The notion of social capital focuses attention on social connectedness within communities and the ways that this connectedness may affect health and well‐being. There are many competing definitions of social capital but most suggest that it involves trust, social networks and reciprocity within communities, not necessarily geographically defined. The usefulness of social capital and related theories that help in understanding the function of nurses in rural communities are explored in this paper. Nurses and health service planners are becoming increasingly aware (...) of the potential contribution of community nurses in rural and/or remote areas, as evidenced in the development of nurse practitioners. Through their interrelational role and status in rural communities, nurses are often ‘immersed’ or ‘embedded’ in the social networks that make up the fabric of rural life and may therefore be important contributors to social capital. For a concept such as social capital to be useful in nursing research, it must have distinct attributes, delineated boundaries, and well‐described preconditions and outcomes in multiple contexts. (shrink)

PREFACE. We present a variety of basic theories involving fundamental concepts of naive thinking, of the sort that were common in "natural philosophy" before the dawn of physical science. The most extreme forms of infinity ever formulated are embodied in the branch of mathematics known as abstract set theory, which forms the accepted foundation for all of mathematics. Each of these theories embodies the most extreme forms of infinity ever formulated, in the following sense. ZFC, and even extensions of ZFC (...) with the so called large cardinal axioms, are mutually interpretable with these theories. This is an extended abstract. Proofs of the claims will appear elsewhere. (shrink)

The subtle, almost ineffable, and ineffable cardinals were introduced in an unpublished 1971 manuscript of R. Jensen and K. Kunen. The concepts were extended to that of k-subtle, k-almost ineffable, and k-ineffable cardinals in 1975 by J. Baumgartner. In this paper we give a self contained treatment of the basic facts about this level of the large cardinal hierarchy, which were established by J. Baumgartner. In particular, we give a proof that the k-subtle, k-almost ineffable, and k-ineffable cardinals define three (...) properly intertwined hierarchies with the same limit, lying strictly above “total indescribability” and strictly below “arrowing ω”. The innovation here is presented in Section 2, where we take a distinctly minimalist approach. Here the subtle cardinal hierarchy is characterized by very elementary properties that do not mention closed unbounded or stationary sets. This development culminates in a characterization of the hierarchy by means of a striking universal second-order property of linear orderings. (shrink)

Let k ≥ 2 and f:Nk Æ [1,k] and n ≥ 1 be such that there is no x1 < ... < xk+1 £ n such that f(x1,...,xk) = f(x1,...,xk+1). Then we want to find g:Nk+1 Æ [1,3] such that there is no x1 < ... < xk+2 £ n such that g(x1,...,xk+1) = g(x2,...,xk+2). This reducees adjacent Ramsey in k dimensions with k colors to adjacent Ramsey in k+1 dimensions with 3 colors.

Religion is more than a matter of worshipping a deity or spirit. For many people, religion pervades every part of their lives and is not separated off into some purely private and personal realm. Religion is integral to many people's relationship with the wider world, an aspect of their dwelling among other beings - both human and other-than-human - and something manifested in the everyday world of eating food, having sex and fearing strangers. Food, Sex and Strangers offers alternative ways (...) of thinking about what religion involves and how we might better understand it. Drawing on studies of contemporary religions, especially among indigenous peoples, the book argues that religion serves to maintain and enhance human relationships in and with the larger-than-human world. Fundamentally, religion can be better understood through the ways we negotiate our lives than in affirmations of belief - and it is best seen when people engage in intimate acts with themselves and others. (shrink)

We consider a number of statements involving restrictions and extensions of algebras, and derive connections with large cardinal axioms.

We axiomatize EFA in strictly mathematical terms, involving only the ring operations, without extending the language by either exponentiation, finite sets of integers, or polynomials.

In mathematics, we back up our discoveries with rigorous deductive proofs. Mathematicians develop a keen instinctive sense of what makes a proof rigorous. In logic, we strive for a *theory* of rigorous proofs.

An assignment is a function f that assigns subsets of N to some atoms. Then f is extended to f* which sends every formula A of HPC to a subset of S(A).

Let ℜ be an o-minimal expansion of (ℝ, <+) and (φk)k∈ℕ be a sequence of positive real numbers such that limk→+∞f(φk)/φk+1=0 for every f:ℝ→ ℝ definable in ℜ. (Such sequences always exist under some reasonable extra assumptions on ℜ, in particular, if ℜ is exponentially bounded or if the language is countable.) Then (ℜ, (S)) is d-minimal, where S ranges over all subsets of cartesian powers of the range of φ.

Gödel's definitive results and his essays leave us with a rich legacy of philosophical programs that promise to be subject to mathematical treatment. After surveying some of these, we focus attention on the program of circumventing his demonstrated impossibility of a consistency proof for mathematics by means of extramathematical concepts.

