Reisenzein, R. (1992). A structuralist reconstruction of ... · Chapter 10 A Structuralist Reconstruction of Wundt's Three-Dimensional Theory of Emotion1 Rainer Reisenzein Free University

Reisenzein, R. (1992). A structuralist reconstruction of Wundt'sthree-dimensional theory of emotion. In H. Westmeyer (Ed.),The structuralist program in psychology: Foundations and applications(pp. 141-189). Toronto: Hogrefe & Huber Publishers.

A Structuralist Reconstruction of Wundt's Three-DimensionalTheory of Emotion 141Rainer Reisenzein

Introduction . 141Informal Description of Wundt's Theory of Emotion . . ' 143Formal Reconstruction of Wundt's Theory 148A Sketch of the Theory-Net of Basic Emotion Theories 174Notes 185References 187

Chapter 10

A Structuralist Reconstruction of Wundt'sThree-Dimensional Theory of Emotion1

Rainer Reisenzein

Free University Berlin

Abstract

A structuralist reconstruction of Wilhelm Wundt's three-dimensional theory ot emotion anaa sketch of its theoretical environment are presented. Wundt's theory, a quantitative theoryof the structure of emotional experience, is reconstructed as a small theory-net consisting ofthe basic theory-element TE(WUNDT) and several specializations. The main substantiveaxiom of TE(WUNDT) postulates that each emotional quality, unless itself basic, results fromthe fusion of a characteristic "mixture" of six basic forms of feeling: Pleasure, displeasure,excitement, inhibition (tranquillization), tension, and relaxation. A second axiom holds thatthese basic feeling qualities are organized into three "bipolar" dimensions; and the thirdaxiom claims that the basic emotions experienced with regard to complex objects are a fusionof the corresponding basic feelings directed at the components of the complex objects. Theconstraint of the theory holds that the mixtures of basic feelings characteristic for the variousnonbasic emotions are the same across different admissible models. Specializations of thetheory result from different possible specifications of the central fusion axiom, as well as fromadditional constraints requiring interindividual and transtemporal constancy.of the emotionalreactions to some kinds of objects. It is suggested that only one concept of the theory, thequality function q (which assigns characteristic proportions of basic feelings to the nonbasicemotions), is T-theoretical. A link.from a theory of emotion measurement to TE{WUNDT)is sketched, and the intended applications of the theory are briefly discussed. Finally, anoutline of the larger theory-net of basic emotion theories to which Wundt's theory belongsis presented.

1. Introduction

Nearly all general theories of emotion which have been proposed throughout history arereductive in the sense that they attempt to reduce the multitude of emotions to a smallerset of presumably "fundamental" or "basic" mental states (which may or may not beemotions themselves). These attempts at reduction seem to have been motivated by twomain considerations. First, the nature of emotional states has always been controversial,and the dominant way of clarifying this issue consisted of the attempt reduce the emo-tions to other mental states that were better understood or less problematic than theemotions, or about the independent existence, of which the theorists were at least morecertain than about that of the emotions. Second, both linguistic (e.g., Averill, 1975;Schmidt-Atzert, 1981) and experimental (e.g., Reisenzein and Hofmann, in press) evi-dence suggests that humans distinguish reliably between a substantial variety of emotions.The successful reduction of these to a small set of basic mental states would make thedomain scientifically manageable and would explain the structural relations that exist

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between different emotions. Theories of emotion which are concerned with these issues(including the pertinent parts of more comprehensive theories of emotion) can be calledstructural theories of emotion, because they seek to elucidate, either the internal structureor composition, and/or the interrelations of emotions.

Depending in part on which of the two considerations just mentioned has been theprimary motive, reductive attempts in the field of emotion have taken several differentforms. Whereas some theorists attempted to reduce emotions to mental states that arethemselves (at least prima facie) not emotions (e.g., cognitive appraisals, patterns ofexperienced physiological changes, action tendencies, or complexes of these elements),others tried to reduce them to a subset of presumably "basic" emotions (e.g., Izard, 1977).These latter theories can be called theories of basic emotions. Their common idea is thatthe multitude of emotions can be understood as being, or resulting from, combinationsof a relatively small number of basic emotional states, which are themselves not furtherreducible, and which are usually also thought to be ontogenetically and phylogeneticallyprimary (see also, Ortony & Turner, 1990). Basic emotion theories come in two mainsubforms. Some theorists take the set of fundamental emotions to be a subset of every-day emotions, such asjoy, sadness, anger, and fear (e.g., Izard, 1977; Tomkins, 1962). Incontrast, other theorists believe that the analysis can be pursued further to still morebasic emotional states, such as pleasure-displeasure and arousal (e.g., Wundt, 1896;Schlosberg, 1954; Russell, 1980).2

In this essay, I present (a) a structuralist (e.g., Balzer, Moulines, & Sneed, 1987;Stegmiiller, 1986; Westmeyer, 1989a) reconstruction of a historically famous basicemotion theory of the second variety, namely, Wundt's (1896; 1910; 1911) three-dimen-sional theory of emotion, and (b) a sketch of the larger theory-net of basic emotiontheories to which Wundt's theory belongs. Although the focus of the article is thus on ahistorical formulation, I believe that the paper is not of historical interest only.First, it also sheds light on some of the contemporary descendants of Wundt's theory andtheir systematic relation to that theory. Second, I think that Wundt's theory is in somerespects more sophisticated than are its contemporary descendants, and that somethingcan therefore still be gained from a reconsideration of Wundt's ideas - at least anincreased awareness of the problems that confront this kind of approach to emotionalexperience.

The formal reconstruction of Wundt's theory is preceded by an informal but alreadysystematic description of the theory, which is intended both to provide historical andbackground information and to enable the reader to judge for herself the adequacy ofthe proposed reconstruction.

Wundt's Theory of Emotion 143

2. Informal Description of Wundt's Theory of Emotion

2.1 General Characteristics of Wundt's Approach to Emotions

Wundt, undertaking to establish psychology as an independent science, postulated thatthe subject matter of psychology is conscious experience, and that the method for itsinvestigation is systematic introspection by trained observers. Guided by the model ofchemistry (cf. Boring, 1953), Wundt assumed that all conscious experiences, howevercomplex, are built up or composed from "absolutely simple and unanalyzable compo-nents" (Wundt, 1896, p. 33), the "psychic elements" of consciousness.3 The task ofpsychology, according to Wundt, consists of analyzing - via introspection - consciousexperiences into their fundamental components; of organizing the elements of conscio-usness obtained in this way into classificatory systems; and finally of explaining, at leastin principle, how these psychic elements are "synthesized" into complex experiences.Originally formulated for sensory psychology (cf. Sander, 1937), this research programcame to be applied in a systematic manner to emotional experience by Wundt (1896) inthe first edition of his Grundrifi der Psychologie (Outlines of Psychology), where he firstproposed his famous three-dimensional theory of emotions (cf. Titchener, 1908).4

The presentation of this theory went hand in hand with a significant change ofWundt's views concerning the ultimate elements of consciousness. In the forth edition ofhis monumental work, Grundzuge der Physiologischen Psychologie {Outlines of PhysiologicalPsychology), Wundt's (1893) official doctrine still was that there is only one kind ofpsychic elements - sensations. Feeling was thought to be a third attribute of sensationsin addition to intensity and quality, termed the affective tone (Gefuhlston) of sensation.Furthermore, only two ultimate forms of this affective tone of sensation were assumedto exist: pleasantness and unpleasantness (cf. Titchener, 1908). In his Outlines of Psycho-logy, Wundt (1896) - most likely in response to an incisive critique by Kiilpe (1893) of the"attribute-of-sensation" theory of feelings - abandoned this position and adopted adualistic view of the elements of consciousness. Now, Wundt claimed that there are "twokinds of psychic elements which result as products of psychological analysis...sensoryelements or sensations ...[and] affective elements or simple feelings" (p. 34).5 Examplesof sensory elements are sensations of touch, tones, heat, or light; examples of elementaryfeelings are the feelings of sensory pleasure or displeasure which may accompany suchsimple sensations. And also in contrast to his earlier views, Wundt now postulated theexistence of several further ultimate forms of elementary feeling qualities (see below).6

All nonelementary conscious experiences were viewed by Wundt as complexes orcompounds of these two kinds of psychic elements. Complexes of sensory elements werecalled ideas (Vorstellungen); complexes of feeling elements, emotions (Gemutsbewegun-gen). Three subtypes of emotions were distinguished: Compound feelings (zusammen-gesetzte Gefiihle), affects (Affekte), and volitions (Willensvorgdnge). Whereas compoundfeelings are "products of a momentary state" (Wundt, 1896, p. 187), affects and volitionsare mental processes, that is, characteristic, temporally extended sequences (Verlaufs-formen) of (compound) feelings (see also, Wundt, 1911, p. 99). This classification ofaffective phenomena is obviously strongly "theory-laden", i.e., strongly influenced by

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Wundt's theory of emotional states. Furthermore, the term "emotion" is used by Wundtin an extended, technical sense; the phenomena typically regarded as emotions incommon sense, such as joy, hope, fear, anger, pity, pride, and sorrow (e.g., Marx, 1982;Fehr & Russell, 1984), belong to Wundt's category of affects.

Note that Wundt's distinction between elementary and nonelementary feelings doesnot correspond to the distinction made in the introduction between basic and nonbasicemotions. The latter distinction is an ontological one, between the ultimate psychicconstituents of-emotions, and the more complex mental states "composed" of theseconstituents. In contrast, Wundt's distinction between elementary and nonelementaryfeelings is purely phenomenological in character, namely, between feelings which presentthemselves to introspection as having a unique quality, however complex their con-stitution or causal genesis may be, and patterns or complexes of simultaneously orsequentially occurring elementary feelings (cf. Titchener's [1908] distinction between"psychophysical" and "psychological" elements of consciousness). In contrast to someother basic emotion theorists, these distinctions are not extensionally equivalent forWundt (i.e., they do not demarcate the same classes of mental events), because heassumed that feelings of a phenomenologically unique, "new" quality (i.e., elementaryfeelings) can arise from the fusion of other elementary feelings (e.g., Wundt, 1896, p.108; 1910, p. 355). Hence, that a feeling is elementary in Wundt's sense does not meanthat it is causally or constitutionally irreducible. It does not even mean that the compo-nent feelings on which a "fused" elementary feeling is based may not also be introspecti-vely discernible to some degree; in fact, such is typically (Wundt, .1896, p. 99) andpossibly always (Wundt, 1896, p. 88) the case. As explained in more detail later, the basicemotions in Wundt's system are a subset of his elementary feelings, whereas the nonbasicemotions comprise (a) all other elementary feelings (which are presumably fusions of thebasic feelings), and (b) the nonelementary feelings (i.e., Wundt's emotions). In the formalreconstruction, the distinction between basic and nonbasic emotions will be made central.In the present, informal description of the theory, however, I will adhere to Wundt'sclassification of affective states into elementary versus nonelementary feelings.

2.2 Elementary Feelings

Wundt's assumptions concerning the elementary or simple feelings can be summarizedas follows:

1. Like sensations, elementary feelings have two essential or constitutive properties("unerlassliche Bestimmungsstucke"): quality and intensity (Wundt, 1896, p. 36).

2. Other than sensations, elementary feelings do not fall into separate quality systems;rather "all simple feelings form a single cohesive manifold, inasmuch as there is nofeeling from which one could not arrive, through intermediate steps and indifferencezones, to any other feeling" (Wundt, 1896, p. 42).

3. As already mentioned, combinations of elementary feelings may give rise to furtherelementary feelings of a new quality, analogous to the combination of chemical elementsinto compounds (Wundt, 1896, p. 35, p. 41).

4. Whereas feelings presuppose sensations or sensation-complexes (i.e., it is notpossible to have feelings without having sensations or ideas), the reverse is not true, as


there are, in fact, instances of affectively neutral sensations (Wundt, 1896, pp. 44-45; p.89). Wundt typically speaks of feelings as "complementing" or "accompanying" sensationsor ideas and rejects a causal interpretation of the "presupposition" relation betweensensations and feelings (Wundt, 1911, p. 102). However, neither is Wundt's anticausalview very clear to me, nor does anything in the reconstruction depend on the avoidanceof a causal interpretation of the sensation-feeling relation. Therefore, in the rest of thisarticle, I will assume that sensation and ideas are the causes of feelings.

5. Although the number of different elementary feeling qualities is very - according toWundt (1896, p. 97) even infinitely - large, this affective manifold can nevertheless beparsimoniously described, for there are, as Wundt calls them, three and only three "maindirections" (Hauptrichtungen, p. 97) or "dimensions" (p. 93) of elementary feeling quali-ties, which "extend between certain feeling-opposites of dominant character...[and] cantherefore...be labelled by pairs of names which suggest opposites" (p. 97): Pleasure-displeasure (Lust-Unlust), excitement-inhibition (or tranquillization) (Erregung-Beruhi-gung) and tension-relaxation (Spannung-Losung)(Wundt, 1896, p. 98). Two clarificationswith regard to these "dimensions of feeling" are necessary. First, the term "dimension" isnot meant to imply that the three dimensions are intrinsic attributes of feeling qualities;rather, they are themselves (classes of, see below) "opposed" pairs of feeling qualities,namely those from which all other affective qualities are ultimately derived (Wundt, 1910,p. 296; see also Kutzner, 1914, p. 165). (However, the dimensions can of course be usedfor a relational description of other, nonbasic feeling qualities; in particular, nonbasicfeeling qualities can be described as being more or less similar to the basic ones, or tocontain the latter as components to varying degrees). Hence, the term "dimension" is usedby Wundt by analogy with its use in phenomenological descriptions of the color space,where the "dimensions" (e.g., red-green) denote pairs of primary color qualities (cf.Wundt, 1896, p. 65ff). Second, although the three dimensions are introduced by Wundtas a classification system of the elementary feeling qualities, it appears that the continuathat "extend between certain feeling-opposites of dominant character" (Wundt, 1896, p.97) represented by the dimensions are by no means pure quality continua - at least giventhe normal use of the terms "emotion quality" and "emotion intensity" that is alsoendorsed by Wundt (1896, p. 36). Rather, each dimension represents only a pair of quali-tatively different feeling types (e.g., pleasure versus displeasure), each of which can varyin intensity. In other words, each dimension is a combination of two opposed, quantitati-vely varying basic feeling qualities. Hence, for example, the pleasure-displeasure continu-um extends from strong pleasure feelings to medium to low pleasure feelings, passesthrough a "zero point" of affective indifference, and then proceeds through low tomedium to strong feelings of displeasure (Wundt, 1910, p. 298). One can therefore alsospeak, and perhaps less misleadingly, of "six basic forms of feelings" (Wundt, 1910, p.298), each of which varies in intensity, and of which two each form phenomenological"opposites". Conceivably, however, Wundt thought that the intensity differences ofemotions are simultaneously also quality differences, analogous to his interpretation ofthe brightness dimension of color experiences (Wundt, 1896, p. 70).

On the background of these clarifications, Wundt's assumptions concerning the three-dimensional system of elementary feelings can be summarized as follows: (1) As alreadymentioned, the three dimensions are, as one might say, bipolar, that is, they "extendbetween certain feeling-opposites of dominant character" (for a more detailed discussion

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of the nature of bipolarity, see the formal reconstruction). (2) The six basic forms offeelings - and consequently the three dimensions, too - are "peculiar forms [of feelings]which cannot be reduced to one another" (Wundt, 1896, p. 99) - i.e., they are basic in thesense explained in the introduction. (3) Elementary, but nonbasic, feelings may involve -that is, may be a fusion of - feelings on all, or just two or one of the three dimensions.According to Wundt (1910, p. 297), "mixed" feelings are the rule, whereas "dimensionallypure" feelings are only rarely experienced; nevertheless, it is the existence of the latterfeelings which makes it possible in the first place to distinguish between the threedimensions (Wundt, 1896, p. 98). Feelings which "belong" to more than one dimensiontypically fuse into feelings of a new quality, but the basic feelings from which they arecomposed can usually (Wundt, 1896, p. 99) and possibly always (p. 88) still be discernedby introspection, even though they normally recede very much into the background ofexperience (p. 88). (4) Finally, it must be noted that, strictly speaking, the three dimen-sions were not meant by Wundt to represent single, uniform feeling qualities. Rather,they were thought to be "dimensional categories" (Titchener, 1908), each of which com-prises many different subtypes of (pairs of) basic feeling qualities, just as the category redcomprises many different shades of red-sensations (Wundt, 1910, p. 300). That is, Wundt(1896, p. 99) assumed, for example, that the displeasure feeling of a painful touch, ofharmonic dissonance, of intellectual failure etc. are all qualitatively different forms ofdispleasure. Indeed, even the quality of the pleasure feeling elicited by the taste of sugarand that associated with the smell of menthol were held to differ by Wundt (1910, p.319). However, for reasons given below, this feature of Wundt's theory will be disregard-ed in the formal reconstruction.

