ABSTRACT With the controversial ethical issues on the creation of human embryos through cloning for therapeutic research, which holds more promise for medical breakthroughs that the world could ever imagine and the acknowledgement by many scientists that this biotechnology may not lead in the near future to therapies; this country report discusses the approach Singapore takes on human stem cell research, interjected with the authors’ own arguments and suggestions especially on research compensation injuries, an often neglected important issue. International comparative (...) viewpoints taken by the major countries in the world are also included in the appendix. (shrink)

Background Supporting physicians in Intensive Care Units s as they face dying patients at unprecedented levels due to the COVID-19 pandemic is critical. Amidst a dearth of such data and guided by evidence that nurses in ICUs experience personal, professional and existential issues in similar conditions, a systematic scoping review is proposed to evaluate prevailing accounts of physicians facing dying patients in ICUs through the lens of Personhood. Such data would enhance understanding and guide the provision of better support for (...) ICU physicians. Methods An SSR adopts the Systematic Evidenced Based Approach to map prevailing accounts of caring for dying patients in ICUs. To enhance the transparency and reproducibility of this process, concurrent and independent use of tabulated summaries, thematic analysis and directed content analysis is adopted. Results Eight thousand three hundred fifty-eight abstracts were reviewed from four databases, 474 full-text articles were evaluated, 58 articles were included, and the Split Approach revealed six categories/themes centered around the Innate, Individual, Relational and Societal Rings of Personhood, conflicts in providing end of life care and coping mechanisms employed. Conclusion This SSR suggests that caring for dying patients in ICU impacts how physicians view their personhood. To resolve conflicts within individual concepts of personhood, physicians use prioritization, reframing and rely on accessible, personalized support from colleagues to steer coping strategies. An adapted form of the Ring Theory of Personhood is proposed to direct timely personalized, appropriate and holistic support. (shrink)

Background and ObjectivesBecause of high skin cancer risks for young women, it is vital that effective interventions reach and influence this demographic. Visual social media platforms, like Instagram, are popular with young women and are an appropriate intervention site; yet, they also host competing images idealizing tan skin. The present study tested the ability of digital sun-safety interventions to affect self-control-related emotions and visual attention to subsequent tan-ideal images as well as sun-safety attitudes.MethodsWomen were recruited from a large public Mid-Atlantic (...) university in the United States. Participants were randomly assigned to view an appearance benefits intervention, a self-control emotions intervention, or a control message, each designed to look like an Instagram sponsored story. After self-reporting self-compassion and anticipated pride, participants then viewed seven pairs of Instagram posts featuring either tan or pale women while an eye tracker assessed visual attention. Finally, participants self-reported their responses to questions assessing sun-safety-related norms, efficacy, and attitudes.ResultsA mixed design analysis of covariance revealed that women who first viewed the appearance benefits intervention story spent less time visually fixated on Instagram images of tan women than did those who viewed the self-control emotions intervention or control message. Regressions also revealed interactions between the intervention conditions and feelings of anticipated pride on both visual attention and sun-safety attitudes.ConclusionSponsored stories on Instagram can promote sun-safety attitudes, depending on the emotional responses they generate. Additionally, sponsored interventions can affect subsequent visual attention. (shrink)

In this paper we will show that Hempel's covering law model can't deal very well with explanations that are based on incomplete knowledge. In particular the symmetry thesis, which is an important aspect of the covering law model, turns out to be problematic for these explanations. We will discuss an example of an electric circuit, which clearly indicates that the symmetry of explanation and prediction does not always hold. It will be argued that an alternative logic for causal explanation is (...) needed. And we will investigate to what extent non-monotonic epistemic logic can provide such an alternative logical framework. Finally we will show that our non-monotonic logical analysis of explanation is not only suitable for simple cases such as the electric circuit, but that it also sheds new light on more controversial causal explanations such as Milton Friedman's explanation of the business cycle. (shrink)

