Context: Strict finitism is usually not taken seriously as a possible view on what mathematics is and how it functions. This is due mainly to unfamiliarity with the topic. Problem: First, it is necessary to present a “decent” history of strict finitism and, secondly, to show that common counterarguments against strict finitism can be properly addressed and refuted. Method: For the historical part, the historical material is situated in a broader context, and for the argumentative part, an evaluation of arguments (...) and counterarguments is presented. Results: The main result is that strict finitism is indeed a viable option, next to other constructive approaches, in mathematics. Implications: Arguing for strict finitism is more complex than is usually thought. For future research, strict finitist mathematics itself needs to be written out in more detail to increase its credibility. In as far as strict finitism is a viable option, it will change our views on such “classics” as the platonist-constructivist discussion, the discovery-construction debate and the mysterious applicability problem . Constructivist content: Strict finitism starts from the idea that counting is an act of labeling, hence the mathematician is an active subject right from the start. It differs from other constructivist views in that the finite limitations of the human subject are taken into account. (shrink)

Open peer commentary on the article “Second-Order Science: Logic, Strategies, Methods” by Stuart A. Umpleby. Upshot: The author makes a strong plea for second-order science but somehow mathematics remains out of focus. The major claim of this commentary is that second-order science requires second-order mathematics.

Everyone is familiar with the measure of beauty that has been proposed by Birkhoff, the famous formula M = O/C. Although I show that the formula in its original form cannot be maintained, I present a reinterpretation that adapts the formula for measuring the beauty of mathematical proofs. However, this type of measure is not the only aesthetic element in mathematics. There exists a 'romantic' side as well, to use the term introduced by François Le Lionnais. Thus, a more complex (...) proposal of mathematical beauty is presented. Finally and as a consequence, I argue against the dichotomy that associates science, including mathematics, with the beauty of simplicity and that associates the arts with the beauty of complexity. As an example, the work of Oulipo, Raymond Queneau in particular, is briefly presented. (shrink)

Open peer commentary on the article “Religion: A Radical-Constructivist Perspective” by Andreas Quale. Upshot: An essential feature of Quale’s point of view is the strict distinction between the cognitive and the non-cognitive. I argue that this position is untenable and hence that a radical constructivist can discuss religious matters.

What is philosophy of mathematics and what is it about? The most popular answer, I suppose, to this question would be that philosophers should provide a justification for our presently most cherished mathematical theories and for the most important tool to develop such theories, namely logico-mathematical proof. In fact, it does cover a large part of the activity of philosophers that think about mathematics. Discussions about the merits and faults of classical logic versus one or other ‘deviant’ logics as the (...) logical basis for mathematical theories, ranging from intuitionist over modal logic to paraconsistent logic, typically belong to this area, as do debates about the natural-number concept, its ‘nature’, its properties, especially its uniqueness, and so on. No doubt sociologists of knowledge could explain why philosophers of mathematics came to select these particular problems and deal with them the way they do. What it does imply, however, is that the question is meaningful whether different kinds of philosophies of mathematics are possible, and—why not?—perhaps even desirable. To a certain extent, the answer is trivial: look at what, e.g., phenomenologists have to say about mathematics and you must notice it does not fit into the scheme sketched above.1 Rather, the question should be whether there are forms that, on the one hand, reinterpret the whole enterprise, and, on the other hand, somehow remain related to the work of ‘mainstream’ philosophers of mathematics today.The book under review here does precisely that. Let me be a bit more precise. The general proposal, present throughout all the contributions, is that even at a first, superficial, glance at what mathematicians do when they do mathematics, it is far more complex than ‘just thinking about and …. (shrink)

Can business humanize its stakeholders? And if so, how does this relate to moral consideration for stakeholders? In this paper we compare two business orientations that are relevant for current business theory and practice: a stakeholder orientation and a profit orientation. We empirically investigate the causal relationships between business orientation, humanization, and moral consideration. We report the results of six experiments, making use of different operationalizations of a stakeholder and profit orientation, different stakeholders, and different participant samples. Our findings support (...) the prediction that individual stakeholders observing a stakeholder-oriented firm see the firm’s other stakeholders as more human than individual stakeholders observing a profit-oriented firm. This humanization, in turn, increases individual stakeholders’ moral consideration for the firm’s other stakeholders. Our findings underscore the importance of humanization for stakeholders’ moral consideration for each other. This paper contributes to a deeper understanding of the firm as a moral community of stakeholders. Specifically, we move away from a focus on managers, and how they can make business more moral. Instead we direct attention to stakeholders, and how business can make these stakeholders more moral. (shrink)

