The First-Order Theories of Dedekind Algebras

A Dedekind Algebra is an ordered pair (B,h) where B is a non-empty set and h is an injective unary function on B. Each Dedekind algebra can be decomposed into a family of disjoint, countable subalgebras called configurations of the Dedekind algebra. There are N₀ isomorphism types of configurations. Each Dedekind algebra is associated with a cardinal-valued function on omega called its configuration signature. The configuration signature of a Dedekind algebra counts the number of configurations in the decomposition of the algebra in each isomorphism type.The configuration signature of a Dedekind algebra encodes the structure of that algebra in the sense that two Dedekind algebras are isomorphic iff their configuration signatures are identical. Configuration signatures are used to establish various results in the first-order model theory of Dedekind algebras. These include categoricity results for the first-order theories of Dedekind algebras and existence and uniqueness results for homogeneous, universal and saturated Dedekind algebras. Fundamental to these results is a condition on configuration signatures that is necessary and sufficient for elementary equivalence.     

Double Agents

Jennifer Herdt's Putting On Virtue argues for the theological and normative superiority of noncompetitive accounts of divine and human agency. Although such accounts affirm the indispensability and sovereignty of divine grace they also acknowledge human agents as active participants in their own moral change. Indeed, Herdt contends we cannot coherently describe the human telos as entailing a transformation of character without affirming that human agents meaningfully contribute to that change. Nevertheless, a recurrent worry in Putting On Virtue is that persons may view their growth in virtue as a personal achievement and that the pleasure of positive self‐regard will displace disinterested—and hence truly virtuous—moral aspiration. This discussion of Herdt's volume sympathetically canvasses her argument. It then looks briefly at the reflexive structure of human agency to consider the relationship between the human telos and the transformation of character, and to encourage a more generous attitude toward positive self‐regard.     

Cognitive processing and time perception

When a visual field is presented for 40 or 80 msec and a subject is asked to judge the duration of the stimulus, judged duration is found to be less when the field is blank than when the field contains three letters, but is the same whether the three letters form a word or not. The perceived difference between “filled” and “blank” fields increases when the subject is required to memorize the presented letters. These data are consistent with a theory which assumes,inter alia, that a stimulus is analyzed by a visual information processor and a timer, that attention is shared between these processors, and that temporal judgments are based on the output of both processors.     

Effect of alcoholic intoxication on the appreciation of different types of humor

Male subjects were placed into one of three intoxication conditions (no ethanol, low dose, high dose) and were exposed to humorous segments from television programs. During manifest intoxication or the corresponding period in the no-intoxication control condition, they were exposed, in a balanced order, to a segment containing blunt (i.e., unsophisticated, raw) humor and to a segment containing subtle (i.e., sophisticated, refined) humor. Subjects' facial reactions to the humorous stimuli were unobtrusively recorded and later analyzed by judges who were naive about the experimental conditions. Subjects also rated the funniness of the segments. The perceived funniness of blunt humor was found to increase with ethanol intoxication. For subtle humor, in contrast, perceived funniness was found to decrease with intoxication. This divergent interaction of reported humor appreciation was less apparent in the analysis of facial expressiveness. Although correlations between ratings and aspects of facial expression were generally positive, clearly corroborative support for the humor appraisals was found only in the frequency of smiles in response to subtle humor.     

Becoming Religious Disbelievers: Retrospective Viewpoints

Pastoral Psychology - Religious disbelief has been increasing in the United States. Many studies have examined this phenomenon. This study examined the factors surrounding the transition to...     

The Sounds of Silence: Inferences from the Absence of Word‐of‐Mouth

While past work has explored some of the reasons why people themselves may remain silent in a group, almost no research has examined the mirror image of this question: How do consumers construe the silence of others? Do they project the opinions of the speakers in a conversation onto the silent individuals, assuming that silence signals agreement? Do they have a usual or “default” naïve theory of silence that they use to explain it across multiple contexts—i.e., “silence usually signals disagreement?” Or does silence act as a mirror, reflecting observers’ own opinions back at them? Three experiments contrasted perceivers’ estimates of conversational silence with their estimates of unknown opinions outside the conversation. Estimates of opinions outside the conversation generally followed an agreement‐with‐the‐speakers rule—the more an opinion was expressed in the group, the more consumers assumed others would support it too. In contrast, silence inside the conversation was interpreted very differently, serving as a mirror for participants’ own thoughts, even when the vocal majority favored the opposite position. Results suggest a process whereby observers project the reason they personally would have been silent in the group (given their opinion) onto silence, leading to an inference that the silents agree with the self.     

König's Infinity Lemma and Beth's Tree Theorem

König, D. [1926. ‘Sur les correspondances multivoques des ensembles’, Fundamenta Mathematica, 8, 114–34] includes a result subsequently called König's Infinity Lemma. Konig, D. [1927. ‘Über eine Schlussweise aus dem Endlichen ins Unendliche’, Acta Litterarum ac Scientiarum, Szeged, 3, 121–30] includes a graph theoretic formulation: an infinite, locally finite and connected (undirected) graph includes an infinite path. Contemporary applications of the infinity lemma in logic frequently refer to a consequence of the infinity lemma: an infinite, locally finite (undirected) tree with a root has a infinite branch. This tree lemma can be traced to [Beth, E. W. 1955. ‘Semantic entailment and formal derivability’, Mededelingen der Kon. Ned. Akad. v. Wet., new series 18, 13, 309–42]. It is argued that Beth independently discovered the tree lemma in the early 1950s and that it was later recognized among logicians that Beth's result was a consequence of the infinity lemma. The equivalence of these lemmas is an easy consequence of a well known result in graph theory: every connected, locally finite graph has among its partial subgraphs a spanning tree.     

A Comparative Analysis of the Psychological Literature on Collaboration Between Clergy and Mental-Health Professionals—Perspectives from Secular and Religious Journals: 1970–1999

A search of the psychological literature was conducted to obtain a better understanding of the issues surrounding collaboration between clergy and psychologists. An electronic search of PsycINFO for 1970–1999 ultimately yielded 52 articles in secular journals and 37 articles in religiously oriented journals that discussed collaboration. Whereas interest in collaboration peaked in religious journals during the 1980's, the number of articles on collaboration appearing in secular journals increased significantly from 1970 to 1999. Content analysis confirmed six major themes about collaboration found by A. J. Weaver, K. J. Flannelly, L. T. Flannelly, and J. E. Oppenheimer (2003). One of the most common themes was the clergy's role as frontline mental-health workers, which was mentioned significantly more often in secular than religious journals. The need for greater education and knowledge was also mentioned significantly more often in secular than religious journals. Insufficient knowledge or education was frequently seen as an obstacle to collaboration. Other factors affecting collaboration are discussed.