Tianxia--conventionally translated as "all-under-Heaven"--in everyday Chinese parlance simply means "the world." But tianxia is also a geopolitical term found in canonical writings that has a deeper historical and philosophical significance. Although there are many understandings of tianxia in this literature, interpretations within the Chinese process cosmology generally begin with an ecological understanding of intra-national relations that acknowledge the mutuality and interdependence of all economic and political activity. This volume contextualizes the tianxia vision of geopolitical order within a variety of strategies (...) drawn from a broad spectrum of cultures and peoples: Buddhist, Islamic, Indian, African, Confucian, European. The conversation among the contributors is guided by several central questions: Is tianxia the only model of cosmopolitanism? Are there ideas and ideals comparable to tianxia that exist in other cultures? What alternative perspectives of global justice have inspired Western, Indian, Islamic, Buddhist, and African cultural traditions? The fundamental premise here is that in order for a planetary tianxia system to be relevant and significant for the present time and for our vision of the future, it must acknowledge the plurality of moral ideals defining the world's cultures while at the same time seek practical ways to formulate a minimalist morality that can provide the solidarity needed to bring the world's people together. (shrink)

Diagnosis theory reasons about incomplete knowledge and only considers the past. It distinguishes between violations and non-violations. Qualitative decision theory reasons about decision variables and considers the future. It distinguishes between fulfilled goals and unfulfilled goals. In this paper we formalize normative diagnoses and decisions in the special purpose formalism DIO2 as well as in extensions of the preference-based deontic logic PDL. The DIagnostic and DEcision-theoretic framework for DEontic reasoning DIO2 formalizes reasoning about violations and fulfillments, and is used to (...) characterize the distinction between normative diagnosis theory and decision theory. The extension of the preference-based deontic logic PDL shows how normative diagnostic and decision-theoretic reasoning — i.e. reasoning about violations and fulfillments — can be formalized as an extension of deontic reasoning. (shrink)

In an attempt to learn from COVID-19, this essay features six responses to the question: what did COVID-19 teach us, expose in us, or purge out of us when it comes to spiritual formation in Christ? Each response was written independently of the others by one of the coauthors. Diane J. Chandler focuses in on how COVID-19 exposed grievous inequities for ethnic groups in the American church and broader society. Kelly M. Kapic reminds us of the goodness of human finitude (...) and how COVID restrictions have forced many of us to embrace our limitations. Siang-Yang Tan reflects on eight lessons he has learned during this pandemic year in his role shepherding a local church. James C. Wilhoit calls us to consider the structures that are needed for local church leadership to make wise and godly decisions in times of crisis. Richard Peace draws our attention to what might be learned from the forced monasticism brought about by COVID-19 quarantines. Finally, Ruth Haley Barton pauses to consider the interdependence of human life that has been dramatically illustrated by this pandemic. While these six responses certainly do not exhaust all there is for the church to learn from COVID, we present them in the spirit of “O Lord, teach us what we do not see” and hope they will inspire your own reflections. (shrink)

This research analyses to what extent the use of debates on literature and cross-cutting themes presented by means of journalistic texts encourages critical thinking in the compulsory secondary education (ESO), concretely within a sample of 128 participants from third year of the secondary school. Firstly, the study investigates the effectiveness of these debates for the correct establishment of literary knowledge from the chosen book, The Life of Lazarillo de Tormes; secondly, the progression (or regression) of critical thinking among the students. (...) To do so, it has been developed and validated a required tool to measure this critical capacity, taking as a starting point Watson Glaser Critical Thinking Test; even if the test was too complex and ambiguous for the level of the students, the test fulfilled most of the requirements to perform this measurement. That is why it was decided to adapt the structure of this test to a new one, Critical Competence Test (CCT), that allows a test to be carried out to assess the key aspects of critical thinking such as identifying assumptions, evaluating arguments, drawing conclusions, and problem solving. The development of the CCT is of great importance because a short test was obtained, with an approximate duration of ten minutes and an understandable language for any level as it has been formulated on purpose for Spanish speakers. All this to facilitate the study participants to carry out the test and the improvement of critical capacity that is intended to be obtained with this research. (shrink)

Network ranging and clock synchronization based on two-way timing stamps exchange mechanism in complex GPS-denied environments is addressed in this paper. An estimator based on the Extended Kalman filter is derived, according to which, the clock skew, clock offset, and ranging information can be jointly estimated. The proposed estimator provides off-line computation by storing the transmitting timing stamps in advance and could be implemented in asymmetrical and asynchronous scenarios. The simulation results show that the proposed estimator achieves a relative good (...) performance than the existed estimators. In addition, a new Bayesian Cramér–Rao Lower Bound is derived. Numerous simulation results show that the proposed estimator meets the B-CRLB. (shrink)