Context: Strict finitism is usually not taken seriously as a possible view on what mathematics is and how it functions. This is due mainly to unfamiliarity with the topic. Problem: First, it is necessary to present a “decent” history of strict finitism (which is now lacking) and, secondly, to show that common counterarguments against strict finitism can be properly addressed and refuted. Method: For the historical part, the historical material is situated in a broader context, and for the argumentative part, (...) an evaluation of arguments and counterarguments is presented. Results: The main result is that strict finitism is indeed a viable option, next to other constructive approaches, in (the foundations of) mathematics. Implications: Arguing for strict finitism is more complex than is usually thought. For future research, strict finitist mathematics itself needs to be written out in more detail to increase its credibility. In as far as strict finitism is a viable option, it will change our views on such “classics” as the platonist-constructivist discussion, the discovery-construction debate and the mysterious applicability problem (why is mathematics so successful in its applications?). Constructivist content: Strict finitism starts from the idea that counting is an act of labeling, hence the mathematician is an active subject right from the start. It differs from other constructivist views in that the finite limitations of the human subject are taken into account. (shrink)

Context: As one of the major approaches within the philosophy of mathematics, constructivism is to be contrasted with realist approaches such as Platonism in that it takes human mental activity as the basis of mathematical content. Problem: Mathematical constructivism is mostly identified as one of the so-called foundationalist accounts internal to mathematics. Other perspectives are possible, however. Results: The notion of “meaning finitism” is exploited to tie together internal and external directions within mathematical constructivism. The various contributions to this issue (...) support our case in different ways. Constructivist content: Further contributions from a multitude of constructivist directions are needed for the puzzle of an integrative, overarching theory of mathematical practice to be solved. (shrink)

Health care professionals often face moral dilemmas. Not dealing constructively with moral dilemmas can cause moral distress and can negatively affect the quality of care. Little research has been documented with methodologies meant to support professionals in care for the homeless in dealing with their dilemmas. Moral case deliberation is a method for systematic reflection on moral dilemmas and is increasingly being used as ethics support for professionals in various health-care domains. This study deals with the question: What is the (...) contribution of MCD in helping professionals in an institution for care for the homeless to deal with their moral dilemmas? A mixed-methods responsive evaluation design was used to answer the research question. Five teams of professionals from a Dutch care institution for the homeless participated in MCD three times. Professionals in care for the homeless value MCD positively. They report that MCD helped them to identify the moral dilemma/question, and that they learned from other people’s perspectives while reflecting and deliberating on the values at stake in the dilemma or moral question. They became aware of the moral dimension of moral dilemmas, of related norms and values, of other perspectives, and learned to formulate a moral standpoint. Some experienced the influence of MCD in the way they dealt with moral dilemmas in daily practice. Half of the professionals expect MCD will influence the way they deal with moral dilemmas in the future. Most of them were in favour of further implementation of MCD in their organization. (shrink)

An international group of distinguished scholars brings a variety of resources to bear on the major issues in the study and teaching of mathematics, and on the problem of understanding mathematics as a cultural and social phenomenon. All are guided by the notion that our understanding of mathematical knowledge must be grounded in and reflect the realities of mathematical practice. Chapters on the philosophy of mathematics illustrate the growing influence of a pragmatic view in a field traditionally dominated by platonic (...) perspectives. In a section on mathematics, politics, and pedagogy, the emphasis is on politics and values in mathematics education. Issues addressed include gender and mathematics, applied mathematics and social concerns, and the reflective and dialogical nature of mathematical knowledge. The concluding section deals with the history and sociology of mathematics, and with mathematics and social change. Contributors include Philip J. Davis, Helga Jungwirth, Nel Noddings, Yehuda Rav, Michael D. Resnik, Ole Skovsmose, and Thomas Tymoczko. (shrink)

