Folk Psychology of Mental Activities

Psycholosical Review 1989, Vo|. 96, No. 2, 187-207

Copyright 1989 by the American I~ycholosical Association, Inc. 0033-295X/89/$00.75

Folk Psychology of Mental Activities Lance J. Rips and Frederick G. Conrad Behavioral Sciences Department University of Chicago A central aspect of people's beliefs about the mind is that mental activities--forexample, thinking, reasoning, and problem solving--are interrelated, with some activities being kinds or parts ofothers. In common-sense psychology, reasoning is a kind of thinking and reasoning is part of problem solving. People's conceptions of these mental kinds and parts can furnish clues to the ordinary meaning of these terms and to the differences between folk and scientific psychology. In this article, we use a new technique for deriving partial orders to analyze subjects' decisions about whether one mental activity is a kind or part of another. The resulting taxonomies and partonomies differ from those of common object categories in exhibiting a converse relation in this domain: One mental activity is a part of another if the second is a kind of the first. The derived taxonomies and partonomies also allow us to predict results from further experiments that examine subjects' memory for these activities, their ratings of the activities' importance, and their judgments about whether there could be "possible minds" that possess some of the activities but not others.

rather than of part to whole. This subset relation provides a taxonomic organization for mental events that is similar to familiar taxonomies of object categories and contrasts with the partonomic or meronomic organization just mentioned (Cruse, 1986; Miller & Johnson-Laird, 1976). Taxonomies, like partonomies, apply to physical as well as to mental events (Cantor, Mischel, & Schwartz, 1982; Rifldn, 1985), although our focus here is exclusively on mental activities. Our aim is to use laymen's judgments of both kind and part relations to examine their knowledge of psychological processes. In the context of scientific psychology, partonomies are common in information-processing models. A typical model of this sort might analyze the task of, say, recognizing a word into subprocesses of encoding the stimulus, searching or activating a portion of memory, deciding on a response, and executing that response. Such a model is committed to the view that encoding, search, decision, and execution are all parts o f the recognition process. The model might go on to analyze the components themselves, generating a multileveled partonomy. Formal taxonomies of mental activities are less common in current research, I but the history of psychology supplies exampies. Many philosophers and psychologists have tried to enumerate the types of mental processes, grouping these processes in meaningful clusters. All faculty psychologies, for example, impose a taxonomic framework on the abilities they analyze. Figure la contains a typical faculty classification proposed by

There is a strong intuition that some mental activities include others. Reading "What Mazie Knew," for example, is a mental activity that involves perceiving individual words, recalling word meanings, parsing the sentences containing these words, inferring missing information, and remembering prior episodes, among other processes. Solving Hilbert's 10th problem is likewise a composite act that might have included recalling related theorems, planning a solution strategy, deducing intermediate consequences, and many other processes. Of course, this nesting of activities in others is not peculiar to mental events; actions of all sorts have their components (Goldman, 1970; Schank & Abeison, 1977; Thalberg, 1977). As an example, washing your hair probably includes finding the shampoo, turning on the water, applying the shampoo, and rinsing your hair (see Abbott, Black, & Smith, 1985, and Galambos & Rips, 1982, for evidence on the organization of such everyday activities). But mental activity is an intriguing special case inasmuch as our ideas about these activities provide clues to our implicit theories of psychology. Analyzing people's beliefs about which mental events involve others may suggest insights into the ordinary meaning of psychological terms such as perceiving, remembering, or reasoning. The act of parsing a novel's sentences is part of the act of reading the novel. Thus, part-whole relations connect some individual mental activities to others. However, when we move from specific activities (or tokens) to types of activities, another important relation becomes apparent. Novel reading (a type of activity) is a kind of reading a relation of subset to superset

i Although complete taxonomies are uncommon, contemporary psycholngists have not hesitated to make claims about the taxonomic relations among specific pairs of mental activities. Examples include (a) "A person recalling material seems to be solving a problem" (Lindsay & Norman, 1972, p. 375), (b) "Deliberate preparation for future retrieval is a form of planning . . . . and could conceivably be as elaborate and variegated as any other form" (Flavell & Wellman, 1977, p. 20), and (c) "In this same sense, perceivingwithout awareness is a form of retrieving without awareness" (Klatzky, 1984, p. 82). We discuss s o m e current taxonomies of mental events from philosophy and anthropology in the final section (Folkpsychologies)of this article.

National Institute of Mental Health Grant MH39633 supported this research. We thank Rob Chametzky, Roy D'Andrade, Anthony Riikin, Roger Schvaneveldt, Howard Karloff, Edward Smith, John-Christian Smith, Barbara Tversky, and Rita Walter for their help with this project. Correspondence concerning this article should be addressed to Lance Rips, Behavioral Sciences Department, University of Chicago, 5848 South University Avenue, Chicago, Illinois 60637. 187

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MENTAL ACTIVITIES McCosh (1886, Section IV) that first divides the "powers of mind" into cognitive and motive groups; cognitive faculties sort into presentative (i.e., perceptual), reproductive (memory), and comparative groups; andCthese categories in turn divide to form a three-tiered hierarchy. Fodor's (1983) distinction between vertical (i.e., domain-specific) faculties and horizontal (or domainindependent) faculties provides a modern example of a taxonomic grouping. Hierarchical models are also common in psychometric theories of intelligence, such as those of Jensen (1970) and Vernon (1950). Vernon, for instance, explicitly rejected faculties in the traditional sense, but nonetheless proposed his own hierarchy of human abilities based on test scores. Figure lb is a presentation by Cronbach (1970), based on Vernon's thinking. Scientific partonomies and taxonomies convey psychological theories based on evidence and argument. Yet it is not too farfetched to suppose that informal hierarchies of this sort are present even in everyday beliefs about thought and emotion. People can gain information about mental processes from introspection, from simple thought experiments, or from opinions of others; indeed, studies of metacognition show that even preschool children possess a great deal of knowledge about cognitive processes in the domains of memory, attention, communication, and problem solving (see Brown, Bransford, Ferrara, & Campione, 1983, and Wellman, 1985, for reviews). Although this information may sometimes be incorrect or incomplete (Churchland, 1981; Stich, 1983), it may still be consistent enough to have a meaningful structure of its own. In our view, if such structure exists, it deserves serious attention on at least three counts. First, it may influence performance in situations in which strategic control is possible. Consider people's belief about whether writing a passage normally includes (as a part) planning which elements to include in it. The presence of this belief may affect the way people actually produce the passage and, ultimately, the quality of the text itself (Flower & Hayes, 1980; Scardamalia, Bereiter, & Steinbach, 1984). Similarly, geometry students' performance may depend on their having the belief that proof is a useful part of solving general mathematical problems (Schoenfeld, 1983). Second, our intuitive psychology may play a crucial role in the explanations we give for others' behavior. These explanations usually involve attributing to people certain mental acts or states: the desire to achieve something and the belief that the action is capable of fulfilling this goal. Moreover, as D'Andrade (1987) pointed out, our culture's folk model of mind is itself part of other systems, including criminal categories, personality types, and speech acts. Whether an instance of killing is an act of murder depends on whether the act was committed "with malice aforethought." Whether we consider a person imaginative obviously depends on whether we believe he or she has a particularly active imagination. And whether a given utterance is a lie usually depends on whether its utterer believes the sentence to be false and intends to deceive (Coleman & Kay, 1981). There is also developmental evidence that folk psychology is a precursor of other forms of nonpsychological knowledge. Thus, Carey (1985) claimed that children's early ideas about biology evolve from a naive psychology that explains behavior at all levels in terms of beliefs and desires. A third reason for studying this structure is pedagogical,

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since we might gain in teaching psychology from knowing the preconceived meanings that students give our terms of art. There is, however, some difficulty in determining subjects' beliefs about mental activities. Although the underlying structure may resemble that in Figure 1, judgments may be variable, both within and between subjects. Answering a question like whether thinking is part of dreaming requires delicate intuition, and the decision process responsible for such answers may introduce noise that obscures the target relations. Finding structure in noise is, of course, the mission of many current techniques for data analysis. But most of these techniques (including factor analysis, multidimensional scaling, hierarchical clustering, and additive or free-tree clustering) are designed to handle numbers that represent symmetric, intransitive relations such as correlations or proximity ratings. In the present case, we are concerned with the relations is-a-part-ofand is-a-kind-of, which are presumably asymmetric and transitive. Proximity-based techniques sometimes accommodate asymmetric data (e.g., Hubert, 1973; Krumhansl, 1978), but where the judgments are systematically asymmetric, we may be able to achieve more revealing solutions by taking this constraint into account. In the first section of this article, we analyze subjects' judgments about kinds and parts of mental activities using a method that we devised specifically for relations of this sort. The second section then evaluates the resulting structures by using them to predict data from further experiments concerning memory for these interrelations, judgments about the importance of mental activities, and judgments about the possibility of minds that can perform some of these activities but not others. The final section considers implications of these results for current issues in categorization and metacognition. A Framework for Representing Mental Activities The basic data with which we will be concerned are subjects' judgments about relations between pairs of mental activities. In discussing these activities, we will stick to the terminology introduced earlier, referring to an individual instance of a mental activity as an activity token and the entire set or kind as an activity type. We assume that subjects' beliefs about kind and part relations conform to certain underlying properties, even though the subjeers might sometimes violate these properties in their overt responses. We therefore attempt to reconstruct the underlying beliefs by finding a set of relations in which these properties hold and which is, in some sense, as close as possible to the subjects' original decisions. The problem of finding this ideal set of relations is easy if the number of mental activities is small (approximately four items or less), since the best-fitting structure can be found through exhaustive search. For larger data sets, though, exhaustive search is too time consuming, and we must resort to other techniques. In the present section, we first take up the question of the underlying nature of part and kind relations and discuss a method of uncovering them. We then apply these considerations to data from an experiment in which subjects judged these relations for pairs of mental activities.

