The history of the Parallelogram Rule for composing physical quantities, such as motions and forces, is marked by conceptual difficulties leading to false starts and halting progress. In particular, authors resisted the required assumption that the magnitude and the direction of a quantity can interact and are jointly necessary to represent the quantity. Consequently, the origins of the Rule cannot be traced to Pseudo-Aristotle or Stevin, as commonly held, but to Fermat, Hobbes, and subsequent developments in the (...) latter part of the seventeenth century. (shrink)

This paper focuses on the mathematisation of mechanics in the seventeenth century, specifically on how the representation of compounded rectilinear motions presented in the ancient Greek Mechanica found its way into Newton’s Principia almost two thousand years later. I aim to show that the path from the former to the latter was optical: the conceptualisation of geometrical lines as paths of reflection created a physical interpretation of dia­grammatic principles of geometrical point-motion, involving the kinematics and dynamics of light reflection. Upon (...) the atomistic conception of light, the optical interpretation of such geometrical principles entailed their mechanical generalisation to local motion; rectilinear motion via the physico-mathemat­ics of reflection and the Mechanica’s parallelogram rule; circular motion via the physico-mathematics of reflection, the Archimedean squaring of the circle and the Mechanica’s extension of the parallelogram rule to centripetal motion. This appeal to the physico-mathematics of reflection forged a realist founda­tion for the mathematisation of motion. Whereas Aristotle’s physics rested on motions which had their source in the nature of the elements, early modern thinkers such as Harriot, Descartes, and Newton based their new principles of mechanical motion upon selected elements of the mechanics of light motion, projected upon the geometry of the parallelogram rule for rectilinear and, ultimately, circular motion. (shrink)

The attempt to find usable diagrams fornterms of the sort devised by John Venn seems to have originated with Venn himself, who published diagrams for up to five classes (the fifth class, however, was shaped like a doughnut, and contained an area outside itself — like the hole in the doughnut). Venn then suggested that “if we wanted to use a diagram forsixterms (x, y, z, w, v, u) the best plan would probably be to taketwofive-term figures, one for theupart (...) and one for the non-upart of all the other combinations …” Such a method would, as Venn admits, be somewhat confusing to the eye, and thus fail to fulfil one of the major purposes of the diagram; nevertheless, it is a method which could be extended to covernclasses.Venn also suggests (but without illustration) another method for drawing diagrams fornterms: “… the rule of formation would be very simple. We should merely have to begin by drawing any closed figure, and then proceed to draw others subject to the one condition that each intersect once, and once only, all the existing subdivisions produced by those which had gone before.” Then, in a rather surprising footnote, he adds: “It will be found that when we adhere to continuous figures, instead of the discontinuous five-term figure given above, there is a tendency for the resultant outlines thus successively drawn to assume a comb-like shape after the first four or five. If we begin by circles or other rounded figures the teeth are curved, if by parallelograms then they are straight. (shrink)

The article presents proofs of the context freeness of a family of typelogical grammars, namely all grammars that are based on a uni- ormultimodal logic of pure residuation, possibly enriched with thestructural rules of Permutation and Expansion for binary modes.

Jesus of Nazareth, like Socrates, left nothing behind written by himself. Yet, the records of his teaching indicate a rich interest in dialogic pedagogy, reflected in his use of the parable, primarily an oral genre, as a dialogic provocation. Working at the interface of pedagogy, theology and philosophy, this article explores the parable of the Good Samaritan from the perspective of dialogic pedagogy. It employs an analytical approach termed diacognition, developed from the notions of dialogue, position and cognition, to analyse (...) the moves within the parable and the teaching situation in which it is located. The article explores how Jesus engages the dialogue of and around the parable to position and reposition his interlocutor, provoking a re-cognition of what it means to love one’s neighbour. It concludes by reflecting on the implications of this analysis for the relation of meaning to knowing and doing. (shrink)

