Boelens' account agree that stimulus equivalence can be viewed as learned, operant behavior, and they also agree on much of the history that might be involved. Proponents of RFT have explicitly stated that "relational frames are a type of generalized operant" (Hayes & Wilson, 1993, p. 286; this has also been developed in some detail in Hayes & Leonhard, 1994). The earliest accounts of the position (e.g., Hayes & Hayes, 1989) laid out possible histories much like those imagined by Boelens, but with less specificity.

Others have correctly interpreted the operant nature of RFT. For example, Sidman (1994) notes that "Relational Frame Theory holds that the establishment of any arbitrary relation, including equivalence, is itself a learned operant" (p. 554; cf. Barnes & Holmes, 1991, and Malott, 1991). Boelens suggests that his account is different from Relational Frame Theory, however, and we will examine this view. Other than the superficial differences in terminology, he suggests two important areas of difference: (a) In his account equivalence is not considered "higher order" responding, and (b) he differs on the necessity of the role of context. To these two we would add an additional point: We see RFT as having substantially broader scope than Boelens' account. In what follows we will examine these three possible differences.

Higher Order Responding

RFT suggests that relational responses can be brought to bear in the absence of a direct history of relational training with respect to the particular relata. The metaphor of a frame is used for precisely the same reason that Skinner (1957) used it to account for grammar. It denotes the general nature of the response and its relative indifference to the formal properties of related events. As noted earlier, such responses may be described variously as "overarching," "generalized," or "higher-order" simply to denote that it is an operant that can only be defined functionally. Once established such operants can encompass an infinite number of topographical and situational forms. Boelens prefers the term generalized, while descriptions of RFT have used all three synonymously because, as noted above, they are mere reminders about the purely functional nature of some operant classes.

Boelens detects a seeming difference between his account and RFT in this area, but the difference is caused entirely by a terminological confusion. Boelens (1994) suggests that, given A1[right arrow]B1, B1[right arrow]C1 training, RFT "presumably leads to the prediction that C1A1 [equivalence] will be found" (p. 600), provided there was a history of direct training in both symmetry and transitivity. Boelens bases this presumption on statements made in an early work by Hayes and Hayes (1989): "it is possible that a child given only a history of symmetry, reflexivity, and transitivity, could derive the frame of coordination and show equivalence classes" (p. 174; emphasis added). Boelens apparently believes that "transitivity" in this passage referred solely to A[right arrow]C responding, and thus his analysis seems to differ very slightly from RFT. He sees RFT as suggesting that there will be relational derivation without any direct training at combining relations and he seems to think this is what is meant by "higher order" responding.

How much and what kind of training is needed for generalization of a relational response is an empirical matter. However, the general logic of RFT suggests that at least some direct training in combining relations (e.g., both A[right arrow]C and C[right arrow]A training) is necessary. Using RFT terms, this point has been made explicitly and clearly in early expositions; for example, equivalence emerges because "mutual entailment, combinatorial entailment and transfer of function are directly trained" (Hayes, 1991, p. 25; emphasis in original). It is important to note here that combinatorial entailment subsumes both A[right arrow]C and C[right arrow]A relations.

In the 1980s many researchers used the term "transitivity generically to refer both to A[right arrow]C and to C[right arrow]A performances. The word "transitivity" was being used in this general way in the quotation above from Hayes and Hayes (1989, p. 174). Under the influence of Fields, Verhave, and Fath (1984), most researchers gradually reserved the term "transitivity" only for the A[right arrow]C relation, using the now ambiguous word "equivalence" to refer both to the C[right arrow]A relation and to the general class (see Sidman, 1992 for a discussion). Boelens' disagreement with RFT in this area seems to be the result of different uses of the term "transitivity." Boelens does not directly quote an RFT prediction that the C[right arrow]A relation would emerge without a history of direct training in the combination of relations, as no such prediction has ever been made. RFT would not make a different prediction than Boelens' account in this area.