Properties of Mental Acts We will suppose, as a working assumption, that both the kindof and part-of relations between mental activities are irreflexive,

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asymmetric, and transitive. In the case of kind-of, these properties seem self-evident: A type of mental activity is not a kind of itself; if activity M~ is a kind of activity M2, then M2 is not a kind ofMj; and for any three activities, M~, M2, and .4/'3, ifMj is a kind of M2 and M2 is a kind of M3, then M~ is a kind of M3 (Thomason, 1969). More generally, these three properties are true of the proper subset relation, and because kind-of is a type of proper subset relation, the same three properties should also be true of kind-of. The semantics of part-of seems to entail the same three properties. Although there are a variety of formal theories of part-whole relations, all of them assume that the notion of (proper) part is at least irreflexive, asymmetric, and transitive (Goodman, 1966, chap. 2; Simons, 1987). This assumption is motivated by the semantics of kind-of and part-off The very meaning of these relations seems to carry a commitment to transitivity, asymmetry, and irreflexivity. Thus, ifa person maintains, for example, that M~ is a kind of M2 and M2 is a kind of M3 but that M~ is not a kind of M3, we might be inclined to suppose that he or she had made a simple processing error or was using the terms or relations in an idiosyncratic or equivocal way; we would not be likely to assume that the person had discovered a truly intransitive set of kinds. This situation is analogous to what we might expect with similar relations, such as is greater than or is the ancestor of. It would be extremely difficult to make sense of the joint assertions that x is greater than y, that y is greater than z, but that x is not greater than z. In all such cases, we tend to hold on to the underlying properties of the relation and attempt to explain the discrepancy as a misunderstanding or temporary slip. There are certain examples, however, that call into question the transitivity, asymmetry, or irreflexivity of kind-of and partof. First, it is sometimes possible to induce subjects to make intransitive judgments about category membership. Most subjects, for example, will affirm that car headlights are lamps and that lamps are furniture, but then deny that car headlights are furniture (Hampton, 1982). It's not hard to imagine similar sorts of intransitivity for part-off Although a foot, for example, is part of a soldier and a soldier is part of an army, a foot is not part of an army. If kind-of and part-of are intransitive for even physical objects, so this objection goes, they are unlikely to be transitive for mental ones, in which the meaning of these relations is perhaps more obscure. Second, one might argue that a mental activity can be a part of itself if we conceive of it on an analogy with a recursive procedure in a language like LISP or PROLOG. A LISPprocedure can contain a reference to itself and in this way be a part of itself. So if mental activities are like recursive procedures, then mental activities are not necessarily irreflexive. For instance, imagine a general-purpose comparison process applied to the job of deciding whether two words are identical. This decision might include a test of the identity of the individual letters performed by the same comparison mechanism, and if so, we might be tempted to say that this procedure is part of itself. Similarly, one LISP procedure can refer to another, which can in turn refer to the first, and this suggests that mental activities are also not asymmetric. Nonetheless, there are some simple ways of countering the foregoing arguments. Intransitivity in judgments of category membership may simply be due to subjects interpreting statements of the form "xs are ys" as meaning that many or most xs are ys or that typical xs are ys. This is, in fact, Hampton's (1982)

own explanation of his data. If this is so, then clarifying the intent of the statement (stipulating that all ~ are ys) should eliminate the intransitivities. In a similar vein, proposed counterexamples to the transitivity of part-of may rest on equivocations. In the example given earlier, the way in which a soldier is part of an army (a member of a collection) appears to be different from the way in which a foot is part of the soldier (a constituent of an object); see Cruse (1979), Macnamara (1986, chap. 8), and M. Winston, Chaffin, and Herrmann (1987). Thus, alleged intransitivities of this kind may be less prevalent if the part relations are of the same sort, as in the case of parts of mental activities. Finally, recursively embedded procedures in languages like LISPare different instantiations or tokens. The comparison process applied to letters is not the same token as the process applied to words. But as we mentioned earlier (and as we emphasized to subjects in the following experiments), partotis a relation among individuals. 2 Ultimately, whether subjects take kind-of and part-of to be irreflexive, asymmetric, and transitive is a question we can examine by determining the extent to which a model based on these assumptions provides a good fit to subjects' judgments. This is the approach we will follow. Individual subjects'judgments. By definition, an irreflexive, asymmetric, transitive relation is a (strict) partial order; so both part-of and kind-of partially order activities. If we represent activities as points and draw a directed link connecting point i to point j whenever activity Mr is a kind of Mj, then the resulting structure will form an acyclic directed graph, that is, a directed graph in which no sequence of links connects a point to itself (Harary, Norman, & Cartwright, 1965, chap. 10). Obviously, the same is true if we connect activities withpart-offinks. Figure 2a-2e shows five possible partial orders for the mental activities thinking, dreaming, and remembering, with links for the kindof relation. In Graph 2a, these activities are totally disconnected, none being a kind of another. Graph 2e exhibits the same activities connected in such a way that dreaming is a kind of remembering, which is in turn a kind of thinking. Both of these structures, as well as the intermediate ones in Graphs 2b-2d, are potential candidates for the underlying subjective organization ofthese activities. Further candidates can be generated by permuting the labels on the points in 2b--2e. On the other hand, Graph 2f is not a possible underlying structure on our account since it violates the transitivity condition. The structures in Figure 1 differ from those in Figure 2 in that the former do not explicitly represent all of the intended kind-of relations. For example, perception is clearly supposed to be a kind of cognitive faculty in Figure la, but this kind-of link is omitted since it is predictable on the basis of the links from perception to presentative faculties and from presentative to cognitive ones, together with the knowledge that kind-of is transitive. We could have followed the same convention in Figure 2 if we had left out the kind-of rink between dreaming and thinking in Graph 2e. Because it is often easier to read graphs that omit these predictable transitive links, we will follow this convention in later examples. A graph produced by removing all of the predictable transitive links is called the transitive reduction of the original. A graph produced by adding all of the predictable transitive links is the transitive closure of the original. We also note that the underlying structures are not necessarily trees, since we allow cases in which two parts of the structure

MENTAL ACTIVITIES

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judgments will not perfectly reproduce a partial order;, decision or response processes can introduce error that obscures the underlying relations. In such a situation, a reasonable hypothesis is that the underlying structure is the partial order that preserves as many o f the subject's actual judgments as possible. Suppose, for example, that Jones stated that dreaming is a kind of remembering, that remembering is a kind o f thinking, but that dreaming is not a kind of thinking. This set of judgments is clearly intransitive. However, we can restore transitivity by adding a single relation (from dreaming to thinking) or by subtracting one relation (either the one from dreaming to remembering or the one from remembering to thinking). Two of these possibilities appear as Figures 2b and 2e. Assuming that adding or subtracting a relation is equally reasonable, we have three nearest partial orders that could serve as hypotheses about Jones's underlying model. Suppose we let s o = I if the subject states that activity Mi is a kind of Mj, and let s 0 = 0 otherwise. Similarly, we can let t 0 = l i f M i is related to Mj in a particular partial order T, and let t o = 0 if Mi is not related to Mj in T Then we can call T a nearest partial order if it minimizes the sum o f the deviations between s and t over all i and j. Clearly, we can treat part-of relations in the same way. Group judgments. Sometimes we are interested in the underlying partial order for a single person, but more often we want to find a structure for the results from an entire group. Obviously, random error can cause group members to differ in their judgments about mental activities even if these members have the same underlying beliefs. We therefore want to identify a partial order over these activities that is closest to some overall measure of the group's judgments. As one possibility, let s0be the proportion of people in the group who say that activity Mi is a kind of Mj. Then we might try to find the partial order T that minimizes the sum of squared differences between the sos and the tos (where t o is as defined previously). In other words, we can take T to be a nearest partial order if it minimizes SSD, where

SSD = Z o ( t O-- SO)2.

Figure 2. Six structures for the activities thinking, remembering, and dreaming. (An arrow between activity Mt and M2 means that M~ is a kind of M2. Graphs a-e meet the requirements of partial orders, whereas Graph fdoes not.)

are disconnected (e.g., in 2a-2b) and cases in which one activity can be nested in two or more others (e.g., conscience in Figure l a and dreaming in Figure 2c). Although all tree structures are partial orders, not all partial orders are trees. Because some of the historical examples (e.g., those in Figure 1) are partial orders but not trees, this more flexible structure seems to be warranted. Partial orders have also been proposed as mental representations for other sorts of entities. Kintsch (1972) argued that partial orders, rather than more specialized structures such as trees or lattices, are the way people represent kind-of relations among categories of physical objects. As we mentioned earlier, we expect that a subject's actual

(1)

The same equation will serve if the judgments are ratings rather than yes/no decisions, as long as the ratings are first rescaled to the 0-to- 1 interval. As an illustration, suppose that the proportion of subjects who say that dreaming is a kind of remembering is .5, the proportion who say that remembering is a kind of thinking is .9, and the proportion who say that dreaming is a kind o f thinking is .3. Suppose, too, that subjects say that no further kind-of relations exist among these three mental activities, so the remaining sos are 0. Then the nearest partial order T, according to Equation 1, is shown in Figure 2b, in which the only connection is the one running from remembering to thinking. For this partial order, SSD = 0.35. The two runners-up are the orders in Figures 2d and 2e (SSD ffi 0.75, in both cases). The remaining partial orders all have SSDs greater than 1.0. 2 2 In applyingthe model to group data, we are explicitlyassuming that subjects have the same underlying beliefs about the relations and objects in the domain. Thus, any discrepancy between the partial orders of individual subjects is ascribed to error. This assumption is likely to be too strong in many domains, and it would clearly be of interest to develop the approach in a way that allows for substantive individual differences.

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Problems in Identifying Nearest Partial Orders Because there are only a small number o f graphs with three labeled points, it is easy to find the nearest partial order in an example like the one we just described. However, even a small increase in the number of points leads to an unwieldy problem. The most obvious method for finding the nearest partial order is to generate all possible directed graphs, checking each for transitivity, asymmetry, and irreflexivity, and then evaluatin~ the SSD. The trouble with this procedure is that there are 2 ~" possible graphs on n labeled points; so for n = 7, the method would have to search through 5.6 × 1014possibilities. In fact, even if it were possible to generate partial orders directly and evaluate the SSDs of just this smaller set, the combinatorial problem would still remain. Although there seems to be no known closed-form expression for the number of partial orders over an arbitrary number of labeled points, Evans, Harary, and Lynn (1967) have used an inductive procedure to enumerate labeled partial orders for n less than or equal to 7. Their results appear in the fourth column of Table 1 and indicate that there are over 6 million partial orders for n = 7. It seems likely that no algorithm for finding the nearest partial order can overcome this exponential increase in the size o f the search space. This is because the problem is formally NPcomplete (Kadoff, 1987); that is, it is equivalent in computational complexity to other better-known examples such as the Traveling Salesman problem or the Knapsack problem, for which no known algorithm requires less time than some exponential function of the problem's dimensions (see Garey & Johnson, 1979, for an exposition of NP-completeness). But although this exponential complexity is unavoidable, it is still possible to come up with algorithms that take less time to execute than others. Clearly, an algorithm that executes in, say, 2 n s is preferable to one that takes l0 n s (where n is the number of items in the partial order). What is needed in finding nearest partial orders is a way of reducing the size of the search space. We have devised an algorithm, which we call TRANSIT, that uses a branch-and-bound technique for this purpose. (For discussions of the advantages of branch-and-bound, see Reingold, Nievergelt, & Deo, 1977, or E H. Winston, 1984.) The basic idea is to use the SSD ofthe best partial order that TRANSIT has obtained so far to avoid considering possibilities that could only lead to partial orders with larger SSDs (i.e., worse fits). The tests that TRANSITcarries out to ensure transitivity are essentially those of Holland and Leinhardt (1976). A fuller description o f t b e algorithm is given in the Appendix. Table 1 contains the results of Monte Carlo simulations with TRANSIT for partial orders of sizes 5 to 8. Column 2 of the table lists the mean number of times the program enters its main loop (see Appendix), and column 3 gives the mean SSD of the resulting nearest partial orders, based on 20 random S matrices. In general, the number of loop executions (the number of adjusted T matrices that the program tests) increases exponentially with each increase in the size ofn. However, in each case, the number

Our assumption, however, may be reasonable in the present context in which all of the subjects are members of the same culture and speech community.

