Manual Stereotyping as Inductive Hypothesis Testing (European Monographs in Social Psychology)

Free download. Book file PDF easily for everyone and every device. You can download and read online Stereotyping as Inductive Hypothesis Testing (European Monographs in Social Psychology) file PDF Book only if you are registered here. And also you can download or read online all Book PDF file that related with Stereotyping as Inductive Hypothesis Testing (European Monographs in Social Psychology) book. Happy reading Stereotyping as Inductive Hypothesis Testing (European Monographs in Social Psychology) Bookeveryone. Download file Free Book PDF Stereotyping as Inductive Hypothesis Testing (European Monographs in Social Psychology) at Complete PDF Library. This Book have some digital formats such us :paperbook, ebook, kindle, epub, fb2 and another formats. Here is The CompletePDF Book Library. It's free to register here to get Book file PDF Stereotyping as Inductive Hypothesis Testing (European Monographs in Social Psychology) Pocket Guide.

Book Description Publication Date: July 31, Traditional social hypotheses have a built-in tendency to verify themselves and so involuntarily resist attempts at stereotype change or correction. This is the insight demonstrated and discussed as the start point for an alternative approach to the problem of stereotyping and hypothesis testing. Stereotyping as Inductive Hypothesis Testing explicates the proposition that many stereotypes originate not so much in individual brains, but in the stimulus environment that interacts with and constitutes the social individual.

This cognitive-ecological approach is then used to analyse the different aspects of language, sign systems and communication that can implicitly govern hypothesis testing procedures and lead to circular or reinforcing outcomes. The authors describe factors in tests such as judgment, memory and expectation and go on to suggest viable ecological learning approaches to them. An original research project based on a classroom situation is used to demonstrate and verify findings.

The cognitive-ecological approach is then contextualised in relation to both the traditional approaches it can replace and the contemporary statistical sampling practices it can improve. Brewer promise of appreciable immediate benefits. The present findings have several intriguing implica- Chaiken, S. Heuristic versus systematic information processing tions. One is that people who have a chronic or dispositional and the use of source versus message cues in persuasion. Journal of tendency to experience happy states may correspondingly be Personality and Social Psychology, 39, It also remains for future Chaiken, S.

The heuristic model of persuasion. Zanna, research to identify the various situational factors that are likely J. Herman Eds. Hillsdale, NJ: Erlbaum. Accountability cues seem to provide one basis for circumvent- Chaiken, S. Heuristic and sys- tematic information processing within and beyond the persuasion ing the stereotyping tendencies of happy social perceivers. Other context. Bargh Eds. New York: Guilford Press. After many years of successfully analyzing Clark, M.

Moods and social judge- the cognitive bases of stereotyping and prejudice, it is becoming ments. Manstead Eds. Chichester, England: Wiley. Affective causes and promises to yield valuable insights into the nature of intergroup consequences of social information processing. Wyer, Jr. Srull Eds. Devine, P. Stereotypes and prejudice: Their automatic and References controlled components. Journal of Personality and Social Psychology, 56, Adelman, P.

  • Account Options.
  • The Coming Crash in the Housing Market: 10 Things You Can Do Now to Protect Your Most Valuable Investment?
  • Textbook of Pediatric Neurology!
  • Product details.
  • Book Description.
  • Stereotyping as Inductive Hypothesis Testing by Klaus Fiedler, Eva Walther -;
  • Recommend to librarian.

Facial efference and the expe- Devine, P. The role of discrepancy-asso- rience of emotion. Annual Review ofPsychology, 40, Hamil- Adorno, T. The authoritarian personality. New "Vbrk: Harper. Allwood, C. Mood and realism of confi- Devine, P. Scandi- Prejudice with and without compunction. Journal ofPersonality and navian Journal ofPsychology, 32, J. Social Psychology, 60, Emotional reactions to ethnic minorities.

  • Cross-Cultural Business Negotiations.
  • The Visible and the Invisible in the Interplay between Philosophy, Literature and Reality (Analecta Husserliana);
  • 1st Edition.
  • European Monographs in Social Psychology - Routledge.