It does seem likely, however, that once the most basic relational unit is established through training in mutual and combinatorial entailment, relatively fewer trained instances of combinatorial entailment will be needed to build out this relational response. Were that not true, every level of relational complexity (e.g., with larger and larger sets of related stimuli) might have to be arduously trained. Consider, for instance, a case in which one was taught to select B in the presence of A, C in the presence of B, D in the presence of C, and so on to the 100th node. We doubt that an individual would have to have a history of direct training at combining relations to match the 100th stimulus to the 1st, the 100th to the 2nd, . . . the 99th to the 1st, . . . the 98th to the 1st, . . . and so on for all possible transitive and equivalence relations among the 100 stimuli. At some point RFT would predict that the operant of combining relations would itself generalize.

It is not completely clear where Boelens stands on this point. However, if he means that a history of direct training would be required for all possible elaborated forms of generalized transitivity and generalized equivalence (combinatorial entailment in RFT terms), then there is in fact a substantial difference between the predictions of the two accounts.

The Role of Context

Boelens also claims to disagree with RFT regarding the role of context in equivalence. According to RFT, arbitrarily applicable relational responses, including stimulus equivalence, must be under contextual control, because by definition responding is not based solely upon the formal properties of the relata or on a history of nonrelational training. Boelens again cites Hayes and Hayes (1989): "a relational response must, by definition, be bought to bear by stimuli other than the relata themselves" (p. 168).

Boelens (1994) disagrees with this but his analysis seems confused. He claims "that these 'stimuli other than the relata themselves' are patterns shared by antecedent stimuli, such as the pattern x[right arrow]y; y(x) in generalized symmetrical responding" (p. 600). This same cue has been discussed by proponents of RFT, and in much the same way as Boelens (e.g., Devany, Hayes, & Nelson, 1986). There is indeed no reason that the matching-to-sample problem pattern itself cannot exert contextual control over relational responding, and at times it seems to do so. However, by the same learning processes Boelens so carefully describes, there is no reason other contextual cues might not also serve the same function, if the history is appropriately arranged. There seems to be no real disagreement here except that Boelens has limited his analysis to one form of cue whereas RFT does not.

Boelens (1994) suggests that contextual control need be assumed "only if the same pattern is followed by different responding in different contexts" (p. 601). This is correct. It is a direct extension of operant principles. Boelens does not explain, however, why as a theoretical matter additional contextual features could not predict differential reinforcement for differential responding, perhaps at times in combination with the problem patterns he emphasizes.

As an empirical matter this may or may not occurs - which cues actually function in a given way is a matter for research, not logical argument. Boelens provides no empirical evidence on this point, but others have. When different relational contexts are experimentally arranged, different relational responses do result, despite the similarity of the problem patterns themselves (e.g., Lipkens, 1992; Steele & Hayes, 1991; Dymond & Barnes, 1995). Thus, Boelens does not disagree with the situated nature of relational operants - he merely wishes to restrict his analysis to one specific cue while RFT is open to the relevance of a range of specific contexts - only the behavioral principles that establish the relevance of these contexts is specified.

Scope of the Accounts

Boelens' position provides a detailed and well worked out operant account of the emergence of generalized symmetry, transitivity, and equivalence. Within the area of equivalence the only real difference we can detect between his position and RFT is that he restricts the relevant context that controls equivalencing. In areas outside equivalence, however, there is a decided difference in the scope of the accounts. Boelens is silent on derived relations other than equivalence. Everything we know about operant behavior suggests that it is flexible with regard to formal and functional details, and if a relation of equivalence can be learned, surely others can be learned as well.

Were Boelens to expand his account, however, he would have to do two things. First, he would have to find an alternative for the descriptive language of equivalence. Boelens could either generate a new term for each relational component of each generalized relational operant (i.e., counterparts for generalized symmetry and transitivity), which would be quite awkward, or he would have to adopt a terminology that is sufficiently general to talk about all possible relations. Second, he would have to make clear that contextual features other than the problem pattern itself could control these various relational operants, given the right history. With these two changes, however, his position would be indistinguishable from Relational Frame Theory.

Summary of Boelens

Boelens' account is important in that it brings attention to equivalence as a historically situated act. Increasing empirical evidence testifies to the utility of such analyses (see Hayes, 1994, for a recent review of the evidence). Boelens has performed a service by showing in great detail how specific histories could lead to equivalencing as an operant. Except that RFT is more general, his detailed analysis is precisely in accord with RFT, and the disagreements Boelens sees are caused by terminological misunderstandings.

