In this paper, we endeavour to give a historically accurate presentation of how Leibniz understood his infinitesimals, and how he justified their use. Some authors claim that when Leibniz called them “fictions” in response to the criticisms of the calculus by Rolle and others at the turn of the century, he had in mind a different meaning of “fiction” than in his earlier work, involving a commitment to their existence as non-Archimedean elements of the continuum. Against this, we show that (...) by 1676 Leibniz had already developed an interpretation from which he never wavered, according to which infinitesimals, like infinite wholes, cannot be regarded as existing because their concepts entail contradictions, even though they may be used as if they exist under certain specified conditions—a conception he later characterized as “syncategorematic”. Thus, one cannot infer the existence of infinitesimals from their successful use. By a detailed analysis of Leibniz’s arguments in his De quadratura of 1675–1676, we show that Leibniz had already presented there two strategies for presenting infinitesimalist methods, one in which one uses finite quantities that can be made as small as necessary in order for the error to be smaller than can be assigned, and thus zero; and another “direct” method in which the infinite and infinitely small are introduced by a fiction analogous to imaginary roots in algebra, and to points at infinity in projective geometry. We then show how in his mature papers the latter strategy, now articulated as based on the Law of Continuity, is presented to critics of the calculus as being equally constitutive for the foundations of algebra and geometry and also as being provably rigorous according to the accepted standards in keeping with the Archimedean axiom. (shrink)

With his clear and accessible prose, impeccable scholarship, and balanced Judgment, Roland Teske, SJ, has been an influential and important voice in Medieval philosophy for more than thirty years. This volume, in his honour, brings together more than a dozen essays on central metaphysical and theological themes in Augustine and other medieval thinkers. The authors, listed below, are noted scholars who draw upon Teskes work, reflect on it, go beyond it, and at times even disagree with it, but always in (...) a spirit of respectful co-operation, and always with the aim of getting at the truth. Essays on Augustine contributed by Gerald Bonner, Charles Brittain, Joseph Koterski, SJ, Joseph T. Lienhard, SJ, David Vincent Meconi, SJ, Ann A. Pang-White, Frederick Van Fleteren, Dorothea Weber, and James Wetzel. Essays on Bernard of Clairvaux, William of Auvergne, and other medieval themes contributed by John P. Doyle, William Harmless, SJ, John A. Laumakis, Edward P. Mahoney, and Philipp W. Rosemann. (shrink)

Once a central topic of philosophy of science, scientific explanation attracted less attention in the last two decades. My aim in this paper is to argue for a newsort of approach towards scientific explanation. In a first step I propose a classification of different approaches through a set of dichotomic characteristics. Taken into account the tendencies in actual philosophy of science I see a local, dynamic and non-theory driven approach as a plausible one. Considering models as bearers of explanations will (...) provide a proper frame for such an approach. In the second part I make some suggestions for a working agenda that will further articulate a sketchy account of explanation through models proposed by Hartmann and Frigg. (shrink)

The aim of this paper is to argue that it is more plausible to approach understanding from a special type of model—the ABS/IBMs models—as a non-explanatory form following some suggestions advanced by Lipton. I will first look to the type of explanation that some authors claimed is disclosed by these models: Weisberg’s analysis of IBMs in ecology and Grüne-Yanoff’s analysis of the Anasazi model. I argue that their analyses fail to show that these models qualify as explanatory understandings. This brings (...) us to Strevens’ “simple view,” which claims the existence of a correct explanation behind any understanding, and his strategy of dismissing the challenges posed by non-explanatory forms. I argue that this strategy incurs damaging costs on his view. In the last part we turn to Khalifa’s critique on Lipton’s proposals and argue that it is based on an unjustified construal of Lipton’s framework. I show how Khalifa’s “argumentative strategy” fails to establish the superiority of actual understanding over possible explanation. (shrink)

Hempel and Oppenheim, in their paper 'The Logic of Explanation', have offered an analysis of the notion of scientific explanation. The present paper advances considerations in the light of which their analysis seems inadequate. In particular, several theorems are proved with roughly the following content: between almost any theory and almost any singular sentence, certain relations of explainability hold.