Table I

Results From Monte Carlo Simulations With Partial Orders of From 5 to 8 Points

No. of points

Mno. of main loop executions

5 6 7 8

1,278 14,346 304,020 7,104,984

MSSD 3.24 __.0.48 4.96 + 0.92 7.18 ___1 . 2 4 10.00 + 1.02

Total no. of partial orders a 4,231 103,023 6,129,859 --

Note. Means are based on 20 observations. From Evans, Harary, & Lynn (1967).

is much smaller than the total number o f partial orders for data sets of that size, as shown in the fourth column of Table 1. Although the program can't overcome the combinatorial difficulty, it can at least postpone the problem long enough to obtain partial orders of up to eight items. In the following section, we take advantage of this potential, using TRANSIT to find underlying partial orders for sets of mental activities. In the final section, we will consider some approximations for partial orders with larger numbers of objects.

Subjective Structures for Mental Activities To explore people's ideas about mental activities, we asked subjects for their judgments of which activities are parts or kinds of others. These judgments provide the type of group data that can be analyzed by the methods just discussed: We can derive partial orders for both the kind-of and part-of relations, on the assumption that these orders represent the subjects' underlying folk psychology. Before we can be confident about the validity of these structures, though, we need to show that the partial orders can themselves predict the results from other types of tasks. As we noted earlier, there is a question whether the properties that we have ascribed to part-of and kind-of correctly describe people's understanding of these relations. One way to test these assumptions is to determine whether the orders derived from them yield correct predictions in relevant experiments. For example, subjects should be able to recognize these orders as better representations than superficially similar ones; they should have an easier time remembering the derived orders than alternatives; and they should rate the importance or centrality of mental activities in ways that conform to the orders. Next, we describe the partial orders themselves and then take up some experimental tests. PreliminarjJ experiments. The textbook terms psychologists use are sometimes specialized phrases (e.g., serial anticipation learning, oral fixation, habituation) with no clear counterparts in ordinary speech. Because our goal is to investigate lay persons' conceptions, we need a set of terms that are part of everyday vocabulary. As a first step, we asked a group of 15 subjects to list as many common mental activities as they could, using a single word or short phrase for each. These subjects were students or persons of student age who had answered an advertisement in the University of Chicago newspaper. None were psychology majors. In tabulating the items from these lists, we combined terms that had the same root (e.g., reason and reason-

MENTAL ACTIVITIES KINDS ORDERINGS

193 PARTS ORDERINGS

ANALYTIC TERMS, a.

t 1,

t

NONANALYTIC TERMS : C.

t

t

t

Figure3. Nearest partial orders obtained by TRANSITfor analytic terms (Graphs a and b) and nonanalytic terms (Graphs c and d). (The left-hand graphs represent ordering by kind-of, and the right-hand graphs ordering by part-of) ing) and combined phrases that differed in their qualifiers (e.g., smelling the air was counted as an instance of smelling). We deemed as idiosyncratic those terms listed by a single subject, eliminating them from further analysis. The final combined list contained 73 entries, with the highest frequency terms being thinking (mentioned by 14 of 15 subjects), dreaming, and remembering (both mentioned by 9 subjects). From these items, we selected 30 for further analysis. These were terms that clearly referred to mental phenomena but spanned a range of types. 3 Our main interest is in part and kind relations, so we asked two new groups to make decisions about them. The two groups contained 20 subjects each, selected from the same pool as in the first experiment; none, however, had participated in that earlier study. Subjects in both groups received booklets containing a randomized list of all possible ordered pairs of the 30 mental activities (with a different random sequence for each subject). The pairs were embedded in simple sentences of the form " x is a kind of y" or "x is a part o f y." (The activities x and y were always distinct; e.g., subjects were not asked whether thinking was a kind of thinking.) Subjects in the kinds group decided whether the first member in each pair was a kind of the second, placing their yes or no answer in a blank to the right. Similarly, subjects in the parts group decided whether the first member of the pair was a part of the second. The instructions emphasized that the relation in question was to apply to all instances of the named activities. That is, subjects were to answer

yes to the kind-ofquestion only if every instance of the one activity was among the instances of the other. Subjects in the parts group were to answer yes only if every instance of the one activity had an instance of the other as a part. These relations were illustrated in the instructions by analogy with physical activities (strolling is a kind of walking, putting a foot forward is a component part of walking). We stressed that subjects should take into account all instances, since we thought this would help them avoid responding on the basis of only a few representative or typical cases. The raw data from this experiment can be conceived as two 30 × 30 S matrices, with the rows and columns corresponding to the different activity terms (imagining, contemplating, etc.). One matrix contains the proportions of subjects from the kinds group who identified the row activities as kinds of the column activities. The second matrix contains the proportions of subjects from the parts group who identified the row activities as parts of the column activities. Because it was impossible to analyze simultaneously the results from matrices of this size, we sampled from them two sets of seven items, one consisting of cognitive or analytic terms (conceptualizing, deciding, plan3 Some of the items in our list, such as loving, could be classified as mental states rather than mental activities on grammatical grounds (see Vendler, 1972). We refer to the items as activities here because that is the category under which subjects listed them.

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ning, reading, reasoning, remembering, and thinking), the other of more nonanalytic terms (contemplating, dreaming, experiencing, having emotions, imagining, loving, and realizing). These groupings distinguish only very roughly between two domains of mental experience, and it is likely that all the activities have both analytic and nonanalytic components. We partitioned the terms into these related groups to increase the chance of finding interesting structure, not because there is a firm theoretical boundary between them. The mean production frequency in our norms was 5.43 mentions per item for the analytic terms and 3.43 mentions per item for the nonanalytic ones (maximum ffi 15). Geometric-mean word frequency for the analytic terms is 21.69 tokens, and for the nonanalytic terms is 9.55 tokens per million words (Francis & Ku~era, 1982).

Sic TRANSIT; Partial orders for analytic and nonanalytic terms. The TRANSITalgorithm was applied to the part-of and kind-of data for both analytic and nonanalytic items, and the resulting partial orders appear in Figure 3. The two graphs on the left depict the kind-of relations, and the two on the right part-of relations. Notice that the kind-of relations are indicated by arrows that run upward, whereas the part-of relations run downward. For example, the bottom left-hand graph shows dreaming as a kind of imagining, whereas the corresponding right-hand graph shows imagining as a part of dreaming. Orienting the graphs in this way brings out the similarity between them, which we discuss later. Looking first at the kind-of graphs (Figures 3a and 3c), we find that the partial orders merge toward the activities thinking and experiencing: The remaining activities are kinds of one of these two general types. More formally, let the indegree of a node be the number of links terminating at that node and the outdegree be the number of links emanating from it (Harary et al., 1965). Thus, the indegrec of conceptualizing is 3 and its outdegrec is 1 in Figure 3a. A graph can be said to be forward branching if the indegre¢ is 0 or 1 at each node in the graph, and backward branching if the outdegree is 0 or I at each node. Thus, both of the kinds graphs are backward branching, following the pattern of most taxonomies. The kinds graphs seem to correspond reasonably well to the everyday meaning of the activity terms. However, most cognitive psychologists would probably view the arrangement of analytic terms as containing too many levels. In the more specialized sense of these terms, planning is not merely a kind of deciding and deciding is not merely a kind of reasoning; rather, reasoning, decision making, and planning are separate, although interdependent, processes. Nevertheless, the hierarchy in Figure 3a presents a consistent view, particularly if we understand deciding in the sense of deliberating: Planning is a way of deciding or deliberating about future actions, and deciding or deliberating is in turn a form of reasoning about what to do or what to believe. If we now turn to the part-of graphs, we immediately notice some resemblance to the corresponding kind-of relations. It is somewhat surprising that for many of the pairs one activity is a part of another when the second is a kind of the first. As a consequence, these graphs tend to branch away from thinking and experiencing, rather than merging toward them as in the kinds graphs. Except for the dreaming node in Figure 3d, these graphs are forward rather than backward branching. Of the 24 pairs of activities linked by kind-of relations, all but 2 are linked

in the opposite direction by part-of. The two exceptions involve contemplating: Dreaming and imagining are kinds of contemplating, but contemplating is not a part of dreaming or imaginin~ according to these results. Similarly, of the 28 pairs linked bypart-of, all but 6 are linked in the opposite direction by kindof. Of the 6 exceptions, 4 have to do with remembering: Remembering is a part of reasoning, reading, deciding, and planning; however, none of the latter activities is a kind of remembering. Thus, with some salient exceptions, subjects treat part-of as the converse of kind-of. Because different groups of subjects judged the kind-ofand part-of relations, this similarity is not due to carry-over effects. The converse relation between kind and part may seem puzzling at first, inasmuch as it normally fails to hold in the domain of physical objects. A hammer is a kind of tool, but a tool is not a part of a hammer; a handle is part of a hammer, but a hammer is not a kind of handle. We discuss the reasons for this difference at length later in the section on Alternative Explanations, but we note that physical activities sometimes behave in this respect like mental ones. It is reasonable to say, for example, that jogging is a kind of exercising and that exercising is a part of jogging (see also Rifkin, 1985). The similarity between the kinds and parts graphs permits us to identify some common features within them. For example, there is a sense in which thinking and experiencing are depicted as focal activities in both types of graphs, whereas planning and dreaming are not. In earlier work we have used the term central to refer to activities that are important or necessary in an operation or process (Galambos & Rips, 1982; Rips, 1984), and this notion seems applicable to items like thinking, near the top of Figures 3a and 3b. By contrast, an activity like dreaming is more peripheral. Later, we define a measure of relative centrality and show that this measure predicts subjects' ratings of the activities' importance and judgments of the likelihood that there could be hypothetical minds lacking some of the activities. Degree of fit. The goodness of fit for these partial orders seems reasonable when compared with those for the random data in the previous section. The SSDs are 2.58 for the nonanalytic kind graph, 4.62 for nonanalytic parts, 3.46 for analytic kinds, and 5.14 for analytic parts. All but the last of these is significantly less than 7.18, the mean SSD for partial orders with seven objects that we obtained in the simulations. (See Table i; the critical value of t at the .05 level with 19 dfis 5.04.) The partial orders appear to provide better fits for the nonanalytic than for the analytic terms, although this may well be due to our particular choice of nonanalytic and analytic items. A more interesting result is that the kind-of relations tend to be better fit than the part-of relations. Lack of fit for the part-of data appears to be the result of symmetric pairs of activities. For instance, 65% of the subjects stated both that reasoning was a part of thinking and that thinking was a part of reasoning, 60% stated both that deciding was a part of reasoning and that reasoning was a part of deciding, and 50% stated both that imagining was a part of dreaming and that dreaming was a part of imagining. These symmetries should make us cautious about accepting the part-of graphs at face value, but it is nevertheless possible that these graphs capture enough of subjects' beliefs about the activities to predict performance in other types of tasks. We return to these symmet-

