Considered by many to be Abraham Robinson's magnum opus, this book offers an explanation of the development and applications of non-standard analysis by the mathematician who founded the subject. Non-standard analysis grew out of Robinson's attempt to resolve the contradictions posed by infinitesimals within calculus. He introduced this new subject in a seminar at Princeton in 1960, and it remains as controversial today as it was then. This paperback reprint of the 1974 revised edition is indispensable reading for anyone interested (...) in non-standard analysis. It treats in rich detail many areas of application, including topology, functions of a real variable, functions of a complex variable, and normed linear spaces, together with problems of boundary layer flow of viscous fluids and rederivations of Saint-Venant's hypothesis concerning the distribution of stresses in an elastic body. (shrink)

Is fertility relevant to evolutionary analyses conducted in modern industrial societies? This question has been the subject of a highly contentious debate, beginning in the late 1980s and continuing to this day. Researchers in both evolutionary and social sciences have argued that the measurement of fitness-related traits (e.g., fertility) offers little insight into evolutionary processes, on the grounds that modern industrial environments differ so greatly from those of our ancestral past that our behavior can no longer be expected to be (...) adaptive. In contrast, we argue that fertility measurements in industrial society are essential for a complete evolutionary analysis: in particular, such data can provide evidence for any putative adaptive mismatch between ancestral environments and those of the present day, and they can provide insight into the selection pressures currently operating on contemporary populations. Having made this positive case, we then go on to discuss some challenges of fertility-related analyses among industrialized populations, particularly those that involve large-scale databases. These include “researcher degrees of freedom” (i.e., the choices made about which variables to analyze and how) and the different biases that may exist in such data. Despite these concerns, large datasets from multiple populations represent an excellent opportunity to test evolutionary hypotheses in great detail, enriching the evolutionary understanding of human behavior. (shrink)

Prologue: on the weakness of education -- Creativity -- Communication -- Teaching -- Learning -- Emancipation -- Democracy -- Virtuosity -- Epilogue: for a pedagogy of the event -- Appendix: coming into the world, uniqueness, and the beautiful risk of education: an interview with Gert Biesta by Philip Winter.

Joshua Gert presents an original account of color properties, and of our perception of them. He employs a general philosophical strategy - neo-pragmatism - which challenges an assumption made by virtually all other theories of color: he argues that colors are primitive properties of objects, irreducible to physical or dispositional properties.

Research integrity is a well-established term used to talk and write about ethical issues in research. Part of its success might be its broad applicability. In this paper, we suggest that this might also be its Achilles heel, since it has the potential to conceal important value conflicts. We identify three broad domains upon which research integrity is applied in the literature: (1) the researcher (or research group), (2) research, and (3) research-related institutions and systems. Integrity in relation to researchers (...) concerns character, although it remains to specify precisely what character traits are the desirable ones in this context and what values researchers should endorse. Integrity in relation to research concerns correct and sufficient description of the research process, data, results, and overall ‘research record’. Hence, it concerns the quality of research. However, whether or not this notion of research integrity covers all ethical aspects of research depends on whether one endorses a wider or a narrower interpretation of the ‘research process’. Integrity in relation to research-related institutions and systems leaves open whether they should be understood as agents in their own right or merely as means to research integrity. Besides the potential lack of clarity that our analysis reveals, we point to how this variety in uses might lead to concealment of value conflicts and propose an open discussion of central values. (shrink)

The central themes of Jesus’ preaching, the kingdom and household of God, are root metaphors expressing the symbolic universe of God’s patronage subverting patronage and patriarchy structuring contemporary Mediterranean society, thus legitimising an anti-hierarchical community of faith. This dominant focus of Jesus’ message was discarded, as society’s prevalent patronage and patriarchy became the societal structure of the later faith communities. Today, patronage and patriarchy still forms the social structure for a large sector of Christian communities and many cultures, resulting in (...) inequality, injustice, exploitation and suffering. This article proposes that the only remedy for the faithful is a return to Jesus’ essential message, by investigating the social dynamics suggested by these root metaphors using metaphor theory and social scientific methods. Patronage is studied within contemporary Roman and Mediterranean aristocratic patriarchal society, forming an a-typical broad-based needle-like power pyramid with multiple similarly structured power pyramids within, based on a morality of indebtedness, honour and power. Jesus accepted God as his father and declared the advent of God’s patronage as king (kingdom of God) and father of the faithful (children of God). Within the kingdom and household of God, there was no hierarchy, except for the primate of the first born son, whom Jesus symbolises as broker for God’s patronage to all his followers. Within the faith communities there should be no hierarchy or any form of clientage other than God’s patronage. Rather, the faithful are equal and should serve each other and their communities with compassion, responsibility and justice.Contribution: The contribution of this research is its focus on similarity and dissimilarity of these patronage metaphors and their application to subvert the power dynamics of patronage and patriarchy within the community of the faithful, in order to proffer God’s patronage of a society of caring, selfless equals today. This research falls within the scope of HTS Theological studies, as it is a multi-disciplinary study of key biblical metaphors investigated with accepted methodology resulting in valid conclusions which are ethically sound. (shrink)