Animism is the label given to worldviews in which the world is understood to be a community of living persons, only some of whom are human. (An older use of the term to label a putative “belief in spirits” is less useful.) Animists inculcate locally meaningful means of communicating with other-than-human persons, especially in order to express respect. Ethnographic accounts of particular animist ways of engaging with animal persons are noted. I argue that ethologists interested in engaging respectfully with animals (...) while researching cognition, behavior, and other critical issues may find their research methods and results enhanced by learning from animists about tested methods of communicating with animals. The mediation of animists in this communicative engagement between animals and those who research among them is proposed not as a romantic gloss on modernist culture but in full recognition that the challenge offered by dialogue with marginalized and excluded “others” may result in a reconfiguration of academic protocols. Nonetheless, this entry into full relationality is seriously posed as an improved means of achieving established goals of understanding animals, humans, and the world we coinhabit. (shrink)

We focus on two formal methods contexts which generate investigations into decision problems for finite strings.

For digraphs G, we write V(G) for the set of all vertices of G, and E(G) for the set of all edges of G. A digraph on a set E is a digraph G where V(G) = E.

Mathematical Logic had a glorious period in the 1930s, which was briefly rekindled in the 1960s. Any Shock Value, such as it is, has surrounded unprovability from ZFC.

An extreme kind of logic skeptic claims that "the present formal systems used for the foundations of mathematics are artificially strong, thereby causing unnecessary headaches such as the Gödel incompleteness phenomena". The skeptic continues by claiming that "logician's systems always contain overly general assertions, and/or assertions about overly general notions, that are not used in any significant way in normal mathematics. For example, induction for all statements, or even all statements of certain restricted forms, is far too general - mathematicians (...) only use induction for natural statements that actually arise. If logicians would tailor their formal systems to conform to the naturalness of normal mathematics, then various logical difficulties would disappear, and the story of the foundations of mathematics would look radically different than it does today. In particular, it should be possible to give a convincing model of actual mathematical practice that can be proved to be free of contradiction using methods that lie within what Hilbert had in mind in connection with his program”. Here we present some specific results in the direction of refuting this point of view, and introduce the Strict Reverse Mathematics (SRM) program. (shrink)

The understanding of conditioned co‐arising is central to Buddhist practice and development. This chapter presents the principle of conditionality, which can be applied to all processes, events, and things, physical or mental, in the universe. Besides explaining the origin of dukkha, the conditioned co‐arising formula also explains karma, rebirth, and the functioning of personality, all without the need to invoke a permanent self. Buddhism sees the basic root of the pain and stress of life as spiritual ignorance, rather than sin. (...) The between‐lives period has three phases: inclining to a further rebirth, seeking it here and there, and falling from one's previous identity into a new rebirth. In the Mahāyāna movement, various uses were made of the conditioned co‐arising. As a general point on conditioned co‐arising, it should be noted that it presents a “middle” way of understanding that echoes the Buddhist path as a “middle way” of practice. (shrink)

It has been accepted since the early part of the Century that there is no problem formalizing mathematics in standard formal systems of axiomatic set theory. Most people feel that they know as much as they ever want to know about how one can reduce natural numbers, integers, rationals, reals, and complex numbers to sets, and prove all of their basic properties. Furthermore, that this can continue through more and more complicated material, and that there is never a real problem.

Among the many themes in which the Irish modernist novelist, James Joyce, was intellectually and emotionally engaged, the issue of British imperialism and Irish nationalism was paramount. While Joyce despised the English colonial occupation of his country, he was equally dismissive of a mythical Irish nationalism, particularly in the way it was endorsed by the Gaelic Athletic Association. While Joyce is not renowned as a writer of sport; nevertheless, sporting pursuits can be found throughout his novels. Joyce’s nuanced understanding of (...) how English culture has permanently altered Irish social subjectivities (and vice versa) can be found in sharp relief in his novels, particularly Ulysses and A Portrait of the Artist as a Young Man. This article takes sport as a theme in Joyce’s work through which to explore fractured national identities through a framework inspired by the discourse theory of Ernesto Laclau and Chantal Mouffe. Their post-Marxist work enables an examination of sport and nationality that goes beyond the existing orthodox Gramscian theory that has proven so productive in the understanding of sport in Cultural Studies. The article will commence with a brief review of existing studies of Joyce with respect to sport and national debates. After summarising the broad Gramscian approaches to understanding sport and nationalism, some of the key concepts in Laclau and Mouffe’s political philosophy are then outlined. The article will apply those concepts to the way Joyce depicts sport, especially cricket and hockey, to deconstruct the binaries in the debate between British colonialism and Irish nationalism. (shrink)