MENTAL ACTIVITIES ries in reviewing alternative accounts o f our data in the third section o f this article .4 We have also applied the algorithm to the judgments o f individual subjects in this experiment, with results that conform to those for the group data. In general, we obtained better fits for nonanalytic than for analytic terms (M SSD over subjects is 4.72 for the nonanalytic graphs and 6.20 for the analytic ones). Similarly, fits were generally better for kinds than for parts ( M SSD is 4.62 for kinds, 6.30 for parts). An analysis of variance (ANOVA) of SSDs confirms that the analytic/nonanalytic difference is significant, 17(1, 38) = 10.43, p = .03, although the kinds/parts difference was not, F ( I , 38) = 1.05, p > . 10. Psychological R e a l i t y o f M e n t a l T a x o n o m i e s and Partonomies The partial orders in Figure 3 would have little interest if they were merely a task-specific product. Our hope is rather that the links in Figure 3 represent relatively permanent features of peopie's beliefs about mental activities. The claim, however, is not that the concepts of thinking, reasoning, remembering, and so on, are stored in long-term memory with connections corresponding to the links in the diagrams. That is, we are not assuming that these links are prestored (Smith, 1978), as they might be in network models like Anderson's (1983) or Collins and Loftus's (1975). Although prestorage is possible, we are here making the weaker suggestion that the links represent the relations people would acknowledge in reflecting on these activities. The links are claimed to be implicit parts of their folk psychology. But even though the links may not be prestored----even though people may never have considered whether, for example, imagining is a kind of contemplating--the links nevertheless have testable psychological consequences. At a minimum, we would suppose that subjects should recognize the Figure 3 diagrams as better representations of this domain than other possible configurations. In addition, subjects' memory for Mnd-ofor part-of relations should be better if the relations conform to those in Figure 3 than if they do not. Finally, these links may predict subjects' ratings of other aspects of mental activities, such as their psychological importance or centrality. In the following, we consider evidence of these sorts.

Diagram Judgments As a simple test of the diagrams in Figure 3, we asked two groups of subjects to rate how good they are as representations of the actual kind-of or part-of relations that exist among these activities. For each of the diagrams in Figure 3, we constructed four foils that had the same shape as the original diagrams but differed in the position of the terms. One foil had an SSD that was approximately 2 units greater than that of the original diagram, the second had an SSD approximately 4 units greater, the third 6 units greater, and the fourth 8 units greater. As an example of a difference of approximately 2 units, the kind-ofdiagram for nonanalytic terms in Figure 3c (SSD = 2.58) differed from the corresponding foil (SSD = 4.68) by an interchange of the positions of contemplating and dreaming. The analytic parts diagram in Figure 3b (SSD -- 5.14) differed from the corresponding foil (SSD -- 7.15) by an interehange of the positions ofthinkingand remembering. We drew the original diagram and its four

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distortions on separate sheets of paper, randomized the order o f the sheets (using a different random order for each subject), and presented them in a booklet. Two groups of subjects took part in the experiment; each group included 12 individuals. Although we selected them from the same pool described earlier, none of the subjects had participated in the earlier experiment. The kinds group received the booklets of diagrams of analytic and nonanalytic kinds, whereas the parts group received the booklets of analytic and nonanalytic parts. One half of the subjects in each group rated analytic diagrams first, and the other half rated nonanalytic diagrams first. The instructions to subjects described the diagram conventions with an example consisting of mental activities that were not used in the experiment proper. The subjects then rated each diagram on a 0-to-10 scale, with 10 meaning that the diagram was exactly right as a description of the relations among the activities and 0 meaning that the diagram was completely wrong. In general, the mean ratings from our subjects decreased with increasing departures from the original diagrams. Figure 4 plots the means for all diagrams and shows a monotonic decrease in ratings for all but the analytic parts. The overall mean is 7.96 for the four original diagrams (the ones in Figure 3), 7.23 for the +2 SSD distortions, 4.98 for the +4 SSD distortions, 4.19 for the +6 SSD distortions, and 3.75 for the +8 SSD distortions. This difference is significant by a test for linear trend, based on an ANOVA, F(1, 88) = 101.02, p < .001. The analysis also produced a significant interaction between the type of term (analytic or nonanalytic) and the degree of distortion, F(4, 88) = 3.14, p < .05. The effect can be seen in Figure 4 as flatter slopes for the analytic diagrams (dashed lines) than for the nonanalytic ones (solid lines). This may be the result of the poorer fits for the analytic diagrams that we noted earlier. Alternatively, the simpler shape of the analytic diagrams may have given subjects fewer clues to the correct ordering of terms. These diagrams are nearly one dimensional, whereas the nonanalytic diagrams have a richer structure. Of course, this experiment does not establish that the diagrams in Figure 3 are the best possible depictions, since graphs with other shapes might have produced higher ratings. 5 We also 4 We also find better fits for the kind-of relation than for the partof relation when we look at the entire set of rated activities from the experiment described earlier. SSDs were lower for kind-ofthan for partof in 18 of 20 random subsets of seven activities each. 5 In an additional experiment, we have compared the TRANSITresults with alternatives that are not partial orders. This experiment had the same design as the one just reported, but with three different foils. We constructed one of the foils, which we call the principalfoil, by drawing a kind-of(part-of) link between two activities whenever more than 50% of the subjects in the original experiment agreed that the first activity was a kind of (part of) the second. The other two foils were randomly constructed, but with the constraint that one contained the same humher of links as in the TRANSITOUtpUtand the other contained the same number of links as the principal foil. In order not to bias the experiment in favor of partial ordering, we displayed the activities in a circular arrangement in all graphs. For the TRANSITgraphs, links connected two activities just in case those activities were linked in the transitive closure of the diagrams in Figure 3. Mean ratings for the TRANSITgraphs in this experiment was 7.59 on the 0-to-10 scale, 7.14 for the principal foils, and 4.66 for the random graphs. As expected, subjects preferred the

196

LANCE J. RIPS AND FREDERICK G. CONRAD I0 9 8

7 Mean Rating

6 Analytic Ports

(O-to-IO scale) 5

Analytic Kinds

4 3

Nonanalytic Parts

2

Nonanalytic Kinds

I

0

I

Originql

I

+2

,I,

!

+4

+8

I

÷8

Sum of Squared Deviations

Figure 4. Mean ratings of how well particular diagrams represent the kind-afar part-ofrelations among groups of mental activities. (Solid lines denote diagrams of nonanalytic terms, and dashed lines diagrams of analytic terms. Circles indicate kind-ofdiagrams,and squarespart-ofdiagrams.)

acknowledge that the ratings may well be based on many of the same intuitions about the activities that provided the input to our partial.ordering algorithm. Nevertheless, it is one thing for subjects to make pairwise judgments of activities and quite another for them to assess entire diagrams, especially since the diagrams have been purged of all violations of partial ordering. The high mean ratings for the original diagrams suggest that they are at least good approximations to subjects' concept of how the activities interrelate. Moreover, subjects' sensitivity to differences in SSD helps confirm its usefulness as a measure of fit.

Memory for Kind-of and Part.of Relations As a more stringent test of the derived partial orders, we asked a new group of subjects to recall the position of the terms within them. One half of the subjects received the partial orders in Figure 3, and the remainder received the +4 SSD diagrams from the previous experiment. We naturally expected better recall for the original diagrams (el. Bower, Clark, Lesgold, & Winzenz, 1969). In addition, we expected that errors subjects make in reconstructing the +4 SSD diagrams would tend to gravitate toward the original diagrams. That is, even though these subjects do not see the original orders in Figure 3, they might displace a term to the position it occupies there. By contrast, subjeets who see the original diagrams should not displace terms to their positions in the +4 SSD diagrams. The logic behind this prediction is essentially the same as in memory experiments based on prototype or schema theories (e.g., Bransford & Franks, 1971; Posner & Keele, 1968). The Figure 3 diagrams

TRANSITgraphs and principal foils to the random graphs, F(I, 36) = 43.38, p < .001. Although the differencebetween the TRANSITgraphs and the principal foils was in the correct direction, it was small and nonsignificant, F( 1, 36) < 1, probably becausethese two graphs differed on only a small number of links (3.5 links on average).

should correspond to underlying schemas that guide subjects as they attempt to reproduce what they saw. During the experiment, subjects inspected two critical diagrams (one containing the analytic terms and a second containing the nonanalytic terms) and two filler diagrams (each conraining mental activity terms not used in Figure 3). For the kinds group, all four diagrams depicted kind-of relations; for the parts group, all diagrams depicted part-ofrelations. Twenty subjects served in each group. Within a group, one half of the subjects received the original (kind-ofor part-of) diagrams, and the other half received the +4 SSD diagrams. At the beginning of the experiment, we informed subjects about the diagramming conventions and told them that their task was to inspect the diagrams to determine how well they represented the true relations among the designated activities. They were not warned of the upcoming memory test. They inspected one of the filler diagrams, then one of the critical diagrams (either analytic or nonanalytic), then the second critical diagram, then the second filler, each for a 30-s period. We balanced the order in which they saw the analytic or nonanalytic terms with type of relation (kinds or parts) and diagram type (original or +4 SSD). Finally, we tested subjects by showing them the empty outline of each diagram they had inspected, together with a randomized list of terms that had appeared in it. They were to write the terms in the outline in exactly the positions they had occupied before. The order of testing was the same as the order of presentation. As we anticipated, our subjects were better at remembering the positions of terms in the original diagrams than in the +4 SSD distortions. Subjects were correct in matching 65% of the terms from the original diagrams, but only 44% of terms from the distorted diagrams, F(l, 36) = 6.24, p = .02. (Chance matching performance would be 14%; so both groups were performing considerably above chance.) The top two rows of Table 2 present the matching probabilities for the four types of diagrams and show that the difference is in the predicted direction for all of them. We observed no significant effects of

MENTAL ACTIVITIES Table 2

Percentage of Matches for Position of Terms in Diagrams by Term Type, Relation, and Level of Distortion Kind-of Distortion level Analytic Correct matches Original +4 SSD Cross matches Original +4 SSD

Part-of

197

either case, the derived orders seem to provide anchors for the correction process.

