The ever-increasing prevalence of chronic conditions over the last half century has gradually altered the demographic of patients admitted to acute care settings; environments traditionally associated with episodic care rather than chronic and complex healthcare. In consequence, the lifeworld of the hospital medical doctor often entails healthcare for a complex, multi-morbid, patient cohort. This paper examines the experience of providing complex healthcare in the pressurised and fast-paced acute care setting. Four medical doctors from two metropolitan health services were interviewed and (...) their data were analysed using a combinatorial framework of phenomenology and complexity theory. The horizon of complex care revealed itself as dynamic, expansive, immersive, and relational, entailing a specialised kind of practice that is now common in acute care settings. Yet this practice has made inroads largely without heralding the unique nature and potential of its ground. Herein lies opportunity for complex care clinicians to expand notions of health and illness, and to shape research, practice, and system design, for a future in which care for health complexity is optimised, irrespective of care settings. (shrink)

This study explores the experiences of nurses that provide ‘complex’, generalist healthcare in hospital settings. Complex care is described as care for patients experiencing acute issues additional to multimorbidity, ageing or psychosocial complexity. Nurses are the largest professional group of frontline healthcare workers and patients experiencing chronic conditions are overrepresented in acute care settings. Research exploring nurses’ experiences of hospital‐based complex care is limited, however. This study aims to add to what is known currently. Four ‘complex care’ nurses undertook in‐depth (...) semistructured interviews and their narratives were analysed using the conceptual framework of complex adaptive phenomenology. Two overarching themes constituting the ‘essence’ of complex care nursing were identified: Contextual factors and attribute/value‐based elements. Creating meaningful patient outcomes and feeling part of a team were experienced as fulfilling, whereas time constraints, institutional settings and systemic barriers to comprehensive caregiving diminished the experience of providing complex care. Overall, work meaning presented as a dynamic phenomenon, shaped by personal and professional values, local settings and systemic factors. It is recommended that more expansive research be undertaken to explore the experience of complex care for nurses. Such knowledge can contribute to initiatives that draw a skilled, effective and engaged hospital‐based complex care nursing workforce. (shrink)

Based on the relevant logic R, the system R# was proposed as a relevant Peano arithmetic. R# has many nice properties: the most conspicuous theorems of classical Peano arithmetic PA are readily provable therein; it is readily and effectively shown to be nontrivial; it incorporates both intuitionist and classical proof methods. But it is shown here that R# is properly weaker than PA, in the sense that there is a strictly positive theorem QRF of PA which is unprovable in R#. (...) The reason is interesting: if PA is slightly weakened to a subtheory P+, it admits the complex ring C as a model; thus QRF is chosen to be a theorem of PA but false in C. Inasmuch as all strictly positive theorems of R# are already theorems of P+, this nonconservativity result shows that QRF is also a nontheorem of R#. As a consequence, Ackermann's rule γ is inadmissible in R#. Accordingly, an extension of R# which retains its good features is desired. The system R##, got by adding an omega-rule, is such an extension. Central question: is there an effectively axiomatizable system intermediate between R# and R##, which does formalize arithmetic on relevant principles, but also admits γ in a natural way? (shrink)

We introduce a reducibility preordering between classes of countable structures, each class containing only structures of a given similarity type (which is allowed to vary from class to class). Though we sometimes work in a slightly larger context, we are principally concerned with the case where each class is an invariant Borel class (i.e. the class of all models, with underlying set $= \omega$, of an $L_{\omega_1\omega}$ sentence; from this point of view, the reducibility can be thought of as a (...) (rather weak) sort of $L_{\omega_1\omega}$-interpretability notion). We prove a number of general results about this notion, but our main thrust is to situate various mathematically natural classes with respect to the preordering, most notably classes of algebraic structures such as groups and fields. (shrink)

Equational Boolean Relation Theory concerns the Boolean equations between sets and their forward images under multivariate functions. We study a particular instance of equational BRT involving two multivariate functions on the natural numbers and three infinite sets of natural numbers. We prove this instance from certain large cardinal axioms going far beyond the usual axioms of mathematics as formalized by ZFC. We show that this particular instance cannot be proved in ZFC, even with the addition of slightly weaker large cardinal (...) axioms, assuming the latter are consistent. (shrink)

A bi-infinite approximate fixed point of type (n,k) is an approximate fixed point of type (n,k) whose terms are biinfinite; i.e., contain infin-itely many positive and infinitely many negative elements.