Previous research has demonstrated that regular exercise modulates motor cortical plasticity and cognitive function, but the influence of short-term high-intensity interval training remains unclear. In the present study, the effect of short-term HIIT on neuroplasticity and executive function was assessed in 32 sedentary females. Half of the participants undertook 2 weeks of HIIT. Paired-pulse transcranial magnetic stimulation was used to measure motor cortical plasticity via short intracortical inhibition and intracortical facilitation. We further adapted the Stroop task using functional near-infrared spectroscopy (...) to evaluate executive function in the participants. The results indicated that, compared with the control group, the HIIT group exhibited decreased ICF. In the Stroop task, the HIIT group displayed greater activation in the left dorsolateral prefrontal cortex and left orbitofrontal cortex even though no significant difference in task performance was observed. These findings indicate that short-term HIIT may modulate motor cortical plasticity and executive function at the neural level. (shrink)

Effective social data governance rests on a bedrock of social support. Without securing trust from the populace whose information is being collected, analyzed, and deployed, policies on which such data are based will be undermined by a lack of public confidence. The COVID-19 pandemic has accelerated digitalization and datafication by governments for the purposes of contact tracing and epidemiological investigation. However, concerns about surveillance and data privacy have stunted the adoption of such contact-tracing initiatives. This commentary analyzes Singapore's contact-tracing initiative (...) to uncover the reasons for public resistance and efforts by the state to address them. The government's contact-tracing program encompassing its proprietary TraceTogether app and physical token initially triggered vociferous public criticisms of Big Brother style surveillance. Using a dialogic communication framework, we analyze the TraceTogether initiative to interrogate the communicative strategies that were used to overcome public resistance. We argue that these strategies reflect a top-down approach that prioritizes transactional dissemination of information, in line with Singapore's technocratic stance toward governance. We further assert that such communicative tactics represent missed opportunities to foster public confidence in social data governance through greater trust building. We propose solutions for more dialogic communicative forms that build trust, so that officials can develop a sound understanding of the public concerns, increase the level of public engagement, and incorporate public feedback into policies that govern data use. (shrink)

The problem of finite-time tracking control is discussed for a class of uncertain nonstrict-feedback time-varying state delay nonlinear systems with full-state constraints and unmodeled dynamics. Different from traditional finite-control methods, a C 1 smooth finite-time adaptive control framework is introduced by employing a smooth switch between the fractional and cubic form state feedback, so that the desired fast finite-time control performance can be guaranteed. By constructing appropriate Lyapunov-Krasovskii functionals, the uncertain terms produced by time-varying state delays are compensated for and (...) unmodeled dynamics is coped with by introducing a dynamical signal. In order to avoid the inherent problem of “complexity of explosion” in the backstepping-design process, the DSC technology with a novel nonlinear filter is introduced to simplify the structure of the controller. Furthermore, the results show that all the internal error signals are driven to converge into small regions in a finite time, and the full-state constraints are not violated. Simulation results verify the effectiveness of the proposed method. (shrink)

Defends an account of mathematical knowledge in which mathematical knowledge is a kind of modal knowledge. Leng argues that nominalists should take mathematical knowledge to consist in knowledge of the consistency of mathematical axiomatic systems, and knowledge of what necessarily follows from those axioms. She defends this view against objections that modal knowledge requires knowledge of abstract objects, and argues that we should understand possibility and necessity in a primative way.

This study examines discrimination in the overseas recruitment print ads of Multinational National Corporations (MNCs) in a lax regulatory environment, Singapore. Institutionalization theory suggests that in a weakly regulated environment, MNC affiliates would tend to adopt the less stringent requirements. With the lack of a strong legal framework in the host country, the home country's legal and cultural imperatives would be more salient, suggesting differences in discrimination as a function of home country imperatives. Some 1122 recruitment print ads of U.S., (...) U.K., and Japanese affiliates of MNCs were examined. While discrimination was found in the print ads of all organizations, U.S. affiliates were least discriminatory, followed by Japan and U.K. affiliates. When Singapore firms were included, they were found to be least discriminatory. However, Singapore firms became more discriminatory when the request for a recent photograph was considered in the discrimination index. Implications of the findings are discussed and suggestions for future research advanced. (shrink)

