From Bayesian epistemology to inductive logic

Inductive logic admits a variety of semantics (Haenni et al. (2011) [7, Part 1]). This paper develops semantics based on the norms of Bayesian epistemology (Williamson, 2010 [16, Chapter 7]). Section 1 introduces the semantics and then, in Section 2, the paper explores methods for drawing inferences in the resulting logic and compares the methods of this paper with the methods of Barnett and Paris (2008) [2]. Section 3 then evaluates this Bayesian inductive logic in the light of four traditional critiques of inductive logic, arguing (i) that it is language independent in a key sense, (ii) that it admits connections with the Principle of Indifference but these connections do not lead to paradox, (iii) that it can capture the phenomenon of learning from experience, and (iv) that while the logic advocates scepticism with regard to some universal hypotheses, such scepticism is not problematic from the point of view of scientific theorising.     

Linguistically invariant inductive logic

Summary Carnap's early system of inductive logic make degrees of confirmation depend on the languages in which they are expressed. They are sensitive to which predicates are, in the language, taken as primitive. Hence they fail to be linguistically invariant. His later systems, in which prior probabilities are assigned to elements of a model rather than sentences of a language, are sensitive to which properties in the model are called primitive. Critics have often protested against these features of his work. This paper shows how to make his systems independent of any choice of primitive predicates or primitive properties.The solution is related to another criticism of inductive logic. It has been noticed that Carnap's systems are too all-embracing. Hisc(h, e) is defined for all sentencesh ande. Yet for manyh ande, the evidencee does not warrant any assessment of the probability ofh. We need an inductive logic in whichc(h, e) is defined only whene really does bear onh. This paper sketches the measure theory of such a logic, and, within this measure theory, provides relativized versions of Carnap's systems which are linguistically invariant.     

Criterion-related construct validity

Established results on latent variable models are applied to the study of the validity of a psychological test. When the test predicts a criterion by measuring a unidimensional latent construct, not only must the total score predict the criterion, but the joint distribution of criterion scores and item responses must exhibit a certain pattern. The presence of this population pattern may be tested with sample data using the stratified Wilcoxon rank sum test. Often, criterion information is available only for selected examinees, for instance, those who are admitted or hired. Three cases are discussed: (i) selection at random, (ii) selection based on the current test, and (iii) selection based on other measures of the latent construct. Discriminant validity is also discussed.This work was supported in part by Grant SES-87-01890 from the Measurement Methods and Data Improvement Program of the U.S. National Science Foundation.     

Factor analysis and construct validity of the Narcissistic Personality Inventory

Three studies are reported which provide evidence for the validity of the Narcissistic Personality Inventory (NPI). Factor analysis of the NPI in Study 1 revealed four factors which were labelled: Exploitativeness/Entitlement, Leadership/Authority, Superiority/Arrogance, and Self-absorption/Self-admiration. In Study 2, scores on the NPI were correlated with basic dimensions of personality, and with relevant self-variables. Narcissism scores were positively related to dominance, exhibitionism, extraversion, self-esteem, and self-monitoring, among others; and negatively related to abasement, deference, and social anxiety, among others. Correlations between the NPI factors and personality variables are also examined. In Study 3, peer ratings of narcissism were obtained and it was found that these were strongly related to scores on the NPI. Taken together, the three studies provide considerable evidence for the construct validity of the NPI, and avenues for future research are suggested.     

An inductive exploration of the social effectiveness construct space

ABSTRACT There is no agreement regarding the nature or number of dimensions that make up the social effectiveness domain. We inductively explore the relationships between a set of social effectiveness measures with the intention of identifying an initial set of dimensions. An exploratory factor analysis of the Social Competence Inventory (SCI, Schneider, 2001 ) resulted in the identification of four factors: Social Potency, Social Appropriateness, Social Emotional Expression, and Social Reputation. A joint factor analysis between the SCI and a set of extant measures resulted in the identification of the same four factors. A fifth factor emerged when a set of scales from an emotional intelligence measure was included in the analysis, suggesting that emotional intelligence is not captured within the common factor space defined by measures of social effectiveness. This study represents a first step in the establishment of a set of common social effectiveness dimensions.     

Carnapian inductive logic for Markov chains

Carnap's Inductive Logic, like most philosophical discussions of induction, is designed for the case of independent trials. To take account of periodicities, and more generally of order, the account must be extended. From both a physical and a probabilistic point of view, the first and fundamental step is to extend Carnap's inductive logic to the case of finite Markov chains. Kuipers (1988) and Martin (1967) suggest a natural way in which this can be done. The probabilistic character of Carnapian inductive logic(s) for Markov chains and their relationship to Carnap's inductive logic(s) is discussed at various levels of Bayesian analysis.     

The construct validity of burnout

Considerable confusion exists in the burnout literature about the similarities and separateness among the constructs of burnout, depression and job satisfaction. This study examined the construct validity of burnout using Campbell & Fiske's multitrait-multimethod approach. The constructs of burnout, depression and orderliness (chosen as a discriminant construct) were assessed by three types of self-report instruments. Data were analysed for 181 females and 139 male faculty members who spent at least 50 per cent of their time in teaching. Results indicated that measures of burnout largely met Campbell & Fiske's criteria for construct validity: burnout measures possessed adequate to good internal reliability and convergent validity. However, burnout measures also correlated substantially with measures of depression. Results are discussed in terms of possible explanations for the substantial overlap that has been demonstrated among measures of burnout, depression and job satisfaction.     

On the complexity of quantifying construct validity

To validate a measure of a construct is to validate a theory: The process includes theory specification, theory elaboration, choice of methods, choice of research design, reliance on necessary auxiliary theories, and empirical observation. Evaluating the success of the process is likely to be enhanced through quantification. To date, scientists have quantified the final step of empirical observation, but earlier steps in the validation process appear more difficult to measure. In this issue, D. Westen and R. Rosenthal (2005) emphasize that threats to validity are often methodological ones that precede empirical observation. Yet, their earlier attempt to quantify construct validity focused only on the final, empirical observation step of the process. For that reason, it can produce positive results despite real theoretical and methodological threats to validity. Nonetheless, the laudable attempt by these distinguished authors to quantify construct validity reminds us of the complexity of the construct validation process.     

Conceptual complexity and construct validity

Despite a century of methodological and conceptual advances in the technology of psychosocial measurement, poor correspondence between indicators and the constructs they are intended to represent remains a limiting factor to the accumulation of scientific knowledge. Longstanding conventions in measurement may contribute to the failure to develop optimal criteria. These conventions include the focus on complex over simple constructs and the use of multi-item measures of disparate content to represent those constructs. Several arguments suggest that such a measurement model compromises the potential for developing measures that accurately reflect psychosocial phenomena. The article concludes with some preliminary suggestions concerning an alternative model that may address this construct validity problem more effectively.     

Second order inductive logic and Wilmers' principle

We extend the framework of Inductive Logic to Second Order languages and introduce Wilmers' Principle, a rational principle for probability functions on Second Order languages. We derive a representation theorem for functions satisfying this principle and investigate its relationship with the first order principles of Regularity and Super Regularity.