Every constitution defines and is defined by a period in time. Like all law the creation and application of constitutions require reference to the past and future respectively. Every instance of constitution‐making is an attempt to control behavior over an extended period of time. Therefore constitutions will be drafted, both in style and substance, to reflect that temporal ambition. The effectiveness of a constitution also requires that its interpretation makes reference to the understanding of its rules held by the constitution‐makers. (...) As a result, and notwithstanding the efforts to make it suitable over a long period by its creators, every constitution is bound to become unsuitable. Courts employ a number of devices to cope with the inevitable obsolescence of constitutions but, sooner or later, every constitution will have to be discarded and a new constitutional era begun. (shrink)

This paper starts by investigating Ackermann's interpretation of finite set theory in the natural numbers. We give a formal version of this interpretation from Peano arithmetic (PA) to Zermelo-Fraenkel set theory with the infinity axiom negated (ZF−inf) and provide an inverse interpretation going the other way. In particular, we emphasize the precise axiomatization of our set theory that is required and point out the necessity of the axiom of transitive containment or (equivalently) the axiom scheme of ∈-induction. This clarifies the (...) nature of the equivalence of PA and ZF−inf and corrects some errors in the literature. We also survey the restrictions of the Ackermann interpretation and its inverse to subsystems of PA and ZF−inf, where full induction, replacement, or separation is not assumed. The paper concludes with a discussion on the problems one faces when the totality of exponentiation fails, or when the existence of unordered pairs or power sets is not guaranteed. (shrink)

We show that Matijasevič's Theorem on the diophantine representation of r.e. predicates is provable in the subsystem I ∃ - 1 of Peano Arithmetic formed by restricting the induction scheme to diophantine formulas with no parameters. More specifically, I ∃ - 1 ⊢ IE - 1 + E ⊢ Matijasevič's Theorem where IE - 1 is the scheme of parameter-free bounded existential induction and E is an ∀∃ axiom expressing the existence of a function of exponential growth. We conclude by (...) examining the consequences of these results to the structure of countable nonstandard models of IE - 1. (shrink)

We generalize Specker's theorem on typical ambiguity, that NF and TST + Ambiguity have the same stratified consequences, to the subschemes Amb(Γ) of ambiguity restricted to classes of sentences Γ with certain natural closure conditions.

This undergraduate textbook covers the key material for a typical first course in logic, in particular presenting a full mathematical account of the most important result in logic, the Completeness Theorem for first-order logic. Looking at a series of interesting systems, increasing in complexity, then proving and discussing the Completeness Theorem for each, the author ensures that the number of new concepts to be absorbed at each stage is manageable, whilst providing lively mathematical applications throughout. Unfamiliar terminology is kept to (...) a minimum, no background in formal set-theory is required, and the book contains proofs of all the required set theoretical results. The reader is taken on a journey starting with König's Lemma, and progressing via order relations, Zorn's Lemma, Boolean algebras, and propositional logic, to completeness and compactness of first-order logic. As applications of the work on first-order logic, two final chapters provide introductions to model theory and nonstandard analysis. (shrink)

Hilbert's tenth problem for a theory T asks if there is an algorithm which decides for a given polynomial p() from [] whether p() has a root in some model of T. We examine some of the model-theoretic consequences that an affirmative answer would have in cases such as T = Open Induction and others, and apply these methods by providing a negative answer in the cases when T is some particular finite fragment of the weak theories IE1 or IU-1.

We expand the notion of resplendency to theories of the kind T + p", where T is a fi rst-order theory and p" expresses that the type p is omitted. We investigate two di erent formulations and prove necessary and sucient conditions for countable recursively saturated models of PA. Some of the results in this paper can be found in one of the author's doctoral thesis [3].

We consider the quantifier hierarchy of Takahashi [1972] and show how it gives rise to reflection theorems for some large cardinals in ZF, a new natural subtheory of Zermelo's set theory, a potentially useful new reduction of the consistency problem for Quine's NF, and a sharpening of another reduction of this problem due to Boffa.

