Objectively reliable subjective probabilities

Subjective Bayesians typically find the following objection difficult to answer: some joint probability measures lead to intuitively irrational inductive behavior, even in the long run. Yet well-motivated ways to restrict the set of reasonable prior joint measures have not been forthcoming. In this paper I propose a way to restrict the set of prior joint probability measures in particular inductive settings. My proposal is the following: where there exists some successful inductive method for getting to the truth in some situation, we ought to employ a (joint) probability measure that is inductively successful in that situation, if such a measure exists. In order to do show that the restriction is possible to meet in a broad class of cases, I prove a Bayesian Completeness Theorem, which says that for any solvable inductive problem of a certain broad type, there exist probability measures that a Bayesian could use to solve the problem. I then briefly compare the merits of my proposal with two other well-known proposals for constraining the class of admissible subjective probability measures, the leave the door ajar condition and the maximize entropy condition.The author owes special thanks to Kevin Kelly, for a number of helpful ideas for the proof of the Bayesian Completeness Theorem, as well as other aspects of the paper. Thanks also to Clark Glymour for some helpful suggestions for improvement of an earlier draft. Part of the work leading to this paper was funded by a Summer Research Grant from the University Research Institute of the University of Texas at Austin.     

Piaget's data and spearman's theory—An empirical reconciliation and its implications for academic achievement

A hierarchical simple structure factor solution was obtained for item scores from a psychometrized battery of Piagetian-type tasks individually administered to 660 kindergarten children. At the first level of factors were the Piagetian theoretical entities of seriation, classification, conservation of number, and temporal and spatial reasoning, with numeration loading on seriation and classification as indicated by the theory. At the second level were two factors identified as Piaget's logicomathematical and infralogical operations. A third-level factor was identified as a g factor. The association of the Piagetian-type tasks with kindergarden and first grade academic achievement was through the third-level g factor. The second-level factors appeared to be similar to Vernon's k:m and v:ed but, like the first level factors, made no important contribution to predicted achievement above that contributed by the g factor. A socioeconomic factor made no unique contribution to predicted first grade achievement. It was concluded that the Piagetian concrete operations variables have no unique role in the prediction of kindergarten or first grade academic achievement.     

Statistical Data and Mathematical Propositions

Statistical tests of the primality of some numbers look similar to statistical tests of many nonmathematical, clearly empirical propositions. Yet interpretations of probability prima facie appear to preclude the possibility of statistical tests of mathematical propositions. For example, it is hard to understand how the statement that n is prime could have a frequentist probability other than 0 or 1. On the other hand, subjectivist approaches appear to be saddled with ‘coherence’ constraints on rational probabilities that require rational agents to assign extremal probabilities to logical and mathematical propositions. In the light of these problems, many philosophers have come to think that there must be some way to generalize a Bayesian statistical account. In this article I propose that a classical frequentist approach should be reconsidered. I conclude that we can give a conditional justification of statistical testing of at least some mathematical hypotheses: if statistical tests provide us with reasons to believe or bet on empirical hypotheses in the standard situations, then they also provide us with reasons to believe or bet on mathematical hypotheses in the structurally similar mathematical cases.     

Contents of volume 145

Volume contents

Contents of volume 145     

Representing tools: how two non-human primate species distinguish between the functionally relevant and irrelevant features of a tool

Few studies have examined whether non-human tool-users understand the properties that are relevant for a tool's function. We tested cotton-top tamarins (Saguinus oedipus) and rhesus macaques (Macaca mulatta) on an expectancy violation procedure designed to assess whether these species make distinctions between the functionally relevant and irrelevant features of a tool. Subjects watched an experimenter use a tool to push a grape down a ramp, and then were presented with different displays in which the features of the original tool (shape, color, orientation) were selectively varied. Results indicated that both species looked longer when a newly shaped stick acted on the grape than when a newly colored stick performed the same action, suggesting that both species perceive shape as a more salient transformation than color. In contrast, tamarins, but not rhesus, attended to changes in the tool's orientation. We propose that some non-human primates begin with a predisposition to attend to a tool's shape and, with sufficient experience, develop a more sophisticated understanding of the features that are functionally relevant to tools.     

Feminist identity and program characteristics in the development of trainees’ social advocacy

Feminism, multiculturalism, and social justice (SJ) are closely related constructs, with an important shared emphasis on societal barriers and client empowerment. Yet, research on the relationships between the three variables in their links to counselor advocacy remains scarce. Employing the Input–Environment–Outcome framework, this study examined the unique contributions of 235 female trainees’ feminist identity, training environment SJ supports, and training multicultural focus in explaining trainees’ advocacy using a three-step hierarchical MMLR model. Findings revealed that all three factors were important to trainees’ advocacy. However, the extent to which each factor influenced advocacy varied. For instance, the more strongly identified trainees were with the Feminist Identity Active Commitment stage, the more likely they were to engage at all four levels of advocacy. Conversely, the more aligned trainees were with Passive Acceptance, the less likely they were to empower clients. Moreover, although both training environment SJ support and multicultural focus were influential, SJ training environment was a better predictor of trainee’s advocacy than multicultural training environment. These findings not only highlight the distinctions between SJ and multiculturalism, but also argue for the importance of SJ training in addition to multicultural training. Implications for theories, training, and practice are discussed.     

Do Religious Affirmations,Religious Commitments,or General Commitments Mitigate the Negative Effects of Exposure to Thin Ideals?

Western pressures for thinness tell women that having a thin body makes a person worthy. Two factors that may provide alternative means of self‐worth are religion and general commitment to a meaningful goal. This study experimentally tested whether religious‐affirming statements buffered against exposure to thin models for everyone, or only for women with strong religious commitment. It also examined the relationships among religious commitment, general commitment, and body satisfaction. One hundred eleven women at a religious‐affiliated college completed the commitment scales and baseline body measures. They were later randomly assigned to read one set of affirming statements, after which they then completed body measures again. Results showed that religious commitment buffered against exposure to ultrathin models. Women who were strongly religiously committed and who read religious statements that affirmed the body showed higher body esteem. Correlation results showed that general commitment was positively related to body esteem, body satisfaction, and healthy dieting. Religious commitment was positively related to body esteem and body satisfaction. Results are discussed in relation to schemas and depth of processing. Practical implications are discussed.