Pure Logic of Many-Many Ground

A logic of grounding where what is grounded can be a collection of truths is a “many-many” logic of ground. The idea that grounding might be irreducibly many-many has recently been suggested by Dasgupta (2014). In this paper I present a range of novel philosophical and logical reasons for being interested in many-many logics of ground. I then show how Fine’s State-Space semantics for the Pure Logic of Ground (plg) can be extended to the many-many case, giving rise to the Pure Logic of Many-Many Ground (plmmg). In the second, more technical, part of the paper, I do two things. First, I present an alternative formalization of plg; this allows us to simplify Fine’s completeness proof for plg. Second, I formalize plmmg using an infinitary sequent calculus and prove that this formalization is sound and complete.     

Does learning to count involve a semantic induction?

We tested the hypothesis that, when children learn to correctly count sets, they make a semantic induction about the meanings of their number words. We tested the logical understanding of number words in 84 children that were classified as "cardinal-principle knowers" by the criteria set forth by Wynn (1992). Results show that these children often do not know (1) which of two numbers in their count list denotes a greater quantity, and (2) that the difference between successive numbers in their count list is 1. Among counters, these abilities are predicted by the highest number to which they can count and their ability to estimate set sizes. Also, children's knowledge of the principles appears to be initially item-specific rather than general to all number words, and is most robust for very small numbers (e.g., 5) compared to larger numbers (e.g., 25), even among children who can count much higher (e.g., above 30). In light of these findings, we conclude that there is little evidence to support the hypothesis that becoming a cardinal-principle knower involves a semantic induction over all items in a child's count list.     

Attitudes of high school students toward carrier screening and prenatal diagnosis of cystic fibrosis

The identification of the common mutations of the cystic fibrosis (CF) transmembrane conductance regulator gene has made it feasible to consider population-based CF carrier screening. However, the demand for such programs will depend largely on the attitudes and perceptions of the general public toward genetic testing. As part of a high school science project, we initiated studies to determine the attitudes of high school students toward carrier screening for CF and other genetic disorders. From a class of 120 biology students, 101 consented to participate in the study. Most of the students were of European ancestry and there were no known family histories of CF. Buccal swabs were obtained for PCR amplification and heteroduplex detection of the most common CF mutation (F508). The students and their corresponding buccal swabs were assigned random numbers and the results were kept confidential unless the student requested his/her test result. A questionnaire was used to assess the students' attitudes toward carrier screening and prenatal diagnosis. This questionnaire was given both before testing and after the class was informed that three individuals were carriers of the F508 mutation. Overall, the data indicate that high school students are receptive to the concepts of carrier screening and prenatal diagnosis. However, their attitudes changed considerably when informed of the possibility that they might actually be a F508 carrier, with marked increases in the level of indecision. At the conclusion of the study, very few students (5/101) requested information about their F508 carrier status.     

The effect of overlearning on transfer of training

The effect of overlearning on transfer of training on the A-B:A-B_r paradigm was studied in paired-associate learning with meaningful material (adjective pairs). One group of subjects was trained to criterion on list A-B, and two additional groups were given 100 per cent and 200 per cent overlearning on list A-B. Rate of learning list A-B_r was found to be directly related to amount of overlearning. Negative transfer on list A-B_r was found for errors with the criterion group, while positive transfer was found for the 100 per cent and 200 per cent overlearning groups. The results were consistent with previous paired-associate experiments, and with results of some maze, reversal learning experiments with infrahuman subjects.

The notation “A-B:A-B_r” will be used for the transfer paradigm in which the same stimuli and responses are used in both the original acquisition phase of paired associate learning and in the subsequent transfer of training phase. In the transfer phase, however, the responses (i.e. B) are rearranged so that they are paired with different stimuli (i.e. A). The notation “A-B:A-C” will be used for the transfer paradigm in which a new set of responses (i.e. C) are paired with the old set of stimuli in the transfer of training phase.     

The evolution of leadership during group development

This paper is based on the view that the theory of the group-as-a-whole is illuminated and clarified by a developmental perspective. Beck's theory of group development is used as the framework within which the evolution of four leadership roles across nine developmental phases are discussed. Leadership is defined as a shared function in which four participants play important roles in a dialectical process through which the structure of a group is developed, maintained, reinterpreted or modified as needed. Data are presented on verbal participation and on a sociometric questionnaire to illustrate changes in the four leaders' behavior and the members' perceptions of them across the phases of group development.