Simpson has claimed that “ATR0 is the weakest set of axioms which permits the development of a decent theory of countable ordinals” [8]. This paper provides empirical support for Simpson's claim. In particular, Cantor's Normal Form Theorem and Sherman's Inequality for countable well-orderings are both equivalent to ATR0. The proofs of these results require a substantial development of ordinal exponentiation and a strengthening of the comparability result in [3].

One of the earliest applications of Cantor's Normal Form Theorem is Jacobstahl's proof of the existence of prime factorizations of ordinals. Applying the techniques of reverse mathematics, we show that the full strength of the Normal Form Theorem is used in this proof.

: This paper considers whether a physician is criminally liable for administering a dose of painkillers that hastens a patient's death. The common wisdom is that a version of the doctrine of double effect legally protects the physician. That is, a physician is supposedly acting lawfully so long as the physician's primary purpose is to relieve suffering. This paper suggests that the criminal liability issue is more complex than that. Physician culpability can be based on recklessness, and recklessness hinges on (...) whether a physician has taken an unjustifiable risk of hastening death. The authors identify three conditions of justifiability. Their analysis helps to explain the distinction between euthanasia, which is legally banned, and the use of risky analgesics, which is permitted in limited circumstances. (shrink)

Carlos F. Gomez, Regulating Death New Yorrk: Free Press, 1991, xx +172 pp.

Some people will confront Alzheimer's with a measure of resignation, a determination to struggle against the progressive debilitation and to extract whatever comforts and benefits they can from their remaining existence. They are entitled to pursue that resolute path. For other people, like myself, protracted maintenance during progressive cognitive dysfunction and helplessness is an intolerably degrading prospect. The critical question for those of us seeking to avoid protracted dementia is how best to accomplish that objective.One strategy is to engineer one's (...) own death while still mentally competent to do so (even in the stage of mild dementia). If I were to use a preemptive strategy in the face of a dementia diagnosis, I would probably choose to stop eating and drinking, a process known as voluntarily stopping eating and drinking. An alternative tactic for avoiding prolonged dementia would be to allow oneself to decline into moderate dementia—thus losing capacity to perform self‐deliverance or even to make serious medical decisions—but before getting to that point to provide advance instructions rejecting prospective life‐sustaining medical interventions. These advance instructions would authorize palliative but not curative measures. My current personal instructions define the point of intolerable cognitive decline triggering medical nonintervention as “mental deterioration to a point when I can no longer read and understand written material such as a newspaper or financial records such as a checkbook.” These instructions dictate allowing my demise at a point of moderate dementia when I may not be perceptibly suffering, when I may still be getting some rudimentary satisfaction from my debilitated life, and when I no longer recall the preoccupation with personally intolerable indignity that motivated my instructions. Can I expect that my advance instructions will be implemented in those circumstances? Is it lawful, and is it moral for a surrogate decision‐maker and associated caregivers to allow an uncomprehending, ostensibly content but demented individual to die? My analysis herein contends that it is not only lawful and moral but also legally required to implement clear, considered advance instructions even at a stage of moderate dementia. (shrink)

The American Journal of Bioethics, Volume 12, Issue 6, Page 12-13, June 2012.

