This book describes a program of research in computable structure theory. The goal is to find definability conditions corresponding to bounds on complexity which persist under isomorphism. The results apply to familiar kinds of structures (groups, fields, vector spaces, linear orderings Boolean algebras, Abelian p-groups, models of arithmetic). There are many interesting results already, but there are also many natural questions still to be answered. The book is self-contained in that it includes necessary background material from recursion theory (ordinal notations, (...) the hyperarithmetical hierarchy) and model theory (infinitary formulas, consistency properties). (shrink)

In their simplest form, hybrid languages are propositional modal languages which can refer to states. They were introduced by Arthur Prior, the inventor of tense logic, and played an important role in his work: because they make reference to specific times possible, they remove the most serious obstacle to developing modal approaches to temporal representation and reasoning. However very little is known about the computational complexity of hybrid temporal logics.In this paper we analyze the complexity of the satisfiability problem of (...) a number of hybrid temporal logics: the basic hybrid language over transitive trees; nominal Until logic; and referential interval logic. We discuss the effects of including nominals, the @ operator, the somewhere modality E, and the difference operator D. Adding nominals to tense logic leads for several frame-classes to an increase in complexity of the satisfiability problem from PSPACE to EXPTIME. On transitive trees, however, the satisfiability problem for this language can be decided in PSPACE. Along the way we make a detour through hybrid propositional dynamic logic: we establish upper bounds for a number of temporal logics by generalizing results due to Passy and Tinchev [29] and De Giacomo [16]. We conclude with some remarks on the relevance of our results to description logic, and draw attention to the utility of the spypoint technique for proving upper and lower bounds. (shrink)

BackgroundResuscitation and treatment of critically ill newborn infants is associated with relatively high mortality, morbidity and cost. Guidelines relating to resuscitation have traditionally focused on the best interests of infants. There are, however, limited resources available in the neonatal intensive care unit, meaning that difficult decisions sometimes need to be made. This study explores the intuitions of lay people regarding resource allocation decisions in the NICU.MethodsThe study design was a cross-sectional quantitative survey, consisting of 20 hypothetical rationing scenarios. There were (...) 119 respondents who entered the questionnaire, and 109 who completed it. The respondents were adult US and Indian participants of the online crowdsourcing platform Mechanical Turk. Respondents were asked to decide which of two infants to treat in a situation of scarce resources. Demographic characteristics, personality traits and political views were recorded. Respondents were also asked to respond to a widely cited thought experiment involving rationing.ResultsThe majority of respondents, in all except one scenario, chose the utilitarian option of directing treatment to the infant with the higher chance of survival, higher life expectancy, less severe disability, and less expensive treatment. As discrepancy between outcomes decreased, however, there was a statistically significant increase in egalitarian responses and decrease in utilitarian responses in scenarios involving chance of survival, life expectancy, and cost of treatment. In the classic ‘lifeboat’ scenario, all but two respondents were utilitarian.ConclusionsThis survey suggests that in situations of scarcity and equal clinical need, non-health professionals support rationing of life-saving treatment based on probability of survival, duration of survival, cost of treatment or quality of life. However, where the difference in prognosis or cost is very small, non-health professionals preferred to give infants an equal chance of receiving treatment. (shrink)

C W Evers, J C Walker; Knowledge, Partitioned Sets and Extensionality: a refutation of the forms of knowledge thesis, Journal of Philosophy of Education, Volume.

Research in the fields of complex problem solving (CPS) and dynamic decision making using microworlds has been mainly conducted in Western industrialized countries. This study analyzes the CPS process by investigating thinking‐aloud protocols in five countries. Participants were 511 students from Brazil, Germany, India, the Philippines, and the United States who worked on two microworlds. On the basis of cultural‐psychological theories, specific cross‐national differences in CPS strategies were hypothesized. Following theories of situatedness of cognition, hypotheses about the specific frequency of (...) problem‐solving strategies in the two microworlds were developed. Results of the verbal protocols showed (a) modification of the theoretical CPS model, (b) task dependence of CPS strategies, and (c) cross‐national differences in CPS strategies. Participants’ CPS processes were particularly influenced by country‐specific problem‐solving strategies. (shrink)

Theories of truth and vagueness are closely connected; in this article, I draw another connection between these areas of research. Gupta and Belnap’s Revision Theory of Truth is converted into an approach to vagueness. I show how revision sequences from a general theory of definitions can be used to understand the nature of vague predicates. The revision sequences show how the meaning of vague predicates are interconnected with each other. The approach is contrasted with the similar supervaluationist approach.