Eu- Wyer, Jr. Dollard, J. Hamilton, D. The influ- Frustration and aggression. In Press. San Lighten, O. Journal ofPersonality and Social Isen, A. Toward understanding the role of affect in cognition. Psychology, 57, The psychology ofattitudes. Worth, Vol. TX: Harcourt Brace Jovanovich. Isen, A. Positive affect, cognitive processes, and social behav- Edwards, J. Depression and the impression- ior. Berkowitz Ed. Some factors influencing decision-making strategy and risk taking.

Clark This article is intended solely for the personal use of the individual user and is not to be disseminated broadly. Fiske Eds. Ekman, P. Autonomic ner- vous system activity distinguishes among emotions. Science, , symposium on cognition pp. Jackson, L. Cognition and affect in evalu- ations of stereotyped group members.

Journal of Social Psychology, Erber, R. Outcome dependency and attention to , Journal ofPersonality and Social Psychol- ogy, 54, Kim, H. Exercise and illusory correlation: Does arousal heighten stereotypic processes? Journal of Experimental So- Esses, V. The role of mood in cial Psychology, 24, Kruglanski, A. Lay epistemics and human knowledge. New Olson Eds. Levenson, R. W, Ekman, P. Voluntary facial Fiske, S. A continuum of impression for- action generates emotion-specific autonomic nervous system activity.

Mackie, D. Affect, cognition, and Zanna Ed. San Diego, CA: Academic Press. Forgas, J. Mood effects on decision-making strategies. Austra- Mackie, D. Processing deficits and the media- lian Journal ofPsychology, 41, Journal ofPersonality and Social Forgas, J. Affect and social perception: Research evidence Psychology, 57, Hewstone Eds. Feeling good, but not thinking ropean review of social psychology Vol. Chichester, straight: The impact of positive mood on persuasion. Forgas England: Wiley. Oxford, England: Forgas, J.

Affect in social judgments and decisions: A Pergamon Press. Zanna Ed. Stereotypes social psychology Vol. Journal Press. After the movies: The effects of Martin, L. W, Achee, J. The aversive form of racism. In Gaertner Eds. Opposites structures, defenses, racism pp.

The trouble of thinking: Activa- 74 8 , Whole No. Journal ofPersonality and Petty, R. The elaboration likelihood model Social Psychology, 60, Kirkland, S. Evidence for terror management Petty, R. Multiple roles for affect theory: II. The effects of mortality salience on reactions to those who in persuasion.

Forgas Ed. Journal ofPersonality and pp. Oxford, England: Pergamon Press. Social Psychology, 58, Stereotyping based on apparently in- Greenberg, J. Terror management and tolerance: Does mortality salience types under attention overload. Journal of Experimental Social Psy- always intensify negative reactions to others who threaten one's chology, 27, The implications of arousal effects Christianson Ed.

A cognitive-attributional analysis of stereotyp- book ofemotion and memory pp. Memory processes and social beliefs. Hamilton Ed. Feelings as information: Informational and moti- reminiscing: The role of time perspective, mood, and mode of think- vational functions of affective states. Sorren- ing. Journal ofPersonality and Social Psychology, 49, Affect and Happy and mindless, but sad and lusory correlations. Journal ofPersonality and Social Psychology, 62, smart? The impact of affective states on analytic reasoning. For- Oxford, En- Stroessner, S.

The impact of induced affect gland: Pergamon Press. Personality and So- cial Psychology Bulletin, 18, Schwarz, N. Mood and persuasion: Stroessner, S. Affect and perceived group Affective states influence the processing of persuasive communica- variability: Implications for stereotyping and prejudice. Interactive processes in group perception pp. Mood, misattribution, and judg- Academic Press. The social identity theory of in- This article is intended solely for the personal use of the individual user and is not to be disseminated broadly. Journal ojPersonality and Social Psychology, 45, Austin Eds.

How do I feel about it? The infor- of intergroup relations pp. Chicago: Nelson-Hall. Forgas Eds. A theoretical approach to sex Affect, cognition, and social behavior pp. Toronto, Ontario, discrimination in traditionally masculine occupations. Organiza- Canada: Hogrefe. Sherif, M. Groups in harmony and tension. New Tetlock, P. Accountability and complexity of thought. Sinclair, R. The influence of mood state Tetlock, P. Accountability and judgment pro- cesses in a personality prediction task.

