We characterize the sets of all Π2 and all equation image theorems of IΠ−1 in terms of restricted exponentiation, and use these characterizations to prove that both sets are not deductively equivalent. We also discuss how these results generalize to n > 0. As an application, we prove that a conservation theorem of Beklemishev stating that IΠ−n + 1 is conservative over IΣ−n with respect to equation image sentences cannot be extended to Πn + 2 sentences. © 2011 WILEY-VCH Verlag (...) GmbH & Co. KGaA, Weinheim. (shrink)

This paper investigates the status of the fragments of Peano Arithmetic obtained by restricting induction, collection and least number axiom schemes to formulas which are $${\Delta_1}$$ provably in an arithmetic theory T. In particular, we determine the provably total computable functions of this kind of theories. As an application, we obtain a reduction of the problem whether $${I\Delta_0 + \neg \mathit{exp}}$$ implies $${B\Sigma_1}$$ to a purely recursion-theoretic question.

In this paper we continue the study of the theories IΔ n+1 (T), initiated in [7]. We focus on the quantifier complexity of these fragments and theirs (non)finite axiomatization. A characterization is obtained for the class of theories such that IΔ n+1 (T) is Π n+2 –axiomatizable. In particular, IΔ n+1 (IΔ n+1 ) gives an axiomatization of Th Π n+2 (IΔ n+1 ) and is not finitely axiomatizable. This fact relates the fragment IΔ n+1 (IΔ n+1 ) to induction (...) rule for Δ n+1 –formulas. Our arguments, involving a construction due to R. Kaye (see [9]), provide proofs of Parsons’ conservativeness theorem (see [16]) and (a weak version) of a result of L.D. Beklemishev on unnested applications of induction rules for Π n+2 and Δ n+1 formulas (see [2]). (shrink)

By a result of L.D. Beklemishev, the hierarchy of nested applications of the $$\Sigma _1$$ -collection rule over any $$\Pi _2$$ -axiomatizable base theory extending Elementary Arithmetic collapses to its first level. We prove that this result cannot in general be extended to base theories of arbitrary quantifier complexity. In fact, given any recursively enumerable set of true $$\Pi _2$$ -sentences, S, we construct a sound $$(\Sigma _2 \! \vee \! \Pi _2)$$ -axiomatized theory T extending S such that the (...) hierarchy of nested applications of the $$\Sigma _1$$ -collection rule over T is proper. Our construction uses some results on subrecursive degree theory obtained by L. Kristiansen. (shrink)

By a theorem of R. Kaye, J. Paris and C. Dimitracopoulos, the class of the Πn+1-sentences true in the standard model is the only consistent Πn+1-theory which extends the scheme of induction for parameter free Πn+1-formulas. Motivated by this result, we present a systematic study of extensions of bounded quantifier complexity of fragments of first-order Peano Arithmetic. Here, we improve that result and show that this property describes a general phenomenon valid for parameter free schemes. As a consequence, we obtain (...) results on the quantifier complexity, finite axiomatizability and relative strength of schemes for Δn+1-formulas. (shrink)

Let T be a second-order arithmetical theory, Λ a well-order, λ < Λ and X ⊆ ℕ. We use $[\lambda |X]_T^{\rm{\Lambda }}\varphi$ as a formalization of “φ is provable from T and an oracle for the set X, using ω-rules of nesting depth at most λ”.For a set of formulas Γ, define predicative oracle reflection for T over Γ ) to be the schema that asserts that, if X ⊆ ℕ, Λ is a well-order and φ ∈ Γ, then$$\forall \,\lambda (...) < {\rm{\Lambda }}\,.$$In particular, define predicative oracle consistency ) as Pred–O–RFN{0=1}.Our main result is as follows. Let ATR0 be the second-order theory of Arithmetical Transfinite Recursion, ${\rm{RCA}}_0^{\rm{*}}$ be Weakened Recursive Comprehension and ACA be Arithmetical Comprehension with Full Induction. Then,$${\rm{ATR}}_0 \equiv {\rm{RCA}}_0^{\rm{*}} + {\rm{Pred - O - Cons\ }}\left \equiv {\rm{RCA}}_0^{\rm{*}} + \,{\rm{Pred - O - Cons\ }}\left \equiv {\rm{RCA}}_0^{\rm{*}} + \,{\rm{Pred - O - RFN}}\,_{{\bf{\Pi }}_2^1 } \left.$$We may even replace ${\rm{RCA}}_0^{\rm{*}}$ by the weaker ECA0, the second-order analogue of Elementary Arithmetic.Thus we characterize ATR0, a theory often considered to embody Predicative Reductionism, in terms of strong reflection and consistency principles. (shrink)