S. Adams, W. Ambrose, A. Andretta, H. Becker, R. Camerlo, C. Champetier, J.P.R. Christensen, D.E. Cohen, A. Connes. C. Dellacherie, R. Dougherty, R.H. Farrell, F. Feldman, A. Furman, D. Gaboriau, S. Gao, V. Ya. Golodets, P. Hahn, P. de la Harpe, G. Hjorth, S. Jackson, S. Kahane, A.S. Kechris, A. Louveau,, R. Lyons, P.-A. Meyer, C.C. Moore, M.G. Nadkarni, C. Nebbia, A.L.T. Patterson, U. Krengel, A.J. Kuntz, J.-P. Serre, S.D. Sinel'shchikov, T. Slaman, Solecki, R. Spatzier, J. Steel, D. Sullivan, S. (...) Thomas, A. Valette, V.S. Varadarajan, B. Velickovic, B. Weiss, J.D.M. Wright, R.J. Zimmer. (shrink)

Provide a formal system that is a conservative extension of PA for Π02 sentences, and even a conservative extension of HA, that supports the worry free smooth development of constructive analysis in the style of Errett Bishop.

Two countable well orderings are weakly comparable if there is an order preserving injection of one into the other. We say the well orderings are strongly comparable if the injection is an isomorphism between one ordering and an initial segment of the other. In [5], Friedman announced that the statement “any two countable well orderings are strongly comparable” is equivalent to ATR 0 . Simpson provides a detailed proof of this result in Chapter 5 of [13]. More recently, Friedman has (...) proved that the statement “any two countable well orderings are weakly comparable” is equivalent to ATR 0 . The main goal of this paper is to give a detailed exposition of this result. (shrink)

The use of x[y,z,w] rather than the more usual y Πx has many advantages for this work. One of them is that we have found a convenient way to eliminate any need for axiom schemes. All axioms considered are single sentences with clear meaning. (In one case only, the axiom is a conjunction of a manageable finite number of sentences).

This paper presents a case study carried out at Sofia University in Bulgaria, describing the relationship between two developments, firstly an expanding involvement with online learning and e-assessment, and secondly the development of institutional approaches to academic integrity. The two developments interact, the widening use of e-learning and e-assessment raising new issues for academic integrity, and the technology providing new tools to support academic integrity, with the involvement in technological developments acting as a catalyst for changes in approaches to academic (...) integrity. The aim of this study is to describe in what ways the integration of technologies for student authentication and authorship checking in this university has begun to influence teachers’ approach to academic integrity, and has also helped to identify specific issues that need to be resolved for the future of academic integrity in the university. Data collected during the implementation of pilots for the project TeSLA - An adaptive trust-based e-assessment system - enabled an examination of the perspectives of administrators, teachers and students on approaches to cheating and plagiarism, and on possible future directions. The data suggests that the piloting of the TeSLA system has triggered a deepening consideration of approaches to academic integrity, and has also helped to identify important issues for future developments. (shrink)

Reflection, in the sense of [Fr03a] and [Fr03b], is based on the idea that a category of classes has a subclass that is “similar” to the category. Here we present axiomatizations based on the idea that a category of classes that does not form a class has extensionally different subclasses that are “similar”. We present two such similarity principles, which are shown to interpret and be interpretable in certain set theories with large cardinal axioms.

How does match-fixing, or other unfair manipulation of matches, that involves under-performance by players, or refereeing and umpiring that prevents fair competition, be thought of in ethical terms? In this article, I outline the different forms that match-fixing can take and seek to comprehend these disparate scenarios within Kantian, Hegelian and contractualist ethical frameworks. I tentatively suggest that, by developing an ethical opposition to match-fixing in sport, we can give much greater substance to popular phrases such as ‘respect for the (...) game’, encompassing the value of sport itself and respect for other players, fans, sponsors and organisers. Arguing that match-fixing denies recognition to these ‘others’ demonstrates how fundamentally match-fixing ‘hollows out’ sport because a fixed match is of no worth: the whole value of the game has literally been evacuated. (shrink)

We address the general problem of determining the validity of boolean combinations of equalities and inequalities between real-valued expressions. In particular, we consider methods of establishing such assertions using only restricted forms of distributivity. At the same time, we explore ways in which “local'’ decision or heuristic procedures for fragments of the theory of the reals can be amalgamated into global ones. Let $Tadd[QQ]$ be the first-order theory of the real numbers in the language with symbols $0, 1, +, -.

The evidence of alienation with respect to work, daily life, politics and inclusion is widespread and has much to do with the increasing influence of right wing populism. Marx changed the basis for his thinking about alienation from a subjective humanist to an objective historical materialist basis. But the relations between the two forms of alienation cannot easily be severed. The contemporary conditions producing subjective states of alienation need to be investigated, chief among these is the rise of personal indebtedness (...) that forecloses upon future possibilities and restricts freedoms. Debt peonage and alienation are in our times a primary material basis for increasing subjective states of alienation. (shrink)

This paper questions the dogmatic stance of the domestic courts toward mandatory orders for treatment, arguing that this has the potential to subjugate patients' interests to clinical discretion, and proposing a via media to accommodate the legitimate concerns of all parties.