是東漢哲學家、思想家桓譚的主要論着，但早己亡佚。今存之輯本有《指海》內佚名氏輯本、清孫馮翼輯本、清嚴可均輯本、黃以周輯本，及近人朱謙之輯本，但均有不足。有鑒於此，吳則虞先生於1962年着有新輯本，收錄 二百餘條，以類相從，分為八卷，並添加附編，匯涵桓譚佚文、存疑、訂訛之文；記載桓譚事跡、著述、評論之文。 桓譚，后漢時人，官至給事中。博學多識，破讖緯迷妄，去虛妄偽飾，先於王充、張衡，具有唯物啟蒙學者之學識，是漢時哲學思想家。《新諭》是桓譚主要論着，但早已亡佚。據歷史記載，明有二卷本，清有孫之騌輯本，皆不 傳。另有《指海》內佚名氏輯本、清孫馮翼輯本、清嚴可均輯本、黃以周輯本及近人朱謙之輯本。從今日的學術、校勘、編排諸方面來看，諸本均有不足：或短椾零篇，漫無倫紀；或望文歸屬，強系篇名；或條目重復，內容雜陳 迭見；或引用刻本，多有遺漏；或雖沿用十七卷篇目之名稱，但其條目已不能再顯現原書各篇的思想內容。有鑒於此，吳則虞先生於一九六二年着有新輯本，收錄二百余條，以類相從，分為八卷，並添加附編，匯涵桓譚佚文、存 疑、訂訛之文；記載桓譚事跡、著述、評論之文；最后殿以輯校引用書目及版本之詳目，以便於讀者查閱與研究。此書成為目前桓譚《新論》集大成之著作。.

This book offers a defence of mathematical fictionalism, according to which we have no reason to believe that there are any mathematical objects. Perhaps the most pressing challenge to mathematical fictionalism is the indispensability argument for the truth of our mathematical theories (and therefore for the existence of the mathematical objects posited by those theories). According to this argument, if we have reason to believe anything, we have reason to believe that the claims of our best empirical theories are (at (...) least approximately) true. But since claims whose truth would require the existence of mathematical objects are indispensable in formulating our best empirical theories, it follows that we have good reason to believe in the mathematical objects posited by those mathematical theories used in empirical science, and therefore to believe that the mathematical theories utilized in empirical science are true. Previous responses to the indispensability argument have focused on arguing that mathematical assumptions can be dispensed with in formulating our empirical theories. This book, by contrast, offers an account of the role of mathematics in empirical science according to which the successful use of mathematics in formulating our empirical theories need not rely on the truth of the mathematics utilized. (shrink)

This paper responds to John Burgess's ‘Mathematics and _Bleak House_’. While Burgess's rejection of hermeneutic fictionalism is accepted, it is argued that his two main attacks on revolutionary fictionalism fail to meet their target. Firstly, ‘philosophical modesty’ should not prevent philosophers from questioning the truth of claims made within successful practices, provided that the utility of those practices as they stand can be explained. Secondly, Carnapian scepticism concerning the meaningfulness of _metaphysical_ existence claims has no force against a _naturalized_ version (...) of fictionalism, according to which our ordinary standards of scientific evidence may show that we have no reason to believe the mathematical existence claims made within the context of our mathematical and scientific theories. (shrink)

A phenomenological approach to mathematical practice is sketched out, and some problems with this sort of approach are considered. The approach outlined takes mathematical practices as its data, and seeks to provide an empirically adequate philosophy of mathematics based on observation of these practices. Some observations are presented, based on two case studies of some research into the classification of C*-algebras. It is suggested that an anti-realist account of mathematics could be developed on the basis of these and other studies, (...) locating the substance of mathematics in the various informal argument methods used by mathematicians. (shrink)

For many philosophers not automatically inclined to Platonism, the indispensability argument for the existence of mathematical objectshas provided the best (and perhaps only) evidence for mathematicalrealism. Recently, however, this argument has been subject to attack, most notably by Penelope Maddy (1992, 1997),on the grounds that its conclusions do not sit well with mathematical practice. I offer a diagnosis of what has gone wrong with the indispensability argument (I claim that mathematics is indispensable in the wrong way), and, taking my cue (...) from Mark Colyvan''s (1998) attempt to provide a Quinean account of unapplied mathematics as `recreational'', suggest that, if one approaches the problem from a Quinean naturalist starting point, one must conclude that all mathematics is recreational in this way. (shrink)