2.3 Compound Feelings and Affects

A singular elementary feeling is only rarely experienced. Usually, the person experiencescompound feelings, that is, affective states which arise from the confluence or simultane-ous occurrence of several elementary feelings. Compound feelings are defined as feelingstates "of unitary character, in which at the same time simpler affective components arediscernible" (Wundt, 1896, p. 187). That is, on the one hand, there is, for each compoundaffective state, an own, irreducible feeling quality, which results from the fusion of all ofits components (Wundt, 1896, p. 214). This unique quality is called the feeling resultant(Gefiihlsresultante) or the total feeling (Totalgefuhl), and it is by definition an elementaryfeeling. According to Wundt's (1896, p. 198) "principle of the unity of the affective state",this feeling resultant always comes into being, regardless of how disparate and indepen-dent the simultaneously experienced sensations or ideas may be which elicit the compo-nent feelings (Wundt, 1910, p. 352). On the other hand, the various components whichmake up the total feeling are also introspectively discernible to a greater or lesser extent.These are called component feelings (Gefiihlskomponenten) or partial feelings (Partialge-fuhle). Hence, the term "compound feeling" does not denote (just) the feeling resultant -which is itself an elementary feeling - but the complex mental state consisting of thefeeling resultant plus the simultaneously present, discernible partial feelings.

According to Wundt (1896, p. 188), the ultimate components of compound feelingsare always "simple sensory feelings", that is, feelings which accompany sensory elements,


i.e., sensations. These feelings are also called "first-order partial feelings". In some cases(e.g., the feeling of bodily well-being; Wundt, 1896, p. 190), the compound feelingconsists only of the total feeling and the first-order partials. In contrast, in other cases(such as with the feelings elicited by tonal sensation-complexes, see below), pairs, triplesetc. of the first-order partial feelings are first fused into partial resultants, or second- andhigher-order partial feelings, "which then enter the total feeling as compound componentfeelings" (Wundt, 1896, p. 188). To illustrate this assumption with Wundt's primaryexample, the compound feeling elicited by the tones c-e-g is construed as follows (Wundt,1896, pp. 188-189). The ultimate components of this compound feeling are the first-orderpartial feelings elicited by the single tones c, e, and g. Next, there are three second-orderpartial feelings, the "feelings of harmony" corresponding to the sensation-complexes c-e,c-g, and e-g, which result from the fusion of the simple feelings elicited by these tones.Finally, there is the third-order partial "feeling of harmony" - which in this case is alsothe total feeling - and which results presumably (this is not entirely clear) from the fusionof the second-order partials.

No question then, that the "structure of compound feelings is in general an extremelycomplicated one" (Wundt, 1896, p. 188). Unfortunately, it is also rather unclearly des-cribed. In particular, it is not clear how, precisely, the fusion of partial feelings is toproceed. The example described above may suggest that this fusion process is strictlyhierarchical, such that only lower-order partial feelings are fused into higher-order ones(see also, Wundt, 1910, p. 354). However, on p. 88 of his Outlines, Wundt (1896) seemsto suggest that the total feeling results from the fusion of only the first-order partials;and according to his "principle of the unity of the affective state" (Wundt, 1896, p. 198),all partial feelings which are present at a given moment are fused into the total feeling.

Finally, Wundt (1896) defines affects as characteristic forms of sequences of com-pound feelings. Little more about them needs to be said here, not only because Wundt'spertinent assumptions are both scarce and unclear, but because he essentially abandonedthe distinction between compound feelings and affects later in his book (Wundt, 1896, p.213) by admitting that temporal course does not furnish a reliable criterion for thedistinction of affects. As with compound feelings, the only reliable discriminating featureis quality. Indeed, it seems that the classification of emotions according to their temporalcourse - i.e., according to changes in their intensity over time (Wundt, 1911, p. 191) - pre-supposes that they are independently identifiable by their quality. For one can hardlyspeak of a change of intensity of a particular emotion over time unless one makes surethat one is indeed dealing with the same emotion quality at the different time points.

2.5 The "Sensory" Character of Wundt's Theory of Emotion

To conclude this section, I would like to point out that - despite the fact that feelingswere conceptualized by Wundt (1896) as a unique kind of basic mental states differentfrom sensations - his theory of emotions remained nevertheless very much "sensory" incharacter (as did his whole approach, to consciousness). As Sander (1937) aptly notes,Wundt conceptualized feelings "in complete analogy to the sensations which up to thenhad alone been accepted as building blocks of the mental" (p. 37). For although feelings

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were held to differ from sensations in a number of respects, they were in other waysconstrued as very similar to sensations (see also Stumpf, 1907). In particular, like sensa-tions, feelings and emotions were taken by Wundt to be intrinsically nonintentional ornonrepresentational mental states. That is, although Wundt acknowledged that emotionstypically have objects - e.g., if one is angry, one is usually angry at or about something(Wundt, 1896, p. 211) - he did not accept Brentano's (1874/1971) and Stumpf s (1899)claim that emotions are intrinsically intentional (cf. Reisenzein & Schonpflug, 1992;Reisenzein, 1992). Rather, according to Wundt, the intentionality of emotions is "derived"from their association with sensations or ideas. In fact, as discussed in more detail later,Wundt's theory can be viewed as including an attempt to explicate this idea of "derivedintentionality" of emotions.

In addition, the idea of a "fusion" of elementary feelings into feelings of a new qualitywas derived, not only from an analogy to chemical composition (Wundt, 1896, p. 36), butalso from an analogy to the phenomenological fusion of tones (Wundt, 1910, p. 353).And the conceptualization of the three-dimensional system of elementary feelings wasclearly modelled on that of the sensory quality systems; in particular, it bears an obviousstructural resemblance to Hering's sphere of color sensations reviewed by Wundt (1896)in the book chapter immediately preceding that on elementary feelings (this analogy isexplicitly drawn by Wundt, 1910, p. 318). Tones and colors were also Wundt's favouriteexamples of studying and illustrating the elementary feelings. As early as 1874, Wundthad already systematized this affective reactions to tones and colors, suggesting, forexample, that the feelings typically elicited by different colors (including the achromaticones) can be arranged in a circular plane corresponding to the color disc, with white ofmedium intensity (i.e., grey) corresponding to the point of affective indifference (Tit-chener, 1908, p. 134; see also Wundt, 1910, p. 340). And it was primarily the study of theaffective reactions to colors and tones that suggested to Wundt the existence of furtherdimensions of feeling in addition to pleasure-displeasure (Wundt, 1910, p. 382). Inter-estingly, however, Wundt (1896) neither accepted that nonprimary color sensations (e.g.,orange) are fusions of primary color sensations (e.g., red and yellow), nor that com-plementary color qualities (e.g., red-green) are psychological "opposites" (rather, theywere thought to represent only "maximal differences"). But - considering particularly thatWundt did make analogous assumptions in the case of feelings - his reasons for rejectingthese assumptions in the case of color experience remain somewhat obscure (cf. Leh-mann, 1914; Titchener, 1908; Hardin, 1985).

3. Formal Reconstruction of Wundt's Theory

3.1 Wundt's Theory as a Structuralist Theory-Net

According to the structuralist view of scientific theories, the entities that are presyste-matically regarded as empirical theories are best characterized, from a systematic per-spective, as particular kinds of set-theoretic structures (Balzer et al., 1987; Stegmiiller,1986; Westmeyer, 1989a), namely, as sets of theory-elements that are in various waysconnected to one another. This is also the case for Wundt's theory of emotion, which is


reconstructed as a small theory-net consisting of the basic theory element TEiWUNDT)containing the fundamental assumptions of Wundt's theory, and a number of morespecific theory-elements, TE(WUNDT1), TE{WUNDT2) etc. that result fromTEiWUNDT) through the more precise specification of existing, or the addition offurther assumptions. This theory-net is itself part of the larger theory-net of basicemotion theories sketched in the last part of this article. In this part, however, thediscussion is restricted to Wundt's theory, i.e., the basic theory element TEiWUNDT) andits specializations.

In accord with the structuralist concept of a theory-element, TEiWUNDT) is definedas the set-theoretical structure TEiWUNDT) = <K(WUNDT),I(WUNDT)> consisting ofthe theory-core KiWUNDT) which contains the formal mathematical structure of thetheory WUNDT, and the set of intended applications I(WUNDT) of the theory-core.Following Balzer et al. (1987; cf. also Westmeyer, 1989a), the theory-core KiWUNDT) istaken to be the set-theoretical structure <Mp(WUNDT),M(WUNDT),Mpp(WUNDT),GC(WUNDT),GL(WUNDT)> consisting of the classes of potential models (A/,), models(A/) and partial potential models (M^,) of WUNDT, as well as the global constraint (GC)and the global link (GL) of the theory. The ensuing presentation of the formalization ofWUNDT approximately follows the order of the elements of the theory-core. First, Ipresent and discuss the definition of the set of potential models Mp(WUNDT), whichintroduces the conceptual apparatus, i.e., the basic concepts of the theory. Second,several important defined concepts are introduced. Third, I present and discuss thedefinition of the set of models MiWUNDT), which contains the substantive axioms of thetheory. Forth, I define and discuss the constraint CiWUNDT) of the theory, whichdescribes an essential connection assumed to hold between different applications of thetheory. Fifth, I sketch a link LiWUNDT) from a theory of emotion measurement,TEifiMM), to TEiWUNDT), which serves to "import" information on measurements ofthe basic and nonbasic feelings to TE(WUNDT). Sixth, the issue of 7-theoreticity andwith it, that of the definition of the partial potential models Mpp(WUNDT) is discussed.Finally, the intended applications of the theory are discussed, and the issue of thecompleteness of the reconstruction is addressed. Possible specializations of TEiWUNDT)are dealt with in the context of the discussion of the models and constraints of WUNDT.

However, before going into the details, I would like to draw the reader's attention tothe fact that the formal reconstruction of Wundt's theory of emotions involves a numberof simplifications. Specifically, (a) volitions were ignored in the reconstruction, becauseI wanted to concentrate on Wundt's theory of emotions; (b) the distinction betweenWundt's compound feelings and affects was ignored, because - as mentioned - Wundthimself in effect admitted that the only reliable criterion for the distinction of feelings istheir quality; (c) Wundt's speculations concerning the physiological origin of feelings(Wundt, 1896, p. 104) and the relations between attributes of sensations and the differentbasic feelings (Wundt, 1896, 1910) were ignored because these assumptions go beyondthe theory here considered, which is intended as a purely psychological theory of thestructure of emotional experience (see Titchener [1908], and Kutzner [1914] on Wundt'spartly conflicting ideas concerning these matters); (d) Wundt's claim that there is a one-sided dependence of feelings on sensations was not explicitly formulated as an axiom; itis however implicitly presupposed in the definition of affective reactions by means of

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their "relativization" to sensations (see below); and finally, (e) Wundt's assumption thateach of the six basic forms of feelings represents a class comprising a multitude ofdistinct feeling qualities was abandoned. However intuitively plausible this assumptionmay seem to be, in the reconstruction it is assumed - in line with more recent dimensio-nal theories of emotion (e.g., Schlosberg, 1954; Russell, 1980) - that there is only onetype of each basic feeling quality.

Note that, except for (e), none of these simplifications significantly changes Wundt'soriginal formulation. And as to the last-mentioned simplification, it was unavoidablebecause Wundt (1896) did not provide enough detail concerning the various subtypes ofthe basic feeling qualities (their number and nature, their relations to one another andto the nonbasic emotions etc.) to permit a formalization. In addition, it can be arguedthat Wundt's suggestion that there are many different subtypes of pleasure, displeasureetc. does not fit well with other assumptions of this theory of emotions. In particular,according to Wundt all of the different feelings within each basic category are, on theone hand, irreducible qualities. On the other hand, Wundt also assumed that, just asfeelings of different basic types can merge into feelings of new qualities, so too canfeelings of different subtypes of one and the same basic category merge into feelings ofanother feeling of the same category (if so, obviously not all of these feelings can bebasic). It would be possible to drop the last-mentioned assumption and hence to assume,for example, that the different pleasure qualities cannot be fused. But this would hardlybe a plausible move as long as one maintains simultaneously that feelings of differentbasic categories can merge into new feeling qualities. And this latter assumption is, afterall, the core of Wundt's theory. It is therefore more plausible to abandon the assumptionthat the different subtypes of pleasure, displeasure etc. are irreducible.

In addition, the feelings within each basic category obviously do have something incommon - a "common character" (Wundt, 1910, p. 295) which justifies using the samename for all of them (p. 294). The most natural assumption - at least within Wundt'selementaristic framework - seems to be that these feelings are "composed" of a commonfeeling component that explains their similarity, plus additional components whichaccount for their differences. These additional components could either be the furtherbasic emotions postulated by Wundt. If so, the set of truly basic emotions has again justsix members (the "pure" basic feelings), as assumed in the reconstruction, whereas theremaining members of the six basic emotion categories are in truth nonbasic feelings -presumably those which contain the respective basic feelings as a dominant component.7

Or the additional components are of a different kind. Then Wundt has failed to specifyall of the basic components of feelings.

3.2 Potential Models of WUNDT

Def-Mp (WUNDT)x is a potential model of the theory WUNDT(x e Mp(WUNDT)) iff there are OBJECTS,,®,BASICS,AFFECTS,q such that(1) x = <OBJECTS, ®,BASICS,AFFECTS, q>;(2) OBJECTS, BASICS, and AFFECTS are finite, nonempty, and pairwise disjoint sets;


(3) ®: OBJECTS x OBJECTS - OBJECTS is an associative, commutative and idem-potent [i.e., © (0,0) = o] operation;

(4) BASICS = {P,D,E,I,T,R}, with all B e BASICS being numerical functions B:OBJECTS - IR0+;

(5) AFFECTS = {...,4,...} , with all A € AFFECTS being numerical functions A:OBJECTS - JR0+;

(6) q: AFFECTS ~ V; with(a) q is a unique (i.e., one-one) function and

6(b) K = {<V,,V2 ,V3 ,V4 ,V5 ,V6> €IR£: E v - 1).

J

Notational conventions'. Arbitrary elements of OBJECTS are denoted by non"o","of etc;those of BASICS by "5", "fl ,","£/' etc.; and those of AFFECTS by "AVA^'Af, etc.

The object of Wundt's theory are the emotional experiences of a given person at agiven time, and its main assumption concerns the "internal structure" or composition ofthese experiences, i.e., Wundt assumes that all emotions, unless themselves basic, resultfrom particular combinations of six basic emotional qualities. To be able to formulatethis, as well as the further assumptions made by Wundt about emotional experiences inset-theoretical terms, the emotional experiences must first be conceptually representedin a suitable format; that is, they must be described by appropriate set-theoreticalconcepts. The basic concepts used for this purpose are collected in the structure<OBJECTS,m,BASICS,AFFECTS,q>. With regard to entities that are describable interms of this conceptual framework - that is, as potential models of WUNDT - it is reaso-nable to ask whether they fulfil the substantive axioms of the theory (Stegmiiller, 1986).