Let ${\mathfrak{M}}$ be a nonstandard model of Peano Arithmetic with domain M and let ${n \in M}$ be nonstandard. We study the symmetric and alternating groups S n and A n of permutations of the set ${\{0,1,\ldots,n-1\}}$ internal to ${\mathfrak{M}}$ , and classify all their normal subgroups, identifying many externally defined such normal subgroups in the process. We provide evidence that A n and S n are not split extensions by these normal subgroups, by showing that any such complement if (...) it exists, cannot be a limit of definable sets. We conclude by identifying an ${\mathbb{R}}$ -valued metric on ${\tilde{S}_n = S_n /B_S}$ and ${\tilde{A}_n = A_n /B_A}$ (where B S , B A are the maximal normal subgroups of S n and A n identified earlier) making these groups into topological groups, and by showing that if ${\mathfrak{M}}$ is ${\mathfrak\aleph_1}$ -saturated then ${\tilde{S}_n}$ and ${\tilde{A}_n}$ are complete with respect to this metric. (shrink)

Yet, the central conviction that informs this volume is that phenomenology provides extraordinary insights into many of the issues that are directly addressed ...

In this paper I reflect upon my personal experience of chronic progressive multiple sclerosis in order to provide a phenomenological account of the human experience of disability. In particular, I argue that the phenomenological notion of lived body provides important insights into the profound disruptions of space and time that are an integral element of changed physical capacities such as loss of mobility. In addition, phenomenology discloses the emotional dimension of physical disorder. The lived body disruption engendered by loss of (...) mobility includes a change in the character of surrounding space, an alteration in one's taken-for-granted awareness of objects, the disruption of corporeal identity, a disturbance in one's relations with others, and a change in the character of temporal experience. The loss of upright posture is of particular significance since it not only concretely diminishes autonomy but affects the way one is treated by others. Such a change in posture is, therefore, particularly disruptive in the social world of everyday life. An understanding of the lived body disruption engendered by disability has important applications for the clinical context in devising effective therapies, as well as for the social arena in determining how best to resolve the various challenges posed by chronic disabling disorders. (shrink)

This essay argues that philosophical phenomenology can provide important insights into the patient-physician relationship. In particular, it is noted that the physician and patient encounter the experience of illness from within the context of different "worlds", each "world" providing a horizon of meaning. Such phenomenological notions as focusing, habits of mind, finite provinces of meaning, and relevance are shown to be central to the way these "worlds" are constituted. An eidetic interpretation of illness is proposed. Such an interpretation discloses certain (...) essential characteristics that pertain to the experience of illness, per se , regardless of its manifestation in terms of a particular disease state. It is suggested that, if a shared world of meaning is to be constituted between physician and patient, the eidetic characteristics of illness must be recognized by the physician. Keywords: phenomenology, patient-physician relationship, illness-as-lived, habits of mind, relevance, eidetic CiteULike Connotea Del.icio.us What's this? (shrink)

This paper suggests that the paradigm of lived body (as it is developed in the works of Merleau-Ponty, Sartre and Zaner) provides important insights into the experience of illness. In particular it is noted that, as embodied persons, we experience illness primarily as a disruption of lived body rather than as a dysfunction of biological body. An account is given of the manner in which such fundamental features of embodiment as bodily intentionality, primary meaning, contextural organization, body image, gestural display, (...) lived spatiality and temporality, are disrupted in illness causing a concurrent disorganization of the patient's self and world. The paradigm of lived body has important applications for medical practice. It provides a fuller account of illness than does the prevailing reductionist Cartesian paradigm of body, more directly addresses the existential predicament of illness, and orients the clinical focus around the personhood of the patient. (shrink)

In this paper I briefly summarize Pellegrino’s phenomenological analysis of the ethics of the physician–patient relationship. In delineating the essential elements of the healing relationship, Pellegrino demonstrates the necessity for health care professionals to understand the patient’s lived experience of illness. In considering the phenomenon of illness, I identify certain essential characteristics of illness-as-lived that provide a basis for developing a rigorous understanding of the patient’s experience. I note recent developments in the systematic delivery of health care that make it (...) difficult for health care professionals to realize Pellegrino’s ethical model of the role of healer. Such developments limit both the physician’s freedom to act on behalf of the patient without the constraint of third parties and the physician’s freedom to act in light of his or her own ethical or religious convictions. Given these difficulties, I note MacIntyre’s call for the development of moral communities, as an alternative to the prevailing culture, and share a first-hand example illustrating how intentional Christian community provides an alternative nurturing context that permits the full development of the healing relationship. (shrink)

In 'On interpretations of arithmetic and set theory', Kaye and Wong proved the following result, which they considered to belong to the folklore of mathematical logic.