We explore the ethics of deliberately exposing consenting adults to SARS-CoV-2 to induce immunity to the virus (“DEI” for short). We explain what a responsible DEI program might look like. We explore a consequentialist argument for DEI according to which DEI is a viable harm-reduction strategy. Then we consider a non-consequentialist argument for DEI that draws on the moral significance of consent. Additionally, we consider arguments for the view that DEI is unethical on the grounds that, given that large-scale DEI (...) would be highly likely to result in some severe illnesses and deaths, DEI amounts to a form of killing. Our thesis is that incorporating a DEI program alongside the status-quo “calibrate-the-curve” responses could have significant advantages at the early stages of pandemics. These potential advantages mean that, at a minimum, research into DEI would have been justified early in the COVID-19 pandemic, and that DEI programs should be explored as potential additions to our overall approach to emerging pandemics in the future. (shrink)

Two kinds of philosophical questions are raised by the current public debate about climate change; epistemic questions (Whom should I believe? Is climate science a genuine science?), and ethical questions (Who should bear the burden? Must I sacrifice if others do not?). Although the former have been central to this debate, professional philosophers have dealt almost exclusively with the latter. This book is the first to address both the epistemic and ethical questions raised by the climate change debate and examine (...) the relationship between them. (shrink)

This paper examines the strategic use of corporate philanthropy in the 1990s by UK building societies faced with an intensification of societal pressure to change legal form from mutual to corporate status. While the economic case for mutuality has been made elsewhere, this paper examines the observation that community relationships were thought by management to be capable of assisting in the strategic positioning of mutual societies with regard to their legal form. By increasing charitable giving to respond to the level (...) of societal scrutiny and discussion on the issue of mutuality, this paper argues that charitable giving, as one proxy for community involvement, was used as a strategic tool to deflect calls for demutualisation, thereby preserving the existing mutual status of building societies. (shrink)

This paper examines the strategic use of corporate philanthropy in the 1990s by UK building societies faced with an intensification of societal pressure to change legal form from mutual to corporate status. While the economic case for mutuality has been made elsewhere, this paper examines the observation that community relationships were thought by management to be capable of assisting in the strategic positioning of mutual societies with regard to their legal form. By increasing charitable giving to respond to the level (...) of societal scrutiny and discussion on the issue of mutuality, this paper argues that charitable giving, as one proxy for community involvement, was used as a strategic tool to deflect calls for demutualisation, thereby preserving the existing mutual status of building societies. (shrink)

Thirty years after the publication of Marr's seminal book Vision the papers in this topic consider the contemporary status of his influential conception of three distinct levels of analysis for information-processing systems, and in particular the role of the algorithmic and representational level with its cognitive-level concepts. This level has been downplayed or eliminated both by reductionist neuroscience approaches from below that seek to account for behavior from the implementation level and by Bayesian approaches from above that seek to account (...) for behavior in purely computational-level terms. (shrink)

The claims by the Building Societies Association (BSA), some mutual building societies and other observers that mutual status is associated with higher levels of charitable and community involvement than public status banks are tested using the proxy of charitable donations in cash as a proportion of profits before tax (PBT). Using a sample of 31 of the remaining 65 mutual societies and the population of U.K.-based retail banks and still-independent demutualised banks, two hypotheses were tested: first, that charitable giving as (...) a proportion of PBT over the period 1990–2003 was higher for mutuals than banks and second, that longitudinal records of charitable donations as a proportion of PBT for former mutuals will show a lower rate after demutualisation. Neither hypothesis was convincingly supported allowing for the conclusion that any claims suggesting that mutuals are structurally more generous than public companies are not supported by empirical evidence. (shrink)

We designed an experiment to explore the learning effectiveness of three different ways of practicing dance movements. To our surprise we found that partial modeling, called marking in the dance world, is a better method than practicing the complete phrase, called practicing full-out; and both marking and full-out are better methods than practicing by repeated mental simulation. We suggest that marking is a form of practicing a dance phrase aspect-by-aspect. Our results also suggest that prior work on learning by observation (...) and learning by mental practice may not scale up to complex movements. (shrink)

This book evaluates the increasingly wide variety of intellectual resources for research methods and methodologies and investigates what constitutes good educational research. Written by a distinguished international group of philosophers of education Questions what sorts of research can usefully inform policy and practice, and what inferences can be drawn from different kinds of research Demonstrates the critical engagement of philosophers of education with the wider educational research community and illustrates the benefits that can accrue from such engagement.

This special issue of the Journal of Philosophy of Education is addressed both to philosophers of education and to the many colleagues in the wider educational.

