Positive modal logic

We give a set of postulates for the minimal normal modal logicK ₊ without negation or any kind of implication. The connectives are simply , , , . The postulates (and theorems) are all deducibility statements . The only postulates that might not be obvious are

Spatial metrics of integral and separable dimensions

Two experiments were conducted to investigate the relationship between dimensional integrality and the form of the combination rule or spatial metric used in a similarity judgment task. In Experiment 1, two groups of eight subjects judged the dissimilarity of all pairwise combinations of 12 rectangles differing in height and width (integral dimensions) or 12 circles differing in size and diameter orientation (separable dimensions). The dimensional organization and spatial metric of both sets of dimensions were determined. The results showed that differences in height and width contributed independently to judgments of the overall dissimilarity of rectangles and that these dimensions were combined using a Euclidean metric. In contrast, substantial interactions between circle size and diameter orientation were found. Combinations of these dimensions also appeared to violate the triangle inequality implying that no spatial metric was appropriate. In Experiment 2, parallelogram size and tilt were similarly analyzed. Although some degree of dimensional interaction was observed, it was found that on the average these dimensions were combined using a city-block metric. In a subsequent speeded classification task, orthogonal interference was observed, which suggested that size and tilt are integral dimensions. The implications of both experiments for the supposed association between the Euclidean metric and dimensional integrality are discussed.     

The rapid-smoking technique: Subject characteristics and treatment outcome

There is a lack of consistency in findings regarding subject (S) characteristics and the effects of smoking-control programmes. Research workers appear to assume that abstinence and reduction in smoking rate are merely different points in the same continuum, and therefore seek to correlate S variables with percentage reductions in smoking rate. It is argued that abstinence and reduced smoking are more appropriately viewed as potentially discrete outcomes. Conceptualizing outcome in this manner, a discriminant function analysis was employed to determine whether it is possible to differentiate between Ss who do, or do not, abstain following participation in a treatment programme involving rapid-smoking. It was found that it is possible to discriminate between the two groups of Ss. Advantages deriving from this approach to the investigation of S characteristics and treatment outcome are discussed.     

Deviation from hierarchical structure in recall: Is there an “optimal” structure?

Past research has suggested that proportionally more superordinate than sub-ordinate propositions are recalled from expository texts, following a hierarchical analysis of the text structure. Since free recall has typically followed this hierarchical pattern, several researchers have assumed that the related memory structures are isomorphic to the text structure. However, few of these studies have examined how individual differences and text structure interact to affect free recall. In two experiments, the assumption of hierarchical patterns of children's recall of expository text was tested. In Experiment 1, high- and average-ability fourth graders (9 years old) were asked to read and recall a passage. Experiment 2 was a replication and extension of Experiment 1. In this experiment, fourth and sixth graders (9 and 11 years old) read and recalled a different passage. The combined results of both experiments support the notion that there is probably no one optimal hierarchical structure for storage and retrieval of expository text.     

Relevant Robinson's arithmetic

In this paper two different formulations of Robinson's arithmetic based on relevant logic are examined. The formulation based on the natural numbers (including zero) is shown to collapse into classical Robinson's arithmetic, whereas the one based on the positive integers (excluding zero) is shown not to similarly collapse. Relations of these two formulations to R. K. Meyer's system R# of relevant Peano arithmetic are examined, and some remarks are made about the role of constant functions (e.g., multiplication by zero) in relevant arithmetic.This paper has been greatly influenced by the (largely unpublished) work of E. K. Meyer (cf. [7]) on relevant arithmetic, and I wish to thank him, and also N. D. Belnap, Jr. and D. Cohen for helpful advice. In fairness to Meyer it must be said that he finds my axioms 13 and 13(1) too strong (they are not theorems of his system R# - cf. §4 below). Meyer tells me be finds vindication for his view in my chief theorem of §2. For myself, I find the insights behind Meyer's work on R# to be both stable and fruitful, and if I now had to make a choice, I would follow Meyer in his rejection of my axioms. However, the systems I explore in this paper themselves have a surprising amount of internal consistency of motivation (cf. §5). Let a hundred formal systems bloom.     

A theorem in 3-valued model theory with connections to number theory,type theory,and relevant logic

Given classical (2 valued) structures and and a homomorphism h of onto , it is shown how to construct a (non-degenerate) 3-valued counterpart of . Classical sentences that are true in are non-false in . Applications to number theory and type theory (with axiom of infinity) produce finite 3-valued models in which all classically true sentences of these theories are non-false. Connections to relevant logic give absolute consistency proofs for versions of these theories formulated in relevant logic (the proof for number theory was obtained earlier by R. K. Meyer and suggested the present abstract development).     

COVID-19 and Religious Ethics

The editors of the JRE solicited short essays on the COVID-19 pandemic from a group of scholars of religious ethics that reflected on how the field might help them make sense of the complex religious, cultural, ethical, and political implications of the pandemic, and on how the pandemic might shape the future of religious ethics.     

Ethnography and Subjectivity in Comparative Religious Ethics

The ethnographic turn in religious studies has responded to important developments, such as the rejection of value neutrality and the need to better address the lived experience of individuals and communities. In this essay, I affirm the value of ethnography as a method in comparative religious ethics, but distinguish between two ways of framing ethnography in relation to ethics. The first way insists on the hard limits of translating values across cultures, and tends to marginalize or dismiss normative inquiry. The second way allows for the interpretation of practices of ethical justification in diverse cultural contexts. I argue that this second category of ethnography is more congenial to the work of comparative religious ethicists, since an integral part of ethical inquiry involves reflecting on, and making arguments about, social norms and practices.