A well known theorem proved by J. Paris and H. Friedman states that BΣn +1 is a Πn +2-conservative extension of IΣn . In this paper, as a continuation of our previous work on collection schemes for Δn +1-formulas , we study a general version of this theorem and characterize theories T such that T + BΣn +1 is a Πn +2-conservative extension of T . We prove that this conservativeness property is equivalent to a model-theoretic property relating Πn-envelopes and (...) Πn-indicators for T . The analysis of Σn +1-collection we develop here is also applied to Σn +1-induction using Parsons' conservativeness theorem instead of Friedman-Paris' theorem.As a corollary, our work provides new model-theoretic proofs of two theorems of R. Kaye, J. Paris and C. Dimitracopoulos : BΣn +1 and IΣn +1 are Σn +3-conservative extensions of their parameter free versions, BΣ–n +1 and IΣ–n +1. (shrink)

We prove that the standard cut is definable in each existentially closed model ofIΔ0+ exp by a (parameter free) П1–formula. This definition is optimal with respect to quantifier complexity and allows us to improve some previously known results on existentially closed models of fragments of arithmetic.

In van Benthem (2008), van Benthem proposes a dynamic consequence relation defined as${\psi _1}, \ldots,{\psi _n}{ \models ^d}\phi \,{\rm{iff}}{ \models ^{pa}}[{\psi _1}] \ldots [{\psi _n}]\phi,$where the latter denotes consequence in public announcement logic, a dynamic epistemic logic. In this paper we investigate the structural properties of a conditional dynamic consequence relation$\models _{\rm{\Gamma }}^d$extending van Benthem’s proposal. It takes into account a set of background conditions Γ, inspired by Makinson (2003) wherein Makinson calls this reasoning ‘modulo’ a set Γ. In the (...) presence of common knowledge, conditional dynamic consequence is definable from (unconditional) dynamic consequence. An open question is whether dynamic consequence is compact. We further investigate a dynamic consequence relation for soft instead of hard announcements. Surprisingly, it shares many properties with (hard) dynamic consequence. Dynamic consequence relations provide a novel perspective on reasoning about protocols in multi-agent systems. (shrink)

Technological developments in the sphere of artificial intelligence (AI) inspire debates about the implications of autonomous weapon systems (AWS), which can select and engage targets without human intervention. While increasingly more systems which could qualify as AWS, such as loitering munitions, are reportedly used in armed conflicts, the global discussion about a system of governance and international legal norms on AWS at the United Nations Convention on Certain Conventional Weapons (UN CCW) has stalled. In this article we argue for the (...) necessity to adopt legal norms on the use and development of AWS. Without a framework for global regulation, state practices in using weapon systems with AI-based and autonomous features will continue to shape the norms of warfare and affect the level and quality of human control in the use of force. By examining the practices of China, Russia, and the United States in their pursuit of AWS-related technologies and participation at the UN CCW debate, we acknowledge that their differing approaches make it challenging for states parties to reach an agreement on regulation, especially in a forum based on consensus. Nevertheless, we argue that global governance on AWS is not impossible. It will depend on the extent to which an actor or group of actors would be ready to take the lead on an alternative process outside of the CCW, inspired by the direction of travel given by previous arms control and weapons ban initiatives. (shrink)

Background: A growing number of frameworks for the practice of clinical ethics are described in the literature. Among these, hermeneutical frameworks have helped highlight the interpretive and contextual nature of clinical ethics practice. Objectives: The aim of this article is to further advance this body of work by drawing on the ideas of Charles Taylor, a leading hermeneutical philosopher. Design/Findings: A Hermeneutical Rapprochement Framework is presented for clinical ethics practice, based on Taylor’s hermeneutical “retrieval” and “rapprochement.” This builds on existing (...) hermeneutical approaches for the practice of clinical ethics by articulating a framework with interpretive and reconciliatory scope that extends beyond the presenting “local” context. A Hermeneutical Rapprochement Framework considers broader socio-historical horizons and imaginaries grounded on Taylor’s expansive work in epistemological, ontological, political, and moral philosophy. Discussion: The framework is discussed in terms of how it can be operationalized for clinical practice as well as normative development. Implications for the educational preparation of clinical ethicists are also discussed. Although this work is directly relevant for clinical ethicists, it can also help inform the ethical practice of all clinicians. (shrink)

