Hausdorff's paradoxical decomposition of a sphere with countably many points removed actually produced a partition of this set into three pieces A,B,C such that A is congruent to B, B is congruent to C, and A is congruent to B ∪ C. While refining the Banach–Tarski paradox, R. Robinson characterized the systems of congruences like this which could be realized by partitions of the sphere with rotations witnessing the congruences: the only nontrivial restriction is that the system should not require (...) any set to be congruent to its complement. Later, J. F. Adams showed that this restriction can be removed if one allows arbitrary isometries of the sphere to witness the congruences. The purpose of this paper is to characterize those systems of congruences which can be satisfied by partitions of the sphere or related spaces into sets with the property of Baire. A paper of Dougherty and Foreman gives a proof that the Banach–Tarski paradox can be achieved using such sets, and gives versions of this result using open sets and related results about partitions of spaces into congruent sets. The same method is used here; it turns out that only one additional restriction on a system of congruences is needed to make it solvable using subsets of the sphere with the property of Baire with free rotations witnessing the congruences. Actually, the result applies to any complete metric space acted on in a sufficiently free way by a free group of homeomorphisms. We also characterize the systems solvable on the sphere using sets with the property of Baire but allowing all isometries. (shrink)

To accept ‘pragmatic encroachment’ is to take the view that whether you are in a position to know is in part a function of practical stakes. This position strikes many as not just unorthodox but extremely implausible. According to Jeremy Fantl and Matthew McGrath (F&M), however, the best account of the prima facie oddity of certain utterances incorporates just such a pragmatist maneuver. In reaching this conclusion, F&M begin with Trent Dougherty and Patrick Rysiew’s (D&R’s) theory as the best (...) on offer (2009a: 63/2009b: 20), but go on to raise objections to D&R’s recent account of the relevant oddity in purely pragmatic (i.e., extra-semantic) terms and to develop it in directions quite inimical to the general outlook established in D&R 2009 and D&R forthcoming. In this brief note, we reply to F&M’s objections and show that their development in the direction of interest-relativism is ill-founded: the relevant phenomena provide no grounds for budging on the issue of pragmatic encroachment. In addition, in the course of meeting F&M’s objections, an original account of certain Moore-paradoxical sentences is given, and the issue of how probable a proposition needs to be to be known is addressed. The result is a quite general defense of a commonsense, evidence-based approach to the relevant phenomena (quite apart from a defense of D&R). (shrink)

R F Dearden; Theory and Practice in Education, Journal of Philosophy of Education, Volume 14, Issue 1, 30 May 2006, Pages 17–29, https://doi.org/10.1111/j.1467-.

R F Dearden; Happiness and Education, Journal of Philosophy of Education, Volume 2, Issue 1, 30 May 2006, Pages 17–29, https://doi.org/10.1111/j.1467-9752.1968.

This volume critically and constructively discusses philosophical questions which have particular bearing on the formulation of educational aims. The book is divided into three major parts: the first deals with the nature of education, and discusses the various general aims, such as 'mental health', 'socialization' and 'creativity' which have been thought to characterize it; the second section is concerned with the nature of reason and its relationship to feeling, will and action; finally the development of different aspects of reason in (...) an educational context is considered. (shrink)

Despite their status as high-income food producing nations, children and their caregivers, both in the United States (U.S.) and Australia can experience food insecurity. Nutrition researchers formed a joint U.S.-Australia collaboration to help advance food security for households with young children aged 0–5 years. This study investigated food insecurity from the perspective of caregivers, especially their perceptions of the impact of food insecurity on their own childhood, their current life, and for the children in their care. Semi-structured interviews were conducted (...) from July to September 2020 during the COVID-19 pandemic. Participants were recruited in Omaha, Nebraska, U.S. (_n_ = 19) and Melbourne, Victoria, Australia (_n_ = 22), during periods of stay-at-home public health orders. These two case study sites enabled an exploration of some universal, and some context-specific, social, economic, and health conditions that buffer, or exacerbate, food insecurity for families in these neo-liberal political settings. An inductive thematic analysis was conducted and established six themes:_growing up poor_, _lessons learned_,_ feeding a family amidst a pandemic_,_ caregiver coping strategies_, _food security in the early years_ and _protecting (young) children_. Perspectives on local anti-hunger strategies were organized to outline participant’s preferred solutions. Household food insecurity is conceptualized in public policy in the U.S. and Australia as a short-term crisis for people, justifying austere, time-limited and patchwork solutions. A narrative of caregivers’ lived experience of food insecurity suggests that it is inter-generational, and exacerbated by a food system shock (i.e., COVID-19). These findings from two varying cities and nations offer a different conceptualization of the timespan and nature of the phenomenon of food insecurity, challenging a dominant policy narrative and highlighting the inadequacy of current so-called solutions. (shrink)