Notwithstanding that there is now widespread interest in the rights of victims, little has been written about the theoretical justification of state compensation. Here we offer an initial exploration of the field in the hope that others might venture further and examine the points at which issues of compensation connect with other general and specific themes in social and political philosophy. For example, there has been much discussion about communitarian conceptions of civil society but the practical implications of such views, (...) other than those relating to multiculturalism, have been largely ignored. The application of theory to social policy needs to take account of existing laws and institutions and these vary from one society and jurisdiction to another. In what follows we are principally concerned with the situation obtaining in the United Kingdom but the underlying issues are general ones [1]. (shrink)

Richard Harvey Brown's pioneering explorations in the philosophy of social science and the theory of rhetoric reach a culmination in Social Science as Civic Discourse. In his earlier works, he argued for a logic of discovery and explanation in social science by showing that science and art both depend on metaphoric thinking, and he has applied that logic to society as a narrative text in which significant action by moral agents is possible. This new work is at once a (...) philosophical critique of social theory and a social-theoretical critique of politics. Brown proposes to redirect the language and the mission of the social sciences toward a new discourse for a humane civic practice. (shrink)

Since then we have been engaged in the development of such results of greater relevance to mathematical practice. In January, 1997 we presented some new results of this kind involving what we call “jump free” classes of finite functions. This Jump Free Theorem is treated in section 2.

This article argues that the quantitative and quasi-experimental approach to evaluating public participation exercises is deficient in at least two respects. First, casting participants in instrumental terms excludes that participants have an experience and that this may be dramatic and emotional. If people are to be invited, even obliged, to participate, then this experience should be considered in event evaluation. Second, current evaluation frameworks tend not to be sensitive to what actually happened in terms of the actions of participants and (...) how these influenced the proceedings and outcome, thus ignoring that such events are fora where positions, values, decisions, and so forth are constructed and constrained rather than simply reported. This article considers the possible contribution of dramaturgical, discourse and conversation analytic, and ethnographic and phenomenological approaches to evaluating participation exercises and illustrates their potential with data gathered during the U.K. “GM Nation?” public debate. (shrink)

We show that “every countable algebra with a nonfinitely generated subalgebra has a maximal nonfinitely generated subalgebra” is provably equivalent to ’11-CA0 over..

The kind of unknowability I will discuss concerns the count of certain natural finite sets of objects. Even the situation with regard to our present strong formal systems is rather unclear. One can just profitably focus on that, putting aside issues of general unknowability.

We present some examples of mathematically natural nonrecursive sets of integers and relations on integers by combining results from Part 1, recursion theory, and from the negative solution to Hilbert’s 10th Problem ([3], [1], and [2]).

An unprovable theorem is a mathematical result that can-not be proved using the com-monly accepted axioms for mathematics (Zermelo-Frankel plus the axiom of choice), but can be proved by using the higher infinities known as large cardinals. Large car-dinal axioms have been the main proposal for new axioms originating with Gödel.

The cognitive and behavioral functions of the frontal lobes have been of great interest to neuroscientists, neurologists, psychologists and psychiatrists. Recent technical advances have made it possible to trace their neuroanatomical connections more precisely and to conduct evoked potential and neuroimaging studies in patients. This book presents a broad and authoritative synthesis of research progress in this field. It encompasses neuroanatomical studies; experiments involving temporal organization and working memory tasks in non-human primates; clinical studies of patients following frontal lobe excisions (...) for intractable epilepsy; metabolic imaging in schizophrenia and affective disorder; neurobehavioral studies of patients with dementia, frontal lobe tumors, and head injuries; magnetic resonance imaging methods for studying human frontal lobe anatomy; theoretical approaches to describing frontal lobe functions; and rehabilitation of patients with frontal lobe damage including their core problem of diminished awareness. Written by a distinguished group of neuroscientists, psychologists and clinicians, Frontal Lobe Function and Dysfunction provides the best current source of information on this region of the brain and its role in cognition, behavior and clinical disorders. (shrink)

We present several selection theorems for Borel relations, involving only Borel sets and functions, all of which can be obtained as consequences of closely related theorems proved in [DSR 96,99,01,01X] involving coanalytic sets. The relevant proofs given there use substantial set theoretic methods, which were also shown to be necessary. We show that none of our Borel consequences can be proved without substantial set theoretic methods. The results are established for Baire space. We give equivalents of some of the main (...) results for the reals. (shrink)

We give a complete proof that all 3 quantifier sentences in the primitive notation of set theory (Œ,=), are decided in ZFC, and in fact in a weak fragment of ZF without the power set axiom. We obtain information concerning witnesses of 2 quantifier formulas with one free variable. There is a 5 quantifier sentence that is not decided in ZFC (see [Fr02]).