This chapter offers a guide to reading Plato’s dialogues, including an overview of his corpus. We recommend first considering each dialogue as its own unified work, before considering how it relates to the others. In general, the dialogues explore ideas and arguments, rather than presenting parts of a comprehensive philosophical system that settles on final answers. The arc of a dialogue frequently depends on who the individual interlocutors are. We argue that the traditional division of the corpus (into Socratic, middle, (...) late stages) is useful, regardless of whether it is a chronological division. Our overview of the corpus gives special attention to the Republic, since it interweaves so many of his key ideas, even if nearly all of them receive longer treatments in other dialogues. Although Plato recognized the limits inherent in written (as opposed to spoken) philosophy, he devoted his life to producing these works, which are clearly meant to help us seek the deepest truths. Little can be learned from reports of Plato’s oral teaching or the letters attributed to him. Understanding the dialogues on their own terms is what offers the greatest reward. (shrink)

Whilst media and political rhetoric in Britain is sceptical and often outright damning of the (presumed) morals and behaviours of the White marginalized poor, our aim is to explore the conditions under which successful communities are nevertheless built. Specifically, we examine the features of community and stress its importance both for belonging and bonding around shared norms and practices and for fostering the necessary bridging essential for interacting and cooperating with others. In considering what it means to foster a community (...) that acts as a breakwater against the tides of stigma or disadvantage, we pay special attention to what we will call enabling conditions – essential features that communities either can or should be able to provide or that exist independent of communities and are indispensable for accessing opportunities in the wider society. We detail the dynamics of White poverty and exclusion before turning our attention to possible responses to these challenges. In searching for viable responses to stigma and disadvantage, we compare some different typologies of community presently available to the White poor in Britain and examine whether these are sufficient to satisfy the enabling conditions associated with more robust forms of group membership. (shrink)

This book evaluates the increasingly wide variety of intellectual resources for research methods and methodologies and investigates what constitutes good educational research. Written by a distinguished international group of philosophers of education Questions what sorts of research can usefully inform policy and practice, and what inferences can be drawn from different kinds of research Demonstrates the critical engagement of philosophers of education with the wider educational research community and illustrates the benefits that can accrue from such engagement.

Contributors in the order of contributions: David Ebrey, Richard Kraut, T. H. Irwin, Leonard Brandwood, Eric Brown, Agnes Callard, Gail Fine, Suzanne Obdrzalek, Gábor Betegh, Elizabeth Asmis, Henry Mendell, Constance C. Meinwald, Michael Frede, Emily Fletcher, Verity Harte, Rachana Kamtekar, and Rachel Singpurwalla. -/- The first edition of the Cambridge Companion to Plato (1992), edited by Richard Kraut, shaped scholarly research and guided new students for thirty years. This new edition introduces students to fresh approaches to Platonic dialogues while (...) advancing the next generation of research. Of its seventeen chapters, nine are entirely new, written by a new generation of scholars. Six others have been thoroughly revised and updated by their original authors. The volume covers the full range of Plato's interests, including ethics, political philosophy, epistemology, metaphysics, aesthetics, religion, mathematics, and psychology. Plato's dialogues are approached as unified works and considered within their intellectual context, and the revised introduction suggests a way of reading the dialogues that attends to the differences between them while also tracing their interrelations. The result is a rich and wide-ranging volume which will be valuable for all students and scholars of Plato. (shrink)

In this unique collection, a distinguished group of social theorists reflect upon the ways in which crime and its control feature in the political and cultural landscapes of contemporary societies. The book brings together for the first time some of today's most powerful social analysts in a discussion of the meaning of crime and punishment in late-modern society. The result is a stimulating and provocative volume that will be of equal interest to specialist criminologists and those working in the fields (...) of social and cultural studies. (shrink)

Respect for autonomy has become a fundamental principle in human research ethics. Nonetheless, this principle and the associated process of obtaining informed consent do have limitations. This can lead to some groups, many of them vulnerable, being left understudied. This book considers these limitations and contributes through legal and philosophical analyses to the search for viable approaches to human research ethics. It explores the limitations of respect for autonomy and informed consent both in law and through the examination of cases (...) where autonomy is lacking (infants), diminished (addicts), and compromised (low socio-economic status). It examines alternative and complementary concepts to overcome the limits of respect for autonomy, including beneficence, dignity, virtue, solidarity, non-exploitation, vulnerability and self-ownership. It takes seriously the importance of human relationality and community in qualifying, tempering and complementing autonomy to achieve the ultimate end of human research - the good of humankind. (shrink)

This is the second of two Special Issues, the first of which appeared as Volume 40, Issue 2 of this year. In the first Issue, our contributors were particularly inclined to question two assumptions that colour thinking about educational research. The first is that educational research is essentially a ‘scientific’ exercise, reaching its apogee in randomised control trials, as if medical research were the ideal to which all other kinds of research should attempt to measure up, and as if education (...) were a process largely analogous to that of administering drugs in order to enhance performance. The second, related assumption is that educational research is to be understood as, at heart, a matter of discovering ‘what works’. This is the background—also explored in other recent publications such as Smeyers and Depaepe (2006)—against which this second Special Issue should be seen. (shrink)