Background: Mental healthcare needs person-tailored interventions. Experience Sampling Method (ESM) can provide daily life monitoring of personal experiences. This study aims to operationalize and test a measure of momentary reward-related Quality of Life (rQoL). Intuitively, quality of life improves by spending more time on rewarding experiences. ESM clinical interventions can use this information to coach patients to find a realistic, optimal balance of positive experiences (maximize reward) in daily life. rQoL combines the frequency of engaging in a relevant context (a (...) ‘behavior setting’) with concurrent (positive) affect. High rQoL occurs when the most frequent behavior settings are combined with positive affect or infrequent behavior settings co-occur with low positive affect. Methods: Resampling procedures (Monte Carlo experiments) were applied to assess the reliability of rQoL using various behavior setting definitions under different sampling circumstances, for real or virtual subjects with low-, average- and high contextual variability. Furthermore, resampling was used to assess whether rQoL is a distinct concept from positive affect. Virtual ESM beep datasets were extracted from 1058 valid ESM observations for virtual and real subjects. Results: Behavior settings defined by Who-What contextual information were most informative. Simulations of at least 100 ESM observations are needed for reliable assessment. Virtual ESM beep datasets of a real subject can be defined by Who-What-Where behavior setting combinations. Large sample sizes are necessary for reliable rQoL assessments, except for subjects with low contextual variability. rQoL is distinct from positive affect. Conclusion: rQoL is a feasible concept. Monte Carlo experiments should be used to assess the reliable implementation of an ESM statistic. Future research in ESM should asses the behavior of summary statistics under different sampling situations. This exploration is especially relevant in clinical implementation, where often only small datasets are available. (shrink)

The aim of this research was to gain insight into the experiences and perspectives of individual members of a Medical Research Ethics Committee regarding their individual roles and possible tensions within and between these roles. We conducted a qualitative interview study among members of a large MREC, supplemented by a focus group meeting. Respondents distinguish five roles: protector, facilitator, educator, advisor and assessor. Central to the role of protector is securing valid informed consent and a proper risk-benefit analysis. The role (...) of facilitator implies that respondents want to think along with and assist researchers in order to help medical science progress. As educators, the respondents want to raise ethical and methodological awareness of researchers. The role of advisor implies that respondents bring in their own expertise. The role of assessor points to contributing to the overall evaluation of the research proposal. Various tensions were identified within and between roles. Within the role of protector, a tension is experienced between paternalism and autonomy. Between the role of protector and facilitator tensions occur when the value of a study is questioned while risks and burdens for the subjects are negligible. Within the role of assessor, a tension is felt between the implicit nature of judgments and the need for more explicit formulations. Awareness of various roles and responsibilities may prevent one-sided views on MREC work, not only by members themselves, but also by researchers. Tensions within and between the roles require reflection by MREC members. (shrink)

The aim of this research was to gain insight into the experiences and perspectives of individual members of a Medical Research Ethics Committee regarding their individual roles and possible tensions within and between these roles. We conducted a qualitative interview study among members of a large MREC, supplemented by a focus group meeting. Respondents distinguish five roles: protector, facilitator, educator, advisor and assessor. Central to the role of protector is securing valid informed consent and a proper risk-benefit analysis. The role (...) of facilitator implies that respondents want to think along with and assist researchers in order to help medical science progress. As educators, the respondents want to raise ethical and methodological awareness of researchers. The role of advisor implies that respondents bring in their own expertise. The role of assessor points to contributing to the overall evaluation of the research proposal. Various tensions were identified within and between roles. Within the role of protector, a tension is experienced between paternalism and autonomy. Between the role of protector and facilitator tensions occur when the value of a study is questioned while risks and burdens for the subjects are negligible. Within the role of assessor, a tension is felt between the implicit nature of judgments and the need for more explicit formulations. Awareness of various roles and responsibilities may prevent one-sided views on MREC work, not only by members themselves, but also by researchers. Tensions within and between the roles require reflection by MREC members. (shrink)

OBJECTIVES: To identify the factors that influence the assessment of reported cases of physician-assisted death by members of the public prosecution. DESIGN/SETTING: At the beginning of 1996, during verbal interviews, 12 short case-descriptions were presented to a representative group of 47 members of the public prosecution in the Netherlands. RESULTS: Assessment varied considerably between respondents. Some respondents made more "lenient" assessments than others. Characteristics of the respondents, such as function, personal-life philosophy and age, were not related to the assessment. Case (...) characteristics, i.e. the presence of an explicit request, life expectancy and the type of suffering, strongly influenced the assessment. Of these characteristics, the presence or absence of an explicit request was the most important determinant of the decision whether or not to hold an inquest. CONCLUSIONS: Although the presence of an explicit request, life expectancy and the type of suffering each influenced the assessment, each individual assessment was dependent on the assessor. The resulting danger of legal inequality and legal uncertainty, particularly in complicated cases, should be kept to a minimum by the introduction of some form of protocol and consultation in doubtful or boundary cases. The notification procedure already promotes a certain degree of uniformity in the prosecution policy. (shrink)