This article examines the relationship between online dispute resolution (ODR) and trust. We discuss what trust is, why trust is important, and how trust develops. Our claim is that efforts to implement online dispute resolution on a site or service in a manner that promotes trust need to consider ODR as just one tool in a broader toolbox of trust-building tools and techniques. These techniques are amongst others marketing, education, trust seals, and transparency. By evaluating ODR in its proper context (...) as one component of a larger trust strategy, we can more accurately set expectations for its results and position our projects for success. (shrink)

Dialogue is a seminal concept within the work of the Brazilian adult education theorist, Paulo Freire, and the Russian literary critic and philosopher, Mikhail Bakhtin. While there are commonalities in their understanding of dialogue, they differ in their treatment of dialectic. This paper addresses commonalities and dissonances within a Bakhtin-Freire dialogue on the notions of dialogue and dialectic. It then teases out some of the implications for education theory and practice in relation to two South African contexts of learning that (...) facilitate the access to education of disadvantaged groups, one in higher education and the other in early childhood education. (shrink)

The information explosion and digital modes of learning often combine to inform the quest for the best ways of transforming information in digital form for pedagogical purposes. This quest has become more urgent and pervasive with the ‘turn’ to online learning in the context of COVID-19. This can result in linear, asynchronous, transmission-based modes of teaching and learning which commodify, package and deliver knowledge for individual ‘customers’. The primary concerns in such models are often technical and economic – technology as (...) a cost-effective ‘solution’ to educational challenges. In this paper I argue for the importance of dialogic learning space in teaching and learning by means of Information and Communication Technologies, whether in the form of fully online learning, blended learning or face-to-face encounters using ICT affordances. Although the 20th Century theorists Mikhail Bakhtin (1895–1975) and Hans-Georg Gadamer (1900–2002) produced their seminal works before the advent of ICTs, they were both concerned with the quality and authenticity of human engagement with texts and with other persons and contexts. Besides a shared interest in dialogue as an ontological feature of human life and being, they both used spatiotemporal concepts for understanding and interpreting texts. The article draws on Gadamer’s notions of dialogue and horizon, and Bakhtin’s notions of dialogue and chronotope, to conceptualize dialogic possibilities for online education. Its purpose is to provide a framework, grounded in Bakhtin’s and Gadamer’s ideas, for a dialogic approach to online teaching and learning in higher education. (shrink)

ALTHOUGH majority rule finds ready acceptance whenever groups make decisions, there are surprisingly few philosophically interesting arguments in support of it.1 Jeremy Waldron’s The Dignity of Legislation contains the most interesting recent defense of majority rule. Waldron combines his own argument from respect with May’s influential characterization of majority rule, tying both to a reinterpretation of a well-known passage from Locke’s Second Treatise (“the body moves into the direction determined by the majority of forces”). Despite its impressive (...) resourcefulness, Waldron’s defense is deficient, and one goal of this essay is to show how. Yet our main concern is not to criticize Waldron, but to demonstrate general deficiencies of arguments for majority rule and to suggest a strategy for a more adequate and more complete defense. Such arguments tend to have one of two weaknesses: Either they assume that collective decisionmaking is done in terms of ranking options and thus neglect both aggregation methods using more information than the relative standing of options in rankings (such as so-called positional methods) and rules that are not aggregation methods at all (such as fair-division procedures); or they also constitute arguments for other decision rules. In the first case, the argument is too narrow, in the second it is too broad. The narrowness problem is bigger than stated so far because arguments for majority rule tend to assume not only that decisions are made by ranking options, but also that only two options are to be ranked. Both problems arise for Waldron’s defense and leave it incomplete. Yet such incompleteness also characterizes the state of the art in arguing for majority rule. So in addition to.. (shrink)