In a modal system of arithmetic, a theory S has the modal disjunction property if whenever $S \vdash \square\varphi \vee \square\psi$ , either $S \vdash \square\varphi$ or $S \vdash \square\psi. S$ has the modal numerical existence property if whenever $S \vdash \exists x\square\varphi(x)$ , there is some natural number n such that $S \vdash \square\varphi(\mathbf{n})$ . Under certain broadly applicable assumptions, these two properties are equivalent.

It is no accident that the book Benjamin wrote as a reader of himself, A Berlin Childhood, also begins with the description of a park, that of the Tiergarten zoo. However great the difference may seem between this collection of short prose pieces and Proust's three-thousand-page novel when viewed from the outside, Benjamin's book illustrates [his] fascination... A sentence in his book points to the central experience of Proust's work: that almost everything childhood was can be withheld from a person (...) for years, suddenly to be offered him anew as if by chance. "Like a mother who holds the new-born infant to her breast without waking it, life proceeds for a long time with the still tender memory of childhood" . Also reminiscent of Proust is the description of the mother who, on evenings when guests are in the house, comes in to see her child only fleetingly to say good night; so, too, is that of the boy attentively listening to the noises which penetrate into his room from the courtyard below and thus from a foreign world. The studied elevation of the newly invented telephone to the level of a mythical object is anticipated in Proust as well. And the relationship to and influence of the earlier work can be demonstrated even in the use of metaphor. But little is gained by this approach, and it would not be easy to refute the objection that such similarities lie in the authors' common raw material: childhood, the fin de siècle epoch, and the attempt to bring them both into the present. Peter Szondi was professor of comparative literature at the Free University of Berlin at the time of his death in 1971. His many influential works include Theorie des modernen Dramas , Versuch über das Tragische , and a five-volume collection of his lectures. Harvey Mendelsohn is the principle translator of the fourteen-volume Dictionary of Scientific Biography; he is currently working on translations of a French commentary on Heraclitus and a selection of Szondi's essays to be published by Yale University Press. (shrink)

Certainty (and the lack thereof) is a major issue in mathematics and computer science. Mathematicians strongly believe in a special kind of certainty for their theorems.

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.

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)

We discuss several axiomatizations of set theory in first order predicate calculus with epsilon and a constant symbol W, starting with the simple system K(W) which has a strong equivalence with ZF without Foundation. The other systems correspond to various extensions of ZF by certain large cardinal hypotheses. These axiomatizations are unusually simple and uncluttered, and are highly suggestive of underlying philosophical principles that generate higher set theory.

We present a range of mathematical theorems whose proofs require unexpectedly strong logical methods, which in some cases go well beyond the usual axioms for mathematics.

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.

This paper proposes a reconsideration of Karl Mannheim and his work from the viewpoint of the needs of sociological theory. It points out certain affinities between Mannheim and some contemporary theorists, such as Gramsci and Foucault, and then reflects on certain problems in Mannheim's work, particularly the response to "relativism" and the hope of creating new "syntheses" through the sociology of knowledge. Finally, it proposes ways to draw on the sociology of intellectuals, inspired by Mannheim, in order to advance the (...) understanding of social theory. (shrink)

We say that R is strictly dominating if and only if for all x,yŒ[1,n], if R(x,y) then max(x) 3k ¥ [1,n], there exists A Õ [1,n] such that R = A. Furthermore, A Õ [1,n] is unique.

ENTIRE BOOK, SINGLE FILE. BOOLEAN RELATION THEORY AND THE INCOMPLETENESS PHENOMENA. 10/30/07 version. Same as 10/01/07 version with Preface added. 568 pages without Appendix B. See above for Appendix B by Francoise Point.

This paper critiques the standard translation of ariya-sacca as ‘Noble Truth’ and argues that the term refers to four saccas as ‘true realities’, rather than as verbalised ‘truths’ about these realities; the teachings about them are not, as such what the term ariya-sacca refers to. Moreover, only one of the ariya-saccas is itself ever described in the suttas as ‘noble’. The four are ‘true realities for the spiritually ennobled’: the fundamental, basic, most significant genuine realities that the Buddha and other (...) noble ones see in the flow of experience of themselves and/or others. The first of them is not best translated as ‘suffering’ but as ‘pain’ – in all its many senses – or indeed ‘the painful’: the up?d?na-kkhandhas as ‘bundles of grasping-fuel’ which are described, adjectivally, as ‘painful’. The paper includes a new translation of the Dhamma-cakka-ppavattana Sutta in line with this analysis. (shrink)

