The Representation of Belief

I derive a sufficient condition for a belief set to be representable by a probability function: if at least one comparative confidence ordering of a certain type satisfies Scott’s axiom, then the belief set used to induce that ordering is representable. This provides support for Kenny Easwaran’s project of analyzing doxastic states in terms of belief sets rather than credences.     

An analysis of response,direction, and place learning in an open field and T maze

Rats were trained to locate food in a response, direction, or place problem on an open field located at 2 positions. In Experiment 1, both the response and direction groups solved the problem. The place group failed to solve the task in approximately 300 trials. Experiment 2 demonstrated that rats need distinguishable start points to solve a place problem when neither a response nor a direction solution is available. Findings from Experiment 3 suggest that a combination of path traveled and distinct cues help to differentiate start points. Experiment 4 replicated the findings using a T maze. These results suggest "place" solutions are difficult for rats. The data are discussed with respect to conditional learning and modern spatial mapping theory.     

Birth order effects in dominance: failure to support Sulloway's view

Contrary to Sulloway's 1996 assertion that firstborns should score higher than laterborns on measures of dominance, the dominance scores for 76 firstborn undergraduate students (50 women, 26 men) did not differ significantly from the scores of 75 laterborn students (48 women, 27 men) on the 16PF dimension of Dominance vs Submissiveness (Factor E). Further research into possible differences in performance strategies between laterborns and firstborns in childhood vs adulthood is necessary to evaluate Sulloway's theory of ordinal position definitively.     

Effects of Interspersing Additional Brief Math Problems on Student Performance and Perception of Math Assignments: Getting Students to Prefer to Do More Work

Three experiments were conducted to assess the effects of the interspersing procedure on students' mathematics performance, perceptions of mathematics assignments, and preference for mathematics assignments when more work was added. In Experiment I, college students worked computation problems from two assignments. The control assignment contained 15 three-digit by two-digit problems (3 × 2) and the experimental assignments contained 18 3 × 2 problems and 6 additional interspersed one-digit by one-digit problems (1 × 1). Students then rated the assignments and chose one for homework. Results showed significantly more students preferred (i.e., chose it for homework) the experimental assignment with the additional target (i.e., 3 × 2) and interspersed problems. Furthermore, significantly more students rated this experiment as requiring less effort and being less difficult. Moreover, students' mathematics performance was not affected by the procedure. Experiment II strengthened the internal validity by showing that students did not prefer the experimental assignment because it contained more target problems. Experiment III showed that the interspersing procedure was not powerful enough to extend findings beyond the 20% level (i.e., 40 and 60% more conditions). Results showed how the interspersing procedure could be used to encourage students to choose to do more target computation tasks. Discussion focuses on the applied value of the interspersing procedure and plausible causal mechanisms that may account for current and past findings related to student choice and interspersing brief tasks.     

Possibility and probability

Conclusion De Finetti was a strong proponent of allowing 0 credal probabilities to be assigned to serious possibilities. I have sought to show that (pace Shimony) strict coherence can be obeyed provided that its scope of applicability is restricted to partitions into states generated by finitely many ultimate payoffs. When countable additivity is obeyed, a restricted version of ISC can be applied to partitions generated by countably many ultimate payoffs. Once this is appreciated, perhaps the compelling character of the Shimony argument will be less overwhelming and the attractiveness of de Finetti's more permissive attitude will become more apparent.I want to push the permissive tendency in de Finetti still further. It seems doubtful that RUIWC should be required as de Finetti apparently suggested. It is also excessively dogmatic and restrictive to require that the credal states of ideally situated rational agents be numerically definite (Levi 1974, 1980). And de Finetti's rejection of objectivism in statistics overreached itself when he dismissed objective probabilities as meaningless metaphysical artefacts (Levi 1986). In this respect, the philosophically most important lessons de Finetti has to teach us are to be found not in his celebrated representation theorem but in his discussions of the relations between 0-probability and possibility, conditional probability and countable additivity. Perhaps, the technical issues involved are remote and pedantic. But the attitude de Finetti sought to inculcate is of profound importance.Thanks are due to Teddy Seidenfeld whose comments have improved this paper substantially. He is not to blame for its lingering defects.     

The duration and perceived intensity of sucrose taste

Thirty-two subjects judged the perceived intensity of each of four concentrations of sucrose over 2 min. Stimuli were either sipped and expectorated or flowed over the subject’s extended tongue. Ratio judgments on a line scale and category ratings were made. Sixteen of the subjects had had extensive training in judging the sensory attributes of food products, and another group of 16 subjects were untrained. The perceived intensity of sucrose rose to a peak within 5 or 10 sec, and then declined over 2 min. In both the sip and the flow conditions, the taste disappeared completely for 26 of 32 subjects. Stronger concentrations were perceived as having greater peak intensities and longer lasting taste. The differences between concentrations were enhanced when sipped rather than flowed over the tongue. Judgments of intensity and duration were largely unaffected by the training level of subjects and the use of different rating scales.