We extend results of Harizanov and Barker. For a relation R on a recursive structure /oA, we give conditions guaranteeing that the image of R in a recursive copy of /oA can be made to have arbitrary ∑α0 degree over Δα0. We give stronger conditions under which the image of R can be made ∑α0 degree as well. The degrees over Δα0 can be replaced by certain more general classes. We also generalize the Friedberg-Muchnik Theorem, giving conditions on a pair (...) of relations R and S under which the images of R and S can be made ∑α0 and independent over Δα0 in a recursive copy of /oA. (shrink)

Kengo Miyazono, in his work Delusions and Beliefs, defends a teleo-functional account of delusions. In my contribution to this symposium, I question one of Miyazono’s motivations for appealing to teleo-functionalism over its main rival, dry-functionalism. Miyazono suggests that teleo-functionalism, unlike dry-functionalism, can account for the compatibility of the theses (i) that delusions are genuine doxastic states (doxasticism about delusions) and (ii) that delusions do not perform the typical causal roles of beliefs (the causal difference thesis). I argue, however, that there (...) are also ways for dry-functionalism to account for this compatibility. If what I have to say is correct, then Miyazono is perhaps too hasty—at least in one important respect—to opt for teleo-functionalism over dry-functionalism. Dry-functionalism has an equally good chance of satisfying some of Miyazono’s explanatory goals. (shrink)

Let be a recursive structure, and let R be a recursive relation on . Harizanov isolated a syntactical condition which is necessary and sufficient for to have recursive copies in which the image of R is r.e. of arbitrary r.e. degree. We had conjectured that a certain extension of Harizanov's syntactical condition would be necessary and sufficient for to have recursive copies in which the image of R is ∑α0 of arbitrary ∑α0 degree, but this is not the case. Here (...) we give examples illustrating some restrictions on the possible ∑α0 degrees. In these examples, the image of R cannot be ∑α0 of degree d unless d possesses an “α-table”. (shrink)

Peter C. Hodgson engages the speculative reconstruction of Christian theology that is accomplished by Hegel's Lectures on the Philosophy of Religion, and provides a close reading of the critical edition of the lectures. He analyses Hegel's concept of the object and purpose of the philosophy of religion, his critique of the theology of his time, his approach to Christianity within the framework of the concept of religion, his concept of God, his reconstruction of central Christian themes, and his placing of (...) Christianity among the religions of the world. Hodgson makes a case for the contemporary theological significance of Hegel by identifying currently contested sites of interpretation and their Hegelian resolution. (shrink)

It is now commonly accepted that N. Goodman's predicate "grue" presents the theory of confirmation of C. G. Hempel (and other such theories) with grave difficulties. The precise nature and status of these "difficulties" has, however, never been made clear. In this paper it is argued that it is very unlikely that "grue" raises any formal difficulties for Hempel and appearances to the contrary are examined, rejected and an explanation of their intuitive appeal offered. However "grue" is shown to raise (...) an informal, "over-arching" difficulty of great magnitude for all theories of confirmation, including Hempel's theory. (shrink)

This volume of essays examines the problem of mind, looking at how the problem has appeared to neuroscientists from classical antiquity through to contemporary times. Beginning with a look at ventricular neuropsychology in antiquity, this book goes on to look at Spinozan ideas on the links between mind and body, Thomas Willis and the foundation of Neurology, Hooke’s mechanical model of the mind and Joseph Priestley’s approach to the mind-body problem. The volume offers a chapter on the 19th century Ottoman (...) perspective on western thinking. Further chapters trace the work of nineteenth century scholars including George Henry Lewes, Herbert Spencer and Emil du Bois-Reymond. The book covers significant work from the twentieth century, including an examination of Alfred North Whitehead and the history of consciousness, and particular attention is given to the development of quantum consciousness. Chapters on slavery and the self and the development of an understanding of Dualism bring this examination up to date on the latest 21st century work in the field. At the heart of this book is the matter of how we define the problem of consciousness itself: has there been any progress in our understanding of the working of mind and brain? This work at the interface between science and the humanities will appeal to experts from across many fields who wish to develop their understanding of the problem of consciousness, including scholars of Neuroscience, Behavioural Science and the History of Science. (shrink)