In the context of the changes and challenges of the 21st century, the main focus of education, especially religious education, is to prepare students to live purposeful and meaningful lives with well-developed analytic, emotional and spiritual abilities to assist them in achieving a life perspective that allows them to face the larger world with greater self-confidence and self-awareness. Therefore, the main objectives of the study are: to bring forward the concepts of religious education, emotional intelligence and spiritual intelligence; to discuss (...) the importance of emotional and spiritual literacy in children’s education; and to discuss the main strategies to enhance the educational process through emotional and spiritual intelligence. This article is a conceptual framework based on a theoretical review. The author reviews literature from books, scientific journals and research reports to develop relevant concepts. Contribution: This study provides information about two important intelligence in Christian Orthodox religious education. Recognising emotional and spiritual intelligence has allowed teachers to engage with students and help them perform at their best. Emotional intelligence and spiritual intelligence promote self-efficacy, self-awareness, self-regulation, motivation, empathy and social skills, which help students perform management tasks in their future occupations but also help them to improve relationships with parents, colleagues and God. (shrink)

Law moves, whether we notice or not. Set amongst a spatial turn in the humanities, and jurisprudence more specifically, this book calls for a greater attention to legal movement, in both its technical and material forms. Despite various ways the spatial turn has been taken up in legal thought, questions of law, movement and its materialities are too often overlooked. This book addresses this oversight, and it does so through an attention to the materialities of legal movement. Paying attention to (...) how law moves across different colonial and contemporary spaces, this book reveals there is a problem with common law's place. Primarily set in the postcolonial context of Australia - although ranging beyond this nationalised topography, both spatially and temporally - this book argues movement is fundamental to the very terms of common law's existence. How, then, might we move well? Explored through examples of walking and burial, this book responds to the challenge of how to live with a contemporary form of colonial legal inheritance by arguing we must take seriously the challenge of living with law, and think more carefully about its spatial productions, and place-making activities. Unsettling place, this book returns the question of movement to jurisprudence. (shrink)

Does greater knowledge help or hinder one’s ability to coordinate with others? While individual expertise can reveal a suitable focal point to converge on, ‘blissful’ ignorance may systematically bias decisions towards it through mere recognition. Our experiment finds in favour of the former possibility. Both specific and general knowledge are significantly associated with success in four of five coordination problems as well as over all. Our analysis suggests that more knowledgeable participants are better able to identify focal decision alternatives because (...) they are aware of more such alternatives and possess more relevant information about each. (shrink)

Background: Spasticity following a stroke occurs in about 30% of patients. The mechanisms underlying this disorder, however, are not well understood. Method: This review aims to define spasticity, describe hypotheses explaining its development after a stroke, give an overview of related neuroimaging studies as well as a description of the most common scales used to quantify the degree of spasticity and finally explore which treatments are currently being used to treat this disorder.

Introduction: Teaching and misleading -- Ethical fables and antifeminist exempla -- From sermon story to novella -- Lives of saints; lives of sinners -- Classical and vernacular exempla -- Magister amoris -- Afterword in time of plague.

This article addresses learning in desktop virtual worlds where students role play for professional education. When students role play in such virtual worlds, they can learn some knowledge and skills that are useful in the physical world. However, existing learning theories do not provide a plausible explanation of how performing non-verbal virtual world actions (e.g. performing a virtual chest examination in a virtual hospital) can lead to the learning of the physical world equivalent. Some theories are particularly implausible because they (...) claim that students learn to perform physical world actions by acting on the virtual world in an embodied way. This is implausible because learning requires a high degree of correspondence between the learning performance and the target performance, and there is insufficient physical correspondence between the performance of a virtual world action where students click on a mouse to make the avatar take actions and the physical-world equivalent where students perform the action with their own body. In this article, we use Austin’s speech act theory to provide a more plausible theory of learning in virtual worlds. We show how non-verbal virtual-world actions performed by avatars can function as performatives and as performatives, they can correspond sufficiently to physical world actions to explain how performing non-verbal virtual-world actions can lead to physical world learning. (shrink)

In this essay Olivia Newman critically examines two opposing rights claims: the liberal claim that children have a right to become liberal choosers and the fundamentalist claim that children have a right to not become liberal choosers. These positions reflect differing views regarding the value of critically choosing, rather than simply accepting, a way of life. Given their assumptions regarding preference formation, both of these rights appear untenable in light of recent scholarship in psychology: we can neither select a (...) way of life independent of our social milieu, as liberals often imply, nor can we predict how different experiences will affect our preferences, as fundamentalists assume. Nevertheless, each position points to important concerns. Children have a substantive right of exit from constraining social milieus, as liberals purport, as well as a right to respect in public institutions, as fundamentalists insist. When liberals and fundamentalists assert these more modest rights claims, educators can and should strive to satisfy both. (shrink)