Journal ofPersonality and So- on judgment and action: Effects on persuasion, categorization, social cial Psychology, 52, Martin Thayer, R. The biopsychology of mood and arousal. It is unlikely that any selectivity arising from this partly subjective procedure will interfere with the primary goal, namely, to elucidate unresolved issues within a unitary framework. A potentially severe problem is whether the term illusory correlation refers to a unitary phenomenon at all or whether it is but a label that unsystematically connects some phenomena and excludes others that may be equally relevant to covariation assessment.

This is, of course, a matter of definition, but definitions need not be arbitrary. The present approach assumes that illusory correlations do, in fact, represent a clearly definable class of phenomena with obvious face validity and a systematic reference to cognitive theory.

Publisher Series: European Monographs in Social Psychology

An illusory correlation is simply defined as a subjective correlation assessment that deviates systematically from an objectively presented correlation. In the simplest, qualitative case, the illusion consists in perceiving a correlation that is actually not there. In the more general case, the definition also includes overestimates, underestimates, reversals, and other distortions of "real" correlations. One might conjecture that normative statistical models may not provide an ultimate criterion of "real" correlations, but this problem can be ignored in the present context, because the experimental comparisons on which illusory correlations are based e.

This definition excludes studies based on summary statistics presented in tables or texts. Thus, the phenomenon under focus is a clearly circumscribed, homogeneous class of cognitive operations: the extraction of a statistical rule from a bivariate or multivariate series of stimuli presented over time. Typical of this cognitive task is the interplay of bottom-up stimulus-driven and top-down knowledge-driven components i. The three paradigms that are the focus of the next three subsections emerge naturally from this field of two complementary forces.

The first paradigm, expectancy-based illusory correlations, highlights the top-down influence of expectations that may override stimulus data. A typical feature of this paradigm is that meaningful stimulus materials are used, and participants' prior knowledge constitutes an essential aspect of the experimental design. In contrast, in the second paradigm, expectations are ruled out so that covariation assessment can be studied as a pure function of stimulus properties e.

In the third paradigm, the emphasis is neither on prior expectations nor on perceptual aspects of individual stimuli; rather, the typical design involves manipulations of the distribution of different stimulus subsets while holding the overall correlation constant. The very fact that research has mainly evolved in these three paradigms and that the present article focuses on these paradigms is not arbitrary but naturally reflects three facets of the dialectic interplay of old knowledge and new stimuli.

Admittedly, one might point to several other paradigms that are also highly relevant to illusory correlations but not commonly associated with this label, such as work on causal and statistical reasoning, attribution errors, or in-group favoritism. That these paradigms are not treated explicitly does not mean that they are neglected or that they would lead to divergent conclusions.

Many of these additional phenomena are easily assimilated by the three major paradigms e. Others that are of distinct theoretical value are mentioned in later sections. Many judgment and evaluation problems call for the fair and impartial assessment of empirical observations, uncontaminated by the observer's subjective beliefs or wishes.

However, the notion of expectancy-based illusory correlations highlights people's inability to keep old expectations apart from new empirical data. Accordingly, the typical research design in this paradigm pits top-down influences of prior knowledge or expectations against bottom-up influences stemming from stimulus data. However, the explicit task is only to assess the correlation in the stimulus data and to disregard prior knowledge.

Much earlier than in cognitive and social psychology, such illusory correlations were introduced as a challenge to standard procedures in diagnostics. Chapman and Chapman , were the first to demonstrate illusions in users of projective techniques such as the Rorschach inkblot test and the draw-a-person test. When presented with a series of test results e. The diagnostic stereotypes that governed these mis perceptions were so superficial and obvious cf.

Shweder, b that even laypeople could anticipate the rules used by the expert diagnosticians.

You May Also Like

After all, associating anomalous heads with intelligence or anal features with homosexuality does not require much professional expertise. A similar point was made, and most strongly articulated, by Shweder , a regarding correlations between personality traits.

When trait-relevant behaviors are observed, the trait correlations that are later memorized closely follow the semantic similarity between trait terms. In fact, semantic similarity is a better predictor of reported correlations than the actually observed statistical relations Shweder, According to Shweder, the whole endeavor of personality research may thus be grounded on an illusory network that confounds likelihood with likeness. It is worth noting that the same expectation effects that govern meaningful observation tasks in diagnostics and personality are also possible at lower levels of learning, such as classical conditioning.