Judgments A bout Possible Minds

Nonanalytic

Analytic

Nonanalytic

.58 .40

.68 .40

.67 .41

.64 .56

.18 .45

.19 .20

.55 .61

.10 .35

whether the terms were analytic or nonanalytic, nor of whether the relation was kind-of or part-of. There was no interaction of these factors, nor any interaction with level of distortion. To assess our second hypothesis---that subjects would tend to err in the direction of the original diagrams--we considered only those terms that subjects placed in incorrect positions and only those positions containing incorrectly placed terms. We then checked the corresponding positions in the diagram that subjects had not seenEthe +4 distortion if the subject had seen the original diagram and the original diagram if the subject had seen the distortionEand calculated the number of incorrect terms that would have been correct with respect to this unseen diagram. This number was divided by the maximum possible number of such cross-diagram matches for this particular set of terms and positions. 6 This conditionalizing is necessary to unconfound the cross-match probability with the probability of a correct match, reported in the preceding paragraph. Our hypothesis is that cross-match probability should be higher for subjects who received distorted diagrams than for subjects who received the original diagrams. In line with this, cross-match probability was .40 for the distorted diagrams and .26 for the undistorted ones, F( 1, 36) = 5.60, p = .02. The crossmatching rates at the bottom of Table 2 show that, once again, the difference is in the correct direction for all four diagram types. This time, however, we also observed significant effects of type of term, F(I, 36) = 23.01, p < .001, type of relation, F(I, 36) = 5.79, p = .02, and the interaction between them, F(I, 36) = 5.57, p = .02. Table 2 suggests that these effects are the result of the relatively large cross-matching rates for diagrams of analytic parts (.58) compared with analytic kinds (.32), nonanalytic parts (.22), or nonanalytic kinds (.20). Subjects' ratings of these diagrams in the previous experiment is consistent with this difference. In that study, the difference between the rating for the original diagram and its +4 distortion was smaller for analytic parts than for the other types (see Figure 4). This suggests that the arrangements of terms in the analytic parts diagram and its distortion may be subjectively similar, leading to more cross matching. Whatever the reason for this last effect, the success of the two basic predictions lends support to the idea that the derived partial orders correspond to subjects' view of this set of mental activities. The results may be due to subjects deliberately placing terms in what seemed the most sensible positions when they had forgotten the true ones. Or the results may have been caused by a more automatic normalization taking place in storage. In

So far we have tried to establish that the Figure 3 diagrams are good representations of mental parts and kinds. But if we are right about this, the diagrams should also predict other judgments that depend on these primary ones. As an example, we could ask subjects to decide whether certain mental activities can exist without others. For instance, is it possible for there to be creatures who have the capacity to remember, reason, and decide but not think? Creatures who can think, remember, and reason, but not decide? As we mentioned earlier, the activities appear to differ in their centrality with respect to overall mental operations. In these terms, we can assume that if an activity Mt is more central than another/142, then it should be easier to conceive of creatures lacking M2 than of creatures lacking Mm. Thus, if thinking is more central than deciding, it should be easier to conceive of a creature that is able to think without being able to decide than one who can decide without being able to think. With respect to the partonomies, central activities should be ones that are parts of many other activities. For example, because thinking is part of all of the other activities in Figure 3b, it should be more central than deciding, which is part of only one. Similarly, because part-of and kind-of relations are near converses in these data, activities that have many subkinds should be more central than those having few, and it should be easier for subjects to imagine a mind lacking an activity with few subkinds than a mind lacking an activity with many subkinds. Of course, we have no way of knowing in general how many other mental activities a given activity is a part of (or a kind of); this depends on the entire population of activities and not just on those we have sampled. Nevertheless, if our sample is a representative one, the predicted relation should emerge. In light of these considerations, a natural measure of centrality for a particular activity is simply the number of other activities it is part of according to the Figure 3 diagrams. This measure is the outdegree of the relevant node in the transitive closure of the part graph--that is, the number of links leading from that node, including both the explicit links and the implicit ones

6 As an illustration, consider the analytic kinds diagram in Figure 3a. Suppose that a given subject receives this diagram and later places the terms thinking, conceptualizing,and readingin their correct positions, but incorrectly permutes remembering, reasoning, deciding, and planning. The +4 distortion contains reading in the position occupied by remembering, conceptualizingin the position occupied by reasoning, planning in the position occupied by deciding,and rememberingin the position occupied by planning. Thus, the maximum possible number of cross-diagram matches for this subject is 2 because he or she could have placed remembering and planning in the positions they occupy in the +4 diagram. The subject's score would he 0 if neither term (cross-)matched, 0.5 ifjust one matched, and 1 if both matched. In some cases--for example, when the subjects placed all seventerms correctly--the maximum number of cross-matches is 0. We treated these trials as missing data. For purposes of analysis of variance, we estimated scores for these observations using the mean from the relevant level-of-distortion by term type by relation cell in the design.

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Table 3

Mean Likelihood and Importance Ratings for Mental Activities M likelihood Outdegree Indegree ofcreatureof parts of kinds missing M graph graph activity importance

Activity Analytic Thinking Conceptualizing Remembering Reasoning Deciding Planning Reading Nonanalytic Experiencing Having emotions Imaging Realizing Contemplating Dreaming Loving

6 5 4 2 1 0 0

6 5 0 2 1 0 0

2.5 4.2 3.1 3.7 3.2 6.5 9.8

8.0 7.0 7.2 7.7 6. I 5.8 6.0

6 2 2 0 0 0 0

6 1 1 0 2 0 0

1.4 4.5 6.1 5.2 6.2 7.1 8. I

6.5 7.3 7.0 5.6 5.8 4.8 6.2

Importance Ratings If subjects conceive of general mental activities such as thinking as more central than specific ones, then the former may

Note. For likelihood ratings, n = 16; for importance ratings, n = 20.

determined by transitivity. Equivalently, it is the sum of the relevant row in the T matrix: Part--centrality(Activity~) -- ~ j t~j.

(2)

Similarly, the indegree of the nodes in the transitive closure of the kinds graph should provide a closely related measure of centrality: Kind-centrality(Activityj) = ~ t~.

(the corresponding creatures are less likely to exist), as should missing activities that have many kinds. The obtained means tend to support this prediction inasmuch as the lowest ratings were associated with thinking and experiencing and the highest ratings with reading and loving. Over all items, the correlation between the ratings and part centrality is - . 7 8 (df= 12, p < .01 ); the comparable correlation for kind centrality is - . 7 0 (dr= 12, p < .01). Of course, these coefficients are not independent since the two centrality measures are themselves highly correlated, r(l 2) = .85. We take these results as evidence that activities near the top o f the Figure 3 graphs provide, in some sense, a common basis for the remaining activities. The central activities are implied by the more specific ones and are therefore more difficult to detach conceptually from this domain. 7

(3)

Thus, we expect subjects to be more likely to agree that a creature could exist without a particular activity if that activity has relatively low part or kind centrality. The values of these measures appear in the first two columns of Table 3. We tested this prediction in an experiment in which subjects read descriptions of hypothetical creatures who could engage in some mental activities but not in others. For each creature, the subject rated "how likely it is that such a creature could exist, given what you know about the different activities mentioned:' We based seven ofthe creatures on the analytic terms and seven on the nonanalytic terms. Each description mentioned that the creature in question was able to engage in six of the activities (e.g., conceptualizing, deciding, planning, reading, reasoning, and remembering) but was not able to engage in the remaining one (e.g., thinking). Every activity in Figure 3 served as the "disabled" item for exactly one of the creatures. We combined the descriptions in a booklet, one description per page, with the order of pages randomized. Subjects made their possibility ratings on a 0-to-10 scale, with 0 indicating that the hypothetical creature was completely impossible and 10 that the creature was completely possible. The mean possibility ratings for our 16 subjects appear in the third column of Table 3, listed according to the activity that the hypothetical creature lacked. As just discussed, missing activities that are parts of many others should produce low ratings

seem more important psychologicallythan the latter. To test this relation, we asked 20 subjects to rate each of a series of mental activities according to "the importance of these activities in how the mind operates" The subjects saw the 14 critical items mixed with 16 other mental-activity fillers in a single randomized list. Subjects rated importance on our usual 0-to-10 scale, ranging from the activity was not at all important in how the mind works (0) to the activity couldn't be more important (10). Subjects gave all of the terms fairly high ratings, as can be seen in Table 3, so the range of variation is compressed. Still, these means correlated highly with part centrality, r(l 2) = .70, p < .01. Note that the correlation is positive in this experiment, rather than negative as in the possible-minds study, because activities at the top of the graphs should be more important. Table 3 shows that the main discrepancy is that experiencing has too low a mean importance rating relative to imagining and having emotions. Although we have no independent evidence for why this should be so, it may have seemed to some of our subjects that experiencing is too vague a term to denote an important activity in mental life. The correlation between kind centrality and importance ratings is also positive, although in this case it is only marginally significant, r(12) = .50, p -- .06. It is worth remembering that these importance ratings come from students who have an obvious interest in skills like thinking and reasoning; ratings from nonstudents may display very different patterns. Nevertheless, the results give us some reason to believe that the partial orders represent at least one aspect of these terms' conceptual roles) 7 We have also considered other measures of centrality suggested in the literature on social networks (e.g., Burr, 1980; Freeman, 1977). These seem not as well adapted to partial orders as the simple measures in Equations 2 and 3 and have lower correlations with ratings. s Apparently, the importance of the activities is not equivalent to their typicality in subjects' view. In a further experiment, we asked a group of 11 subjects to rate the typicality of the same set of mental activities. Although these data showed a typicalitygradient, there was no correlation between these ratings and the structural or rating measures reported earlier. The correlation of typicality with part centrality is .01, and the correlation with kind centrality is .03. Nor does typicalitycorrelate significantly with the importance ratings or "possible mind" ratings. This hints that typicalityhas a different basis from that of the kind

MENTAL ACTIVITIES Implications and Extensions People's beliefs about mental activities have a specific relational structure. They conceive of some activities as types or kinds of more general ones, some as parts of more complex ones. We began by assuming that these kind and part relations would partially order the activities since both relations appear to be transitive, asymmetric, and irreflexive, and we attempted to test this idea by developing an algorithm that finds best-fitting partial orders for pairwise judgments. Our initial assumptions turned out to be better met by the kind decisions than by the part decisions: Goodness o f fit was more adequate for kinds than parts, and the parts data exhibited a fair number of symmetric pairs. In general, though, subjects took one activity to be a part of another if the second was a kind of the first. The derived partial orders for both kinds and parts were able to predict the results of further experiments. Subjects rated the derived orders as better representations than distorted orders, and they remembered the derived orders better than the distortions. Memory errors, when they occurred, tended to drift in the direction of the derived orders. Finally, simple graph-theoretic measures o f centrality defined on the partial orders predicted subjects' ratings of the psychological importance of the activities and ratings of the possibility of minds lacking some of them. The more kinds a given activity contains and the more often it is part of other activities, the more important and less dispensable it seems. We believe these results point to some advantages for the techniques we have introduced, but they also leave some open questions, both methodological and substanfive, which we consider in the remainder of this article.