THEOREM 1 The first-order theories of Peano arithmetic and Zermelo-Fraenkel set theory with the axiom of infinity negated are bi-interpretable.

In this note, I describe a theory of sets that is bi-interpretable with the theory of bounded arithmetic IDelta0 + exp. Because of the weakness of this theory of sets, I cannot straightforwardly adapt Kaye and Wong's (...) interpretation of the arithmetic in the set theory. Instead, I am forced to produce a different interpretation. (shrink)

This essay argues that, while much has been gained by medicine's focus on the spatial aspects of disease in light of developments in modern pathology, too little attention has been given to the temporal experience of illness at the subjective level of the patient. In particular, it is noted that there is a radical distinction between subjective and objective time. Whereas the patient experiences his immediate illness in terms of the ongoing flux of subjective time, the physician conceptualizes the illness (...) as a disease state according to the measurements of objective time. A greater understanding of this disparity in temporal experiencing provides insights into the lived experience of illness and can preclude difficulties in communication between physician and patient. (shrink)

Book reviewed in this article: The Meaning of Illness. By S. Kay Toombs.

In this essay I discuss Edith Stein's analysis of empathy and note its application in the field of clinical medicine. In identifying empathy as the basic mode of cognition in which one grasps the experiences of others, Stein notes, 'I grasp the Other as a living body and not merely as a physical body'. The living body is given in terms of five distinctive characteristics - characteristics that disclose important facets of the illness experience. Empathy plays an important role in (...) clinical practice in aiding physicians to grasp the content of first-person reports of bodily disorder, and to comprehend the meaning of illness-as-lived. I suggest that an important task for medical education should be that of developing students' capacity for empathic understanding and I note several ways in which this task might be accomplished. (shrink)

In order to gain greater insight into the nature of corporate social responsibility (CSR) during a time of crisis, the study examines the commitment of firms to continue to engage in CSR activity despite financial pressures to divert their slack resources elsewhere. The setting of the study is CSR activity during the perhaps unprecedented global crisis associated with the COVID-19 pandemic. Based on a qualitative research method approach, both a variety of media sources and the relevant academic literature are reviewed (...) in order to identify examples of CSR activity related specifically to COVID-19. The examples are then categorized and situated according to Professor Archie Carroll’s well-known CSR Pyramid framework describing the economic, legal, ethical, and philanthropic domains of CSR. As such, this study is the first to extend the rich literature stream utilizing Carroll’s CSR Pyramid within the unique context of a global pandemic. (shrink)

While it seems to be evident that the vision of the eternal return of the same is the solution to the riddle mentioned in "On the vision and the riddle," exactly what constitutes the riddle is anything but clear. Li ke all good riddles the solution demands a paradigm shift. Nietzsche's riddle is solved by a radical rethinking of the concept of time, from a straight line to a circle. I give a detailed account of how Nietzsche's riddle is formulated (...) in such a way tha t the eternal return of the same is the only possible solution. (shrink)

How transcription factors achieve their in vivo specificities is a fundamental question in biology. For the Homeotic Complex (HOM/Hox) family of homeoproteins, specificity in vivo is likely to be in part determined by subtle differences in the DNA binding properties inherent in these proteins. Some of these differences in DNA binding are due to sequence differences in the N‐terminal arms of HOM/Hox homeodomains. Evidence also exists to suggest that cofactors can modify HOM/Hox function by cooperative DNA binding interactions. The Drosophila (...) homeoprotein extradenticle (exd) is likely to be one such cofactor. In HOM/Hox proteins, both the conserved ‘YPWM’ peptide motif and the homeodomain are important for interacting with exd. Although exd provides part of the answer as to how specificity is achieved, there may be additional cofactors and mechanisms that have yet to be identified. (shrink)