The difference in generality is not a major issue until other derived relational responses are considered. This is not a flaw per se - Boelens is free to limit his analysis. For the field at large, however, RFT provides the additional advantage of using technical terms with sufficient scope to account for a variety of arbitrarily applicable relations while taking the same conservative approach as Boelens' narrower analysis.

Reply to Sidman's Account

Several theorists have critically discussed Sidman's mathematically derived description of equivalence (e.g., Barnes, 1994; Hayes & Hayes, 1992; Saunders & Green, 1992), and we will not repeat or expand on those points here. Sidman (1994) has recently provided his first detailed criticism of RFT (pp. 554-561). In the present paper we will respond to Sidman's position only as it relates to his criticisms of RFT.

Must Equivalencing be Learned?

Sidman, (1994) makes two points about RFT in this area. First, he does not see why "'equivalencing' - must itself be a learned response" (p. 556). There is indeed no reason that equivalencing must be a learned response. It is an empirical question. RFT suggests that it is, and research has subsequently been done that provides some support for this idea (see Hayes, 1994), but it could still turn out not to be so. The value of RFT is to lay out how it could be so, so that the idea that equivalencing is a learned phenomenon can be assessed.

Second, Sidman goes well beyond this to argue, essentially, that equivalencing cannot be learned, even if RFT is correct about the histories and resultant response properties involved. The argument is as follows. Sidman is concerned that "a linguistically naive organism's abstraction of commonalities from a set of exemplars that share no physical features requires more of an explanation than just a history of experience with the exemplars" (p. 557). Sidman agrees that stimulus relations can be taught this way when the relation is physically defined, and he further agrees that "linguistically proficient organisms can indeed abstract the properties of arbitrary relations" (p. 556). However, he argues that even if equivalence relations can be shown to emerge exactly as envisioned by RFT "that very finding would require an explanation that is not currently available among the principles of behavior analysis" (p. 557).

This line of criticism can be boiled down to a central point: Purely functional response classes that share no physically defined situational or topographical features cannot be learned operant behavior. By this line of reasoning, generalized imitation, autoclitic frames, or the emission of novel response forms as operants could not be learned merely by exemplars, and if they could, they could not be explained by the existing principles of behavior analysis. Although Sidman makes this criticism of RFT, presumably it would apply equally well to any operant account of equivalence - including that of Boelens.

To the contrary, RFT suggests (and presumably Boelens would also) that whether or not equivalencing is learned operant behavior is entirely an empirical, not a conceptual, problem for behavior analysis. Sidman (1994) criticizes RFT, saying "each relation has its own properties; placing those properties within the borders of an empty frame and then giving the frame a label does not account for them" (p. 561). This is very true, but the description of the frame is not the account of derived stimulus relations within RFT. The suggested reinforcement history is the account. The relational frame is the result. If a reinforcement history with many exemplars leads to an abstraction of commonalities that do not share physical features, and if the response class that results shows the other defining features of an operant (e.g., stimulus control, consequential control, response flexibility, response development), then the behavior analytically adequate explanation for this result is that the response is an operant. What other kind of account is required within behavior analysis?

Sidman rules out a priori operant classes that are based on "generalization from physically unalike exemplars by a nonverbal organism" (p. 557). Other than making this puzzling claim, Sidman does not explain why such classes cannot occur. No finding in behavior analysis of which we are aware requires such a limitation.

Let us consider an example. A pre-verbal child is taught to touch serially any three different objects out of several that are available. Any series of three distinct objects is reinforced. Say the child touches first the green ball, then the red truck, and then the blue cup. The child is then given one of the three objects, say the cup. Imagine that in the presence of a characteristic tone, touching serially the two remaining objects from the set of three (i.e., the truck and the ball) will be reinforced, but not touching any other object. Conversely, in the presence of another tone, touching any two objects other than the truck and ball will be reinforced. This pattern is repeated with an entirely new set of objects (other than balls, trucks, and cups), and then another, and so on for many, many sets. Sidman seemingly must argue that the child cannot in principle learn such a pattern because this is "generalization from physically unalike exemplars by a nonverbal organism." But the contingency defines the response class, not any physical similarity of the exemplars. It would be worth hearing how Sidman would describe such performances, or those of generalized imitation (e.g., Baer et al., 1967; Gewirtz & Stengle, 1968), or novelty as an operant (e.g., Neuringer, 1986; Page & Neuringer, 1985).