This book presents an account of normative practical reasons and the way in which they contribute to the rationality of action. Rather than simply 'counting in favour of' actions, normative reasons play two logically distinct roles: requiring action and justifying action. The distinction between these two roles explains why some reasons do not seem relevant to the rational status of an action unless the agent cares about them, while other reasons retain all their force regardless of the agent's attitude. It (...) also explains why the class of rationally permissible action is wide enough to contain not only all morally required action, but also much selfish and immoral action. The book will appeal to a range of readers interested in practical reason in particular, and moral theory more generally. (shrink)

When did the concept of model begin to be used in mathematics? This question appears at first somewhat surprising since “model” is such a standard term now in the discourse on mathematics and “modelling” such a standard activity that it seems to be well established since long. The paper shows that the term— in the intended epistemological meaning—emerged rather recently and tries to reveal in which mathematical contexts it became established. The paper discusses various layers of argumentations and reflections in (...) order to unravel and reach the pertinent kernel of the issue. The specific points of this paper are the difference in the epistemological concept to the usually discussed notions of model and the difference between conceptions implied in mathematical practices and their becoming conscious in proper reflections of mathematicians. (shrink)

This chapter contains sections titled: Learner Student Speaker Coda Notes References.

Joshua Gert offers an original account of normative facts and properties, those which have implications for how we ought to behave. He argues that our ability to think and talk about normative notions such as reasons and benefits is dependent on how we respond to the world around us, including how we respond to the actions of other people.

Plagiarism is a major problem for research. There are, however, divergent views on how to define plagiarism and on what makes plagiarism reprehensible. In this paper we explicate the concept of “plagiarism” and discuss plagiarism normatively in relation to research. We suggest that plagiarism should be understood as “someone using someone else’s intellectual product, thereby implying that it is their own” and argue that this is an adequate and fruitful definition. We discuss a number of circumstances that make plagiarism more (...) or less grave and the plagiariser more or less blameworthy. As a result of our normative analysis, we suggest that what makes plagiarism reprehensible as such is that it distorts scientific credit. In addition, intentional plagiarism involves dishonesty. There are, furthermore, a number of potentially negative consequences of plagiarism. (shrink)