Extending the Partial Orders: R a p i d TR,4NSlT Although TRANSITdelivers reasonable results for up to eight objects, it bogs down badly for larger numbers of items, limiting the size of the taxonomies and partonomies we can construct. As we noted earlier, a slow down is inevitable, given the NPcompleteness of the partial-ordering task; however, there are ways of avoiding this limitation if we are willing to accept approximations to the nearest partial orders. One possibility for extending the partial orders in Figure 3 stems from the fact that certain stimulus pairs may be more important than others, allowing us to restrict the minimization process to these important items. In typical data, subjects will agree that some of the pairs bear the specified relation (e.g., reasoning is certainly a kind of thinking) and agree that some others do not (reasoning is clearly not a kind of dreaming). These pairs will be associated with values near I and 0 in the data matrix S and will count most in the search for the nearest partial order. Excluding from the partial order a pair with a value near I or including a pair with a value near 0 will produce large

and part relations we have been investigating. We introduced the term centrality earlier to mean the relative importance or necessity of an activity in overall mental operations. Our present point is that, although centrality may sometimes be related to typicality, they are distinct properties and impose different organizations on their domains. By analogy, Ronald Reagan is a central figure in American life, but is hardly typical, whereas Ronald Shmengan, manager of the Omaha branch of Kentucky Fried Chicken, is typical but not central.

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increases in SSD. By contrast, values in the middle range will make less of a difference (e.g., ifa pair has a value of exactly .5, then SSD will be the same whether or not the pair is included in the partial order.) The trouble is that TRANSITgenerally spends more time worrying about these intermediate values than about the extreme ones. Misclassifying an extreme value produces an abrupt increase in SSD that will often cause the search to be redirected, whereas misclassifying an intermediate value will produce only a small increase and lead to deeper search. This suggests that we might restrict the optimizing to pairs with extreme values, allowing these pairs to determine the fate of the remaining ones. We have modified TRANSITto take advantage of this idea. The essential change is that the subroutines in the program (see Appendix) operate only on pairs for which s o is less than a lower cutoff or is greater than an upper cutoff. Pairs with intermediate values are included in the partial order only if they are forced in by the extreme pairs, excluded only if they are forced out by the extreme pairs, and otherwise are left undetermined. They can be forced in by transitivity: For if Pair 0 and Pair~k are in the partial order, then Pair~k will also be included whether the latter is an extreme item or not. A pair can be forced out by asymmetry: For if Pair 0 is in the partial order, then Pairj~ will be excluded. Although this procedure obviously can't guarantee that the partial order it uncovers will be the nearest one, it often produces good approximations. Figure 5 shows the result of applying the modified algorithm to the full set of data in the first experiment described earlier. In this application, the cutoff values were .05 and .95, resulting in 52 extreme pairs from the parts data and 70 extreme pairs from the kinds data. The part-of ordering produced an SSD of 0.998, and the kind-of ordering an SSD of 1.970, as calculated on just the extreme items. We have omitted individual activities from the figure ifthey were detached from all other items; hence only 15 of the 30 activities appear in the parts graph, and 18 of 30 in the kinds graph? These graphs share some of the properties ofthose in Figure 3wfor example, the converse relation of part-of and kind-of, as well as the central position allotted to thinking and (in the kinds graph) to experiencing. But by comparison to the earlier diagrams, these appear flattened, especially in the case of kinds. This is the result of disagreement among subjects about the relations among the horizontally arrayed activities---whether, for example, analyzing is a kind of conceptualizing or conceptualizing a kind of analyzing. These pairs received intermediate scores, and their status was not resolved by the final partial ordering. However, as these diagrams illustrate, this disadvantage is partly offset by the graphs highlighting links that are particularly strong. I° We return to these 9 The graphs shown in Figure 5 are not unique since there are slightly different configurations with exactly the same SSDs. In the case of parts, there is one such fled graph that differs from that in the figure by the relative positions of items within the deciding-choosing-planningcluster. In the case of kinds, there are three additional graphs that differ in the relative positions of investigatingand examining and of figuringout and solvingproblems. It is likely that these multiple graphs are due to subjects regarding decidingand choosing, investigatingand examining, and solvingproblems andfiguring out as synonyms rather than as terms for distinct activities. ,o Another approach to the problem of large data sets is to settle for an approximation based on the followingprocedure. Let S be defined as before, and let the initial value ofT be such that to = 1 ifs~ ~ .5, and

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tr~

°111

il il

MENTAL ACTIVITIES diagrams in the final section when we discuss some other proposed taxonomies.

Alternative Explanations At the outset we adopted as a working hypothesis the idea that people's underlying conception of mental kinds and parts could be described by a partial order. Although this partial-order assumption was motivated by semantics, it has the advantage that we can use it in the domain of mental activities to detect underlying structure among the kind and part judgments. This led us to the idea of a nearest partial order and to the diagrams in Figures 3 and 5. However, in following this path we have so far side-stepped recalcitrant findings like the symmetric part judgments for pairs like thinking and reasoning. Likewise, the unexpected reciprocal relation between kinds and parts, although consistent with the partial-order assumption, may nevertheless raise some doubts about our methods because this reciprocity does not seem to hold for object categories. We therefore need to reevaluate our premises in light o f these findings.

Do partial orders reflect subjects" beliefs about mental activities? The most serious piece of evidence against partial ordering is the moderate fits to the parts data, especially for the analytic items. As we've noted, many subjects apparently believe that some of these activities are symmetrically related: for example, that thinking is part of reasoning and that reasoning is part of thinking. This obviously violates our partial-order assumption; moreover, we can't easily dismiss these symmetries as mere processing error since some ofthem appeared among the responses of more than one half of the subjects. Perhaps the simplest way to reconcile this violation with the partial order assumption is to suppose that subjects were not fully following our instructions. Although we had told them to respond yes only if every instance of one activity had an instance of the other as a part, this directive may have been confusing or hard to obey for closely related activities such as thinking and reasoning. In this situation, the subjects may have answered by relying on typical or representative cases of the activities in question (Hampton, 1982), which may have caused symmetric judgments. Typical instances of thinking (e.g., solving a problem on a quiz) may contain reasoning as a part, and

tij = 0 ifs 0 < .5. The SSD of this initial T is minimal, though T is not in general a partial order. For each entry in T we can calculate two quantities: the increment in SSD that would result from changing its value, and the net increase or decrease in intransitivitiesthat would result from changing its value (to 0 ift 0 is currently 1, or to 1 if it is currently 0; see Holland & Leinhardt, 1976). At the first stage in the procedure, we select the entry in T that would produce least increase in SSD and check to see whether changing its value would reduce total intransitivities. If so, we make the change, readjust the weight, and restart the procedure. If not, we advance to the entry that would make the next smallest increase in SSD. We can continue in this way until all intransitivities are eliminated. The resulting T will be a partial order of relatively low SSD, although not necessarily the nearest one. The advantage of the procedure is that its running time is much faster than TRANSIT,and we have found it useful for ordering sets of up to 50 objects. In simulations with 5, 6, 7, and 8 objects, the procedure produced mean SSDs of 3.63, 5.62, 8.40, and 12.05, respectively, which can be compared with the mean SSDs for the nearest partial orders in Table 1.

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a typical case of reasoning (e.g., proving a theorem) may include thinking. Such an account is similar to that discussed in the first section in connection with apparent violations of transitivity of kinds. It permits us to keep the idea that part-of is a partialorder relation but denies that subjects are always in a position to assess this relation for arbitrary pairs of activities. Subjects' knowledge of activities like thinking and reasoning may be too meager to allow them to make perfectly accurate judgments and may force them to use heuristics that sometimes result in inconsistencies. A somewhat similar move is to suppose that the activity terms are ambiguous or contextually sensitive and that the different questions we posed evoked different interpretations. For example, the meanings that subjects gave to the terms thinking and reasoning may have shifted between the time they were asked if thinking is part of reasoning and when they were asked if reasoning is part of thinking. This account again retains the idea that part-of is a partial-order relation, but it assumes that violations o f partial ordering are the result, not of inaccuracies on subjects' part, but of their willingness to reconstrue the activity terms (perhaps in an effort to make the questions themselves as sensible as possible). We believe there is some truth to both of these accounts of the symmetric pairs, but we also think they should not be allowed to obscure the orderliness of the results from these experiments. For one thing, the number ofsymmctric pairs (i.e., pairs for which more than one half the subjects stated both that Mt was a part o f M2 and that M2 was a part o f M 0 was relatively small: only 17% of the data. More important, the departures from partial ordering--whetber due to heuristic processing or context sensitivity--were obviously not severe enough to keep us from using the Figure 3 diagrams to predict the ratings of possible minds or the ratings of importance of the activities. This suggests that we might regard these diagrams as approximating subjects' beliefs under conditions in which the meaning o f t b e activity terms is constant and in which heuristics do not produce inconsistent decisions. There are limits, of course, to such an idealization, but it may be worth making if it permits us to predict the data we have examined. Ambiguity and heuristics may help account for some puzzling aspects of the results, but there are other, more systematic, findings that they don't readily explain. Why, in particular, should mental parts and kinds be reciprocally related in the way we have observed7 An explanation for this phenomena may yield a more complete picture of subjects' intuitive psychology and o f the nature of the differences between conceptions o f activities and objects. We can think of two possible explanations along these lines, which we discuss in the remainder of this section. A generality-based explanation. Let's begin by considering the activities thinking and planning that follow the reciprocal pattern: Figure 3a shows planning as a kind of thinking whereas Figure 3b has thinking as a part of planning. The kindo f relation in this case seems unproblematic, but the part-of relation is more troublesome; if thinking is really more general than planning (as seems sensible), how could it be that thinking is a part of planning? More general classes of objects don't seem to be parts of more specific o n e s - - m a m m a l s are not parts of elephants, tools are not parts of hammers, and so o n - - s o why are mental activities like thinking and planning an exception?

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I~rt-of kind-of

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Activity3

Activity1 '

Activity2

Predicate-I

"Predict- I

Predicate-2

Predicate-2

Predi~te-i

Predicate-i Predicate-k

Figure 6. Two views of the relations between kinds and parts: (a) in terms of a generality-based explanation, and (b) in terms of a propertybased account.