3.2.1 BASICS and AFFECTS

The central concepts are the sets BASICS and AFFECTS, the elements of which are in-tended to represent, respectively, the various basic and nonbasic feeling qualities. It mustbe emphasized that these concepts are not meant to capture Wundt's phenomenologicaldistinction between elementary and nonelementary feelings mentioned in the informaldescription of the theory. Rather, they are intended to represent the more important,ontological distinction between affective qualities which - according to Wundt - resultfrom fusions of other feelings (I chose to call them affects) and those which don't (basicfeelings). BASICS has therefore exactly six elements, which represent the six basicelementary feeling qualities proposed by Wundt: Pleasure (P), displeasure (D), excite-ment (E), inhibition or tranquillization (/), tension (7), and relaxation (R). (I introducethem as six basic feelings and later state their "bipolarity" axiomatically). The exactnumber and kind of the elements of AFFECTS depends on the specific application of thetheory (i.e., which nonbasic feelings are measured in that application), but two generalthings can be said: First, because AFFECTS' and BASICS are assumed to be mutuallydisjoint, AFFECTS never contains any of the basic feelings; and second, AFFECTS maycontain any affective quality which - according to Wundt - is "nonbasic", i.e., is a fusionof basic feelings, or of other elements e AFFECTS. In particular, as argued below,

152 R. Reisenzein

AFFECTS may contain any of the mental states regarded as typical emotions in common-sense, such as joy, pride, anger, and fear.8

In sum, the basic concepts of the formalization capture only Wundt's elementaryfeelings; and these are not represented by a single set, but are split into two sets, BASICSand AFFECTS. Wundt's compound feelings (i.e., feeling complexes which consist of thesimultaneous occurrence of basic, partial and total feelings) are later introduced bydefinition. It may be objected that this procedure is unnatural, because Wundt's com-pound feelings are certainly also nonbasic and should therefore be included among theelements of AFFECTS (and perhaps be singled out later). This would be possible, but Ithink there is a good reason for proceeding in the way I did: I think - in contrast toWundt - that all that is really important about compound feelings is their component"total" feeling, which, because it is an elementary (fused) feeling, is already contained inAFFECTS. For I assume, in full agreement with Wundt (1896, p. 36), that all nonbasicaffective states can be meaningfully said to have an intensity, including in particular alsoparadigmatic emotions such as joy, fear, and sorrow, which are held to be compoundfeelings by Wundt. The notion of a unique intensity of a compound feeling (i.e., a patternof coocurring feelings) is however by no means intuitively evident. The only plausible wayto explicate this notion seems to consist of assuming that the intensity of feeling patternsis a quantity which is in some way derived from the intensities of the partial feelingsinvolved in the compound. And the simplest and most plausible assumption, withinWundt's theory, is that it is just the intensity of the total feeling resulting from the fusionof all components (which, according to Wundt's [1896, p. 198] principle of the "unity ofthe affective state", should always exist). If so, however, one can just as well identify pre-sumably compound feelings such as joy and sorrow with the total feeling (i.e., with afused elementary feeling, rather than a compound feeling) and hence, there is no needto consider compound feelings separately. In fact, compound feelings play no role in theaxioms. Their subsequent definitional introduction is mainly useful for purposes ofdescribing a person's total emotional reactions in a parsimonious way.

Set-theoretically, the various feeling qualities are represented by numerical functions.Hence, the elements of BASICS and AFFECTS are numerical functions; different func-tions represent different basic (e.g., pleasure) or nonbasic (e.g., anger) feeling qualities,and different values of the same function represent different intensities of the samefeeling quality. As will be seen, this set-theoretical representation of feeling qualities bynumerical functions allows for a rather natural description of emotional experiences,particularly when OBJECTS is interpreted as a set of propositions.9

3.2.2 OBJECTS and e

The arguments of the affect functions are provided by the elements of OBJECTS, whichcan be interpreted in two different ways: (a) as the sensations or sensation-complexeswhich "accompany" (Wundt, 1896) or - as I assume - cause the emotions; or (b) aspropositions which serve as the intentional objects of the emotions. (The formulation"emotion E of intensity v is experienced toward object o" is meant to cover both of thesepossibilities). Inasmuch as emotions are mental states of people in which they find them-


selves at certain times, it may at first seem natural to use - at least in addition toOBJECTS - persons and time points as arguments of the affect functions. However,closer examination of this issue reveals that - analogous to the structuralist reconstructionof Jeffrey's (1965) decision theory (cf. Balzer et al., 1987; Stegmuller, 1986) - conceptsrepresenting people and time points are not needed in the formalization. The reason isthat each intended application of the theory can be regarded as dealing with the affectiveexperiences of a single (although largely arbitrary) person at a single (although arbitrary)time point. Therefore, both the affective experiences of different people and those of thesame person at different time points constitute different potential applications of thetheory.10

That an intended application of the theory concerns a single individual can be seen byconsidering that the theory says nothing about possible interactions of any sort betweendifferent people; the only way other people may enter the picture is as (components of)objects of emotions (contrast, e.g., Westmeyer's [1989b] theory of behavior interaction).That an intended application concerns a person's emotional experiences at a single timepoint is less apparent, but note (a) that temporally extended sequences of feelings(Wundt's affects) are' disregarded in the formalization (for reasons given above), and (b)that none of the axioms is formulated as a law of succession (the two fusion axioms couldperhaps be so interpreted, but it is not necessary to formulate them explicitly as laws ofsuccession). This holds also true for the further theories of the theory-net of basicemotion theories considered later in this article; therefore, time points are unnecessaryfor the reconstruction of these theories, too. A set of time points would however beuseful for the precise formulation of constraints dealing with the temporal constancy ofaffective reactions toward particular objects (which are proposed for certain specializa-tions of Wundt's theory). However, if one is satisfied with a semi-formal definition ofthese constraints, a set of time points is not necessary even for this purpose.

As mentioned, the set OBJECTS can be interpreted in two different ways. Accordingto the first interpretation, which is closer to Wundt (1896) in letter, the elements ofOBJECTS represent different types (see below) of Wundt's elementary sensations andsensation-complexes, namely those which the person experiences at the time pointconsidered, and which may thus potentially function as elicitors of basic and nonbasicfeelings. (As mentioned in the informal description of the theory, Wundt assumed thatemotional reactions always presuppose sensations). Given this interpretation of OB-JECTS, the associated binary operation ® is to be interpreted as a "combination" or "con-catenation" operation which serves to build more complex sensations or ideas fromsimpler ones (cf. the informal description of the theory). That is, the intended inter-pretation of "9(01,Oβ) = vk" is "ok is a sensation-complex (an idea in Wundt's terminolo-gy) consisting of the component ideas (or sensations) 0, and of. The set-theoreticalsentence "A(o) = v" thus means "the person experiences, at the time considered, an affectof quality A and intensity v, which accompanies (or: is caused by) an idea or sensation oftype o". Hence, the feelings are "relativized" to the ideas or sensations which theyaccompany or, as I assume, by which they are caused. \A{p) = 0 captures the case whereo has no emotional effect]. This relativization of the affective reactions to ideas is neededfor the following reasons. First, according to Wundt, different sensations or sensation-complexes experienced by a person at the same time can theoretically cause feelings of

154 R. Reisenzein

the same quality, and even of the same intensity. Without a set of objects, these affectivereactions could not be distinguished. Second, OBJECTS is needed for the formalizationof Wundt's idea that pairs of basic feelings (e.g., pleasure and displeasure) are "opposi-tes", because, as will be explained later, the corresponding axiom holds true only forthose basic feelings that are caused by "simple" objects, i.e., sensations. And third, therelativization of feelings to ideas captures Wundt's attempt to deal with the object-directedness of emotions.

Finally, note that the elements of OBJECTS are intended to be types of sensationsrather than tokens (i.e., unrepeated, dated particulars; cf. footnote 6), which differ atleast in quality and intensity (e.g., "vanilla-taste-sensation of intensity u"). (It may in ad-dition be necessary to consider the phenomenal localization of sensations, at least forsome sense modalities; cf. Carnap, 1928/1979). However, I do of course not want to saythat mental state types - abstract objects - are causes. Therefore, "A(o) = v" must beinterpreted, more precisely, as "the person experiences, at the time point considered, anaffect of quality^! and intensity v, which is caused by (the event of)/?'s exemplifying sen-sation-type o at this time point." (Hence, I construe concrete, particular events asexemplifications of properties by objects; cf. Kim, 1973). In my view, the present con-struction of sensations as types of mental states is preferable to the alternative approachof construing them as particulars (e.g., Balzer & Marcou, 1989). Events as particulars areby their very nature unique occurrences. Hence, the same person cannot experience thesame particular sensation at different times, nor can different persons experience thesame particular sensation at the same or at different times.

Although the interpretation of OBJECTS as a set of sensations or sensation-complexesstays close to Wundt (1896) in letter, the alternative possible interpretation of OBJECTSas a set of propositions may actually be closer in spirit. For Wundt (1896) clearly meanthis theory to be applicable to all emotional experiences, not just to those which are infact caused (directly) by sensations or sensation-complexes. In contrast to Wundt,however, it is today widely believed that at least paradigmatic emotions are usually if notnecessarily mediated by more or less complex cognitions concerning the eliciting state ofaffairs (e.g., Lazarus, 1991; Reisenzein & Schonpflug, 1992). Fortunately, Wundt'sassumptions about the causation of emotions are completely detachable from his theoryof emotion (considered purely as a theory of the structure of emotional experience). Thatis, Wundt's theory is neither restricted to emotions that are in fact caused by sensations,nor does it presuppose the acceptance of Wundt's sensualistic and elementaristic view ofperception (which is generally seen as inadequate today). This is demonstrated by theproposed alternative interpretation of OBJECTS as a set of propositions. Furthermore,part of what Wundt (1896) attempted to achieve by means of the "relativization" ofemotions to ideas and sensations - namely, to account for the object-directedness ofemotions - is achieved in a more straightforward and adequate manner by the proposedreinterpretation. Many contemporary philosophers regard propositions as the properobjects of intentional mental states, including beliefs, desires, and emotions (see e.g.,Gordon, 1974; Jeffrey, 1965; Schiffer, 1988; Searle, 1983). According to this alternativeinterpretation of OBJECTS, "A(o) = v" means "the person experiences, at the time pointconsidered, the emotion of quality A and intensity v, which is intentionally directed at thepropositional object o". For example, let o be the proposition, currently believed-as-true


by Franziska, that she was invited to the party. "Happiness (o) = v" then means thatFranziska's degree of happiness about being invited to the party was v units on anappropriate scale. It may be seen that, particularly when OBJECTS is interpreted as a setof propositions, the present set-theoretical representation of emotions by numericalfunctions allows for a rather "natural" description of emotional experiences, i.e., one thatis close to everyday descriptions of emotional experiences, being essentially a quantitativerefinement of these descriptions.

Note also that the interpretation of OBJECTS as a set of propositions is compatiblewith both the view that emotions are intrinsically intentional, as are beliefs and desires(e.g., Stumpf, 1899; cf. Reisenzein & Schonpflug, 1992); and with the view that theintentionality of emotions is a "derived" feature, that is, a feature due to the association,specifically the causal dependence of emotions on beliefs (cf. Husserl, 1901/1975). If thelatter interpretation is preferred, one ought to interpret "A is intentionally directed at o"as "the person's experience of A was caused by her believing (or thinking) that o" (andanalogously for the basic feelings B).

Given the interpretation of OBJECTS as a set of propositions, the operation ® is mostsensibly interpreted as logical conjunction (A). The assumed properties of © - associative-ness, commutativeness, and idempotency - are then mandatory, because these are just theproperties of logical conjunction." The properties required of © are however alsoplausible if OBJECTS is interpreted as a set of sensations or ideas, because in this casetoo, they can be traced back to the properties of A. For, as mentioned above, the ele-ments of OBJECTS are meant to be sensation-types, which I take to be a special kind ofproperties. Therefore, © can be interpreted as the "concatenation" of simpler propertiesinto more complex properties. For example, let P be the property of having a red-sensation, and Q the property of having a yellow-sensation. Then P © Q can be inter-preted as the property of having a blue-and-yellow-sensation. It is thus plausible to define[P © Q] as follows: [P © Q] (x) ** P(x) A Q(x). The properties of © can then again bededuced from those of A.

3.2.3 Quality Function q

Finally, q assigns to each of the elements of AFFECTS, in a unique way, a six-tuple orvector of real numbers q{A) = <v,,v2,v3,v4,v5,v6>, with the additional requirementsthat the vector components are nonnegative and add up to 1. These requirements weremade to permit a transparent interpretation of q(A) as a proportion, namely, the propor-tion of the six basic feelings that is characteristic for the affect A. By using q, it ispossible to formulate both the central fusion axiom and the constraint of the theoryWUNDT in a concise way.

3.3 Defined Concepts

With the help of the basic concepts just introduced, several further concepts can be de-fined. These defined concepts are in part needed for the concise formulation of the

156 R- Reisenzein

substantive axioms; in part they are formal reconstructions of some of Wundt's centralconcepts, such as his "dimensions of feeling" and his "compound feelings".

Dl: Simple objects

SOBJECTS = {ok : ok € OBJECTS A - 3 o»Oj € OBJECTS such that ok ± o, A)}ok ± OjAok = ©

D2.1 to D23: Object components

D2.1 ("o,- is a component of of):C c OBJECTS x OBJECTS;<oi,Oj> € C - 3 oA (ok =£ o, /\ok ± Oj A o;- = o, © o*).

D2.2 ("o,- and o;- have a common component"):CC c OBJECTS x OBJECTS;<oi,oj> E CC ~ 3ok (<ok,Oi> e C A <ok,Oj> e C).

D23 ("the maximal common component of o, and of):MC: OBJECTS x OBJECTS -+ OBJECTS;<Oj,Oj> e CC - MC{Oi,Oj) = that o t , for which:<oA,o(> e C A <ok,Oj> € C A -i 3 o, (<o,,oi) € C A <ol,oj> e CA <oA, o, > e C).

D3.1 to D3.4: Compound feelings

D3.1 TBASIC: OBJECTS -»• IR6;TBASIC{o) = <P(o),D(o)Mo)Ao),T(o),R(o)>.

D3.2 TAFFECT: OBJECTS - • IR"; TAFFECT(o) = <... , ,4»,. . .>.D33 TEMOTION: OBJECTS -» IR6+";

TEMOTION(o) = <TBASIC(o),TAFFECT(p)>.D3.4 7OL4L = <TEMOTION{o,),...,TEMOTION{or)>.

D4.1 to D4.4: The three dimensions of feelings

D4.1 PD: SOBJECTS -* IR;D4.2 £/: SOBJECTS -*• IR; £/(o) = £(o) - /(o);D43 T/?: SOBJECTS —• IR; 77?(o) = T(o) - /?(o);D4.4 TRIDIM: SOBJECTS -* IR3; TRIDIMip) = <PD(p),EI(o),TR(o)>.

D5 For any m, a function g: IRm —>• IR is strictly monotonically increasing(g € MON) iff V <xlv..;cm > e IRm V <yx,...ym > 6 JRm:(*, ylA ... Axm ym) A (3 i (i s m Ax, < >>,)) -

In Definition Dl, a subset SOBJECTS of simple objects is singled out from the setOBJECTS with the help of the operation ©. As mentioned, SOBJECTS is later needed


for the formulation of the 'TDipoIarity" axiom of Dei-MQVUNDT). As can be seen fromDl, simple objects are those objects which are not composed of other elements ofOBJECTS. Wundt, of course, assumed that such absolutely simple objects do exist; andthis seems to be reasonable if OBJECTS is interpreted as a set of sensations and sensa-tion-complexes. If OBJECTS is interpreted as a set of propositions and © as logicalconjunction, I suggest that SOBJECTS should be interpreted as the set of those proposi-tions currently "entertained" by the person which are atomic in the given context; that is,they constitute the most fine-grained conceptualization of the situation considered by theperson at the moment. Whether one thinks that there are "ultimately" atomic proposi-tions (with regard to A) depends in part on whether one believes that there are ab-solutely unanalyzable predicates (i.e., "semantic primitives" of the "language of thought";cf. e.g., Wierzbicka, 1972; Miller & Johnson-Laird, 1976). Even if they existed, it isunlikely that they play a substantial role in applications of the present theory.

Definitions D2.1 to D2.3 concern common components of (complex) objects. Theseconcepts are later needed in the context of the formalization of axiom 2 of Def-M(WUNDT), the first fusion axiom. In D2.1, an object ot is defined as being a componentofoj iff there is an object ok distinct from both o, and Oj which, if concatenated with olt

results in or In D2.2, two objects are defined as having a common component iff thereis a (simpler) object ok which is a component of both o, and or Finally, D2.3 defines theconcept of the maximal common component of two objects ot and ot as that common com-ponent ok of the two objects which is not a component of any other common componentO[ of the two objects. For example, assume that a,b, and c have no common components,and that ol, = (a © b © c), and Oj = (b © c © d). The maximal common component of o,and Oj, MC(Oi,Oj) is (b © c), for (b © c) is a component of both objects, and there is nofurther, "larger" common component of the two objects, i.e., one of which (b © c) is itselfa component. Note that D2.3 is a conditional definition, i.e., MC is defined only for thecase where the two objects o, and o} in fact have a common component. If they have nocommon component, MC is left undefined. By using a conditional definition, it is possibleto make do without assuming a "null element" in the set OBJECTS that could serve asthe value of MC if the two objects have no common components.

In D3.1 to D3.4, four further concepts are defined which capture Wundt's ideasconcerning compound feelings (cf. the informal discussion of the theory). TBASIC repre-sents the person's compound of basic feelings toward an object o [this concept is alsoused in the formulation of axiom 3 of Dci-M(WUNDT)}; TAFFECT represents the com-pound of nonbasic feelings toward an object o (it is assumed that \AFFECTS \ = n);TEMOTION represents the compound of both basic and nonbasic feelings toward anobject; and finally, TOTAL is the compound of all basic and nonbasic feelings toward allobjects considered (i.e., the person's total affective state compound). More precisely, ina given application of the theory, one would have to say that TBASIC, TAFFECT andTOTAL represent those basic and fused feelings toward those objects which are explicitlyconsidered (e.g., assessed) in that application (cf. the discussion of the intended ap-plications of WUNDT).