In this article I argue for an interpretive approach to bioethics with critically ill children. I begin by highlighting the dominant Anglo-American bioethical framework that defines standards for ethical care in critically ill children and then outline a critique of this framework. Drawing predominantly on the ideas of Charles Taylor, Michael Walzer and Richard Zaner, I call for a reconception of bioethics and propose an interpretive ‘thick’ framework that is centred on culture and context. Finally, I illustrate this interpretive approach (...) through a comparative study of two cases in pediatric intensive care: the narratives of Marc and Larry. These case studies reveal that ethical dilemmas in pediatric critical care can be traced to relational tensions over respect, trust and power rooted in the disparity of moral horizons among the persons involved. (shrink)

The modern West has vigorously sought to overcome death, or at the very least minimize the suffering that it entails. Whereas the former has been predominantly pursued through modern scientific medicine, the minimization of the adversity of death and dying has been sought through ‘death technologies’. This technologization of death is analyzed in light of Martin Heidegger’s phenomenological philosophy. The analysis begins with an outline of the fundamental tenets of Heidegger’s ‘philosophy of Being’. In turn, his philosophical framework is utilized (...) to highlight the manner in which the technologization of dying serves to conceal the central existential questions about being and finitude that dying gives rise to. The paper concludes with a discussion of how Heidegger’s work can inspire a more authentic stance toward dying. Leo Tolstoy’s The Death of Ivan Ilych is referred to in order to illustrate Heidegger’s construal of this existential struggle toward dying. (shrink)

Nursing scholars have called for nursing approaches with children that ensure the promotion of their childhood, contesting dominant adult-based approaches that are adapted for practice with children. Although the nursing literature includes many important advances in the promotion of child-centered approaches, there are still significant gaps in fully recognizing the complexities of childhood within nursing. Within this paper, I (a) outline some key advances in nursing approaches with children, sometimes referred to as “Children's Nursing” (shifting away from “Pediatric Nursing” conceptions (...) that may be focused more on diseases than childhood); (b) highlight key gaps in current conceptions of Children's Nursing, namely the inadequate integration of work from the interdisciplinary field of Childhood Studies which challenges dominant age-based developmental models which discount children's voices and experiences as “immature”; and (c) propose a Childhood Ethics-based framework that bridges advances in Children's Nursing with those within Childhood Studies, which I refer to as the VOICE Children's Nursing Framework. The latter is rooted in the recognition of (a) children as active agents with capacities and interests in participating in discussions and decisions that affect them, and (b) best interests as the foundational basis for determining the nursing care required by a child which should be defined in an individualized manner, informed by a child's expressed aspirations and concerns. This Framework integrates biological, relational, and ethical dimensions of children's wellbeing and draws on hermeneutic approaches for eliciting and interpreting children's agential expressions, which involves continuous part/whole shifting to meticulously discern what is meaningful within a situation. The Framework is operationalized for clinical practice through the use of orienting questions, which is demonstrated through discussion of a clinical exemplar. The paper closes with proposed future directions for Children's Nursing development in practice, education, and research. (shrink)

This analysis presents an epistemological and moral examination of suffering. It addresses the specific questions: (1) What is suffering? (2) Can one's suffering be assessed by another? and (3) What is the moral significance of suffering? The epistemological analysis is orientated by Peter Hacker's framework for the investigation of emotions, demonstrating that suffering is an emotion. This leads to a discussion of whether suffering is a phenomenon that can be evaluated objectively by another person who is not experiencing the suffering, (...) questioning the validity of some decisional models for limiting life-sustaining therapies with the aim of preventing suffering. This analysis highlights that understandings of suffering are value laden. It is conventionally implied that suffering is `bad' and that it should be eliminated. Suffering is commonly regarded as a moral wrong that needs to be made right by health care. This article concludes with a recommendation for a paradigm shift in how suffering can be better understood, through the practice of empathic attunement. (shrink)