To see what's going on here, it's helpful to ask what the parts of planning really are. From an intuitive standpoint, most or all cases of planning seem to include the steps of gathering relevant information, assessing one's goals, considering possible scenarios, and finally producing a plan. Not all of the steps in planning are easy to name, however. There must be some way of combining the relevant constraints with goals in generating the plan, but there seems to be no simple term for this crucial synthetic step. We might use a longer phrase or sentence, as we just did, to name this process, or if pressed for a shorter label, we might use some more general term. In fact, because this generation process is clearly a type of thinking, why not use the label thinking itself?. The point is that there is a genuine exemplar of thinking (e.g., the process ofcomhiniog constraints and goals) that is a part of planning. Furthermore, it's likely that every instance of planning contains such an instance of thinking as a part. But we defined the part-of relation for our subjects as a case in which each instance of the one activity had an instance of the other as part; so by our definition, thinking is indeed a part of planning. From this perspective, it is no longer difficult to see why mental parts and kinds are converses, and Figure 6a illustrates the type of situation in which these opposite connections will arise. Suppose Activity2 is a kind of Activity~ and Activity3 is a part of Activity2. It may often be the case in these circumstances that Activity3 is also a kind of Activity~. These relations are shown at the left of Figure 6, with solid arrows for the kind-ofrelations and dashed arrows for part-of. For example, planning is a kind

of thinking and parts of planning (e.g., the combining activity just discussed) also tend to be kinds of thinking. In this situation, it follows logically that Activityl (e.g., thinking) is itself a part of Activity2 (e.g., planning), as represented by the dashed arrow at the right. This is a consequence of the fact that every instance of Activity2 has an instance of Activity, (namely, Activity3) as a part. The kind-ofand part-ofarrows running in opposite directions between Activityt and Activity2 are the converse relations that we obtained. Of course, this analysis does not imply that all pairs of activities linked by the kind-of relation will also he linked in the reverse direction by part-of To get the converse link, we need all three of the relations shown at the left of Figure 6, and this may account for some of the exceptions we noticed in surveying the Figure 3 diagrams. What remains mysterious in this explanation is why the con. verse relation fails to hold for classes of physical objects. If all this is correct, why aren't mammals parts of elephants? In terms of the present explanation, the answer seems to be that although activities and their parts are often members of the same proximal kinds, objects and their parts are not. With respect to Figure 6a, what's missing in the case of objects is the kind-of link at the extreme left: Although elephants are kinds of mammals and knees (for example) are parts of elephants, knees are not kinds of mammals. Without this last relation, we can't deduce the critical part-of connection. The fact that activities, but not objects, have parts belonging to the same superordinate categories may he a fundamental difference between our conceptions of these two types ofentities. It is possible, however, to break down this object-activity distinction if we go to very abstract levels of the object taxonomies. That is, we can get a situation parallel to that of Figure 6a if we choose a very high-level category for the topmost class. For example, we can say that knees are parts of elephants and that both knees and elephants are kinds of physical objects. In this case, our analysis predicts that we should be able to say that physical objects are parts of elephants, and this does seem to he correct. At this level of abstraction, then, we get an analogous converse relation among object classes (e.g., physical objects are parts of elephants, and elephants are a kind of physical object). Finally, we note that the generality hypothesis can also offer an explanation of the symmetric part relations. Consider a situation like that of Figure 6a, except that Activity2 is a part, rather than a kind, of Activity,. As before, every instance of Activity2 has an instance of Activity3 as a part. But because Activity3 is a kind of Activity~, the latter instance is also an instance of Activity1. It follows that every instance of Activity2 has as a part some instance of Activity~. Hence, Activity~ is a part of Activity2, according to our definition, and this yields the symmetric relation. Note that on this hypothesis, part-of could still be asymmetric at the level of individual activity tokens. According to this explanation, symmetries arise in generalizing over these tokens to get statements like Reasoning is part of thinking. A property-based explanation. A second way ofapproaching these results follows the lines of what Smith and Medin (1981) call probabih'sti¢ models of concepts. In models of this sort, categories are mentally represented in terms of a collection of mental predicates, corresponding to properties of the category members. In these terms, people might represent an activity such as planning by means of predicates like temporally extended, intellectual, purposeful, and so on. The predicates may

MENTAL ACTIVITIES not necessarily be true of every category member, but will be assumed to hold, all else being equal. The exact details of the representation are not crucial for our purposes; for example, we can think ofthe predicates as being arrayed in a larger structure (schema or frame), and the predicates themselves can be simple or highly relational ones. We are interested in how people decide about kind-of and part-of relations with representations like these since this may provide a clue to the patterns we have found in our data. For kind-of, the usual decision rule is that one category will be a kind of another if a sufficient number of the predicates of the second category are among the predicates of the first. (The predicates could be weighted for importance in this comparison, although this will not concern us here.) So planning will be deemed a kind of thinking if enough of the predicates in the thinking representation are also predicates in the planning representation. This predicate comparison procedure enables probabilistic models to explain a large body of data concerning subjects' speed and accuracy in classification judgments (Smith &Medin, 1981), although these models have generally been applied to object categories rather than to activities. Probabilistic modelers have given less attention to the process of deciding whether one entity is a part of another. At first glance, it appears that if one activity has another as a part, then all of the properties of the part are also properties of the larger activity. This suggests that we might base our decision about parts on whether a sufficient number of the predicates of the paws representation are among the predicates of the surrounding activity's representation. For example, if enough of the predicates of thinking are also predicates of planning, then we can say that thinking is a part of planning. Figure 6b illustrates this state of affairs. Activityt (e.g., thinking) has Predicates 1 through i, and Activity2 (e.g., planning) has all of these plus some additional predicates of its own. Thus, according to the rule for parts just given, Activityt should be a part of Activity2. What's interesting about this is that the same relation that establishes Activity~ as a part of Activity2 also implies that Activity2 is a kind of Activity,. Because Activity2 has all the predicates ofActivityt, it must be a kind of Activity,, according to the classification principle mentioned in the previous paragraph. Although this relation is a tidy one, it again leaves us with the problem of why it doesn't hold for classes of physical objects. In the case of objects, the decision rule for kind-of generally yields the correct result, but the decision rule for part-of would lead to the erroneous judgment that superordinate categories were parts of their subordinates. The difficulty is not hard to trace. In proposing the part-of rule, we assumed that all of the properties of a part are also properties of the activity that ineludes it. But this assumption does not usually hold for physical objects. Knees, for example, join an upper and lower leg, but an elephant does not join an upper and lower leg. Evidently, physical parts have properties of their own, in virtue of their spatial distribution or functional role, and these are not always inherited by the including objects. This means that in order to decide whether one object is part of another, we must ordinarily check whether the properties of the part are properties of some cohesive spatial or functional region of the object. This conclusion is reinforced by the observation that we would probably not say that an object had a particular part if the properties of that part were satisfied by scattered object areas. A car

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would not have a lawn mower as a part, even if all predicates in the representation of lawn mower were true of discontinuous regions of the car. Simply matching predicates of an object and a part, then, is usually neither necessary nor sufficient for establishing the part-of relation. A probabilistic model will work in this context only if the notion of a part is explicitly built into the representation of the object (Smith, Rips, & Shoben, 1974). The probabilistic model, then, leads to the following hypothesis. The converse relation between kinds and parts holds for activities but not objects because activity parts are organized in a different way than object parts. Whereas object parts are more or less clearly segregated in spatial-functional terms, activity parts are often more diffuse. People will agree that thinking is a part of planning as long as planning manifests a sufficient number of the properties of thinking. But they set more stringent standards for deciding that something is a part of an object: The part must have the right coherence with respect to the object. To be sure, some activities do have welldefined subactivities--physical, scripted activities like washing one's hair are cases in point. However, in people's everyday conception, many simple mental acts may not have clearly segmented, stable subactions; hence, if these amorphous activities have parts at all, they have them in virtue of overlap with the properties of other mental activities. To get a feel for this amorphous character, ask yourself about the parts of a mental activity for which we have no scientific analysis. What are the stages of imagining, for example? Our experience with imagining apparently doesn't yield intuitive activity segments in the way that our encounters with objects yield intuitive spatial ones. Summary The explanations we have considered offer some contrasting costs and benefits. The accounts based on ambiguity or heuristics offer ways to explain some of the departures from partial ordering that we have encountered, but (without further elaboration) they are too unsystematic to clarify the reciprocal part-kind effect or even to help us understand why the partial orders were successful in predicting our memory and rating data. The generality- and property-based explanations provide some deeper insights. The generality theory, in particular, gives an especially clear account of the reciprocal effect (and its exceptions). Its main drawback is that it fails to explain how subjects arrive at the part and kind relations in the first place. The property-based model also seems to provide a good overall account. First, this model explains the derivation of kind and part judgments through the decision rules we have described. Moreover, because both decision rules are based on subset relations among the predicates of the activities and because the subset relation is itself a partial order, this model yields structures like those of Figures 3 and 5. Second, we also get the reciprocal effect as a by-product of the decision rules, as discussed earlier. Third, the model is consistent with probabitistic theories that have been successful in other domains. (See Rips, in pressa, for further discussion of these advantages.) But, although these pluses seem attractive, we must also acknowledge some minuses. One is that we need to posit different decision rules for parts of objects and for parts of activities. Another is that the model falters in explaining exceptions to the reciprocal effect, which are rather easily handled by the generality explanation. Of course, it is possible that more than one of these explanations is correct. For example, a property-based model could ac-

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knowledge ambiguities or be combined with a heuristic component (as is usual on probabilistic accounts). It seems quite likely that some such compromise is needed to handle all of the data. Our goal has been to try to uncover some of the main aspects of subjects' beliefs about mental parts and kinds, but much remains to be done in specifying the mechanisms underlying these characteristics.

Consequences for the Study of Metacognition Clearly, there are many ways to study people's conceptions of psychological activities. Fine-grained psycholinguistic analyses are valuable in understanding the precise meanings that subjeers attach to individual terms (see, e.g., Just & Clark, 1973, for a study of remember and forget, and Johnson & Maratsos, 1977; Johnson & Wellman, 1980; and Shatz, Wellman, & Silber, 1983, for the acquisition of think, remember, kno~, and guess). However, if people's beliefs about mental activities are systematic and connected--if they truly constitute a "common-sense psychology" (Heider, 1958) or"folk model" (D'Andrade, 1987) or "theory of mind" (Wellman, 1985)--we also need methods that will reveal more global facts about this domain. Proximity analysis. Most earlier empirical attempts to study psychological terms globally have been confined to clustering and multidimensional scaling of emotions such as happiness or fear. In such studies, subjects judge the similarity of pairs of emotion words or pairs of photographed faces posed for specific emotions. The investigator then submits these similarities to scaling or factor analysis and uses the output as evidence of taxonomic or componential structure. The results of such studies, however, have produced a somewhat meager view of taxonomic relations in this domain. Apart from a dimension that represents the emotions' pleasantness or unpleasantness (and sometimes a second excitement/nonexcitement dimension), no clear-cut distinctions or groupings have emerged across experiments. This uncertainty may be the product of differences between experiments in methods of collecting data or sampling emotion terms or photos. It may also be, as Fillenbaum and Rapoport (1971, chap. 6) suggested, that subjects' beliefs about such terms are idiosyncratic because of the private character of emotional experience. Our own hunch, though, is that techniques for analyzing similarity judgments are too indirect to uncover the complex web of taxonomic relations. We take this difficulty with emotions as the symptom of a more general problem. The attempt to find taxonomic structure in similarity data presupposes that similarity is constitutive of such structure: Activities belong in the same taxonomic category, according to this story, either because they are all highly similar to each other or highly similar to some representative of the category as a whole. Therefore, an analysis of similarity judgments should reveal the important categories within the domain. However, we suspect this line of reasoning is false for many kinds of everyday categories. In the case of physical objects, it is possible to demonstrate that subjects will judge an instance to be more similar to Category A than Category B, yet judge the very same instance more likely to be a member o r b than of A (see Rips, in press-b, for several experiments of this sort with natural and artifact categories). If this is true, then grouping instances by similarity (via scaling) may have little to