Wundt claims that his six basic feelings form three pairs of opposites, which make uphis three "dimensions of feeling", pleasure-displeasure, excitement-inhibition (tranquilliza-

158 R. Reisenzein

tion), and tension-relaxation. Rather than being introduced as basic concepts, thesedimensions are defined in D4.1 to D4.3. In D3.1, the degree of pleasure-displeasure ex-perienced toward an object, PD{o), is defined as the difference between the degree ofpleasure and the degree of displeasure experienced toward that object. In D3.2 andD3.3., the dimensions EI (excitement-inhibition) and TR (tension-relaxation) are definedin an analogous way. Note that, in contrast to the basic emotion functions, the dimensionfunctions are not defined on OBJECTS, but on SOBJECTS, the set of simple objects (cf.the discussion of the bipolarity axiom for an explanation). In addition, the range of thedimension functions is IR, because they can also take on negative numbers. However, thisis obviously a purely formal expedient.

Finally, in D5 the concept of a strictly monotonically increasing function of m-tuplesof reals, g: IR", —*• IR is defined as a function for which g(<xu...,xm >) < g(<y\,...,ym >)if at least one of the components yt of <yi,...,ym> is greater than the correspondingcomponent *,- of <xu...,xm >, and none of the remaining components^- are smaller thanthe corresponding^ (see Balzer et al., 1987, p. 131). This concept is used in the formula-tion of axiom 3 of Def-M(WUNDT). g is not included among the basic concepts of thetheory, because it is an auxiliary mathematical concept that represents a (roughly speci-fied) law or connection between basic concepts of the theory (cf. axiom 3).

3.4 Models of W U N D T

Def-M(WUNDT)x is a model of the theory WUNDT (x e M{WUNDT)) iffx € Mp(WUNDT) and(1) V o e SOBJECTS: P{o) • D(p) = 0 A E(o) • I(o) = 0 A T(p) • R(o) = 0;

(2) VB € BASICS V o e OBJECTS:

<oi,oj> $CC - B(o, © Oj) = B(o,) + B(oj);

(3) VAe AFFECTS 3 g e MON V o e OBJECTS:

A(o) .. ig(TBASIC(o)) if 3 a e JR+: TBASICS(o) = a q(A)^ ' 1 0 otherwise

(See D5 for the definition of MON).

Wundt's substantive assumptions are captured by the three axioms (1) to (3) of thedefinition oiM{WUNDT). Axiom (1) concerns the "bipolarity" of the basic feeling dimen-sions, whereas axioms (2) and (3) concern the fusion of feelings.

3.4.1 Axiom (1)

The first axiom is intended to capture Wundt's (1896, p. 97) assumption that two eachof the basic feelings from BASICS are "opposite" conscious qualities (which can thereforebe labelled by pairs of antonyms).12 According to Wundt (1910, p. 347), the "movementbetween opposites" is an essential characteristic of feelings, which reveals itself time andagain to introspection.


A first possibility of formalizing this idea that comes to mind is to define a similarityordering on the set of all affective qualities (i.e., BASICS u AFFECTS), and then to re-quire that P, E and T are maximally dissimilar to D, I, and R, respectively. However,although recourse to the perceived similarity of feelings may be of value in the contextof empirical tests of Wundt's theory, several reasons speak against using this approachto formulate the bipolanty assumption. First, Wundt (1896; 1910) would not haveaccepted this formalization, because he believed that the relation of maximal differencebetween conscious qualities (exemplified, for example, by the relation that exists betweenhigh and low tones) must be sharply distinguished from the relation of oppositionexisting between the basic feelings. Indeed, Wundt thought that the phenomenon ofopposition or contrast "has its original right of domicile only in the domain of feelings,and wherever else it is being used, it has been deliberately or nondeliberately transferredfrom this original domain" (1910, p. 348-349; cf. Osgood, 1969). Second, this approachrequires the introduction of a further basic concept (i.e., a similarity relation; cf. Orth,1974). And third, it accepts the similarity ordering of feeling qualities as a phenomenolo-gical "given", whereas I think that the perceived similarity of feelings, and more specifi-cally the perceived opposed character of the basic feelings is a phenomenon which needsitself to be explained.

The second, actually used possibility of formalizing the bipolarity assumption avoidsthe introduction of an additional concept and also goes some way toward explaining theperceived oppositeness of the basic feelings. It constitutes a formalization of a character-istic feature of the properties denoted by gradable antonyms (Lyons, 1977): Namely, thatthey cannot be "had" or exemplified simultaneously by the same objects. That is, the basicintuition behind axiom 1 is that opposed basic feeling qualities cannot be experiencedsimultaneously. This interpretation of the oppositeness of feelings can also be found inWundt (1910): "Each dimension contains two opposed directions [of feeling] whichexclude each other, whereas each of the...six basic directions can coexist with feelingsfrom the two other dimensions" (p. 298). However, in axiom 1 this assumption wasrestricted to opposed basic feelings directed at the same simple object (as defined inDl). ,3

This restriction can be justified as follows. First, it is clear that Wundt would not haveaccepted the axiom without some kind of restriction of its domain of application; i.e., hewould not have accepted without qualification the claim that one cannot simultaneouslyexperience opposed basic feelings. For he explicitly posited the existence of "conflicting"feelings, such as the feeling induced by tickling (Wundt, 1896, p. 192), fearful anticipa-tion, and nostalgia (Wundt, 1910, p. 331). According to Wundt, these feelings are causedby sensation-complexes, of which some components elicit pleasure, whereas others elicitdispleasure. This may suggest that the bipolarity axiom should be restricted to the "total"basic feelings elicited by a given object (cf. axiom 2 discussed below). However, thisrestriction of the bipolarity axiom would be incorrect. For although Wundt held that allpartial feelings which exist at a given moment are ultimately fused into a total feeling(Wundt, 1896, p. 198), including the fusion of partial feelings of opposed character (p.192), he also claimed that the total feeling resulting from the fusion of pleasure anddispleasure "cannot itself be called a feeling of either pleasure or displeasure" (p. 191).That is, Wundt rejected the idea that the pleasure and displeasure feelings elicited by a

160 R- Reisenzein

complex object are "summed" into an overall feeling of (dis-)pleasure, analogous to theintegration of the perceived positive and negative aspects of a state of affairs into anoverall evaluation. This "resistance to summation" of emotions has in fact been repeated-ly posited as a characteristic difference between emotions and evaluative judgments (e.g.,Robinson, 1983). The bipolarity axiom turns out all right, however, if it is restricted tosimple objects, at least if OBJECTS is interpreted as a set of sensations and ideas. ForWundt assumed indeed that sensations (i.e., the sensory elements of consciousness)cannot simultaneously elicit opposed basic feelings. The restriction of axiom 1 to simpleobjects is however also plausible if OBJECTS is interpreted as a set of propositions. Inthis case, the restriction means that people do not experience opposed basic feelingstoward those currently entertained propositions that are atomic in the given context; i.e.,those which constitute the person's most fine-grained conceptualization of the situation.

Axiom 1 remains silent about why people don't simultaneously experience opposedfeelings toward simple objects, a question which Wundt (1896) also failed to answer.However, it seems that the reasons could be either conceptual or nomological. A concep-tual explanation of bipolarity may be most adequate for the dimension of excitement-inhi-bition (or excitement-tranquillizatiori), which is similar to the arousal dimension postulatedby several contemporary emotion theorists (e.g., Russell, 1980). That is, this dimensionmay refer to an intrinsically unidimensional phenomenal quality, ranging from low tohigh arousal, which is only conceptually represented by bipolar concepts, with "excitement"representing above-baseline (resting-state) levels of arousal,. and "inhibition" below-baseline levels. An analogous explanation may also be possible for tension-relaxation,which is in any case difficult to distinguish, both conceptually and empirically, fromexcitement-inhibition (cf. Titchener, 1908; but see also Wundt, 1910, p. 347). In contrast,with regard to the pleasure-displeasure dimension, it seems more plausible to assume thatit reflects the operation of two distinct mechanisms which produce, respectively, pleasureand displeasure feelings; the perceived opposed character of pleasure and displeasuremay then be due either to the fact that these two mechanisms mutually inhibit each other(e.g., Diener & Iran-Nejad, 1986), or that they are aroused by mutually incompatiblecauses.

Finally, note that axiom 1 provides a "justification" for the definition of the threedimensions of emotion, pleasure-displeasure (PD), excitement-inhibition (EI), andtension-relaxation (TR) introduced in D4.1 to D4.3. There, the dimension values weredefined as the difference of the values of the two basic feelings combined into therespective dimensions [e.g., PD(o) = P(o) - D(o)]. Axiom 1 guarantees that the combi-nation of the values of the basic feeling functions into the dimension values by the sub-traction operation is a unique (one-one) function. Hence, for example, if one knows avalue of PD, one can always recalculate the values of the "combined" functions P and Dand thus, no information about the basic feelings (toward simple objects) is lost if theyare combined into the dimensions. Without the restriction imposed by axiom 1 on thebasic feelings toward simple objects, the function PD would for example take on thevalue 0 for all value combinations of P and D for which P(o) = D(o).


3.4.2 Axiom (2)

According to Wundt, fused feelings (i.e., the elements at AFFECTS in the present recon-struction) are always either fusions of basic feelings, or fusions of other fused feelings. Inthe latter case, their components are themselves either fusions of basic feelings or fusionsof "lower-level" affects, and so on down to their most basic constituents, which are alwaysbasic feelings. However, as noted in the informal description of Wundt's theory, Wundtremained somewhat vague about the principles that govern this fusion process, and heapparently assumed that it can vary to some degree from one affect to the other andpossibly also for the same affect at different times. This suggests that the quality andintensity of nonbasic (fused) feelings is difficult to predict, and hence that it is difficultto reconstruct this part of the theory. However, I think that the apparent complexitysuggested by Wundt is largely illusory, and that all that is important about the fusion offeelings can be captured by two axioms, which concern, respectively, the fusion of basicfeelings of the same quality toward different objects (axiom 2); and the fusion of basicfeelings of different quality toward the same object into a "new", nonbasic affectivequality (axiom 3).

To motivate axiom 2, consider the case where somebody experiences basic emotionsof just a single quality B toward two different objects, o, and or For example, Franziskamight be simultaneously displeased that she missed her train (o,), and also displeased thatshe lost her wallet (oy). It is reasonable that the quality of the total feeling resulting fromthe fusion of these two displeasure feelings - if such a fusion takes place at all, whichaccording to Wundt's (1896, p. 198) principle of the unity of the affective state shouldhowever always be the case - is also displeasure. Less evident is how the intensity of thetotal feeling is determined. I assumed that it is simply the sum of the intensities of thecomponent feelings, because this seemed to be the most reasonable of the simplerprinciples of affect integration that come to mind. It is, for example, in accord with theeveryday observation that pleasures or displeasures can "accumulate". In contrast, forexample, the assumption that the intensity of the total displeasure is the arithmetic meanof the component displeasures would imply that it is always equal to or less than themaximum displeasure intensity experienced toward any component object. This isintuitively implausible.

Axiom 2 consists of, on the one hand, a generalization of these assumptions to caseswhere further basic feelings of different quality toward the same object are also present,and on the other hand, a restriction to those cases in which the objects of the basicfeeling qualities, o, and ojy have no components in common (cf. D2.2). (For the casewhere o, and ot do have common components, see the theorem given below). This re-striction was necessary, first, to avoid a logical inconsistency. For the assumed idempo-tency of the operation © [i.e., (o, © o,) = ot] entails that B{ot® ot) = B(pt). If axiom 2were unconditionally valid, it would permit the deduction that B{o, © o,) is equal to B(p{)+ B{ot) = 2 B(o-\ thus leading to a contradiction. Apart from this, however, theproposed restriction of axiom 1 is intuitively compelling, both if OBJECTS is interpretedas a set of propositions, and if it is interpreted as a set of sensations. As to the first case,it is for example intuitively clear that the intensity of Franziska's displeasure that she

162 R. Reisenzein

missed her train AND missed her train, B(Oj © o,), should be equal to the intensity of herdispleasure that she missed her train, #(<?,); after all, she missed her train only once. IfOBJECTS is interpreted as a set of sensations, B(ot) and B(o}-) can be regarded as thosecomponents of the total feeling intensity, £(<?,• © o;), that were caused by the sensationsot and Oj, respectively; and axiom 2 claims that the various sensory causes of emotionscontribute to the total emotion intensity in a strictly additive fashion. The requirementthat <oi,oj> ( CC is again plausible in this case, because the common components oftwo objects should not contribute twice to the total intensity of the basic feelings.

A possible objection to axiom 2 is that the generalization from situations where onlysame-quality feelings are experienced to the general case is unwarranted. This objectioncould be supported by pointing out that Wundt did not explicitly say that coocurringbasic feelings of the same quality are always fused into "total" basic feelings, and that hispertinent remarks actually suggest the opposite (such a fusion happens in some, but notin all cases). This objection is acknowledged, but I do not consider it decisive. For evenif one accepts it, one can still hold on to the present formulation of axiom 2 by claimingthat the basic "totals" in such cases are to be understood as intervening variables whichrepresent the intensity of the total basic feelings which the person would have experiencedif the corresponding fusion had taken place.

The intensity of the "total" basic emotional reactions to objects which do have com-mon components can be derived from axiom 2 and the assumed properties of the opera-tion © according to the following theorem:

VB e BASICS Wo € OBJECTS:<o,,Oj> G CC -5(o, . ooj) = B(o,) 4- B(pj) - B(MC(oi)Oj));

i.e., as the sum of the intensities of the basic feelings toward the individual objects minusthat toward their maximal common component (as defined in D2.3).

Proof: Let AfC(<? ,•,<?,) be ok, and let o, = {ok © o,) and Oj = (ok © om). Then, fromaxiom 2 we get B(o}) = B(ok © o,) = B{ok) + B{o,), and B(oj) = B(ok © om) = B(ok)+ B(om). Furthermore, 2?(o, © Oj) = B((ok © o,) © (ok © om)) = B(ok © o, © om). Becau-se ok,o, and om have no common components, this is equal to B(ok) + B(o,) + B(om)according to axiom 2. But this is again equal to £(<?,) + B(oj) - B{ok) - B{ot) + B{p)-B(MC(oi)Oj)).n

Axiom 2 can furthermore be easily generalized, by means of induction, to cases of nobjects. Let O = {ouo2,...,on} c OBJECTS be a set of n objects which have no compo-nents in common, i.e., for all <o,, o, > e O, <oit os > £ CC. Then

VB s BASICS: B{ox © o2 ©...© o, ©...© on) = £i - i

And because all complex objects are ultimately concatenations of simple objects, the totalbasic feeling reaction B toward a complex object is equal to the sum of the feelings Btoward the simple objects which make up the complex object.


3.4.3 Axiom (3)

Axiom 3 conveys the central assumption of Wundt's theory, namely, that each nonbasicfeeling quality (each A e AFFECTS) is a "fusion" of two or more of the basic feelings(the B e BASICS); or expressed differently and somewhat more generally, that thenonbasic feeling qualities can be reduced to the six basic ones. The formalization of thisassumption required again some degree of reconstruction, because Wundt (1896) was notfully explicit about the precise form of the reduction of nonbasic to basic emotions.However, I think that the proposed reconstruction can be justified.

At the very least, the general schematic form of axiom 3 should be unproblematic.For, given that the basic feelings B and the nonbasic feelings A are represented in thereconstruction by numerical functions defined on the same domain (OBJECTS), it isnatural to formalize Wundt's assumption of the "reducibility" of the nonbasic emotionsto the basic ones by requiring that, for each nonbasic emotion A, the function valuesA{p) are determined by - or in other words, are expressible as a function $A of - thevalues of the six basic, emotion functions. In addition, one should allow for the possibilitythat-<4(0) also depends on one or several parameters px—pn (cf. Stegmuller, 1986, p.437). The general schematic form of axiom 3 is therefore: V ^ e AFFECTS V o €

(cf. definition D3.1). Note that, because neither the form of the function $A, nor theparameterspx...pn have been specified, this is strictly speaking not an axiom but only aschema of an axiom (cf. Stegmuller, 1986, p. 437); i.e., a sentential formula which cannotbe said to be true or false. However, axioms can be obtained from this schema byspecifying the function $A and the necessary parameters.