This book offers the fullest and most sophisticated account of Gert's influential moral theory, a model first articulated in the classic work The Moral Rules: A New Rational Foundation for Morality, published in 1970. In this final revision, Gert makes clear that the moral rules are only one part of an informal system that does not provide unique answers to every moral question but does always provide a range of morally acceptable options. A new chapter on reasons includes (...) an account of what makes one reason better than another and a second new chapter is devoted to the question of justifying violations of the rules. Moral impartiality, the moral ideals, and virtue and vice, are all treated in greater detail. Throughout, Gert attempts to answer all of the challenges that his work has provoked. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:“Above and Beneath Classification”: Bartleby, Life and Times of Michael K, and Syntagmatic ParticipationGert Buelens (bio) and Dominiek Hoens (bio)The history of the relation between the law, norm, or rule on the one hand and what forms an exception to that rule on the other is complex and multifaceted.1 In the most general terms, one could posit that the exception is that which escapes from the rule. Thus, confronted (...) with the strangeness of Michael K, his noncommunicativeness, his odd combination of meekness and intransigence, the medical officer in J. M. Coetzee’s Life and Times of Michael K assigns K a place “above and beneath classification” [Coetzee 151]. Michael K is at once too large and too small to fit into the administrative and humanitarian categories that pertain at the prisoner camp. He appears to the medical officer—whose good intentions and patient, selfless interest in K cannot be doubted—as a recalcitrant, nonidentifiable object that flirts with dehumanization. To put it in Bataille’s terms, Michael K is formless (informe), and his existence can, by mere virtue of that fact, be called scandalous.2Let us take a closer look at the expression “above and beneath classification.” We can note that (1) it names something that situates itself on the outside of any classification; (2) this something must have a paradoxical status, since it is at once above and beneath classification; (3) the nonclassifiable is regarded as such from a classifying perspective. Although the latter point may sound tautological, it nonetheless touches upon one of the most difficult dimensions of the exception: if the exception is always an exception to the rule, how can it exist otherwise than by virtue of that rule? how can it be more than just the rule’s negative? But if the exception radically breaks away from the rule, then how is it possible for that rule to identify the exception and recognize it as such? This crucial problem has formed the basis for reflection on the relation between rule and exception. Freud, for instance, saw the exception (crime) as constitutive of social ties and the social order. Lacan needed a special topology to show the extimate character of what is at once inside and outside the symbolic order [Lacan, Miller]. Religious ways of thinking could be said to have located the exception as transcendent to any human order. For Badiou, the secularization of the infinite cannot be thought apart from an immanent, rather than transcendent, event that is disruptive of all order. In Derrida’s subtle analyses, the originary supplement appears as both constitutive and deconstructive. Agamben regards the exception as having become the political rule. These interpretative frameworks, in spite of some deep distinctions, all show not only that the rule cannot do without the exception, but that the exception is just as dependent on the rule. Even when the exception is regarded as a kind of pure, ruleless being-as-such, the rule is at the very least conceptually [End Page 157] indispensable for this pure, mere being to be thinkable in the first place. In brief, however much one may want, for political or other reasons, to assign the exception a central place at the expense of the rule, that rule remains inescapable.Nonetheless, the inevitability of the rule should not lead us to conclude that it is also immutable, nor that we should adopt a conservatism that accepts the rule as a repressive normativity or as an inclusive and exclusive apparatus of judgment. That this is as impossible as it is undesirable is suggested by what we indicated under the second item: the exception is both above and beneath. The exception is the paradoxical given of that which at once escapes from existing categories and lacks all identity in that escape. The problem that Michael K and Bartleby, the second figure of exception we consider in this essay, present for the rule resides not just in the recalcitrance that allows them to show up the limits of the rule, but also in the doubling with which this goes hand in hand. Michael K and Bartleby are as pliant as they are obdurate, show great loyalty even... (shrink)

We discuss three aspects of the intuitionistic reformulation of Mally’s deontic logic that was recently proposed ). First, this reformulation is more similar to Standard Deontic Logic than appears at first sight: like Standard Deontic Logic, it is Kanger reducible and Anderson reducible to alethic logic and it has a semantical interpretation that can be read in deontic terms. Second, this reformulation has an extension that provides 100% of the theorems stated by Mally himself. Third, it is interesting to view (...) Mally’s original deontic logic as an extension of this reformulation. (shrink)

In this essay, Gert Biesta provides a critical analysis of the idea of evidence‐based practice and the ways in which it has been promoted and implemented in the field of education, focusing on the tension between scientific and democratic control over educational practice and research. Biesta examines three key assumptions of evidence‐based education: first, the extent to which educational practice can be compared to the practice of medicine, the field in which evidence‐based practice was first developed; second, the role (...) of knowledge in professional actions, with special attention to what kind of epistemology is appropriate for professional practices that wish to be informed by the outcomes of research; and third, the expectations about the practical role of research implicit in the idea of evidence‐based education. Biesta concludes that evidence‐based practice provides a framework for understanding the role of research in educational practice that not only restricts the scope of decision making to questions about effectivity and effectiveness, but that also restricts the opportunities for participation in educational decision making. He argues that we must expand our views about the interrelations among research, policy, and practice to keep in view education as a thoroughly moral and political practice that requires continuous democratic contestation and deliberation. (shrink)

In contemporary societies, there is a strong push toward seeing education as an instrument for the delivery of particular societal agendas. On such a view, the only questions that remain are how effective education is at delivering such agendas and how its effectiveness can be increased. While this might be a desirable way forward for those who believe that a consensus about the agenda for education can easily be achieved, it is at odds with the idea that a democratic society (...) is characterized by a fundamental plurality of visions about what schools are supposed to be for. Yet the democratic critique of educational instrumentalism cannot be confined to giving each and every vision its own school, as this would simply multiply educational instrumentalism rather than oppose it. A true democratic response thus needs to take education's own interest seriously as well, which, as Gert Biesta argues in this paper, amounts to a defense of the school as institution. (shrink)