Reading the Republic without reference to the less familiar Laws can lead to a distorted view of Plato's political theory. In the Republic the philosopher describes his ideal city; in his last and longest work he deals with the more detailed considerations involved in setting up a second-best 'practical utopia.' The relative neglect of the Laws has stemmed largely from the obscurity of its style and the apparent chaos of its organization so that, although good translations now exist, students of (...) philosophy and political science still find the text inaccessible. This first full-length philosophical introduction to the Laws will therefore prove invaluable. The opening chapters describe the general character of the dialogue and set it in the context of Plato's political philosophy as a whole. Each of the remaining chapters deals with a single topic, ranging over material scattered through the text and so drawing together the threads of the argument in a stimulating and readily comprehensible way. Those topics include education, punishment, responsibility, religion, virtue and pleasure as well as political matters and law itself. Throughout, the author encourages the reader to think critically about Plato's ideas and to see their relevance to present-day philosophical debate. No knowledge of Greek is required and only a limited background in philosophy. Although aimed primarily at students, the book will also be of interest to more advanced readers since it provides for the first time a philosophical, as opposed to linguistic or historical, commentary on the Laws in English. (shrink)

R F Dearden; Play and Pleasure, Journal of Philosophy of Education, Volume 5, Issue 1, 30 May 2006, Pages 37–41, https://doi.org/10.1111/j.1467-9752.1971.tb0044.

The question of what counts as a successful outcome of the process of genetics counselling has recently become central because of the increasing calls for efficiency in health care, and for means of measuring efficiency. Angus Clarke has drawn attention to this trend, and has argued against both a measure in terms of the number of terminations of pregnancy performed as a result of counselling, and an assessment in terms of the contribution of genetics counselling to a national eugenics policy. (...) He suggests instead a measure of workload. There are good arguments for supporting Clarke's position up to a point. In looking for an appropriate measure, much turns on how genetics counselling is defined. It is here understood in the context of an autonomy model of health care. It is argued that there is a contradiction between such an interpretation and the termination measure of outcome. The political philosophy underlying this outcome is also defective. Workload is not sufficient as a measure of outcome however; it is essential to look at the proper goals of an activity. It is argued that these must be connected in some way with the genetic health of the population; that the promotion of reproductive autonomy itself is not sufficient as a goal. The concern for genetic health, however, is interpreted in a way that avoids Clarke's concerns about a national eugenics policy. (shrink)

Arvind Thomas has written a remarkable book. That said, however, it must be quickly added that it is not a book for everyone, not even for all students of medieval literature. It is a very thoughtf...

It has come to be expected that collections issued by the Royal Institute of Philosophy will contain work that has quality or is otherwise interesting. This volume runs true to form and presents plenty of both. It gives the proceedings of the conference arranged by the Institute at Exeter in 1973, consisting of five symposia together with Chairman's remarks of about eight pages or so for each symposium, and in three cases postscripts by the first speaker. The contributors and topics (...) are: R. F. Dearden and Elizabeth Telfer on ‘Autonomy as an Educational Ideal’ with R. M. Hare as Chairman; R. K. Elliott and Glenn Langford on ‘Education and the Development of the Understanding’ with Paul Hirst as Chairman; David Cooper and Timothy O'Hagan on ‘Quality and Equality in Education’ with R. F. Atkinson as Chairman; Mary Warnock and Richard Norman on ‘The Neutral Teacher’ with Alan Montefiore as Chairman; Stuart Brown and A. Phillips Griffiths on ‘Academic Freedom’ with R. S. Peters as Chairman. (shrink)

Historical materialism I take to be the view expressed in the well-known Preface to the Critique of Political Economy (1859) and exemplified in Capital and in many other writings by Marx and by Marxists. I shall begin with a few introductory remarks, next sketch in the theory, and finally contend that, despite real attractions, it too far limits the scope of legitimate historical enquiry to be ultimately acceptable.

R F Deaden; In Defence of Children's Enquiry, Journal of Philosophy of Education, Volume 11, Issue 1, 30 May 2006, Pages 170–175, https://doi.org/10.1111/j.1467.

„My sole purpose in this paper is to try and correct what I take to be a common misinterpretation of Hume’s opinions on mathematics. I shall not enquire whether he was right or wrong in holding these opinions. Nor shall I offer opinions of my own.“.

Rapid developments in Artificial Intelligence are leading to an increasing human reliance on machine decision making. Even in collaborative efforts with Decision Support Systems (DSSs), where a human expert is expected to make the final decisions, it can be hard to keep the expert actively involved throughout the decision process. DSSs suggest their own solutions and thus invite passive decision making. To keep humans actively ‘on’ the decision-making loop and counter overreliance on machines, we propose a ‘reflection machine’ (RM). This (...) system asks users questions about their decision strategy and thereby prompts them to evaluate their own decisions critically. We discuss what forms RMs can take and present a proof-of-concept implementation of a RM that can produce feedback on users’ decisions in the medical and law domains. We show that the prototype requires very little domain knowledge to create reasonably intelligent critiquing questions. With this prototype, we demonstrate the technical feasibility to develop RMs and hope to pave the way for future research into their effectiveness and value. (shrink)

R F Dearden; Education and Politics, Journal of Philosophy of Education, Volume 14, Issue 2, 30 May 2006, Pages 149–156, https://doi.org/10.1111/j.1467-9752.198.