Garcia and Koelling have long demonstrated that an unconditional stimulus such as sickness can be easier associated with conditional stimuli in the olfactory modality, whereas electrical shock can be more effectively paired with distinct auditory signals. In recent times, expectancy-based illusory correlations have continued to attract research interest. However, whereas the challenging idea has been extended to many domains, the basic psychological principle has received little modification.

CRC Press Online - Series: European Monographs in Social Psychology

As summarized in Table 1 , recent applications concern illusory correlations in clinical e. However, these moderator analyses are guided by pragmatic issues rather than distinct theoretical questions. In social psychology, illusory correlations have reached a prominent status in stereotype research. A stereotype is commonly defined cf. Given this analogous definition, stereotypes are special cases of expectancy-based illusory correlations. In the social domain, expectations may not always originate in semantic or epistemic knowledge; rather, they may sometimes originate in affective goals or wishful thinking.

Thus, perceivers who are themselves members of one group are typically biased to perceive correlations that assign more positive attributes to the in-group than to the out-group Brewer, A similar variant of wishful thinking can be found in self-perception. Alloy and Abramson presented their participants with a simple contingency game in which they could try to control the onset of a light by either pressing or not pressing a button. Normal participants as opposed to depressives typically overestimated the degree of control they exerted over the light onset, even when it was noncontingent.

Note that the apparatus was free of any meaning, so epistemic expectations could hardly have influenced this variant of unrealistic optimism cf. Weinstein, In any case, the literature on illusory correlations is replete with provocative and partly ingenious demonstrations of expectation effects in social and applied contexts.

However, the contribution of this prominent research field remains mainly empiristic. The fascination of this phenomenon mainly arises from its power and robustness and the irrational flavor of people's inability to keep old knowledge and new data apart. At the level of psychological theory, the impact of prior knowledge, the Kantian notion that human intelligence does not start as a tabula rasa, is simply taken for granted as an axiom or theoretical primitive. No explicit attempt is made to explain how and why it is that events that are expected to go together or resemble each other appear to be more frequent than unexpected or dissimilar pairings.

Publisher Series by cover

Note that quite heterogeneous sources of expectation were used in the studies reviewed here, ranging from stereotypical beliefs to semantic similarity, biological preparedness, and wishful thinking. Note, in particular, that no systematic distinction was made between similarity-based and expectancy-based illusory correlations. No explicit process theory seems to be required for such a fully normal expectation effect.

Implicitly, the interplay of inductive and deductive influences is assumed to follow a simple compromise: When observing the contingency between events, the intelligent organism does not start from zero but is already prepared with prior expectations rooted in older knowledge. To the extent that empirical stimulus data are incomplete, impoverished, masked, or forgotten as a consequence of imperfect memory, the resulting uncertainty gap can be filled with epistemic expectations, which afford useful default knowledge.

Within this plausible and seemingly uncontestable compromise model, there has been little controversy between competing theories, and reflections on the underlying cognitive process have been largely confined to locating the stages in the cognitive process that are sensitive to expectancies. Most experiments have emphasized the role of expectancy-driven encoding and selective recall Hamilton, ; C. Expectancy-based illusory correlations have been observed in hundreds of experiments, showing that correlation judgments under uncertainty stimulus load and memory loss reflect a compromise between actual observations and prior expectancies.

Theoretical explanations have taken for granted that expectancy-congruent biases can occur at different stages of cognitive processing information search, perception, encoding, recall, judgment, and communication , although stages may differ in sensitivity. The notion of expectancy-congruent processing is so plausible and self-evident that it is presupposed as a theoretical primitive that need not itself be explained. Cacioppo, Gardner, and Berntson have recently identified this sense of obviousness as a major block in scientific progress.

Note that the congruency concept, as a theory heuristic, is deeply rooted in a priori gestalt principles that hold not only for experimental participants but for researchers as well. If the target of observation is female, the expectancy linking females to leadership inability will cause ambiguous behavioral observations to be interpreted accordingly i. Just as balanced structures can be learned more readily than unbalanced ones de Soto, , the basic gestalt principle of congruency predicts that stimulus observations should be adjusted to preexisting expectancies.

Because the expectancy paradigm is mainly governed by the gestalt heuristic of congruency, it contributes little to cognitive theory. Neither the question of stimulus encoding and representation nor an algorithmic description of the assessment process is illuminated within this paradigm. It does not even afford an explicit model of the interaction between new stimuli and old expectancies. Incongruent, expectancy-deviant, surprising, or conflict-prone observations are particularly likely to be salient during perception, to be elaborated deeply at encoding, and therefore to be highly accessible in recall.