Slippery-slope arguments typically question a course of action by estimating that it will end in misery once the first unfortunate step is taken. Previous studies indicate that estimations of the long-term consequences of certain debated actions, such as legalizing physician-assisted suicide, may be strongly influenced by tacit personal values. In this paper, we suggest that to the extent that slippery-slope arguments rest on estimations of future events, they may be mere rationalizations of personal values. This might explain why there are (...) proponents even for strikingly poor slippery-slope arguments. (shrink)

_Obstinate Education: Reconnecting School and Society_ argues that education is not just there to give individuals, groups and societies what they want from it, but that education has a duty to resist.

The standard models for what doctors must tell their patients are based on the idea of informed consent: physicians must provide the information that patients need to make treatment decisions. In fact, though, they usually provide considerably more information than this model requires. And rightly so: patients should receive enough information that they will not be surprised by whatever happens—unless the physician is also surprised.

This paper briefly surveys previous analyses of implicitness and proposes a new, two-dimensional account. The first dimension concerns whether an assumption follows or not in terms of analytical or contextual implications or because it is a reasonable interpretation. The second dimension concerns the intentions of the author. Both dimensions are needed for identifying implicit assumptions in critical analyses of texts. A definition of clear cases of implicit assumptions is given. /// Este artículo examina brevemente análisis previos sobre lo implícito y (...) propone una nueva explicación bidimensional. La primera dimensión es sobre si se sigue o no una suposición en términos de implicaciones analíticas o contextuales, o porque la interpretación es razonable. La segunda dimensión se ocupa de las intenciones del autor. Ambas dimensiones son necesarias para identificar suposiciones implícitas en los análisis críticos de textos. Se proporciona una definición de los casos claros de supuestos implícitos. (shrink)

Connectionist models aiming to reveal the mechanisms of atypical development must in their undamaged form constitute plausible models of normal development and follow a developmental trajectory that matches empirical data. Constructivist models that adapt their structure to the learning task satisfy this demand. They are therefore more informative in the study of atypical development than the static models employed by Thomas & Karmiloff-Smith (T&K-S).

In this article, I explore the impact of the contemporary culture of measurement on education as a professional field. I focus particularly on the democratic dimensions of professionalism, which includes both the democratic qualities of professional action in education itself and the way in which education, as a profession, supports the wider democratic cause. I show how an initial authoritarian conception of professionalism was opened up in the 1960s and 1970s towards more democratic and more inclusive forms of professional action. (...) I then show how, in the wake of the transformation of the welfare state and the rise of neo-liberal forms of governing, the democratic dimension of professionalism became distorted. I discuss three distortions: having to do with the position of clients, the nature of accountability and the status of professional knowledge. While at first sight, the developments in each of these areas can be seen as furthering the democratisation of the professions, I argue that in fact they have eroded the democratic dimension of the professions and show the contribution of the culture of measurement to this erosion process. In the final step of my argument, I suggest how a more democratic mode of professional action might be regained and how such a mode of professional action might contribute to wider processes of democratisation. (shrink)

An updated and expanded successor to Culver and Gert's Philosophy in Medicine, this book integrates moral philosophy with clinical medicine to present a comprehensive summary of the theory, concepts, and lines of reasoning underlying the ...

Bioethicists have for quite some time discussed the right to know and the right not to know personal health information, such as genetic information acquired in health care and incidental health-related findings in research. Several international ethical guidelines explicitly defend these rights.My own interest in these matters stems from my participation in ethics-related research tied to a longitudinal screening study on Type I diabetes involving young children. A few of the participating parents did not want to be informed if the (...) study revealed their child had a high risk of developing diabetes. This response was troublesome, not least since the information would concern the child's and not the parents’ health. Our inclination was that there cannot be a right not to know that should be granted without qualifications. Furthermore, other contextual factors, e.g., that parents experienced pressure to participate and felt concern about some of the personal data handled in the study, gave reason to question whether autonomous decisions were made regarding participation. The autonomy of their expressed desire not to know was therefore questionable. (shrink)

This comment is analysing the last section of a paper by Piotr Blaszczyk, Mikhail G. Katz, and David Sherry on alleged misconceptions committed by historians of mathematics regarding the history of analysis, published in this journal in the first issue of 2013. Since this section abounds of wrong attributions and denouncing statements regarding my research and a key publication, the comment serves to rectify them and to recall some minimal methodological requirements for historical research.