This was done in the formulation of axiom 3. Specifically, it was assumed: (a) Foreach nonbasic emotion A, the intensity of A toward an object o is greater than zero (i.e.,the emotion of quality A is experienced toward object o) if the person experiences aspecific "mixture" or proportion q(A) = <vl,v2,v3tvA,vi,v6> of the six basic feelingscharacteristic for the affect A; otherwise, A(o) - 0, i.e., the person does not experiencean emotion of that quality toward o (although she may experience an emotion of adifferent quality); and (b) as long as the basic feelings occur in the characteristic propor-tion q(A), the intensity of A increases strictly monotonically, in the sense defined in D5,with increased intensities of the basic feelings. To illustrate, assume that the affect of fearis characterized by equal amounts of displeasure and excitement, i.e., q(Fear) = <0,1/2,1/2,0,0,0>. The intensity of fear toward object o, Fear(o) is then greater than zero aslong as the person experiences equal amounts of displeasure and excitement (and noother basic emotions); otherwise, Fear(o) — 0. And as long as the proportion of basicemotions characteristic for fear is present, the intensity of fear increases with increasinglevels of displeasure and excitement. It should also be noted that - by means of generali-zing over the A € AFFECTS - axiom 3 actually summarizes a whole series of axioms (onefor each A) of the form:

î(o) = g(TBASIC(o)) if 3 a € IR+: TBASIC(o) = a • q(Ax)\ 0 otherwise;A2(o) = g(TBASIC(o)) if 3 a € IR+: TBASIC{o) = a -<7(<42); 0 otherwise; etc.

164 R. Reisenzein

In contrast to the general schematic form of axiom 3, the more specific assumptionthat nonbasic emotions are characterized by particular quantitative mixtures of basic emo-tions may seem to be more problematic as a reconstruction of Wundt's (1896) ideas.However, I think that this assumption does find sufficient basis in Wundt's writings. Forone reason, Wundt certainly gave numerous examples which are suggestive of such aninterpretation. For instance, according to Wundt the tone c elicits a feeling of "calmseriousness" or "quiet cheerfulness", which is a fusion of pleasure and tranquillization(Wundt, 1910, p. 355). Similarly, emotions such as rage or fear are explicitly said to be"mixed forms" (Wundt, 1896, p. 209); for example, rage is said to be an affect of "exciteddispleasure" (Wundt, 1896, p. 210), and joy presumably contains pleasure, excitement,and tension (Wundt, 1911, p. 201). Admittedly, Wundt did not explicitly say that thedifferent affects are uniquely related to different proportions of the basic feelings; that is,he did not explicitly formulate a quantitative version of his idea that nonbasic feelingsresult from a mixture of the basic ones. However, the mere fact that Wundt used qualita-tive language in his examples is hardly decisive, because he also used qualitative languagein the discussion of color experience even though a quantitative model was being des-cribed (cf. Hardin, 1985). More important is the consideration that a quantitative versionof the fusion axiom seems to be required by Wundt's remaining assumptions, in particu-lar the assumptions (a) that the distinctive feature of affects is their quality (Wundt,1896, p. 213); (b) that the quality of affects is determined by the basic emotions; and (c)that the number of nonbasic feelings is very large, whereas there are only six basicemotions. In addition, the proposed fusion axiom is also suggested by the analogy tocolor perception to which Wundt (e.g., 1910, p. 318) alludes (see also Hardin, 1985;Hurvich, 1981; Titchener, 1908).,4 Finally, I know of no other, more plausible inter-pretation of Wundt's fusion assumption.

3.4.4 Specializations of Axiom (3)

Axiom 3 is still not a complete specification of the axiom schema mentioned above. First,except for a number of qualitative hints, the function q was left unspecified by Wundt.Therefore, the substantive content of axiom 3 is in effect only that there exists, for eachaffect A, a unique "characteristic proportion" of basic feelings q(A), such that A(o) =(...). The form of q is however restricted by the constraint of the theory WUNDT formu-lated below, which requires that each affective quality A is assigned the same "charac-teristic proportion" q{A) of basic emotions in different potential models of the theory.Second, the function g occurring in axiom 3 is not specified any further than by therequirement that it is strictly monotonically increasing (in the sense defined in D5), acondition that is of course satisfied by a great number of specific functions. In attemptingto specify g further, the question arises whether there are additional plausible restrictionsthat could be imposed on its form. One such restriction can be gleaned from axiom 2: Itseems reasonable to require that what was postulated in axiom 2.for basic emotionsshould also be true, in a similar form, for nonbasic emotions. More precisely, it isreasonable to require that if A(ot) > 0 and A(oj) > 0, <oi,oi> € CC - A{o, © Oj) =A(o,) + A(Oj). It can be shown that the following two specifications of g fulfil this requi-rement:15


(1) g(TBASIC(p)) = E *,(*); (2) 8(TBASIC(o)) =i - l i - l

In both cases, simple geometrical interpretations of A(p) are possible: In the second case,A(p) is equal to the length of the vector TBASIC(p), i.e., the Euclidian distance of thisvector from the origin of the six-dimensional space <0,0,0,0,0,0>; in the first case,y4(o)is equal to the "City-Block" distance from the origin (see e.g., Coxon, 1982). In addition,one could either make the assumption that g has the same form (e.g., 1 or 2) for allaffects, or that different kinds of functions gug2 etc. e MON characterize differentaffects. These and further conceivable specifications of axiom 3 are however best relega-ted to specializations of WUNDT. To illustrate, I sketch one possible specialization ofWUNDT, here called WUNDT1, which assumes that the proposed specification (2) of thefunction g holds for all A e AFFECTS.

Def-TE(WUNDT1)TEiWUNDTl) is specialization 1 of the theory-element WUNDT iff there existK(WUNDT1) and IQVUNDT1) such that:(1) TEiWUNDTl) = <K(WUNDT1),I(WUNDT1)>;(2) K(WUNDT1) = <Mp(WUNDTl),M{WUNDTl),Mpp(WUNDTl),GC(WUNDTl),

GL(WUNDT1)> is the core of TEiWUNDTl);(3) I(WUNDT1) is the set of intended applications of K(WUNDT1).

The elements of the core of WUNDT1 are defined as follows:Mp(WUNDTl) = Mp(WUNDT); Mpp{WUNDTl) = Mpp(WUNDT); GC(WUNDT1) =GC(WUNDT); and GLQVUNDT1) = GL(WUNDT). Only M(WUNDT1) differs fromM(WUNDT); it is defined as follows:

Def-M(WUNDT1)x e M(WUNDT1) iff(1) x € Mp(WUNDTl);(2) x € M(WUNDT);(3) V ^ e AFFECTS V o e OBJECTS:

if 3 « e IR+: TBASICS{6) = a • q(A);A(o)i-l

6 otherwiseFinally, I(WUNDT1) c (WUNDT).

3.5 Constraints of WUNDT

Let n: AFFECTS -*• 1N+; n^4,) = i (i.e., the function n assigns to each affect/1, the index/ of its name), and let «x and ny be the two name-index functions of two arbitrary potenti-al models x and y of WUNDT.

166 R. Reisenzein

Def-GC(WUNDT)X satisfies the global constraint of the theory WUNDT (X e GC(WUNDT)) iff X satisfiesthe constraint C of WUNDT. That is, GCQVUNDT) = C(WUNDT).

Def-C(WUNDT)X satisfies the constraint C of the theory WUNDT (X e C(WUNDT)) iff(1) XzMp (WUNDT) and X ± 0;(2) V^y € AT with x = <BASICSx,ex,AFFECTS',q*> and

y = <BASICSy,&,AFFECTS',q*> VA*. € AFFECTS' VAy € AFFECTS':

The structuralist concept of constraints refers to a special kind of laws which placeadditional restrictions on the admissible models of a theory (i.e., in addition to thosecaptured by the axioms; cf. Balzer et al., 1987; Stegmiiller, 1986). One could say that,whereas the axioms of a theory characterize the models of a theory intrinsically, or asconsidered by themselves, constraints additionally characterize them relationally, that is,they specify in which relation they must stand to certain other models of the theory,usually those with which they "overlap" in some respect. Constraints are typically used toexpress assumptions of identity, constancy, or stability of properties across these "over-lapping" models of the theory.

In the case of the theory WUNDT, there is only one constraint, CiWUNDT), which istherefore identical to the global constraint GC(WUNDT) (which is defined as theintersection of all constraints). Additional constraints can however be formulated forspecializations of the theory. They will be discussed below.

3.5.1 Constraint C(WUNDT)

The cojistraint of WUNDT concerns the identity, across different potential models, of thecharacteristic proportions of basic feelings assigned to the various affects.16 For exam-ple, assume again that the affect of fear is characterized by equal amounts of displeasureand excitement; i.e., q(Fear) = <0, l/2,l/2,0,0,0>. Clearly, q(Fear) was meant byWUNDT to be the same in different models of the theory. That is, the specific mixtureof basic feelings presumably characteristic of fear should be the same for differentpeople, as well as for the same person at different times. A violation of this constraintcould arise in the case of a (partial) "affective blindness" of a person or an idiosyncraticreversal of the affective spectrum (if that's a possibility; cf. Shoemaker, 1975). Such"emotionally deviant" people are to be excluded from the domain of intended applica-tions, just as color-blind people are excluded from the domain of application of thetheory of normal color perception.17 It is later argued that q is T-theoretical; hence,C(WUNDT) is a theoretical constraint (Kuokkanen, 1989).

Condition (1) of C(WUNDT) states general conditions required by the elements of aconstraint, namely, that they are nonempty subsets of the set of potential models (cf.Balzer et al., 1987; Stegmiiller, 1986). The condition specific to the theory WUNDT iscontained in (2). Expressed semi-formally, this condition requires that for each of two


"corresponding" affect qualities A* and Ay (e.g., Fear1 and Fear") that occur in two dif-ferent potential models x andy, qx(Ax) = qy{Ay). In the fully formalized version of theconstraint, the notion of "corresponding" functions is also expressed set-theoretically. Thisinvolves a slight technical complication, because "corresponding" is not the same as"identical". Set-theoretically, functions are simply sets (of tuples) and are thus identicalwhenever they contain the same elements. Agreement in elements of two functions Ax

and A) from AFFECTS1 and AFFECTS, is however neither necessary nor sufficient forcorrespondence as here asked for. It is not necessary because, for example, Fear" andFear, will already differ whenever the sets OBJECTS' and OBJECTS, are different, or theintensities of the affects experienced toward at least one object differ. And it is notsufficient, because the functions which represent two different affects in two potentialmodels (e.g., Fear1 and Anger,) may happen to be identical by pure coincidence. What ismeant by "corresponding" functions is intensional identity, i.e., identity of the properties(e.g., fear or anger) represented by the functions. (This entails, for example, that corre-sponding functions must be measured in the same or "compatible" ways across potentialmodels). Given the present conceptual framework, functions from different potentialmodels that correspond in this sense are formally identifiable only by their name, that is,they are those pairs KAx

iyAyj> which have the same name or - what amounts to the same

in the present context - those which have the same name-index, i.e., for which / = ;.Therefore, I first defined an auxiliary function n that assigns to each affect function theindex of its name, i.e. n: AFFECTS -*• IN+; n(At) = i. I did not include this functionamong the basic concepts of the theory because it is purely auxiliary and besides meta-linguistic in character.

3.5.2 Constraints for Specializations of WUNDT

Further conceivable constraints concern (a) the temporal stability of the affective reac-tions of a given person toward the same object, and (b) the identity of the affectivereactions of different people toward the same object. At first sight, constraints of thistype may perhaps seem to be difficult to justify considering that affective reactions, evento the same objects, tend to be variable from one person to another and within oneperson over time (cf. Wundt, 1896, p. 44). Some constraints of this sort were howeverclearly assumed to exist both by Wundt (1896) and Titchener (1908). That is, bothauthors assumed that at least the affective reactions to some objects, particularly simplesensations, are fairly stable across time points and across different persons. Consideragain Wundt's (1896) example concerning his affective reactions to tones, which is alsodiscussed by Titchener (1908). Both Wundt and Titchener observe their basic and fusedaffective reactions to the tones c, e, and g. First, each tone is presented alone (c, then e,then g); next, the tones are presented as pairs (c-e, c-g, e-g); and finally, they are presen-ted as a triple (c-e-g). Presumably, this introspective experiment was also repeated severaltimes (surely Titchener [1908] repeated it: "I have, for myself, repeated the test often andagain...always...I get the same meagre affective result", p. 158). Hence, both Wundt andTitchener assumed implicitly (a) that their affective reactions to these tones across thedifferent replications of the experiment remained largely constant, as well as (b) that thebasic feelings elicited by a single tone at time tx were of the same quality and and inten-sity as those elicited by this tone when it was presented at t2 in the context of more

168 R- Reisenzein

complex tonal combinations. And Titchener (1908), who repeated Wundt's experimentseveral years after Wundt, must have assumed that neither the change of person, nor theconsiderable time span which had elapsed between the two tests of the theory, invalida-ted his observations, for he compared them with Wundt's. True, Titchener came to quitedifferent conclusions than did Wundt, but his suggestion that the reader who repeats thisexperiment for him- or herself must surely agree with his (Titchener's) observations (p.157), and "that it is fair to test the theory...by the judgment of a group of psychologicallytrained observers" (p. 158) suggests that he did not attribute his divergent results togeneral time-related changes of people's affective reactions to these-tones, nor tointerindividual differences between the observers. Although he did not explicitly say so,I think Titchener doubted whether Wundt's example was really based on careful observa-tion rather than being constructed more or less in an armchair manner to fit the theory.

Hence, at least with regard to simple sensations, considerable stability of the affectivereactions was assumed to exist by Wundt and Titchener across people and times. Thisconclusion is explicitly confirmed by Wundt (1910), who claims that an approximatelyconstant feeling is attached to some simple sensations, such as the color red or the bittertaste of quinine (p. 321). Some amount of affective constancy may however also be as-sumed to exist if OBJECTS is interpreted as a set of propositions.,8 Certainly, however,interpersonal and transtemporal constancy of emotional reactions cannot be assumed tohold for all objects which might occur in any of the potential models of WUNDT.Therefore, it would not be correct to incorporate a corresponding constraint into theglobal constraint of WUNDT. Rather, it should be incorporated into a specialization ofWUNDT. Let us call this specialized theory-element WUNDT2.

Def-C(WUNDT2)X satisfies the constraint C of the theory WUNDT2 (X € C(WUNDT2)) iff(1) X € C(WUNDT) and(2) Vx,y e X with x = <BASICSZ, *\AFFECTSX, q* > and

y = <BASICSy, ÂFFECTS", qy> Vo e OBJECTS1 n OBJECTS':p*(6) = py(o) A Dx{p) = Dy{o) A Ex{p) = Ey(p) A Ix(o) = P(o)A f ( o ) = F(o) A Rx(o) = Ry(o);

(3) Vx,y eX VAX e AFFECTS1 VAy € AFFECTSy V o e OBJECTS1 n OBJECTS':n(Ax) = n(Ay)-Ax(o)=Ay(o).

Condition (2) requires the constancy of the basic feelings toward (a restricted set of)objects across potential models (i.e., across people and time points); condition (3) theconstancy of nonbasic feelings. These conditions could in various ways be weakened, e.g.,by assuming that affective reactions remain stable only over restricted time periods, onlyfor certain people, or both; that they remain only approximately constant; that primarilytheir quality remains constant, etc. The nature of the objects for which the constraint isfulfilled (e.g., "simple sensations") cannot be formally specified; this is part of the infor-mal description of I(WUNDT2).


3.6 Links of the Theory WUNDT

To become testable, empirical theories usually presuppose certain other theories, such astheories of measurement for their basic terms. Within the structuralist framework, suchrelations of presupposition between theory-elements belonging to different theory-netsare represented by intertheoretical links. These links serve to "import" meaning, informa-tion or data from other theories T, 7" etc. to the theory considered, T. Although itwould be formally possible to construe intertheoretical links as relations that are com-pletely "external" to the theories considered, this seems often to be inappropriate,because links frequently help to define the very identity of the theory in question. Balzeret al. (1987) have therefore suggested to incorporate the essential intertheoreticalconnections of a theory into its formal core, where they are represented by the global linkGL. GL is defined as the set of all potential models of the theory T to which appropriatepotential models of other theories are connected by the various links LuL2,...,Lm rele-vant for T. In the present case, then, a potential model x of WUNDT satisfies the globallink of the theory (x e GL(WUNDT)) if 3 yuy2,...ym: <yux> € LX(WUNDT) and<y2,x> eL2(WUNDT) and...and <ym,x> e Lm{wUNDT).