Let k be a positive integer. There is a longest finite sequence x1,...,xn in k letters in which no consecutive block xi,...,x2i is a subsequence of any other consecutive block xj,...,x2j. Let n(k) be this longest length. We prove that n(1) = 3, n(2) = 11, and n(3) is incomprehensibly large. We give a lower bound for n(3) in terms of the familiar Ackerman hierarchy. We also give asymptotic upper and lower bounds for n(k). We view n(3) as a particularly (...) elemental description of an incomprehensibly large integer. Related problems involving binary sequences (two letters) are also addressed. We also report on some recent computer explorations of R. Dougherty which we use to raise the lower bound for n(3). (shrink)

We present some new decision and comparison problems of unusually high computational complexity. Most of the problems are strictly combinatorial in nature; others involve basic logical notions. Their complexities range from iterated exponential time completeness to (0 time completeness to ((((,0) time completeness to ((((,,0) time completeness. These three ordinals are well known ordinals from proof theory, and their associated com- plexity classes represent new levels of computational complexity for natural decision problems. Proofs will appear in an extended version of (...) this manuscript to be published elsewhere. (shrink)

• Wright Brothers made a two mile flight • Wright Brothers made a 42 mile flight • Want to ship goods • Want to move lots of passengers • Want reliability and safety • Want low cost • ... Modern aviation • Each major advance spawns reasonable demands for more and more • Excruciating difficulties overcome • Armies of people over decades or more • Same story for any practically any epoch breaking advance in anything..

We have been particularly interested in the demonstrable unremovability of machinery, which is a theme that can be pursued systematically starting at the most elementary level - the use of binary notation to represent integers; the use of rational numbers to solve linear equations; the use of real and complex numbers to solve polynomial equations; and the use of transcendental functions to solve differential equations.

Extrapolating from the work of Mahlo , one can prove that given any pair of countable closed totally bounded subsets of complete separable metric spaces, one subset can be homeomorphically embedded in the other. This sort of topological comparability is reminiscent of the statements concerning comparability of well orderings which Friedman has shown to be equivalent to ATR0 over the weak base system RCA0. The main result of this paper states that topological comparability is also equivalent to ATR0. In Section (...) 1, the pertinent subsystems of second-order arithmetic and results on well orderings are reviewed. Sections 2 and 3 overview the encoding of metric spaces and homeomorphisms in second-order arithmetic. Section 4 contains a proof of the topological comparability result in ATR0. Section 5 contains the reversal, a derivation of ATR0 from the topological comparability result. In Section 6, additional information about the structure of the embeddings is obtained, culminating in an application to closed subsets of the real numbers. (shrink)

This textbook carefully develops the main ideas and techniques of statistical and thermal physics and is intended for upper-level undergraduate courses. The authors each have more than thirty years' experience in teaching, curriculum development, and research in statistical and computational physics. Statistical and Thermal Physics begins with a qualitative discussion of the relation between the macroscopic and microscopic worlds and incorporates computer simulations throughout the book to provide concrete examples of important conceptual ideas. Unlike many contemporary texts on thermal physics, (...) this book presents thermodynamic reasoning as an independent way of thinking about macroscopic systems. Probability concepts and techniques are introduced, including topics that are useful for understanding how probability and statistics are used. Magnetism and the Ising model are considered in greater depth than in most undergraduate texts, and ideal quantum gases are treated within a uniform framework. Advanced chapters on fluids and critical phenomena are appropriate for motivated undergraduates and beginning graduate students. Integrates Monte Carlo and molecular dynamics simulations as well as other numerical techniques throughout the text Provides self-contained introductions to thermodynamics and statistical mechanics Discusses probability concepts and methods in detail Contains ideas and methods from contemporary research Includes advanced chapters that provide a natural bridge to graduate study Features more than 400 problems Programs are open source and available in an executable cross-platform format Solutions manual. (shrink)

My paper addresses a number of questions raised in the Statesman by the Eleatic Visitor’s identification of certain ontological conditions for the existence of art of due measure, and therefore of all the technai. My view is that evidence relevant to these questions can be found in the Philebus, and specifically, in an ontological doctrine presented at 23c–27c. What emerges from an examination of the Statesman and Philebus is a highly developed conception of technê, one that affords a place for (...) such ordinary human activities within the broader framework of Plato’s philosophy. (shrink)

With gripping archival detail, The Logic of Hatred scrutinizes the witch hunts and the Great Terror during the French Revolution to elaborate a theory and critique of what Jacob Rogozinski names the persecution apparatus. When this process is set into motion, sovereign power excludes and persecutes minoritized groups of humans deemed unworthy of inclusion, ultimately annihilating them. The author’s purpose is to break the seemingly inexorable cycle.