Where does the human aesthetic come from? How does it develop? By introducing the notion of the ‘niche’ as a key term in an empirically and evolutionarily informed aesthetics, this paper aims to take a fresh look at these and similar questions. It also aims to shed new light on the development and functioning of the aesthetic capacity in humans and its trans-generational transmission. Drawing on recent research developments in evolutionary biology, developmental psychology, and cognitive sciences, I shall argue that (...) the human aesthetic capacity—which I understand as the capacity, involving perceptual, cognitive and emotional processes, to enter into a pleasurable/non-pleasurable and expressive relation with objects, artworks, natural phenomena, or other people—relies on constructed environmental resources for its emergence and its ontogenetic development. (shrink)

Few automated legal reasoning systems have been developed in domains of law in which a judicial decision maker has extensive discretion in the exercise of his or her powers. Discretionary domains challenge existing artificial intelligence paradigms because models of judicial reasoning are difficult, if not impossible to specify. We argue that judicial discretion adds to the characterisation of law as open textured in a way which has not been addressed by artificial intelligence and law researchers in depth. We demonstrate that (...) systems for reasoning with this form of open texture can be built by integrating rule sets with neural networks trained with data collected from standard past cases. The obstacles to this approach include difficulties in generating explanations once conclusions have been inferred, difficulties associated with the collection of sufficient data from past cases and difficulties associated with integrating two vastly different paradigms. A knowledge representation scheme based on the structure of arguments proposed by Toulmin has been used to overcome these obstacles. The system, known as Split Up, predicts judicial decisions in property proceedings within family law in Australia. Predictions from the system have been compared to those from a group of lawyers with favourable results. (shrink)

The central issue that I consider in this paper is the use of the so‐called ‘Rule of Rescue’ in the context of resource allocation. This ‘Rule’ has played an important role in resource allocation decisions in various parts of the world. It was invoked in Ontario to overturn a decision not to fund treatment for Gaucher's Disease and it has also been used to justify resource decisions in Israel concerning the same condition. -/- In the paper I consider (...) the nature of the Rule of Rescue and its moral justification. The latter involves consideration of the distinction between agent‐relative and agent‐neutral obligations. If the Rule of Rescue is to be justified, it is plausible to think that it will be in the context of agent‐relative obligations. Two problems with this suggestion are considered: the role of identifiability in the Rule of Rescue and the extent to which policy makers in a health care system can be taken to have such obligations. It is argued that in both cases these problems can be overcome and hence that there is a prima facie obligation to follow the Rule of Rescue. (shrink)

Through detailed and trenchant criticism of standard interpretations of some of the key arguments in analytical philosophy over the last sixty years, this book ...

The Dead Donor Rule is intended to protect the public and patients, but it remains contentious. Here, I argue that we can abandon the Dead Donor Rule. Using Joel Feinberg’s account of harm, I argue that, in most cases, particularly when patients consent to being organ donors, death does not harm permanently unconscious (PUC) patients. In these cases, then, causing the death of PUC patients is not morally wrong. This undermines the strongest argument for the Dead Donor (...) class='Hi'>Rule—that doctors ought not kill their patients. Thus, there is nothing wrong with abandoning the Dead Donor Rule with regard to PUC patients. Importantly, the harm-based argument defended here allows us to sidestep the thorny debate surrounding definitions of death. What matters is not when a patient dies but whether their death constitutes some further harm. (shrink)

In this essay, I provide a new argument for Intellectualism about knowing how, one that does not rest on controversial assumptions about how knowing how is ascribed in English. In particular, I argue that the distinctive intentionality of the manifestations of knowing how ought to be explained in terms of a propositional attitude of belief about how to perform an action.

The dead donor rule justifies current practice in organ procurement for transplantation and states that organ donors must be dead prior to donation. The majority of organ donors are diagnosed as having suffered brain death and hence are declared dead by neurological criteria. However, a significant amount of unrest in both the philosophical and the medical literature has surfaced since this practice began forty years ago. I argue that, first, declaring death by neurological criteria is both unreliable and unjustified (...) but further, the ethical principles which themselves justify the dead donor rule are better served by abandoning that rule and instead allowing individuals who have suffered severe and irreversible brain damage to become organ donors, even though they are not yet dead and even though the removal of their organs would be the proximal cause of death. (shrink)