“Small” large cardinal notions in the language of ZFC are those large cardinal notions that are consistent with V = L. Besides their original formulation in classical set theory, we have a variety of analogue notions in systems of admissible set theory, admissible recursion theory, constructive set theory, constructive type theory, explicit mathematics and recursive ordinal notations (as used in proof theory). On the face of it, it is surprising that such distinctively set-theoretical notions have analogues in such disaparate and (...) relatively constructive contexts. There must be an underlying reason why that is possible (and, incidentally, why “large” large cardinal notions have not led to comparable analogues). My long term aim is to develop a common language in which such notions can be expressed and can be interpreted both in their original classical form and in their analogue form in each of these special constructive and semi-constructive cases. This is a program in progress. What is done here, to begin with, is to show how that can be done to a considerable extent in the settings of classical and admissible set theory (and thence, admissible recursion theory). The approach taken here is to expand the language of set theory to allow us to talk about (possibly partial) operations applicable both to sets and to operations and to formulate the large cardinal notions in question in terms of operational closure conditions; at the same time only minimal existence axioms are posited for sets. The resulting system, called Operational Set Theory, is a partial adaptation to the set-theoretical framework of the explicit mathematics framework Feferman (1975). The.. (shrink)

In the sole extended break from his life and varing in this way we can associate a sysied career in England, Alan Turing spent the tem of logic with any constructive ordinal. It may be asked whether such a years 1936–1938 doing graduate work at..

Logical Options introduces the extensions and alternatives to classical logic which are most discussed in the philosophical literature: many-sorted logic, second-order logic, modal logics, intuitionistic logic, three-valued logic, fuzzy logic, and free logic. Each logic is introduced with a brief description of some aspect of its philosophical significance, and wherever possible semantic and proof methods are employed to facilitate comparison of the various systems. The book is designed to be useful for philosophy students and professional philosophers who have learned some (...) classical first-order logic and would like to learn about other logics important to their philosophical work. (shrink)

State health departments are at the core of the United States public health infrastructure. Surveillance to monitor trends in disease and injury; the development, coordination, and delivery of services; and public education are some of the core functions health department employees oversee every day. As such, agencies and their employees are well positioned to inform policy decisions that affect the public’s health. However, little is known about the role of health department staff — a sizeable proportion of the public health (...) workforce — as advocates for public health policies, independent of their agency roles. Anecdotally, some health department employees with whom we have spoken expressed reluctance to engage in policy advocacy for fear of violating little known or understood agency or state rules. (shrink)

Abstract Energy typically is discussed in terms of science, technology, economics, and politics. Little attention has been given to fundamental religious and ethical questions surrounding the upcoming transition to renewable energy. The essays in this thematic section seek to redress that deficiency. This introductory essay raises some key questions and summarizes various presentations on energy and religion, as these were held at the 2010 conference of the Institute on Religion in an Age of Science (IRAS). Some presentations described the energy (...) landscape and provided data and perspectives needed for sound policy. Others raised ethical and religious considerations for energy decisions as the transition from nonrenewable to renewable sources is faced. Some posed the challenges of the energy transition to religion itself. Yet others offered examples of sustainable energy use and/or promising sources for meeting future needs sustainably. At the conclusion of the conference, presenters crafted a common “Statement on Energy and Climate Change” that includes a “Call to Action.” The “Energy Statement” follows as an appendix. (shrink)

At the onset of the COVID-19 pandemic in the United States, stay-at-home orders disrupted normal research operations. Principal investigators (PIs) had to make decisions about conducting and staffing essential research under unprecedented, rapidly changing conditions. These decisions also had to be made amid other substantial work and life stressors, like pressures to be productive and staying healthy. Using survey methods, we asked PIs funded by the National Institutes of Health and the National Science Foundation (N = 930) to rate how (...) they prioritized different considerations, such as personal risks, risks to research personnel, and career consequences, when making decisions. They also reported how difficult they found these choices and associated symptoms of stress. Using a checklist, PIs indicated those factors in their research environments that made their decisions easier (i.e., facilitators) or more difficult (i.e., barriers) to make. Finally, PIs also indicated how satisfied they were with their decisions and management of research during the disruption. Descriptive statistics summarize PIs’ responses and inferential tests explore whether responses varied by academic rank or gender. PIs overall reported prioritizing the well-being and perspectives of research personnel, and they perceived more facilitators than barriers. Early-career faculty, however, rated concerns about their careers and productivity as higher priorities compared to their senior counterparts. Early-career faculty also perceived greater difficulty and stress, more barriers, fewer facilitators, and had less satisfaction with their decisions. Women rated several interpersonal concerns about their research personnel more highly than men and reported greater stress. The experience and perceptions of researchers during the COVID-19 pandemic can inform policies and practices when planning for future crises and recovering from the pandemic. (shrink)

This book presents views of the concept of intention and its relationship to communication from three perspectives: philosphy, linguistics, and artificial intelligence. The book is a record of a workshop held in 1987.

This is a “bottom-up” paper in the sense that it draws lessons in defining disciplinary categories under study from a series of empirical studies of interdisciplinarity. In particular, we are in the process of studying the interchange of research-based knowledge between Cognitive Science and Educational Research. This has posed a set of design decisions that we believe warrant consideration as others study cross-disciplinary research processes.