George Annas serves a critical function as an incisive commentator on the interactions between law and medicine and law and public health. Along with Alex Capron, Dena Davis, Rebecca Dresser, and Larry GostinProfessor Annas analyses legal aspects of a spectrum of medicolegal issues both in a forum and in a manner that makes them accessible and understandable to a broad community of healthcare providers. His latest book, SomeChoice, continues that valuable tradition. The bulk of the volume (17 out of 22 (...) chapters) is drawn from essays originally published as the feature of the NewEnglandJournalofMedicine. The topics include such staples of patients' rights debate as the boundaries of informed consent, authorization of medical experiments, and physician-assisted suicide. A treat is the inclusion of less frequently covered issues, such as access to health information concerning presidential candidates and constitutional bounds of limits on cigarette advertising. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Criminal Law, Pain Relief, and Physician Aid in DyingFaye Girsh, Ed.D., Executive DirectorMadam:The article by Cantor and Thomas on “Pain Relief, Acceleration of Death, and Criminal Law” (KIEJ, June 1996) was a tortured attempt to develop criteria for the humane and compassionate physician who tries to serve the needs of a patient in unremitting pain. There are three areas that merit comment.The authors dealt with pain medications that (...) might have the undesirable side effect of causing death. They did not mention tolerance, which usually occurs in a patient with chronic pain and which would require exceedingly high doses to be effective. They did not mention barbiturates, which are preferable to opiates in causing death and which are used increasingly by compassionate physicians to answer the pleas of their suffering patients, but for which there is no excuse about alleviating pain. Would the criminal law just call the prescription of a lethal dose of barbiturates a reckless act and require conviction? Fortunately, juries, as the authors point out, do not balance these formulas on the head of a pin. When they see the circumstances under which these doctors do help their patients, they choose to nullify the law and would ignore the suggestions made in this article.The authors refer to the “consent” of the patient. They do not mention that these doctors are operating with more than consent; they are administering these medications because suffering patients are begging them to put them out of their pain and the indignities of the dying process. The article discusses the process as though it were the same as consent to elective surgery. These patients—with AIDS, cancer, and hopeless neurological degeneration—are not simply agreeing to a procedure; they are desperately seeking a way out. If the criminal law were to develop criteria for physician aid in dying, certainly one of them should be the active, witnessed, repeated request of such a patient for a certain, quick, painless, gentle death.The third point is that physicians do not face prosecution when administering no treatment to a patient whose life could be saved with treatment but who chooses not to receive it. This has been upheld by the U.S. Supreme Court; no criteria for suffering, alternatives, terminality, justifiability, or unbearability are required. The doctor can stand by while the patient dies what may be a protracted, difficult death, but it is within the law. What matters in this situation is the decision of the patient to refuse treatment, and that is absolute. How ironic that the patient who cannot refuse treatment must, with his or her doctor, jump through all these hoops to achieve a peaceful death.One worries that the physician who must balance the risk of “risky pain relief” against the accusation of recklessness will err in the direction of allowing [End Page 103] the patient to bear the pain rather than help with a dose of analgesics that might be considered beyond the stipulated “risk.”Why don’t we just be honest about it? Allow dying or hopelessly ill patients to make the decision about what they want by passing a carefully defined law allowing euthanasia rather than balancing the risk and trying to determine the “purpose” of the physician’s ministrations. We protect some patients from themselves while allowing others almost complete autonomy to make the choice of ending their lives. The authors were right in saying that proponents of rational laws consider this sheer hypocrisy.Faye Girsh, Executive DirectorHemlock Society U.S.A. Denver, COFaye Girsh misconceives our article’s objective as an “attempt to develop criteria” for the humane physician. Our goal in writing the paper was to analyze the current criminal law framework in the hope of sharpening debate and engendering normative critiques. We readily acknowledge tensions in the current legal framework and would support changes in that framework.Copyright © 1997 The Johns Hopkins University Press... (shrink)

This rich and varied collection of essays addresses some of the most fundamental human questions through the lenses of philosophy, literature, religion, politics, and theology. Peter Augustine Lawler and Dale McConkey have fashioned an interdisciplinary consideration of such perennial and enduring issues as the relationship between nature and history, nature and grace, reason and revelation, classical philosophy and Christianity, modernity and postmodernity, repentance and self-limitation, and philosophy and politics.

Ever since the 1960s, when medical science became capable of prolonging the dying process beyond bounds that many patients would find acceptable, people have sought “death with dignity,” or “a natural death,” or “a good death.” Once debilitation from a fatal affliction has reached a personally intolerable point, dying patients have sought to control the manner and timing of death via diverse techniques. Some sought the disconnection of life-sustaining medical interventions, such as respirators and dialysis machines. Beyond freedom from unwelcome (...) interventions, some patients intent on avoiding suffering sought access to pain relief medication—even in dosages posing some risk of hastening death. Other dying patients sought access to deep sedation, even knowing that they would never emerge from the resultant unconsciousness. Still other patients voluntarily refused to eat or drink or to accept artificial nutrition and hydration. (shrink)

Ever since the 1960s, when medical science became capable of prolonging the dying process beyond bounds that many patients would find acceptable, people have sought “death with dignity,” or “a natural death,” or “a good death.” Once debilitation from a fatal affliction has reached a personally intolerable point, dying patients have sought to control the manner and timing of death via diverse techniques. Some sought the disconnection of life-sustaining medical interventions, such as respirators and dialysis machines. Beyond freedom from unwelcome (...) interventions, some patients intent on avoiding suffering sought access to pain relief medication—even in dosages posing some risk of hastening death. Other dying patients sought access to deep sedation, even knowing that they would never emerge from the resultant unconsciousness. Still other patients voluntarily refused to eat or drink or to accept artificial nutrition and hydration. (shrink)

This collection of essays, offered in honor of the distinguished career of prominent political philosophy professor Clifford Orwin, brings together internationally renowned scholars to provide a wide context and discuss various aspects of the virtue of “humanity” through the history of political philosophy.

This collection of essays, offered in honor of the distinguished career of prominent political philosophy professor Clifford Orwin, brings together internationally renowned scholars to provide a wide context and discuss various aspects of the virtue of “humanity” through the history of political philosophy.