Critics contend that Aristotelianism demands too much of the virtuous person in the way of knowledge to be credible. This general charge is usually directed against either of two of Aristotelianism’s apparent claims about the necessary conditions for the possession of a single virtue, namely that 1) one must know what all the other virtues require, and 2) one must also be the master of a preternatural range of technical/empirical knowledge. I argue that Aristotelianism does indeed have a very high (...) standard when it comes to the knowledge necessary for the full possession of a virtue, in both of these respects. However, focus on the necessary conditions for full virtue tends to obscure an important fact: some kinds of knowledge are much more important to various virtues than others are. A proper appreciation of the significance of this fact will go a long way toward answering critics’ worries about Aristotelianism’s knowledge requirements. (shrink)

A model of corporate ethics and social responsibility (CESR) was developed and empirically tested among Chinese business undergraduates in Hong Kong and Singapore. As predicted, it was found that CESR beliefs were negatively related to Machiavellianism and two Confucian concepts, guanxi (interpersonal connections) and mianzi (face). CESR beliefs were also lower among Hong Kong than Singaporean youths. The negative effects of guanxi, mianzi, and Machiavellianism were more pronounced for the Hong Kong than Singapore sample. Implications of these findings are discussed (...) and directions for future research suggested. (shrink)

Background: Nursing practice takes place in a social framework, in which environmental elements and interpersonal relations interact. Ethical climate of the work unit is an important element affecting nurses’ professional and ethical practice. Nevertheless, whatever the environmental circumstances, nurses are expected to be professionally competent providing high-quality care ethically and clinically. Aim: This study examined newly graduated nurses’ perception of the ethical climate of their work environment and its association with their self-assessed professional competence, turnover intentions and job satisfaction. Method: (...) Descriptive, cross-sectional, correlational research design was applied. Participants consisted of 318 newly graduated nurses. Data were collected electronically and analysed statistically. Ethical considerations: Ethical approval and permissions to use instruments and conduct the study were obtained according to required procedures. Data were rendered anonymous to protect participant confidentiality. Completing the questionnaire was interpreted as consent to participate. Findings: Nurses’ overall perception of the ethical climate was positive. More positive perceptions related to peers, patients and physicians, and less positive to hospitals and managers. Strong associations were found between perceived ethical climate and self-assessed competence, turnover intentions in terms of changing job, and job satisfaction in terms of quality of care. Nurses at a higher competence level with positive views of job satisfaction and low turnover intentions perceived the climate significantly more positively. Conclusion: Nursing management responsible for and having the power to implement changes should understand their contribution in ethical leadership, as well as the multidimensional nature of nurses’ work environment and the interaction between work-related factors in planning developmental measures. Future research should focus on issues in nurse managers’ ethical leadership in creating ethical work environments. There is also a need for knowledge of newly graduated nurses’ views of factors which act as enhancers or barriers to positive ethical climates to develop. Interventions, continuing education courses, and discussions designed to promote positive ethical climates should be developed for managers, nurses, and multi-professional teams. (shrink)

The historiography of sexology is young. It is also expanding at a remarkable pace, both in terms of the volume of publications and, more notably, in terms of its geographical, disciplinary, and intersectional reach. This special issue takes stock of these new directions, while offering new research contributions that expand our understanding of the interdisciplinary and transnational formation of this field from the late 19th through to the mid 20th century. The five articles that make up this special issue stage (...) historiographical interventions by challenging the tendency within sexological history to focus on the medical, the homosexual, the human, and the Western European at the expense of other disciplines, diagnoses, non-human subjects, and geographical locations. A particular strength of these contributions is their focus on mapping conversations among and between sexologists on both sides of the Atlantic in the early to mid 20th century – particularly in Germany, Britain, and the US – and between East and West in the early Cold War era. (shrink)

Are there genuine mathematical explanations of physical phenomena, and if so, how can mathematical theories, which are typically thought to concern abstract mathematical objects, explain contingent empirical matters? The answer, I argue, is in seeing an important range of mathematical explanations as structural explanations, where structural explanations explain a phenomenon by showing it to have been an inevitable consequence of the structural features instantiated in the physical system under consideration. Such explanations are best cast as deductive arguments which, by virtue (...) of their form, establish that, given the mathematical structure instantiated in the physical system under consideration, the explanandum had to occur. Against the claims of platonists such as Alan Baker and Mark Colyvan, I argue that formulating mathematical explanations as structural explanations in this way shows that we can accept that mathematics can play an indispensable explanatory role in empirical science without committing to the existence of any abstract mathematical objects. (shrink)