Although such an incongruency effect is clearly at variance with a universal congruency principle, it is rooted in an equally common gestalt metaphor, the contrast of a figure against the ground.

Recommend to librarian

Salient, distinctive stimuli that deviate markedly from the background or baseline are likely to become the focus of attention and to give rise to illusory correlations distorted toward distinctive, salient, unexpected, and attention-grabbing stimuli. Empirical evidence for this principle has developed in two paradigms.

In the other paradigm, distinctiveness refers to the contrast of outstanding stimuli against the remaining list. It is addressed in the next section. In an early investigation conducted by Jenkins and Ward , the task was to figure out the extent to which an outcome a lighted circle symbolizing "success" could be controlled by pressing one of two buttons. When the actual contingency was zero, in that both buttons had the same success rate, participants experienced more control when the constant success rate was high e.

This control illusion was obviously due to the fact that subjective contingency is mainly sensitive to the number of successful trials and rather insensitive to complementary feedback on negative trials. This bias to attend to present features more than to absent features was also highlighted by Nisbett and Ross and confirmed by numerous studies conducted since Jenkins and Ward's seminal article e.

For example, when judging therapy success, people usually consider the number of patients recovered after psychotherapy and fail to consider the rate of spontaneous recovery without psychotherapy Eysenck, Or when judging correlations between a symptom and a disease, they usually assign the greatest weight to the number of cases in which both the symptom and the disease are present Smedslund, In a similar vein, judgments of the observed impact of a cause e. Instead, the bias toward positive information is evident in the so-called density bias Allan, , showing that, when delta is held constant, judged causality or control increases with the absolute occurrence rate of the effect e.

Thus, even when an effect occurs at the same rate in the presence as in the absence of a cause, the judged contingency is higher when the constant rate is high e. Whenever one level of a dichotomous variable is more informative or diagnostic than the other level, contingency judgments will give more weight to observations representing the positive level.

As mentioned earlier, the asymmetric impact of positive versus negative information reflects a general gestalt principle: Present features e. Absent features an absent traffic sign or a missing symptom are less informative because they do not reveal the nature of what is missing Garner, However, research in this area has not made a systematic attempt to explain why, how, and under what boundary conditions positive features are more informative than negative features.

In this notation see Figure 1 , a is the number of observations in which both attributes e. Rather sophisticated methods and designs have been developed to test and quantify the impact of the four cell frequencies, based on the systematic variation of a , b , c , and d in the stimulus series Wasserman et al.

However, whereas the empirically obtained weighting rules may afford "paramorphic" models P. Hoffman, of correlation judgments, they cannot be regarded as models of the cognitive process. The extra distinctiveness of positive observations, which constitutes the major theory heuristic of this paradigm, can be considered a well-established law of inductive learning. However, aside from their implications for general learning models, these findings reveal little about the cognitive representation of positive and negative information or the underlying memory algorithm.

Moreover, the impact of expectations and content specificity, which is central to the former paradigm, is largely excluded from this paradigm in which prior knowledge is typically ruled out as a factor to be controlled experimentally. The power of distinctive, attention-grabbing events in regard to producing illusory correlations is not confined to the perceptual salience of present positive as opposed to absent negative features.

Distinctiveness may also arise from the infrequency of outstanding stimuli within a list. This variant dates back to the famous von Restorff effect. The typical task used by Hedwig von Restorff, a student of Koehler in Berlin, consisted of a series of numbers in which, say, one letter string was inserted, or pairs of nonsense syllables with singular pairs of other materials in between. In subsequent memory tests, the outstanding stimuli were shown to have a clear memory advantage. Although the von Restorff effect is rarely cited explicitly, it had a huge impact on empirical approaches to illusory correlation.

Chapman showed that the frequency of outstanding pairs of stimulus events e. In a well-known experiment conducted by Taylor, Fiske, Etkoff, and Ruderman , participants observed a videotaped group discussion in which one Black White and five White Black individuals took part or one woman man and five men women took part. The relative contribution of the less frequent type of discussant was regularly overestimated.