It is a celebrated result of McKinsey and Tarski [28] thatS4is the logic of the closure algebraΧ+over any dense-in-itself separable metrizable space. In particular,S4is the logic of the closure algebra over the realsR, the rationalsQ, or the Cantor spaceC. By [5], each logic aboveS4that has the finite model property is the logic of a subalgebra ofQ+, as well as the logic of a subalgebra ofC+. This is no longer true forR, and the main result of [5] states that each (...) connected logic aboveS4with the finite model property is the logic of a subalgebra of the closure algebraR+.In this paper we extend these results to all logics aboveS4. Namely, for a normal modal logicL, we prove that the following conditions are equivalent: (i)Lis aboveS4, (ii)Lis the logic of a subalgebra ofQ+, (iii)Lis the logic of a subalgebra ofC+. We introduce the concept of a well-connected logic aboveS4and prove that the following conditions are equivalent: (i)Lis a well-connected logic, (ii)Lis the logic of a subalgebra of the closure algebra$\xi _2^ + $over the infinite binary tree, (iii)Lis the logic of a subalgebra of the closure algebra${\bf{L}}_2^ + $over the infinite binary tree with limits equipped with the Scott topology. Finally, we prove that a logicLaboveS4is connected iffLis the logic of a subalgebra ofR+, and transfer our results to the setting of intermediate logics.Proving these general completeness results requires new tools. We introduce the countable general frame property (CGFP) and prove that each normal modal logic has the CGFP. We introduce general topological semantics forS4, which generalizes topological semantics the same way general frame semantics generalizes Kripke semantics. We prove that the categories of descriptive frames forS4and descriptive spaces are isomorphic. It follows that every logic aboveS4is complete with respect to the corresponding class of descriptive spaces. We provide several ways of realizing the infinite binary tree with limits, and prove that when equipped with the Scott topology, it is an interior image of bothCandR. Finally, we introduce gluing of general spaces and prove that the space obtained by appropriate gluing involving certain quotients ofL2is an interior image ofR. (shrink)

The Human Genome Project (HGP) has been criticised from an evolutionary perspective for three reasons: completely ignoring genetic variation; improperly treating either all or some genetic variation as deviation from a norm; and mistakenly seeking to define species in terms of essential properties possessed by all and only member organisms. The first claim is unfounded; the second and third claims are more on target. Nevertheless, it is a mistake to use the typological-population distinction to oppose molecular genetics and evolutionary genetics (...) in order to characterise HGP mapping and sequencing aims, especially the production of a DNA reference sequence, as 'anti-evolutionary' and 'pre-Darwinian.' These aims are consistent with certain strands in twentieth-century evolutionary thought: Muller's classical theory, Kimura's neutral and 'effectively neutral' theories, and, to a lesser extent, Dobzhansky's balance theory of the genetic structure of natural populations. In practice, population-based approaches to human genetic variation are similarly vulnerable to charges of 'typological' and 'essentialist' thinking in their treatment of genetic variation as deviation. This means that the Human Genome Diversity Initiative will not provide a population-based panacea for an overly typological HGP, as its proponents contend. Substituting related, and less rhetorically-charged, conceptual, empirical, and metaphysical distinctions for the typological-population distinction furnishes a better way to assess the concept of the normal genome from an evolutionary perspective. (shrink)

This article raises the question of ‘normality’ today and the fracturing of health ideals along new lines of enablement and function. In particular the study asks if ‘functional’ and ‘dysfunctional’ are displacing ‘normal’ and ‘pathological’ as master biopolitical binarisms, and if so, what distinctions can be drawn between them. The discourse of ‘function’ and ‘dysfunction’ is certainly ubiquitous in two areas of research and practice: gerontology and sexology. In the former case ‘functional health’ is linked to successful aging represented (...) by technical tests around activities of daily living (ADLs) and risk-assessment profiles. In the latter case, sexual function and dysfunction have become all-encompassing markers of heterosexual competence, now largely detached from reproductive imperatives, but refashioned as integral to responsible and successful self-management. Presenting examples from both cases, the article concludes that functionality, circulating under the signs of ‘normal’, ‘natural’ and ‘healthy’, furnishes economic, technological, educational, professional, pharmacological and policy fields with a rich intellectual, practical and regulatory resource. (shrink)

Three variants of Beth's definability theorem are considered. Let L be any normal extension of the provability logic G. It is proved that the first variant B1 holds in L iff L possesses Craig's interpolation property. If L is consistent, then the statement B2 holds in L iff L = G + {0}. Finally, the variant B3 holds in any normal extension of G.

À l'heure où tant de discours prônent des sociétés dites 'inclusives,' dans nos vies quotidiennes, la vulnérabilité est encore trop souvent perçue comme le versant négatif de l'autonomie, un moment de l'existence qu'il faut impérativement dépasser pour pouvoir construire l'identité d'un sujet libre et autonome. Et si, à l'inverse, la construction d'une identité forte ne pouvait advenir que grâce à l'articulation entre vulnérabilité, comme condition normale de l'existence, et autonomie? Fruit d'un travail collectif, cet ouvrage souhaite prouver, à l'aide de (...) la pensée de philosophes comme Paul Ricoeur, Emmanuel Levinas, Michel Henry, Martha Nussbaum ou encore Platon et Aristote, comment le déni de la vulnérabilité, bien que compréhensible, peut devenir "toxique" lorsqu'il n'est pas démasqué. Cela aussi bien pour l'individu que pour la société. Un livre qui croise de multiples regards, la philosophie, le droit, les sciences de la santé, la politique, pour éclairer la façon dont nos modes de vie et l'organisation de nos sociétés pourraient changer, y compris d'un point de vue pratique, si vulnérabilité et autonomie étaient considérées comme des moments indispensables et complémentaires du développement de l'identité du sujet."--Back cover. (shrink)