For illustrative purposes, I sketch one link, LiWUNDT), assumed to exist from atheory of emotion measurement by means of rating scales, TE(EMM), to TEQVUNDT)(ignoring Wundt's [1910, p. 329] skepticism concerning the possibility of quantitativemeasurement of emotions). The elements x = <OBJECTS,MBASICS,MAFFECTS,...>oiMp(EMM) are assumed to contain at least a set of objects and two sets MBASICS ={MP,MD,ME,MI>MT,MR} and MAFFECTS = {..MA,...}, the elements of which arenumerical functions/: OBJECTS -*• IR0+ that represent actual measurements of basic andnonbasic emotions such as check-marks on rating scales." The axioms of TE(EMM) arenot needed for the formulation of L(WUNDT); their specification is relegated to anotheroccasion. However, a constraint of TE(EMM) shall be formulated which expresses thescale level required of the affect measurements. This constraint makes again use of anauxiliary function n, now defined as n: MAFFECTS -*• 1N+; n(MA,) = i.

Def-C(EMM)X satisfies the constraint C of the theory EMM (X e C{EMM)) iff(1) XzMp (EMM) A X # 0;(2) Vx,y e ^ w i t h * = <OBJECTSZ, MBASICS*,MAFFECTS*,...> and

y = <OBJECTSy,MBASICSy,MAFFECTS",...> 3 a e IR+ Vo e OBJECTS* n OB-JECTS3,: MP*(o) = a • MPy(p) A MD*^) = a • MDy(o) A ME*(p) = a • MEy(o)A MI*(o) = a -MP(p)A MT(o) = a • MV{o) A MR*(o) = a • MRy(o);

(3) V MA* e MAFFECTS* V MA] e MAFFECTSy 3 b e JR+

Vo € OBJECTS* n OBJECTS": n(MA*) = n(MAy) - MA*(o) = b • MA](o).The link from TE(EMM) to TE{WUNDT) can now be formulated as follows:

Def-L(WUNDT)<y,x> satisfies the link L from the theory of emotion measurement EMM to the theoryWUNDT (<y,x> € L(WUNDT)) iff(1) y = <OBJECTSy,MBASICSy,MAFFECTS',...> e Mp{EMM)\

770 R. Reisenzein

x= <OBJECTSX, rf,BASICS*,AFFECTS*,qx> G Mp(WUNDT);(2) OBJECTS1 = OBJECTS";(3) BASICS1 a MBASICSy;(4) AFFECTS* * MAFFECTSy.

The central conditions (3) and (4) ofDef-L(WUNDT) require that the basic and nonba-sic affect functions of WUNDT (the B* and A*) are, at least approximately (•), deter-mined by the corresponding functions MBy and MAy in the linked structures. These canbe regarded as constituting "operationalizations" of the functions Bx and A*, respectively(e.g., check-marks on rating scales). The constraint C(EMM) requires that the measure-ments MB, MA are determined up to the multiplication by a (positive) scalar. This meansthat the affect functions are measured in EMM on a ratio scale level (cf. Orth, 1974).More precisely, the basic emotion measurements MB are dependent ratio scales (cf. alsoOrth, 1987), i.e., the admissible transformations for these scales consist of the simultane-ous multiplication of the values of all six functions by the same positive real number. Thisrequirement must be made to preserve the constancy of the proportions of basic emo-tions across scale transformations. In contrast, the nonbasic emotion measurements MAare independent ratio scales. The reason for the more complicated formulation of condi-tion (3) of C{EMM) is again that the number and identity of the nonbasic emotions maydiffer in different potential models of EMM.

3.7 Partial Potential Models of WUNDT

Def-Mpp (WUNDT)x is a partial potential model of the theory WUNDT (x e Mpp(WUNDT)) iff there areOBJECTS, ©, BASICS, AFFECTS,q such that(1) x = <OBJECTS,®,BASICS,AFFECTS>;(2) <OBJECTS, ®,BASICS,AFFECTS,q> € Mp(WUNDT)(3) exactly q is WTO/DT-theoretical.

The potential models of WUNDT are those entities that can be described as set-theo-retical structures using all of the basic concepts of the theory. Partial potential models ofWUNDT are fragments of potential models that result from the latter by the omission of7-theoretical terms. Hence, the distinction between potential and partial potential modelsis based on the distinction between 7-theoretical and 7-nontheoretical terms. T-theoreti-cal terms, in turn, are those concepts of a theory T that cannot be determined in atheory-independent manner. That is, a concept / is T-theoretical iff "every determinationof.../ in any application of T presupposes the existence of at least one actual model of 7"(Balzer et al., 1987, p. 55; see also, Kuokkanen, 1989). In other words, the claim to havedetermined the value of a T-theoretical function / for an object or a tuple of objects, orto have ascertained that a T-theoretical property t is exemplified by an object or a tupleof objects, logically entails that the axioms of the theory are also fulfilled by at least oneempirical entity.

Concerning the theory WUNDT, the concepts OBJECTS, BASICS and AFFECTS seemto be 7-nontheoretical. As to OBJECTS, one can simply ask people to indicate the things


at which various emotions are directed, or one can "present" appropriate objects experi-mentally (as is in fact done in paradigmatic applications of WUNDT concerned withemotional reactions to simple sensations). As to the emotion functions, their values canbe determined by appropriate measurement instruments based on self-observation. True,the theory in the present form requires that the emotions are measurable on a ratio-scalelevel, and one may doubt whether such measurement is possible. However, I cannot seehow the axioms of the theory could be of aid to solve this problem (if it is a problem).Nor do the axioms of WUNDT provide a solution to the problem that people maysometimes be incapable of distinguishing their simultaneous affective or arousal reactionsto different objects (e.g., Reisenzein, 1983; Schwarz, 1990).

In contrast to OBJECTS and the affect functions, the quality function q appears to beJfTWDT-theoretical. For q was neither specified a priori (and it is hard to see how thiscould be done), nor can it be directly observed in any given application. What can beobserved are only the basic and nonbasic feelings directed at the different objectsconsidered by the person at the time. If an affect A is observed to occur with greaterthan zero intensity toward some object, one can then calculate the value of q for thataffect. However, for this purpose one has to rely on axiom 3. Specifically, it can beshown that axiom 3 (together with the definition of q) entails the theorem:

MA e AFFECTS Vo e OBJECTS: A(o) > 0 ~ q(A) = TBASIC{o)l E B,(p).i - l

Using this theorem, one can calculate q(A) from the observed TBASlC(p) for those caseswhere A{6) > 0. There may in fact be several such cases for a given A in a single appli-cation of a theory (e.g., when someone is simultaneously angry at two different states ofaffairs).

3.8 Intended Applications of WUNDT

A fundamental tenet of structuralism is that a theory T is not universally applicable, butonly to a certain basically open set of intended applications I(T). The elements of I(T)are empirical entities which can be described by the non-theoretical concepts of thetheory, i.e., as partial potential models of T [hence, I(T) c Mpp(T)]. I(T) is normallyanchored in a subset /0 of / containing those intended applications which are regardedas exemplary of the theory (Westmeyer, 1989a).

In the present case, I{WUNDT) contains those emotional experiences of people atgiven time points which can be described as structures <OBJECTS,®,BASICS, AF-FECTS^, hence, I(WUNDT) c Mpp(WUNDT). Inasmuch as Wundt intended his theoryto be a general theory of the structure of emotional experience, I{WUNDT) was certainlymeant to comprise at least all emotional experiences of "normal" adults.- However,Wundt's actual examples of intended applications concern nearly exclusively the emotio-nal reactions to simple sensations such as tones, colors, odors and tastes. These lattercases therefore seem to make up the set of paradigmatic examples of intended applica-tions, IQ{WUNDT), and it would be better in line with the tenets of structuralism tospecify I(WUNDT) as containing all those cases that are "sufficiently similar" to these

172 R. Reisenzein

paradigmatic examples, rather than to claim from the outset that the theory is alsoapplicable to all other emotional experiences. In fact, Izard (1971) has suggested that"the investigators, in their efforts to reduce affective stimuli to their simplest forms(tastes, smells, colors), were probably not dealing with emotional stimuli and emotionsat all. They were investigating qualities of sensation, or perhaps an aspect of whatTomkins (1962) has termed drive pleasure" (p. 86).

The description of emotional experiences as structures <OBJECTS,®,BASICS,AFFECTS> will usually require some degree of active conceptualization and idealizationby the researcher (cf. Stegmiiller, 1986, p. 26) that involves the use of more basic theo-ries, in particular theories of emotion measurement (cf. the link described above). In fact,inasmuch as only those objects and affect qualities {A € AFFECTS) are explicitly con-sidered in a partial potential model that are measured by the researcher, it can be saidthat these measurement activities in part determine the specific nature of a partialpotential model.

The empirical claim of the theory (cf. Balzer et al., 1987; Stegmiiller, 1986) can beformulated as follows: Each intended application of WUNDT (i.e., each empirical struc-ture <OBJECTS,®,BASICS,AFFECTS>) can be extended to a full potential model bysupplementing it with a quality function q in such a way that the laws, constraints andlinks of the theory are satisfied.

3.9 On the Completeness of the Reconstruction of Wundt's Theory

The question can be raised whether the present reconstruction of Wundt's structuraltheory of emotions is complete or exhaustive in the sense that all of Wundt's importantstructural assumptions about emotions have been considered. Three possible objectionsagainst this assumption will be discussed.

1. The reader may miss an axiomatic statement of Wundt's assumption that theelements of BASICS are indeed basic emotions, that is, cannot be reduced to still furtheremotions; in particular, that they cannot be reduced to one another in a manner analo-gous to that formulated in axiom 3 of Def-M(WUNDT) for the reduction of nonbasic tobasic emotions. Indeed, nothing in the present formalization explicitly prevents thispossibility. Rather, I assumed20 that the irreducibility of the basic feelings is "built into"the conceptual system, i.e., is implicitly contained in the distinction between the setsBASICS and AFFECTS. In this way, a number of difficulties associated with the formula-tion of an irreducibility axiom within the present, deterministic conceptual frameworkcould be avoided. Such an axiom could however be formulated with the help of probabi-lity theory (see below), by requiring that none of the basic emotions is entirely statistical-ly dependent on the remaining emotions. " .

2. Particularly when compared with contemporary dimensional theories of emotionalexperience, such as pleasure-arousal theory, a further axiom may appear to be missingfrom the formalization of WUNDT. Proponents of pleasure-arousal theory usually assumethat the two postulated dimensions of affect, pleasure-displeasure and arousal, are


"independent" or "orthogonal" (e.g., Russell, 1980). This independence is meant to bestochastic independence (β-independence), i.e., it is assumed that the conditional proba-bility distribution of the values on one dimension is the same for each value of the otherdimension.2. The question therefore arises whether an analogous or related assumptionwas made by Wundt (1896) with regard to his three dimensions of feeling. Certainly, thedimensions were not assumed to be completely S-dependent (this is implied by theassumption that they are not reducible to one another). On the other hand, somethinganalogous to complete S-independence was nowhere explicitly claimed by Wundt, al-though also not explicitly denied. Wundt's assumptions concerning this issue can therefo-re probably be best expressed by saying that the dimensions are independent in the sensethat all logically possible combinations of their values are also nomologically possible (let'scall this form of independence W-independence). Note that the assumption of W-indepen-dence - which is stronger than that of irreducibility, but weaker than that of S-indepen-dence - is not self-evident. For example, in his discussion of color perception, Wundt(1896) points out that maximum degrees of saturation are observed only for colorsensations of medium brightness; brighter and darker colors are always less than fullysaturated.

However, although W-independence is not the same as S-independence, it appearsthat the formalization of both assumptions requires recourse to probability theory. Tokeep the theory simple and deterministic, I therefore did not state the assumption of W-independence as an axiom.22 However, I will at least briefly sketch how the probabilisticformulation of these independence assumptions could look like.

Intuitively, the probabilistic formulation of W-independence holds that, for each ofthe possible combinations of values <u, v, w> of the three dimensions PD,TR, and EI,the probability is greater than zero that <PD(o), TR(o),EI(o)> = <u, v, w>. The assum-ption of S-independence holds that the probability of all value combinations is equal tothe product of the probabilities of the single values. The precise axiomatic statement ofthese axioms necessitates a probabilistic extension (Suck, this volume) of the potentialmodels of WUNDT, as defined in Det-Mp(WUNDT). That is, the structure <OBJECTS,©,BASICS,AFFECTS,q> must be supplemented by a probability space PS = <C1,AQ,P>. In this structure, Q is the sample space, AQ is a o-algebra [e.g., Po(Q)], and P is theprobability measure defined onAQ. The main problem is the construction of Q. Onepossibility is to choose as elements of Q the triples a> = <u, v, w> representing all combi-nations of the possible values of the dimensions PD, EI, TR. Next, three random variables

4>/>D»4>£/>4>7S: Q -*• IR are defined as follows (see also Steyer, 1989): <J>/»D(w) = <i>«>(<«,v, w>) = u; 4>£/(o>) = <J>£/(<w,v, w>) = v; and <{>„,(o>) = 4>TR(<u, v, w>) - w. With thehelp of these random variables, appropriate events - subsets of Q - can be defined towhich the probabilities are assigned. Specifically, {o>: §PD (o>) = u} represents the eventthat the person experiences a pleasure-displeasure feeling of degree u toward someobject; {&>: 4>ra(o)) = v} represents the event that the value v on the excitement-inhibi-tion dimension is exemplified by the person toward some object, and so on. The twomentioned independence assumptions can now be formalized as follows:23

W-independence:û,v,w: P({o>: $PD(<x>) = u A 4>£/(w) = v A 4)^(0)) = w}) > 0.

174 R- Reisenzein

S-independence: V u,v, w: P({o>: $PD(o) = u A 4>£/(w) = v A <j>ra(o>) = w}) =: ^ ( o > ) = u}) P({o: <J)£/(co) = v})

The further elaboration of this probabilistic extension of the present formalization mustbe left to another occasion.

3. Finally, it could be argued that condition 4 of Def-Mp(WUNDT) - which holds thatBASICS = {P, D, E, I, T, R} - should be incorporated as a further substantive axiom intothe definition of the models of the theory. For this assumption was historically by nomeans regarded as uncontroversial or as empirically untestable. On the contrary, bothwith regard to Wundt's theory (cf. Titchener, 1908) and its contemporary descendants,assumptions concerning the number of basic dimensions of feelings have stirred muchcontroversy and empirical research (see e.g., Russell, 1978).

However, if one heeds the requirement that those axioms which appear in the defini-tion of the models of a theory should state a connection between two or more of thebasic relations or.functions of the theory (Balzer et al., 1987; Stegmuller, 1986), then thecurrent condition 4 of Def-Mp (WUNDT) clearly does not qualify.

One can, however, reconcile these two apparently conflicting intuitions by realizingthat empirical tests of Wundt's theory do not begin only at the level of the models of thetheory. Rather, already the attempt to find or construct empirical entities that are(partial) potential models of the theory is, at least in part, an empirical activity that mayremain unsuccessful. This includes the possibility that, if the axiom BASICS = {P, D, E,I, T,R} is generally false - as contended by Titchener [1908], who thinks that there are atbest two basic dimensions of feelings - no empirical partial potential model of the theorycan be found at all.

4. A Sketch of the Theory-Net of Basic Emotion Theories

Wundt's theory (i.e., in the reconstruction, the theory-net consisting of the theory-ele-ment TE(WUNDT) and its specializations) is itself part of the larger theory-net of basicemotion theories, which were defined in the introduction as those theories of emotionwhich claim that the different emotional qualities can be reduced to a limited set of basicemotions. In this final section, I present a sketch of this larger theory-net.

4.1 Theory-Element TE(BASE)

The defining assumption of the theory-elements belonging to the net of basic emotiontheories is the assumption of the reducibility of nonbasic to basic emotions. Everythingelse is controversial. Therefore, only the reducibility assumption should appear in thedefinition of the models of the basic theory element of the net, TE(BASE).


Def-TE(E SE)TE(BASE is the theory-element "basic emotion theories" iff there are K(BASE) andI(BASE) such that(1) TE(BASE) = <K{BASE), T(BASE)>;(2) K(BASE) = <Mp(BASE),M(BASE)Mpp(BASE),GC(BASE),GL(BASE)> is the

theory-core of TE(BASE);(3) I(BASE) is the set of intended applications of K(BASE).