The aim of this article is to analyse the contemporary ‘futility discourse’ from a constructivist perspective. I will argue that bioethics discourse typically disregards the con text from which controversies emerge and the processes that inform and constrain such discourse. Constructivists have argued that scientific knowledge is expressive of the dominant paradigm within which a scientific community is working. I will outline an analysis of ‘medical futility’ as a construction of biomedical and bioethical communities (and their respective paradigms). I will (...) trace the emergence and utilization of futility in the literature. My analysis of the context (i.e. the historical circumstances, the particular actors involved) within which the futility discourse emerged suggests that medical futility was constructed, in part, as a means of enhancing physician domination of a context wherein medical authority was threatened. The actors in this debate express widely divergent frameworks of ‘the good’, arguing from distinctive representations of moral agency. At times, this controversy has been argued from incommensurate moral horizons wherein the discussants debate incomparable problems. This discussion is related to a study of the ‘practice’ of futility in the clinical context. Further studies on the construction of bioethical problems are a necessary condition for supporting the truth claims of bioethical arguments. (shrink)

Accepted standards of parental decisional autonomy and child best interests do not address adequately the complex moral problems involved in the care of critically ill children. A growing body of moral discourse is calling for the recognition of `tragedy' in selected human problems. A tragic dilemma is an irresolvable dilemma with forced terrible alternatives, where even the virtuous agent inescapably emerges with `dirty hands'. The shift in moral framework described here recognizes that the form of conduct called for by tragic (...) dilemmas is the practice of phronesis. The phronetic agent has acquired a capacity to discern good agency in tragic circumstances. This discernment is practiced through the artful creation of moral narratives: stories that convey that which is morally meaningful in a particular situation; that is, stories that are `meaning making'. The phronetic agent addresses tragic dilemmas involving children as a narrator of contextualized temporal embodied human (counter)stories. (shrink)

This article reviews empirical evidence and ethical norms in cross-linguistic nursing. Empirical evidence highlights that linguistic barriers between nurses and patients can perpetuate discrimination and compromise nursing care. There are significant organizational and relational challenges involved in ensuring adequate use of interpreters by nurses. Some evidence suggests that linguistic barriers are particularly problematic for nurses when compared with physicians. A comparative analysis of nursing ethical norms for cross-linguistic nursing was conducted using the codes of ethics of the American Nurses Association, (...) the Canadian Nurses Association, and the International Council of Nurses. Five principal ethical norms for cross-linguistic nursing were identified: (1) respect for the patient as a unique person; (2) respect for the patient’s right to self-determination; (3) respect for patient privacy and confidentiality; (4) responsibility for one’s own competence, judgment, and action; and (5) responsibility to promote action better to meet the needs of patients, families, and groups. (shrink)

Hermeneutics, also referred to as interpretive phenomenology, has led to important contributions to nursing research. The philosophy of Charles Taylor has been a major source in the development of contemporary hermeneutics, through his ontological and epistemological articulations of the human sciences. The aim of this paper is to demonstrate that Taylor's ideas can further enrich hermeneutic inquiry in nursing research, particularly for investigations of ethical concerns. The paper begins with an outline of Taylor's hermeneutical framework, followed by a review of (...) his key ideas relevant for ethics research. The paper ends with a discussion of my empirical research with critically ill children in Canada and France in relation to Taylor's ideas, chiefly Social Imaginaries. I argue that Taylor's hermeneutics provides a substantive moral framework as well as a methodology for examining ethical concerns. (shrink)

In this article, the nursing health history is revisited with a hermeneutic lens to uncover means by which this tool can better serve nursing practice. It is argued that further distanciation from the developmental and medical model is necessary to accurately uncover health and history in the nurse–client encounter. Based on the works of prominent hermeneutic philosophers, such as Heidegger, Gadamer, Merleau‐Ponty, Ricoeur, and Taylor, four orientations to health history and nursing are explored: orientation to caring, orientation to narrative, orientation (...) to time, and orientation to the body. The nursing health history is used as a vehicle for illuminating the usefulness of a hermeneutic perspective in everyday nursing practice. This article reveals views of health, history, and health history that are already known to nurses and the nursing milieu but are concealed by more dominant outlooks. The hermeneutical perspective presented in this article can help to reveal the important dimensions of everyday nursing practice and foster a richer attunement with the complex health experiences of individuals. (shrink)