Likewise, McArthur reviewed research showing that salient stimulus persons are given more attention and are perceived to exert more "social causality" than less salient persons. By far the most important elaboration of the von Restorff phenomenon took place in social psychology, following the seminal work of Hamilton and Gifford Their stimulus series consisted of 26 behavior descriptions pertaining to Group A the majority and 13 behavior descriptions pertaining to Group B the minority.

The correlation between group membership and the desirability positivity of behaviors was zero in that the same ratio of positive to negative behaviors held for both groups i. As it turned out, however, the larger group was consistently associated with the predominant valence of behavior i. Minorities are, by definition, less numerous than majorities, and negative behavior is norm deviant and therefore less frequent than positive, norm-conforming behavior Taylor, Given the same ratio of prevailing positivity in large and small groups, the impressions and cognitive representations of minorities will be relatively negative.

This raises a pessimistic perspective on the problem of minority discrimination. A synopsis of relevant literature is provided in Table 3. Adopting von Restorff's gestalt notion of distinctiveness, Hamilton and colleagues cf. As a consequence, stimulus items that belong to the most distinctive category should be encoded more deeply and should therefore have a memory advantage, which is assumed to mediate the resulting illusory correlation.

Over many years, no theoretical alternative was apparent to this account, which was regarded as empirically well established. Crucial to these accounts is sample size; if positive behavior prevails by the same ratio in two groups, this prevalence will be more apparent in the larger group because of the larger number of observations or learning trials. Theoretically, this approach places illusory correlations in the context of a basic law of learning, namely, that a constant "reinforcement ratio" i.

It is not necessary to assume changes in the learning parameters i. Almost all research in this paradigm is related to judgments of majority versus minority groups. Applications of the major theory heuristic, distinctiveness, to formally analogous stimulus distributions in other content areas have been rare see Table 3. In the absence of a comprehensive cognitive model, the latent conflict with the expectancy paradigm which predicts a stronger influence of expected rather than distinctive information has not been addressed explicitly.

Nor has the relation to the second paradigm, the perceptual asymmetry of present versus absent features, been delineated systematically. With regard to the cognitive underpinnings, modern research tools of cognitive psychology have rarely been applied to substantiate the supposed memory advantage for infrequent observations as described later. Cognitive boundary conditions are only crudely apparent in the general finding that infrequency-based illusory correlations are most pronounced under suboptimal encoding conditions.

It entails the danger of being circular on the one hand and contradictory or incoherent on the other. Circularity is present when a judgment bias toward expected correlations e.

European Monographs in Social Psychology

Moreover, the contradiction between the two gestalt notions of congruency and distinctiveness cannot be discarded as merely rhetorical. Congruency implies enhanced weight given to expected information, whereas distinctiveness gives superiority to unexpected, outstanding information.

Thus, a priest's benevolent behavior should override his criminal behavior congruency , but a priest's criminality should be particularly attention grabbing, leading to an opposite judgment bias. From a metatheoretical view, it seems fair to characterize the situation as follows. Depending on what outcome is obtained in one particular context i. This post hoc feature, or hindsight reasoning, creates theoretical dissatisfaction.

What is strongly needed is a comprehensive theoretical framework that allows for the forward prediction of illusory correlations, from antecedent conditions to observed consequences. Stangor and McMillan offered an elegant solution to this problem in an elucidating meta-analysis. On the basis of signal-detection analyses, these authors drew a systematic distinction between genuine memory of original stimuli and guessing inferences involving prior knowledge.

When the experimental task relies heavily on memory for original stimuli, the deeper encoding of incongruent information determines the outcome. However, when the task invites top-down inferences from prior knowledge structures, an advantage for expectancy-congruency information becomes apparent. This solution relies on process dissociation. However, this peaceful solution of the conflict is more apparent than real.

In fact, there is evidence that expectancies affect not only final judgments but also the perception, encoding, and disambiguation of stimuli from the beginning Fiedler et al. In the preceding example, the priest's behavior is more likely to be perceived, classified, and encoded as benevolent than mean cf. Moreover, these congruency effects on memory are correlated with later judgment biases. Thus, the conflict does exist and cannot be discarded beforehand as belonging to two genuinely separate situations.

What are the properties that one would expect of a unifying theoretical framework? Three indispensable criteria are that the framework should indicate an algorithm that is valid, fertile, and noncircular.