Sidman goes on to avow that if such operants did occur, it would "be unwise to use that phenomenon as the explanatory basis for other phenomena" (p. 557) because it is not "itself understood" (p. 557). However, nothing either in operant theory or in the empirical findings of behavior analysis requires that operants be based on physically alike exemplars. What law of operant classes would be violated by this performance? The whole idea of a three-term contingency and of functional response classes seems to argue against Sidman's claim.

Symmetry

Sidman suggests that RFT requires only trained symmetry to produce equivalence, and he criticizes this idea. This is an empirical question, but as with Boelens, this interpretation of RFT is seemingly a misunderstanding caused by an overextension of a section of an early paper. Proponents of RFT have argued that generalized symmetry is possible merely with training in symmetry. Generalized symmetry might be enough to produce equivalence, but RFT holds that at least some training in combinatorial entailment will probably also be needed to produce a relational frame (see Hayes, 1991, p. 25, as quoted above in the section on higher order responding).

Sidman also raises the same point about generalized symmetry as he did about equivalencing - that generalized symmetry cannot be learned because the exemplars share no physical features. He goes on to note that the S-R learning theorists understood this problem and tried to solve it by mediational explanations. He concludes that "to interpret equivalence as a learned response is, despite protestations to the contrary, merely to summarize a complex set of variables by postulating a hypothetical entity - in this instance, an inferred but undemonstratable response - as a mediator of equivalence relations" (p. 558). This is an unusual line of reasoning. Sidman seems to be saying that because RFT fails to see a problem that others solved mediationally, that RFT must be making mediational claims. To the contrary, no mediational solution is necessary for a problem that does not exist. In part, RFT denies the existence of the problem because of the very different understanding of what constitutes a stimulus in behavior analysis, as opposed to S-R psychology.

Mechanistic S-R learning theory required mediators to deal with situations in which responses or controlling stimuli shared no physical features because associations had to be between stimuli conceived of as objects and responses conceived of as forms. Behavior analysis has a more powerful, nonmediational alternative: the functional response class. The need for mediation thus seems to emerge not from RFT which explicitly rejects it but from Sidman's unwillingness to allow for operant classes unfettered by shared physical properties.

In that context it is not surprising to find Sidman himself embracing the very idea he wrongly attributes to RFT. Sidman (1992) has suggested that "because equivalence is always an inference, never directly observed, it is vital to have an unequivocal test for determining whether or not that inference is correct in any instance" (p. 20). Similarly, Saunders and Green (1992) suggest that "a relation, including an equivalence relation, is neither a stimulus nor behavior; a relation is inferred from the observation of behavior" (p. 239). In sharp contrast, the RFT approach holds that a relational operant is not "inferred," it is not "undemonstratable," and it does not "mediate" the performances that result. Rather it is nothing more nor less than the entire class of those very performances, functionally defined as produced by their reinforcement histories and as maintained by current contingencies. Functional classes are not synonymous with any given topographical instance of behavior, but they are not thereby inferences. They are observed, empirical classes of organism-environment interactions.

Elegance and Predictive Power 

Sidman complains that RFT "in throwing away the mathematically derived description [of equivalence] . . . also throws away its predictive power" (p. 558) and that "the mathematical description of the equivalence relation has an elegance and simplicity that Relational Frame Theory is unable to match" (p. 559).

Sidman could be correct about elegance and simplicity - this is a matter of taste. Others can decide for themselves whether things outside psychology such as mathematics or set theory are more elegant than the behavior analytic concepts of reinforcement history and contextually controlled functional response classes.

Comparing the positions predictively is possible, however. RFT predicts that equivalence will develop and behave like an operant (see Hayes, 1994, for some examples of specific predictions this view produces). In a few areas, this idea does lead to predictions that are not readily made by Sidman's procedural/mathematical/nativistic account of equivalence, but the predictive differences are not large (Barnes, 1994). The biggest difference emerges with regard to other relations (cf., Saunders & Green, 1992).