In this paper I present a range of substructural logics for a conditional connective ↦. This connective was original introduced semantically via restriction on the ternary accessibility relation R for a relevant conditional. I give sound and complete proof systems for a number of variations of this semantic definition. The completeness result in this paper proceeds by step-by-step improvements of models, rather than by the one-step canonical model method. This gradual technique allows for the additional control, lacking in the canonical (...) model method, that is required. (shrink)

The survival of a unique set of drawings, complemented by a contemporary description and a sale catalogue, enable us to ‘reconstruct’ the cabinet of Bonnier de la Mosson , a miscellaneous collection formed in Paris c. 1740. A brief assessment is offered of the status of such cabinets in the growth and diffusion of science in ancien régime France. We also point to a link with the decorative arts: in a study of such a subject the intellectual and aesthetic dimensions (...) must be treated as a unity if we are fully to evoke the context of the cabinet in the age of the rococo. Only the modern ‘discipline’-oriented viewpoint forces a separation between the history of science and the history of art. (shrink)

The popular concept and practice of science as an exclusively objective exercise ignores the study of rich and unavoidable subjective phenomena relating to mind. This article proposes that as a process of generating knowledge from perceptual experiences, science-skill is innate to man, which demands precision and effective management of bias, and relies on faith for communication. It manifests in man along two dimensions, one of precision and the other of need and interest. Two more dimensions influence its practice and communicability. (...) This dimensionality accommodates scientific study of diverse human experiences, including religion and spirituality. Evolution of scientific study of mind requires complementing the existing objective techniques with development of techniques for investigating subjective and intuitive experiences. It would also benefit by borrowing concepts and methodologies from ancient Indian philosophies and spiritual practices. Swami Vivekananda's observations are presented in this connection. (shrink)

In Campbell Soup Co. v. Allstate Insurance Co. ), the United States District Court for the Western District of Michigan, Southern Division, held that a health plan's coordination of benefits clause, covered under the Employee Retirement Income Security Act, does not preempt a similar no-fault automobile insurance clause in the absence of irreconcilable conflict. The court found that ERISA's policy of shielding plans from unanticipated claims could only be furthered when the plan had expressly disavowed such claims. Because the ERISA (...) plan in this case did not specifically subordinate itself to the no-fault policy, the district court found that the no-fault COB clause controlled. However, to escape this ruling, ERISA plans need only redraft their COB clauses specifically to disclaim liability in case of conflict with provisions of no-fault insurance policies. This caveat substantially limits the scope of the court's ruling. (shrink)

In many systems, the tensors used to describe physical properties must acquire their structure from one vector. Knowledge of that fact alone leads to an interesting line of analysis for such systems. The analysis begins with a discussion of the types of dyadics that can be constructed from one vector. Attention is focused on certain exemplary dyadic operators, which, because of their geometrical properties, would appear particularly basic; the algebra of these dyadics is developed in detail. The algebra is then (...) used in a derivation of the expansion of general functions of these dyadics. Several applications of the general expansion are presented: the inverse of a general dyadic operator (when it exists), a general rotation operator that includes strains and reflections, the determinant of a general dyadic operator, and operators, including some new ones, used in constructing Lorentz boosts. Finally, a coordinate-free representation of the Levi-Civita tensor is provided. (shrink)

The coordinate-free methods of the preceding paper are illustrated in three problems. First, the electrodynamics of a homogeneous, isotropic, and gyrotropic medium is investigated; it is shown that such a medium can exhibit optical activity, and the propagation of a plane electromagnetic wave in such a medium is discussed. Then, the electrodynamics of a homogeneous system made anisotropic by a uniform external magnetic field is considered; a description of Faraday rotation is provided, the ionosphere being used in an example. Finally, (...) the reflection and refraction of a plane electromagnetic wave at the interface of two media are described by coordinate-free operators. (shrink)