BackgroundFollowing the SARS pandemic, jurisdictions around the world began developing ethical resource allocation frameworks for future pandemics—one such framework was developed by Thompson and colleagues. While this framework offers a solid backbone upon which decision-makers can rest assured that their work is driven by rigorous ethical processes and principles, it fails to take into account the nuanced experiences and interests of children and youth (i.e., young people) in a pandemic context. The current COVID-19 pandemic offers an opportunity to re-examine this (...) framework from young people’s perspectives, informed by advances in childhood ethics and children’s rights.Main bodyIn this paper, we revisit the Thompson et al. framework and propose adaptations to the ethical processes and values outlined therein. This work is informed by expertise in clinical ethics and literature related to impacts of COVID-19 and other pandemics on the health and well-being of children around the world, though with particular attention to Canada. During the processes of drafting this work, stakeholders were consulted—aligned with the approach used by Thompson and colleagues—to validate the interpretations provided. We also propose a new principle, namely practicability, to indicate the complex balance between what is possible and what is convenient that is required in ethically sound decisions in the context of services affecting young people. We outline and discuss the strengths and limitations of our work and indicate next steps for scholars in the areas of childhood studies and child health.ConclusionEfforts to ensure frameworks are truly child-inclusive should be the status-quo, so pandemic impacts and policy implications can be considered in advance of emergency preparedness contexts. (shrink)

Within his earliest contributions to the human sciences, Charles Taylor challenged dominant behavioral views by advancing a hermeneutical conception of human agency. For Taylor, persons continually...

The aim of this article is to highlight the under-recognized merits of clinical ethics committees (CECs), to help ensure that the development of roles for clinical ethics consultants do not unwittingly compromise the valuable contributions that CECs can continue to provide. I argue that CECs can offer distinctive contributions to the clinical ethics consultation process that can complement and enrich the input provided by a clinical ethics consultant. These distinctions and complementarities should be further examined and developed. This will help (...) to optimize the synergistic contributions that CECs and clinical ethics consultants can make to promote the ethical treatment of patients and their families. (shrink)

In this note we provide new results of interest in the portfolio choice problem when the risky opportunities are correlated: for a general vector (X 1, X 2,..., X n ) of risky opportunities we give new conditions for stochastic comparison among different portfolios choices and new necessary and sufficient conditions to characterize the portfolio which gives the maximal expected utility.

This dissertation deals with the political uses of anger, focusing on those cases in which anger is mobilized against socially structural forms of injustice (henceforth, “radical anger”). The author provides a philosophical defence of the legitimacy and usefulness of this kind of anger, together with a set of conceptual tools for distinguishing among different instances of anger in the political realm. The text consists of seven chapters, an introduction and a short conclusion. The first chapter offers a genealogy of the (...) pathologization of radical anger, investigating the linguistic and conceptual entanglement of rage and rabies. The following chapter reviews a few cases in which oppressed groups successfully reclaimed radical anger in spite of widespread pathologizing and criminalizing tendencies, drawing mainly from the radical feminist and antiracist traditions. Special attention is also paid to the relationship between anger and violence, as well as to the opportunity for structurally discriminated groups to politically embrace anger. The metaphor of a ballistics of anger is introduced to heuristically distinguish among specific occurrences of political anger. The third chapter outlines the essential features of a political philosophy of radical anger, starting from a re-reading of Michel Foucault’s interpretation of ancient Cynicism which emphasises the angry character of the latter. After asking whether radical anger can be considered philosophically true and reactionary anger defined as untrue, three possible arguments in favour of an affirmative answer are considered. Since the first two arguments, based respectively on the works of Rahel Jaeggi and Giorgio Agamben, prove unsuccessful, a third alternative, relying mainly on the works of Foucault and Hannah Arendt, is proposed by the author. Chapters from 4 to 6 look for contemporary reprises of Cynical anger, proposing a philosophical reading of the lives and works of three figures who angrily confronted several kinds of structural injustice: Valerie Solanas, Malcolm X and Audre Lorde. The dissertation shows that each of them can offer useful additions to the political philosophy of radical anger already sketched. In particular, Solanas can help us thinking the connections between anger, negation, utopia and abolition; X testifies to the importance of the link between radical anger and the notion of care of the self (ἐπιμέλεια ἑαυτοῦ); Lorde allows us to understand the deep implications of the use of radical anger and paves the way for an erotic conception of this feeling. Finally, Chapter 7 presents the international trans-feminist movement Ni Una Menos-Non Una di Meno as an example of the practical and theoretical strengths of radical anger. (shrink)