RFT has real advantages predictively in what it was designed to be: a general behavior analytic approach. to arbitrarily applicable relational responding. The Steele and Hayes (1991) study, for example, is entirely obvious from the point of view of Relational Frame Theory. Even today, however, when the study is described to behavioral convention audiences, they generally predict incorrect outcomes for it - outcomes that are seemingly implied by a contemporary understanding of equivalence classes but not by RFT. For example, if subjects learn A - B. and A - C relations in the presence of a given cue, equivalence alone predicts that B will be selected in the presence of C and vice versa. Steele and Hayes (1991) showed this to be false. If the cue had been previously associated with the nonarbitrary relation of oppositeness, for example, subjects would avoid B given C and vice versa. An opposite of an opposite is the same, not opposite. Others have shown this phenomena with other derived relations such as "larger than" (Lipkens, 1992; Dymond & Barnes, 1995).

We know of no well-developed alternative contemporary behavioral approaches against which to evaluate RFT regarding arbitrary relational responses considered broadly. Like Boelens' analysis, Sidman's technical vocabulary has no obvious application to arbitrary relations generally. Sidman claims (but does not actually attempt to show) that "differing relations such as same, opposite, different, and so forth, can be handled by any formulation of equivalence that recognizes the role of context" (p. 561). This may or may not be so. We suspect that it is; computers can model virtually any relation by strings of ones and zeros, and thus any relation can probably be modeled by enough combinations of equivalence and nonequivalence. However, these computer models are horrendously complex. RFT addresses all arbitrarily applicable relational responses in precisely the same manner. At the least, it seems that Sidman's procedural analysis will have to be highly modified and elaborated to account for relational networks containing dozens of different kinds of arbitrary relations. Only after Sidman attempts such an account will the assessment of the relative elegance, simplicity, and predictiveness of RFT as compared with Sidman's procedural/mathematical view be possible as applied to derived and arbitrary relations generally. We hope that Sidman will take this point seriously and will attempt to account in technical language for all these other relations so that the field can make the comparison.

The Role of Theory in Behavior Analysis

Behavior analysts have been very cautious about the development of theoretical accounts because of the tendency for researchers to lose touch with the actual phenomena of interest in the service of theory testing. This becomes especially likely when theories give ontological status to concepts and then go on to explain what is "really" going on with these supposed entities, or worse, lead to a research program about the theoretical processes that underlie these newfound ontological entities. RFT is not a traditional hypothetico-deductive theory of this kind: It is merely an application of behavior analytic principles to a kind of responding that is of interest. It is designed to show how an unusual response form could be an operant, so that the needed research can be done to see if it is.

The purpose of our responding to these criticisms is the same. We are not arguing that RFT is "true." Rather, we are laying out the conceptual and empirical implications of taking the view that deriving stimulus relations is operant behavior. It could be that Sidman is correct: Stimulus equivalence may be a new type of basic stimulus process. However, before the field adopts this rather liberal idea, a more conservative approach seems worth attempting.

The need for theorizing (rather than only producing more data) is shown by Sidman's apparent willingness on theoretical grounds to rule out equivalence as an operant learned by exemplars, which he correctly sees as the essence of RFT. By laying out a broad analysis, a "theory," others can carefully examine the behavioral reasoning involved. This is what RFT has done, and Sidman's now has clearly stated his disagreement with our reasoning. His objections, he himself says, are not merely empirical. All of this can be a very positive development.

This disagreement can be good for the field if it focuses attention on the theoretical and empirical issues involved in the analysis of derived stimulus relations and related phenomena, not merely to an abstract conceptual quarrel. If the field agrees that responses without shared physical properties cannot be operants taught by exemplars, then there is no need to continue to go through the extremely difficult task of assessing empirically whether equivalencing and other forms of relational activity are interesting operant classes trained in this way. Conversely, if Sidman's reasoning is faulty in this area, the process of detecting the fault in this reasoning may lead to more refined descriptions of the kinds of data that will be needed to assess whether arbitrarily applicable relational responding is learned. Either way, the field will benefit, if we keep our eye on the prize: an adequate behavioral analysis of derived stimulus relations arid the psychological events they may contribute to such as speaking, listening, planning, and reasoning.

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