do with the kinds that subjects recognize as defined over these instances, t Of course, if we broaden our definition of similarity sufficiently, then "similarity" can capture taxonomy by fiat. For example, if we say that bats and whales are "similar" by virtue of sharing the property of mammalness, then "similarity" and taxonomy can be brought into alignment. But, for one thing, this can become blatantly circular (Goodman, 1970; Murphy & Medin, 1985): Once we've explained that bats and whales are similar by virtue of mammalness, it's no good trying to explain that subjects classify bats and whales as mammals because of their similarity. For another, there is no reason to think that subjects' similarity judgments respect this special sense of the word (Rips, in press-b). We certainly don't mean to imply that scaling of similarity is never helpful in understanding subjects' beliefs about a domain. One of us has used this technique in earlier studies (e.g., Rips, Shoben, & Smith, 1973), and in many cases it has brought to light nontrivial relations among instances. However, similarity judgments are no doubt sensitive to many types of relations besides taxonomic ones; so the evidence they provide about kinds in particular is likely to be diluted. Our conclusion is simply this: If you want to know which taxonomic or kind-ofrelations subjects recognize within a given domain, ask the subjects about kinds, don't ask them about similarity. The techniques we have introduced in this article are intended to provide tools for discerning relevant structure in this type of data. Folk psychologies. Folk beliefs about mental processes are elaborate, including ideas about the processes' causes and effects, origins and development, types, components, pleasantness, typicality, importance, and temporal course. The system of these relations and properties can be likened to cultural systems such as religious beliefs or moral obligations. Accordingly, there have been several recent attempts to reconstruct the folk psychology of different cultures on the basis of linguistic evidence and interviews with informants. To our knowledge, the best-developed systems for Western folk psychology are those of D'Andrade (1987) and Vendler (1972). Because both of these systems include a taxonomy of mental states and activities, it is ofinterest to compare their theories to the present findings. The taxonomy that Vendler (1972) developed is intended to display a parallel between speech act verbs (e.g., say orpromise) and verbs of propositional attitude (e.g., think, decide). Although propositional-attitude verbs describe mental states or acts, they tend to occur in the same sorts of grammatical constructions as speech-act verbs. Both think and say, for example, can take that-complement clauses, as in "Sam thinks (said) that Dukakis will win." Similarly, both promise and decide take tocomplements (e.g., "Meagan decided (promised) to be home by 1:00"). Thus, Vendler distinguished classes of mental verbs on H Probabilistic models of the sort discussed in the previous section typically include similarity as one factor determining classification judgments. For example, in the models of Miller and Johnson-Laird (1976) and Smith et al. (1974), similarity provides heuristic information about class membership. However,these models also include more analytic or core information as the final arbiter in categorization. Thus, there is no contradiction in holding both that probabilistic models can explain the data from the present experiments and that similarity is not sufficient for many kind-ofdecisions.

MENTAL ACTIVITIES grammatical grounds: that-complement mental verbs (e.g., think that, learn that), to-complement verbs (e.g., decide to, plan to), wh-eomplement verbs (e.g., wonder whether), as.construction verbs (e.g., recognize as, consider as), and for-construction verbs (e.g.,forgive...for, blame...for). Each of these classes is subdivided into mental state verbs and mental act verbs, again according to grammatical criteria. This classification does not include verbs like love or hatethat do not take complements. D'Andrade's (1987) taxonomy, on the other hand, divides mental verbs according to the broader role they play in mental lifemfor example, whether their cause is inside or outside the mind, whether they are controllable or not, and so on. These criteria produce six main classes: those having to do with perceptions (e.g., see and look), beliefs (remember and reason), feelings (love and enjoy), desires (desire and wish), intentions (intend to and decide to), and resolutions (resolve to and force oneself to). As in Vendler's (1972) system, each of these classes split into state and process verbs, according to the verbs' aspect. In this account, these groups are situated in a causal framework in which perceptions tend to induce beliefs, which in turn influence feelings; feelings can then give rise to desires, desires to intentions, intentions to resolutions, and resolutions to external actions. We did not sample mental activities with these proposals in mind, and our results do not provide a specific test of these frameworks. Nevertheless, the kinds diagram in Figure 5 provides some hints about ways in which our subjects' intuitions differed from these prior taxonomies. Looking first at Vendler's (1972) system, we find that our derived hierarchy does not always respect the complement-type distinctions. Verbs of different types sometimes end up in the same clusters, whereas verbs of the same type sometimes appear in different ones. For example, the group headed by thinking contains members of several of Vendler's categories. Learn, reason, figure out, and think itself can all take that clauses, but analyze, conceptualize, and interpret cannot. You can learn that Jones is a criminal, but not analyze that Jones is a criminal. Conversely, dream and imagine, which are both that-clause verbs are segregated from the other that verbs, such as learn and think. D'Andrade's (1987) taxonomy does a somewhat better job at capturing the main clusters in Figure 5. Certainly, the thinking cluster seems consistent with D'Andrade's belief/knowledge group, and the loving-feeling-emotions cluster at the left of Figure 5 may be representative of the feeling-emotions group. Still, there are some obvious departures. First, choosing appears as a kind of deciding in Figure 5, although they belong to different groups in D'Andrade's theory (choosing in the desires/wishes group and deciding in the intentions group). Second, terms like experiencing, dreaming, and imagining (in the sense in which it is a superordinate of dreaming) don't fit comfortably in this theory. Is dreaming, for example, a perception verb, a belief/ knowledge verb, or something else? Similarly, experiencing might be considered either a perception verb, a feeling/emotion verb, or perhaps a representative of some higher type not included in this system. Further analysis would be required to determine whether these differences reflect genuine gaps in the theory. At a more general level, however, our results may supplement D'Andrade's and Vendler's theories by establishing aspects of folk beliefs that may not be obvious to informants or observers.

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Appendix A Branch-and-Bound Algorithm for Nearest Partial Orders The TRANSIT algorithm for finding nearest partial orders is outlined in the program of Table A 1. Its main routine takes as input (a) a matrix S of the s# values that represent the proportion of subjects who judge that activity i is related to activity j and (b) an array called INDEX, conraining pairs (i,j)~, (i,j)2 . . . . . (i, J)~,-~l, which are the indices of the off-diagonal entries of S, sorted according to decreasing value of the corresponding entry. For example, if s3.~ is the largest entry in S and s4.s is next largest, then INDEX[I] = (3, 1) and INDEX[2] = (4, 8). (The computer program that implements TRANSITcalculates the INDEX values automatically from S, but we omit this sorting step here to simplify Table A i.) As output, TRANSIT produces the nearest partial order, or the nearest k orders if there is a k-way tie. To find the nearest order, TRANSIT COnstructs a matrix T that will eventually come to represent that partial order. If an entry t# of T is equal to 1, then TRANSITassumes that there is a link connecting Item i to ltemj. If t# is 0, then there is no link. And if t# is - 1, then TRANSIT is temporarily undecided about the status of the link. T starts offwith O's on its main diagonal and - i's elsewhere (see Lines 4-6 of Table A 1). During the course of the algorithm, TRANSITdecides in a series of steps which potential links should be included in the partial order (i.e., which of the - 1 entries should be changed to 1) and which should be excluded (which - 1 entries should be changed to 0). In doing so, it keeps track ofthe minimum SSD over the partial orders it has found so far, called current-min in Table A I. The value o f current-rain is initialized in Line 2 to the sum of the squared sos, which is the SSD associated with the totally disconnected graph with no links at all (all t ~ = 0). Because this graph is a partial order, it makes a convenient starting point.

The basic procedure is to insert a 1 in T at the position corresponding to the largest entry in S, then at the position corresponding to the next largest entry, and so on, until TRANSIT discovers some fault with T (we will discuss the nature of these faults momentarily). This insertion of l's is handled by the subroutine ADVANCE (Lines 21-26). During the insertion process, TRANSIT keeps a running record of the SSD, computed over each link in T that it is so far committed to (i.e., that is either 1 or 0); this is the value of the variable current-SSD in Table A 1. If current-SSD becomes greater than current-rnin, then the links to which TRANSIT is presently committed cannot be part of the nearest partial order; we already have a nearer partial order. So in this situation, TRANSIT should abandon its strategy and back up. Similarly, if the last entry in T produces an intransitivity, then TRANSIT should also back up. These tests are the ones in Lines 11-12 of Table A 1. The simple subroutine TRANSITIVE that tests for intransitivities is not shown here. Its only important characteristic is that it need only decide whether the current entry t~j produces an intransitive triple; it needn't worry about triples that do not contain this entry. The basic conditions of the test are given by Holland and Leinhardt (1976). (TRANSITdoes not need to check the asymmetry of the matrix because transitivity and irreflexivity are jointly sufficient for asymmetry; see, e.g., Enderton, 1977, Theorem 7A. Irreflexivity is ensured by setting the diagonal entries in T to 0.) Backing up is the responsibility of subroutine RETREAT (Lines 27-37), which moves to the last choice-point in which a 1 was inserted, changes this value to 0, adjusts the value of currentSSD accordingly, and returns to the main routine.

Table A 1 A B r a n c h - a n d - B o u n d R o u t i n e f o r F i n d i n g N e a r e s t Partial Orders

I. procedure TRANSIT(n, S, INDEX) 2. current-min 4- ~# s~ 3. last-entry ,.- n (n - 1) 4. for/.*- 1 t o n d o 5. forj .,-- I to n do 6. if i f j then t# .,- O else t# .,- - I 7. k,,--O 8. current-SSD ~-- 0 9. ADVANCE(T, current-SSD, k, i, j ) 10. whilek> 0do 11. if current-SSD < current-rain 12. and TRANSITIVE(T, i, j ) = 1 13. then 14. if k 4~ last-entry then ADVANCE(T, current-SSD, k, i, j ) 15. else 16. current-rain ,,- current-SSD 17. STORE(T) 18. RErREA 7( T, current-SSD, k, i, j ) 19. else RETREAT(T, current-SSD, k, i, j ) 20. end TRANSIT

21. 22. 23. 24. 25. 26.

procedure ADVANCE( T, current-SSD, k, i,j ) k~-k+ 1 (i,j ) 4- INDEX[k] tij ~ 1 current-SSD ,,-- current-SSD + (1 - so) 2 end ADVANCE

27. procedure RETREAT(T, current-SSD, k, i , j ) 28. iftij = 0 a n d k = 1 t h e n k 4 - 0 29. else 30. while tij ~ 1 do 31. tij "~" -- 1 32. current-SSD .,-- current-SSD - s 2 33. k~--k- 1 34. (i,j ) ~ INDEX[k] 35. t~j .,-- 0 36. current-SSD ~ current-SSD + 2s# - 1 37. end RETREAT

Received F e b r u a r y 26, 1988 Revision received August 30, 1988 Accepted S e p t e m b e r 29, 1988 •