The potential models of BASE are defined as follows:

Def-Mp(BASE)x is a potential model of the theory BASE (x e Mp(BASE)) iff there are OBJECTS,®,BASICS, AFFECTS, q such that(1) x= <OBJECTS,9,BASICS, AFFECTS, q>;(2) OBJECTS, BASICS, and AFFECTS are finite, nonempty, and pairwise disjoint sets;(3) ©: OBJECTS x OBJECTS -*• OBJECTS ist an associative, commutative and idem-

potent [i.e., ®(o,o) — o] operation;(4) BASICS = {BuB2...,Bm} is a set of functions B: OBJECTS - • IR0+;(5) AFFECTS = {...,4,...} is a set of functions A: OBJECTS - • IR0+;(6) q: AFFECTS -* JRm (with m = \BASICS\) is a unique (one-one) function.As a consequence of the more general (as compared with WUNDT) characterization ofBASICS, the concept TBASIC (cf. D3.1 of WUNDT) is now defined as follows:

TBASIC: OBJECTS - • JRm0 + ; TBASIC(p) = <B,(o),...,Bm(o)>.

The models of A45£ are defined as follows:

Def-M(BASE)x is a mcxfe/ of the theory BASE (x € M(BASE)) iff(1) XGMP(BASE);(2) V^ e AFFECTS V o e OBJECTS: A(o) = $^ (ra4S/C(o),<7(,4)).

Condition (2) is essentially the axiom schema that was previously mentioned as represen-ting the general form of the fusion axiom 3 of Def-M(WUNDT), except that the parame-ters P\...pn have been reduced to one parameter, i.e., <7(4). Because (2) is an axiomschema, TE(BASE) is, strictly speaking, only a schema for a theory (for an analogouscase, cf. Diederich's [1982] structuralist reconstruction of Marx's economics, reported inStegmiiller, 1986, p. 432ff).

The general constraint of BASE, GC(BASE), can be regarded as a straightforwardgeneralization of the corresponding constraint of WUNDT. Using analogous notation, itcan be defined as follows:

Def-GC(BASE)X satisfies the general constraint of the theory BASE (X € GC(BASE)) iff X satisfies theconstraint C of BASE.

176 R- Reisenzein

Def-C(BASE)X satisfies the constraint C of the theory BASE (X e C(BASE)) iff(1) XzMp (BASE) and X * 0;(2) \fx,yeX V Ax e AFFECTSX V/1J e AFFECTS': n(Ax) = n

) K)Assuming that the various basic emotion theorist accept a general method of measu-

rement of the emotions considered in their theories, it would be reasonable to additional-ly define a link L(BASE) from a theory of emotion measurement to TE(BASE), analo-gous to L(WUNDT).

4.2 Specializations of TE(BASE)

TE(BASE) contains the common assumptions of different basic emotion theories. Thesetheories differ from one another primarily in the following respects: (a) with regard to thenumber and identity of the basic emotions that are postulated to exist; (b) whether someor all of the basic.emotions are held to form "bipolar opposites"; (c) whether the basicemotions (or dimensions) are assumed to be statistically independent; (d) whether or notthe theories, in particular the fusion assumptions, are formulated in quantitative terms orat least strongly suggest a quantitative formulation; and finally, (e) whether the theoriesexplicitly take into account the - depending on interpretation - different elicitors, orintentional objects of the emotions. The task of reconstructing the theory-net of basicemotion theories requires to deal with all of these issues. Let me address them in turn.

4.2.1 Identity of the Basic Emotions, Bipolarity Assumptions, andStatistical Independence

The present conceptual framework is easily accommodated to different numbers andkinds of basic emotions by appropriate specifications of the potential models of BASE(i.e., by appropriate specifications of the set BASICS). The set of potential models of thespecialized theory-elements is then a subset of Mp (BASE). This constitutes an instanceof specialization in the wider sense (cf. Stegmiiller, 1986, p. 101). If a bipolarity assump-tion is being made in a theory, it is simply included into the definition of the models ofthat theory; if necessary, it is restricted to a subset of the basic emotions. The issue ofstatistical independence was already discussed in the context of the formalization ofWundt's theory.

4.2.2 Qualitative Formulations

Like Wundt (1896), most basic emotion theorists use qualitative language to describetheir theories, including specifically the proposed fusion of basic emotions. However, asin Wundt's case, this does not necessarily mean that the theorists intended their theoriesto be purely qualitative; in fact, they may well have had in mind a quantitative formula-tion. If so, it is reasonable to attempt to quantify these theories in the formal recon-struction. Indeed, it can be argued that, inasmuch as emotions do have an intensity, thisfeature of emotions will ultimately have to be addressed by any basic emotion theory.


However, in some cases quantification is difficult or would at least require a sub-stantial degree of interpretational activity on the part of the reconstructionist. To illustra-te the problems that can arise if one tries to quantify the formulations of some basicemotion theorists, consider how the claim "guilt is (or results from) a mixture of joy andfear" (Millenson, 1967) could be quantified. Should it be assumed that guilt is experien-ced only if a specific quantitative "mixture" of fear and joy (e.g., 1:1) is present, analo-gously to WUNDT! If yes, what about different proportions of fear and guilt, such as 1:2,which also seem to be covered by the qualitative claim? Should one assume that arbitraryproportions of joy and fear lead to guilt as long as both basic emotions are felt at all? Ifso, how should the intensity of guilt be determined? Is it the sum or the arithmetic meanof the intensities of the basic emotions, or more generally, should one assume that thecomponent basic emotions work together in a compensatory fashion with regard to guilt(such that pne, for example, feels equal degrees of guilt if one experiences 1 unit of joyand 5 units fear, or 5 units of fear and 1 unit of joy)? Intuitively, these "mixtures" offeelings certainly feel different. Or should one assume that each specific quantitativemixture of joy and fear corresponds to a specific subtype of guilt, and hence, that "guilt"is the name of a whole class of affect functions {GX,G2,...}, with all G: OBJECTS -*•IR0+? If so, how should apparently straightforward ordinary language claims such as"John felt very guilty about p" be interpreted?

If one wants to avoid to deal with these problems for the time being - if only becauseone does not want to impute too much to the theorists - it may be preferable to leavethe theories in their qualitative form. The only problem that must be solved in this caseis the question of how to accommodate the present, quantitative conceptual frameworkto the qualitative formulations. As a matter of fact, this can be achieved rather easily asfollows: (a) The range of the functions B € BASICS and A € AFFECTS is restricted to{0,1}, with 0 representing the absence and 1 the presence of the respective basic andnonbasic emotional qualities; and (b) the axiom schema of T)ti-M(BASE) is specified toan axiom which states that there is, for each A from AFFECTS, a particular combinationof basic emotions from BASICS, such that the person has the affect A exactly if she ex-periences that "characteristic" combination of basic emotions. In more detail, the axiomcould be formulated as follows: First, the range of the quality function q is restricted to{0, l} m ; with TO being the number of basic emotions. Second, the axiom schema ofM(BASE) is specified to the following axiom:

VA G AFFECTS Vo e OBJECTS: A(o) = 1 if TBASIC(o) = q(A); 0 otherwise.

To illustrate, assume that a theory postulates four qualitative basic emotions, BUB2,B3,B4 and that a particular nonbasic emotion A is experienced whenever BX,B3 and BA

but not B2 are present. That is, A(p) = 1 exactly if TBASIC(o) = < l ,0 , l , l> . q{A) isthen simply < 1,0,1, l>.24 In this formulation of the fusion axiom, I assumed that aperson can only experience a single nonbasic emotion toward one and the same object.Specifically, if, for example, q(At) = < l ,0 , l , l> andq(A2) = <l,0,l ,0>, thenA2(o) =0 \iAx(p) > 0, i.e., the person experiences only the "more complex" emotion Ax towardo, but notA2. This assumption, which appears to be plausible in the quantitative case (cf.the theory WUNDT), may seem to be too strict in the qualitative case. That is, one may

178 R. Reisenzein

prefer to assume that the simpler affects toward an object (e.g.,A2 in the example) "con-tained" in the more complex affects (e.g., A,) are also experienced whenever the morecomplex affects are experienced. If so, the fusion axiom would have to be modifiedappropriately. Note, however, that such a modification is not absolutely necessary if itsaim is only to account for the simultaneous experience of several affects toward anobject. For this is already achieved to a fair degree with the original formulation by theassumption that different affects can be experienced toward different components of anobject. One would only have to interpret the presystematic notion of "multiple affectsdirected at object o" as "affects directed at o or components of o".

A qualitative fusion axiom for basic emotions experienced toward different objects[analogous to axiom 2 of Def-Ai\WUNDT)] could be formulated as follows:

VB € BASICS Vo 6 OBJECTS: B(o( © o}) = 1 if B(o,) = 1 VB(o;) = 1; and 0 otherwi-se.

That is, a basic emotion is experienced toward a complex object (o, © o;) wheneverthat basic emotion is experienced toward at least one of the components of (o, ®o;). Therestriction of the axiom to objects which have no common components [cf. axiom 2 ofDei-MQVUNDT)] is not necessary for the qualitative formulation, because B{ot © o,) =B(pi) according to the axiom.

4.2.2 Object-Directedness of Emotions

As mentioned previously, most basic emotion theorists including Wundt take emotionsto be intrinsically nonintentional or nonrepresentational mental states similar to sensa-tions. The connection of emotions to their objects in these theories is achieved throughthe association, specifically the causal connection, of emotions with "intellectual" ele-ments such as sensations or, more plausibly, beliefs. For example, if the object o ofJohn's anger is that Sally ruined John's tape-recorder, then "John is angry that o" is inter-preted as "John experienced an anger-feeling, which is caused by his belief that o".25

This nonrepresentational view of emotions suggests that it may be possible to do com-pletely without "intellectual" elements in a structural theory of the emotions; or formallyspeaking, that the set OBJECTS could be entirely dispensed with. Of course, there maybe cogent reasons to use a set of OBJECTS even if emotions are regarded as intrinsicallynonintentional mental states - as was argued in the case of Wundt's theory - but thesereasons may be less apparent for other basic emotion theories. In fact, in contrast toWundt, most contemporary basic emotion theorists, including the proponents of dimen-sional theories, don't even attempt to deal with the object-directedness of emotions. Forexample, they do not usually consider the case where someone experiences simultaneous-ly two instances of a basic feeling or an affect directed at different objects. As a conse-quence, they do not say whether, and if yes how, a "total" emotion results in these cases.

How should the fact that the objects or causes of emotions are not being explicitlyconsidered in most basic emotion theories be dealt with in the formal reconstruction?One possibility would be to dispense with the set OBJECTS and the operation © in


TE(BASE), as well as in all those specializations of TE(BASE) in which objects are notexplicitly considered. For those theory-elements - such as TEfWUNDT) - in which objectsare needed, the concepts OBJECTS and © would be introduced by means of a differen-tiation of the conceptual apparatus (cf. Stephan, 1989, 1990; Westermann, 1989). Thesecond possibility consists of using the more elaborated conceptual apparatus from thebeginning. At least in the present case, this second approach seemed to be preferable.First, according to the standard structuralist concept of a theory-net (i.e., a set of theory-elements that are hierarchically linked by the specialization relation; cf. Balzer et al.,1987), all theory-elements of a net should share the same conceptual apparatus. Second,using this second approach toward reconstructing the theory-net, the consequences whichresult from the neglect of objects in various theories can be systematically studied (cf. thediscussion below) and the theories can easily be expanded or modified if desired. Apossible disadvantage of this approach is that it can lead to the impression that thetheorists did, after all, explicitly consider the objects or causes of the emotions in theirtheories. However, I think that this impression can be avoided by appropriate informalexplanations.

How, precisely, the neglect of the objects or causes of emotions by a theorist ishandled within the conceptual framework of TE(BASE) depends on how one interpretsthe reasons, of the theorist for this neglect. I can think of at least three possible inter-pretations.

1. Even though a theorist does not explicitly say so, she may always have had in minda specific object or eliciting circumstance when speaking about emotions. The object ofthe emotions was only "kept constant", as it were; that is, the theorist considered anarbitrary, but fixed o* € OBJECTS and therefore did not deem it necessary to explicitlymention this object. In this case, there is no need to change the present formalization.Specifically, the central fusion axiom does not have to be changed, because this axiomconstitutes the permitted generalization from o* to all o € OBJECTS. However, simulta-neously to making this generalization, one has to decide (a) whether an axiom concerningthe fusion of basic feelings toward different objects is needed [cf. axiom 2 of Def-M(WUNDT)], and if so, how, precisely, this axiom should look like; and (b) whether a"bipolarity axiom" [cf. axiom 1 of Def-M(WUNDT)] is to be adopted, and if yes, whetherthis axiom concerns only simple objects (as in WUNDT) or all objects.

2. A theorist may implicitly assume that a person can only experience emotionstowards a single (even though arbitrary) object during the considered time interval t -perhaps because the person can only concentrate on one object at a time during / andonly attended-to objects influence emotions; or because, if the person's attention isfocused on a particular object, only that part of the total affect which is caused by thisobject is subjectively salient. This case can be handled within the present conceptualframework by requiring that \OBJECTS\ = 1. Assumptions concerning the fusion ofemotions directed toward different objects would be absent in this version of basicemotion theory, but a bipolarity axiom (if desired) could be formulated either for simpleobjects, as in WUNDT (in which case it would be reasonable to require that OBJECTS= SOBJECTS), or for all objects. A problem of this second position is that the singleconsidered object could be complex, i.e., composed of simpler objects, which could elicit

180 R. Reisenzein

different and conflicting feelings. It seems difficult to rule out such cases in principle. Inaddition, if it is assumed - as in WUNDT - that a person always experiences only onenonbasic emotion toward a given object, then the assumption \OBJECTS\ = 1 impliesthat people cannot simultaneously experience several emotions. Empirical observationsseem to speak against this conclusion (e.g., Smith & Ellsworth, 1987).26

3. Finally, some basic emotion theorists may not have explicitly considered the objectsor causes of emotions in their theories because they believe that all simultaneouslyexperienced emotions of the same quality are "fused" into an overall affect, and theywanted to deal only with the resultant total emotion. This assumption does have someplausibility if emotions are interpreted as intrinsically nonintentional, sensation-likestates, and the different B(o,) or A(oj) are interpreted as those "parts" of the totalintensity of the emotion B or A that are elicited by the various o, and op respectively [cf.the discussion of axiom 2 of Def-M(WUNDT)]. Within the present conceptual frame-work, this assumption could be formally expressed by considering only the basic andnonbasic emotion "totals".

More precisely, two cases must be distinguished. Let "oy" denote the "total object",i.e., the object that results from the concatenation of all o e OBJECTS. (Because of theassumed properties of ©, oy is of course identical with the object resulting from the con-catenation of all simple objects). If one assumes (a) that the various affects which resultfrom different components of oy - or more precisely, from the fusion of the basicemotions elicited by these components - are not experienced in addition to the affectdirected toward oy, then the total intensity of each A-t e AFFECTS is simply A,(oy).This case can therefore be handled by taking OBJECTS to be {oy}. More precisely,OBJECTS only needs to be interpreted as {oy}; oy does not have to be actually deter-mined, nor need one explicitly measure the A (and B) directed toward oy. What ismeasured are simply the "objectless" A's and B's. That is, one simply asks people, forexample, how angry they feel, and interprets the obtained function values as the intensityof the "fused" anger that exists at the time toward all objects. However, it is clear that,if one wants to test whether the so-defined "objectless" emotions are indeed fusions of thesimultaneously existing component emotions - rather than to simply presuppose this -then the set OBJECTS has again to be enlarged, and one will in effect arrive at theoriginal formulation. A problematic aspect of this position is furthermore that it impliesthat, if o, elicits an emotion of type/l, and o} an emotion of type/12, the total emotionelicited by oy = (o, © os) is always different from both Ax and A2. In addition, thisposition implies again that people can only experience a single affect (i.e., nonbasicemotion) toward an object (namely, oy) at a time.

Alternatively, (b) it could be assumed - with Wundt - that the affects which resultfrom the fusion of the basic emotions of various components of oy are experienced inaddition to those directed at oy. In this case, the "total" intensity ofy4 cannot be identi-fied with ^(Oγ).27 However, one could define, for each affect A that is experienced atall, an object oyA as oyA = ox © o2...© ok, with ox..x>k being all those objects for whichA(o,) > 0. The "total" affective reactions/4 can then be represented by A(oyA), and thecorresponding basic emotions as B{oyA). Hence, this case could be dealt with by choo-sing as OBJECTS the set ioyAi,oyAj...}. In this case, it is necessary, when measuring the


affects, to take into account the various oyAi if one wants to test the fusion axiomresulting from a specification of the axiom schema of Dcf-M(BASE). For example, onewould have to ask people to indicate first at which things they are angry, happy, or sadat the moment, and then to measure the intensities of the affects and basic emotionstoward the various objects.