Gert Scobel zeigt in seinem kenntnisreichen Buch, dass uns heute kaum etwas so sehr fehlt wie Weisheit: Im Umgang mit der Welt, mit anderen und uns selbst. Denn in unserer immer komplexer werdenden Umwelt, die uns mit Widersprüchen ebenso konfrontiert wie mit immer mehr Faktenwissen, brauchen wir Orientierung. Doch die fehlt. Und Weisheit stellt sich auch im Alter nicht von selbst ein. Gert Scobel belegt fundiert, dass man sie erlernen kann - und sollte. Dabei speist sich die Gelassenheit, (...) von der der Autor spricht, nicht aus esoterischen Höhenflügen, die oft mit einer unsanften Bauchlandung enden. Vielmehr ist sie inspiriert von den Lehren des Buddhismus, die Scobel überraschend mit der westlichen Geistesgeschichte versöhnt. Er verfolgt die Weisheit bis zu ihren Ursprüngen, ins Mittelalter und in den fernen Osten. Das Buch bringt uns aber auch die neusten Erkenntnisse zur Weisheit aus Psychologie, Neurowissenschaften, Biologie, Glücks- und Komplexitätsforschung nahe. Entstanden ist die faszinierende und anschaulich erzählte Geschichte einer Geisteshaltung, die sich nicht nur unterhaltsam und spannend liest, sondern auch mit großem persönlichem Gewinn. Denn Weisheit ist die Grundvoraussetzung für ein sinnvolles und geglücktes Leben. (shrink)

Moral problems do not always come in the form of great social controversies. More often, the moral decisions we make are made quietly, constantly, and within the context of everyday activities and quotidian dilemmas. Indeed, these smaller decisions are based on a moral foundation that few of us ever stop to think about but which guides our every action. Here distinguished philosopher Bernard Gert presents a clear and concise introduction to what he calls "common morality" -- the moral system (...) that most thoughtful people implicitly use when making everyday, common sense moral decisions and judgments. Common Morality is useful in that -- while not resolving every disagreement on controversial issues -- it is able to distinguish between acceptable and unacceptable answers to moral problems. In the first part of the book Gert lays out the fundamental features of common morality: moral rules, moral ideals, and a two-step procedure for determining when a violation of a moral rule is justified. Written in a non-technical style, the ten general moral rules include rules on which everyone can agree, such as "do not kill," "do not deceive," and "keep your promises." The moral ideals include similarly uncontroversial precepts such as "Relieve pain" and "Aid the needy." In the second part of the book Gert examines the underlying concepts that justify common morality, such as the notions of rationality and impartiality. The distillation of over 40 years of scholarship, this book is the most accessible version of Gert's influential theory of morality as well as an eye-opening look at the moral foundations of our everyday actions. Throughout the discussion is clear enough for a reader with little or no philosophy background. (shrink)

Studies of the association between wealth and fertility in industrial populations have a rich history in the evolutionary literature, and they have been used to argue both for and against a behavioral ecological approach to explaining human variability. We consider that there are strong arguments in favor of measuring fertility (and proxies thereof) in industrial populations, not least because of the wide availability of large-scale secondary databases. Such data sources bring challenges as well as advantages, however. The purpose of this (...) article is to illustrate these by examining the association between wealth and reproductive success in the United States, using the National Longitudinal Study of Youth 1979. We conduct a broad-based exploratory analysis of the relationship between wealth and fertility, employing both cross-sectional and longitudinal approaches, and multiple measures of both wealth (income and net worth) and fertility (lifetime reproductive success and transitions to first, second and third births). We highlight the kinds of decisions that have to be made regarding sample selection, along with the selection and construction of explanatory variables and control measures. Based on our analyses, we find a positive effect of both income and net worth on fertility for men, which is more pronounced for white men and for transitions to first and second births. Income tends to have a negative effect on fertility for women, while net worth is more likely to positively predict fertility. Different reproductive strategies among different groups within the same population highlight the complexity of the reproductive ecology of industrial societies. These results differ in a number of respects from other analyses using the same database. We suggest this reflects the impossibility of producing a definitive analysis, rather than a failure to identify the “correct” analytical strategy. Finally, we discuss how these findings inform us about (mal)adaptive decision-making. (shrink)