TE(BASE)

(Bipolarity Axiom)

(Nondimensonal)

(Nature of B)

TEOZARD)

Specification of fusion axiom2. fusion axiomNature of BAdditional axioms

TE(2-DIMENS)

(Number of dimensions)

TEO-DIMENS)

TE(PA) TE(WATSON-TELLEGEN) TE(SCHLOSBERG) TE(WUNDT)

Further specificationof the fusion axiom /Additional constraint!

TE(WUNDT1) TE(WUNDT2)

TE(WUNDT1.1) TE(WUNDT12)

Figure 1: The theory-net of basic emotion theories

182 R. Reisenzein

4.3 Structure of the Theory-Net

Finally, it must be decided in which order additional relevant axioms are to be "added"to Def-M(BASE) or Def-Mp(BASE) to obtain the various specializations of the basictheory-element. The following order seems to be the most natural one, inasmuch as itleads to a clear hierarchical structure and also agrees with a common psychologicalclassification of basic emotion theories (e.g., Izard, 1971): (a) If a bipolarity axiom isadded to Dct-M(BASE), the resulting theory-element defines the common structure ofso-called dimensional theories; otherwise, the theories are nondimensional. However, toinclude all of the existing versions of dimensional theories, a somewhat weakened versionof the bipolarity axiom known from WUNDT should be used, according to which it is notnecessary that all basic emotions have a bipolar opposite, but only that at least one pairof opposites exists (cf. e.g., Schlosberg's [1954] theory), (b) Next, both the dimensionaland nondimensional theories are further specialized by means of different specificationsof BASICS (the set of basic emotions). Different variants of dimensional theories thatresult in this step are, for example, those by Wundt (1896), Schlosberg (1954), thepleasure-arousal (PA) theory proposed by Russell (1980), or Watson and Tellegen(1985); variants of nondimensional theories are, for example, those by Izard (1977) orMillenson (1967). (c) Further specializations -result from the specification of the fusionaxiom of M(BASE) and the addition of further axioms or constraints. Hence, the theory-net of basic emotion theories could look as in Figure 1 (links to other theories areomitted).

4.4 Three Further Elements of the Theory-Net:TE(DIMENS); TE(IZARD); and TE(SCHLOSBERG)

For illustrative purposes, three further theory-elements of the theory-net of basic emo-tion theories will be sketched.

TE(DIMENS): Dimensional Basic Emotion TheoriesDef-TE(DIMENS)x € TEiDIMENS) iix = <K(DIMENS),I(DIMENS)>, with K(DIMENS) and I(DIMENS)being defined as usual;Def-Mp(DIMENS)Mp(DIMENS) = Mp(BASE);Def-M(DIMENS)x e MiDIMENS) iff x € M(BASE) A 3 Bi,Bi € BASICSVo eSOBJECTS: B,(o) Bj(p) = 0;Def-MW(DIMENS)Mpp(DIMENS) = Mpp(BASE);Def-GC(DIMENS)GC{DIMENS) c GC(BASE);Def-GL(DIMENS)GL(DIMENS) c GL(BASE).


The following two theory-elements, TE(IZARD) and TE(SCHLOSBERG) are, respec-tively, examples of nondimensional and dimensional basic emotion theories.

TE(IZARD): Izard's Basic Emotion TheoryDef-TE(IZARD)x e TE(IZARD) iff x - <K(IZARD),I(IZARD)> with K(IZARD) a theory-core andI{IZARD) a set of intended applications; K(IZARD) and I(IZARD) are defined as usual.Def-MP(IZARD)x is a potential model of IZARD (x e Mp{IZARD)) iff(1) x € Mp(BASE);(2) BASICS = {Interest, Joy, Surprise, Distress, Anger, Disgust, Contempt, Fear, Shame,

Guilt}, with all B e BASICS being functions:B: OBJECTS -+ {0,1};

(3) AFFECTS = {.../I,-...}, with all ^ e AFFECTS being functionsA: OBJECTS - • {0,1};

(4) 4: AFFECTS -+ {0,1}10.Def-M(IZARD)x is a mode/ of /Z4flD (r e Af(/Z4flD)) iff* e Mp{IZARD) and(1) VB € &4S/CS Vo,,o7 e OBJECTS: B(p, 9 o}) = 1 if B(o.) = 1 VB(o,) = 1;(2) VA € AFFECTS V o e OBJECTS: A(p) = 1 if TBASIC{o) = q(A); 0 otherwise.

As concerns the remaining components of K(IZARD), it may be assumed thatMpp(JZARD) c MW(B>I5£); GC(IZARD) c GC(&4S£) and GL{IZARD) c GL(BASE).

Izard's (1971,1977) complete theory of emotion is much more comprehensive than its"basic emotion theory" component, of which a qualitative version is sketched here. Axiom2 of Dei-Mp(IZARD) indicates that Izard assumes the existence of 10 basic emotions;axiom 2 of Def-M(IZARD) captures Izard's assumption that a subset of the remainingemotions are combinations of two or more of the basic ones. However, in contrast toWundt, Izard does not claim that all nonbasic emotions are reducible to basic emotionsonly; for example, hate is assumed to be a combination of basic emotions and cognitions(cf. Izard, 1977, p. 97). It would be possible to further specify the set AFFECTS tocapture Izard's suggestions about which nonbasic emotions are combinations of basicones, but it may be more reasonable to leave this issue to empirical inquiry.

Going beyond what Izard explicitly says, I assumed that the axioms of the theory aremeant to apply to arbitrary o* e OBJECTS (cf. the previous discussion), and that peopleexperience a basic emotion toward a complex object (o, © o,) if they experience thatbasic emotion toward at least one of the component objects o, or ot [cf. axiom 1 of Def-M(IZARD)].

TE(SCHLOSBERG): Schlosberg's Dimensional Theoiy of EmotionsDef-TE(SCHLOSBERG)x € TE(SCHLOSBERG) iff x = <K{SCHLOSBERG),I(SCHLOSBERG)> withK{SCHLOSBERG) a theory-core and I{SCHLOSBERG) a set of intended applications,defined as usual.

184 R- Reisenzein

Def-Mp (SCHLOSBERG)x is a potential model of SCHLOSBERG (x e Mp(SCHLOSBERG)) iff(1) x e Mp(DIMENS);(2) OBJECTS = {oy}-OT {...oyAi...Y,(3) BASICS = {Pleasure, Displeasure, Activation, Attention, Rejection};(4) q: AFFECTS -+ IR2;Defined Concepts of the Theoiy SCHLOSBERGPD(o) = Pleasureip) - Displeasure(o);AtR(o) = Attention(o) - Rejection(p).Def-M(SCHLOSBERG)x is a model of SCHLOSBERG (x e M(SCHLOSBERG)) iffx e Mp(SCHLOSBERG) and(1) V o e OBJECTS:

Pleasureip) • Displeasureip) = 0 A Attentionfp) • Rejectionip) = 0;(2) Vy4 e AFFECTS 3 g V o € OBJECTS:

Ai } = /S('4cftvflriow(o)) if <PD(p),AtR(o)> = <7(/l)*• ' 10 otherwise

The function g is assumed to be strictly monotonically increasing in the usual sense,i.e., Vx,y e D^) : x < y -*g(x) < giy).

As to the remaining components of K(SCHLOSBERG), it may be assumed that theyare the same as the corresponding components of K(DIMENS).

Schlosberg's (1954) theory of emotion is a specialization of TE(DIMENS). Five basicemotions are assumed to exist, of which pleasure-displeasure and attention-rejection formbipolar opposites [axiom 1 of Def-M(SCHLOSBERG)]. The activation dimension is as-sumed to be unipolar.28 Objects of emotions are disregarded by Schlosberg (1954), soI have in this case assumed that one of the possible interpretations (2) or (3) discussedearlier applies [cf. axiom 2 of Def-M, (SCHLOSBERG)]. Therefore, the bipolarity axiomwas formulated for OBJECTS rather than SOBJECTS, and an axiom dealing with thefusion of same-quality basic emotions toward different objects was omitted. As seen fromaxiom 2 of Def-M(SCHLOSBERG), Schlosberg (1954) apparently assumes that differentemotion qualities are determined by different value combinations of pleasure-displeasureand attention-rejection, whereas the intensity of emotions is determined by the activationdimension. The plausibility of this assumption is left for the reader to decide.

To conclude, I emphasize that this sketch of the theory-net of basic emotion theoriesis only preliminary. A detailed reconstruction would undoubtedly necessitate variousmodifications. Furthermore, it would be possible in principle to extend the theory-net toinclude further, e.g. cognitive theories of the structure of emotion.


Notes

1 A previous version of this paper was presented at the 5th symposium "Psychological Theories froma Structuralist Point of View" (Bad Homburg, Nov 1-3, 1990). The present version has greatlyprofited from the comments of the participants of the symposium. For their unusally extensive andthorough comments, I would especially like to thank Wolfgang Balzer and Hans Westmeyer. Allremaining inadequacies are of course solely my own responsibility.

2 In the present article, I follow Wundt (1896) in regarding such feelings as arousal, excitement-tranquillization, and tension-relaxation as emotions (for Wundt's criteria of emotion, see Wundt,1910; Titchener, 1908; and Kutzner, 1914).

If feelings of arousal etc. are taken to be nonemotionaJ in character, then the dimensionaltheories of Wundt, Schlosberg and Russell have to be characterized as attempts to reduce emotionsto partly emotional (pleasure-displeasure) and partly nonemotional mental states. In this case, theconcept of "basic emotion theories" should be redefined to denote the set of all theories whichattempt to reduce emotions at least inter alia to basic emotions.

3 All translations from German are mine. Concerning the translation of technical terms, I stayed asclose as possible to Titchener (1908).

4 The theory is also extensively described in the second and third volume of Wundt's Grundziige derphysiologischen Psydiologie (6th edition, 1910; 1911), and in summary form in his Vorlesungen uberdieMenschen- und Tierseele (1906). However, these publications contain no essential changes of thetheory as originally presented by Wundt (1896).

5 As Titchener (1908) points out, Wundt had in fact already endorsed - if only implicitly - a similarposition in the first edition of his Physiologische Psychologie of 1874. Hence, Wundt's (1896) theorymay be regarded as a return to this earlier position.

6 Note that the terms "sensation(s)" and "feeling(s)" (as well as "emotion(s)", "cognition(s)" etc.) arepotentially ambiguous, because they can be used to refer either to types or tokens of mental states.In speaking of the sensations of blue and green, the feelings of pleasure and displeasure, or of thesix basic emotions, one is speaking about types of mental states (these can be regarded as propertiesthat are exemplified by people at certain times; cf. Kim, 1973). In contrast, when saying that sensa-tions and feelings have both a quality and an intensity, one is speaking about tokens or instances ofmental states, e.g., John's having a blue-sensation at time t, or John's experience of pleasure at time/. Mental state tokens are particulars, i.e., concrete, dated, unrepeatable events. As Wundt (1896) andTitchener (1908) point out, mental states are usually grouped into types according to their quality.

Usually, the intended meaning can be inferred from the context, but I have occasionally used theterm "feeling qualities" or "sensation types" to emphasize that types rather than tokens are meant.

7 This seems in fact to be Kutzner's (1914) interpretation of Wundt's claim that each basic emotioncategory contains many different subtypes.

8 Note that the terms for nonbasic emotions 'A","Aw 'An e tc- a r e meant to have a constant meaningacross different potential models. Hence, for example, if "A 10" means fear, then it means fear in allpotential models of WUNDT, even though, as said, AFFECTS may contain different elements indifferent potential models.

9 In the context of a graphical illustration of the system of elementary feelings, Wundt (1910, p. 299)writes that a singular feeling can be represented by a single point in the three-dimensional continu-um. However, as becomes clear from the context, in this case either a feeling-token or a quality-plus-intensity type is meant.

10 It would be possible to make this explicit in the formalization, for example by including among thebasic concepts the two singletons {/?} and {r}, whose elements represent the person and time pointconsidered in the specific intended application of the theory, and by defining the affect functions on{/?} x {t) x OBJECTS rather than on OBJECTS only. However, inasmuch as the sets {p} and {r}play no substantive role in the axioms, this would only lead to an unnecessary complication of theformalization.

11 If one decides to use exclusively the propositional interpretation of OBJECTS, it may be reasonableto supplement the conceptual framework by disjunction and negation operators to obtain a Booleanalgebra of propositions (cf. Stegmiiller, 1986, p. 397).

186 R- Reisenzein

12 I ignore here the question of whether the words chosen by Wundt (1896) to name the dimensionscan indeed be regarded as antonyms (Titchener, 1908, doubts this for Erregung-Beruhigung andSpannung-Losung). This question may however become important in the context of measurement ofthe basic emotions by means of self-reports.

13 Note that axiom 1 is logically equivalent to the less concise, but perhaps more transparent formu-lation: V o e SOBJECTS:(P(o) > 0 - D(p) = 0) A (£>(o) > 0 - P{o) = 0);(£(o) > 0 - /(o) = 0) A (/(o) > 0 - E(o) = 0);(T(o) > 0 - R(o) = 0) A (R(o) > 0 - T(o) = 0).The current, more concise formulation of axiom 1 was suggested by Wolfgang Baker.

14 Besides, the qualitative formulations of affective fusion (e.g., "rage results from a mixture of dis-pleasure and excitement") are ambiguous (cf. the discussion of the theory-net). The quantitativeformulation also resolves these ambiguities.

15 That is, given these specifications of the function g, this requirement is entailed by axioms 2 and 3.16 An interesting parallel to this constraint exists in the structuralist reconstruction of DaJtonian

stoichiometry (see Balzer et al., 1987). In this case, the constraint requires that the same chemicalsubstances are assigned identical composition formulas in different potential models.

17 In contrast, an idiosyncratic use of the ordinary-language emotion words used for the measurementof the emotions by means of self-reports would presumably have to be excluded by appropriate con-straints of the corresponding measurement theories.

18 In fact, it can be argued that, because other people's feelings cannot be directly observed, a fairdegree of interpersonal and transtemporal constancy of the affective reactions to some objects mustbe assumed to exist in order to explain how ordinary-language emotion words could have acquiredan intersubjective meaning.

19 Note that, in contrast to TE(WUNDT), the potential models, models etc. of TE(EMM) are meant torefer to a. particular person's experience of emotion at & particular time point. To keep the formaliza-tion simple, this was not explicitly considered here.

20 Following a suggestion by Wolfgang Balzer.21 Although this is not stated explicitly, S-independence is probably thought to reflect the causal

independence of the mechanisms responsible for the basic feelings.22 This seemed additionally justified by the consideration that an axiom should restrict the set of

potential models, by placing additional requirements on them. In the present case, such a restrictionwould exist, for example, if Wundt had claimed that certain combinations of values on the threedimensions do not occur. The assumption of W-independence, however, is precisely that suchrestrictions do not exist, i.e., that all combinations of values are nomologically possible. Hence, ratherthan excluding certain potential models, the assumption that the dimensions of feeling are W-independent requires that certain potential models are, or at least could be, empirically realized. Theomission of the axiom means only that the possibility is left open that certain combinations ofdimension values do not occur empirically.

23 In these formulations, I have assumed that the number of possible dimension values is at bestcountably infinite. If one makes the idealizing assumption (Hays, 1973) that the number of dimensionvalues is noncountably infinite, then probability densities have to be used in the axioms (cf. Bosch,1976).

24 It may be noted that the axiom could even be formulated using the same format as that of axiom 3of WUNDT:VA e AFFECTS Vo e OBJECTS: A(p) = 1 if 3 a e IR+: TBASICip) = a -q(A); 0 otherwise.In this case, the "characteristic proportion" q(A) of the example is < 1/3,0,1/3, l/3>, and a = 3.

25 In Wundt's theory, the "intellectual elements" (i.e., sensations and sensation-complexes) seem to bethemselves nonintentional mental states; hence it is prima facie not clear how they could explain theintentionaliry of emotions. In fact, however, Wundt identified his sensation-complexes with what arenormally called (intentional) perceptions. Thus, the problem here lies with Wundt's inadequateanalysis of perception. This consideration speaks additionally in favor of a reinterpretation ofOBJECTS as a set of propositions.


26 Adherents of position (2) could however object that these empirical findings reflect sequentialemotional experiences that occurred within a time span much longer than the considered timeinterval t. In addition, it could be assumed that people constantly "switch" back and forth betweendifferent affects. To formalize these ideas, a set of time points would be needed.

27 However, assuming that the elements of O = {ot ,o2...} have no components in common, one couldidentify the total intensity of A with Y,A(Oj).

28 It would of course have been possible to conceptually split the dimension into two parts, but theformulation of the fusion axiom is easier if one begins right away with an unipolar dimension.

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