In this paper we look at some of the ingredients and processes involved in the understanding of mathematics. We analyze elements of mathematical knowledge, organize them in a coherent way and take note of certain classes of items that share noteworthy roles in understanding. We thus build a conceptual framework in which to talk about mathematical knowledge. We then use this representation to describe the acquisition of understanding. We also report on classroom experience with these ideas.

Many philosophers subscribe to the view that philosophy is a priori and in the business of discovering necessary truths from the armchair. This paper sets out to empirically test this picture. If this were the case, we would expect to see this reflected in philosophical practice. In particular, we would expect philosophers to advance mostly deductive, rather than inductive, arguments. The paper shows that the percentage of philosophy articles advancing deductive arguments is higher than those advancing inductive arguments, which is (...) what we would expect from the vantage point of the armchair philosophy picture. The results also show, however, that the percentages of articles advancing deductive arguments and those advancing inductive arguments are converging over time and that the difference between inductive and deductive ratios is declining over time. This trend suggests that deductive arguments are gradually losing their status as the dominant form of argumentation in philosophy. (shrink)

Inspiring and empowering, this journey behind the scenes of humanity's greatest creations reveals the surprising way we make something new. What do Thomas Jefferson's ice cream recipe, Coca Cola, and Chanel No. 5 have in common? They all depended on a nineteenth-century African boy who, with a single pinch, solved one of nature's great riddles and gave birth to the multimillion-dollar vanilla industry. Kevin Ashton opens his book with the fascinating story of the young slave who launched a flavor (...) revolution to show that invention and creation come in unexpected shapes and sizes. From the crystallographer's laboratory where the secrets of DNA were first revealed by a long-forgotten woman, to the electromagnetic chamber where the stealth bomber was born on a 25-cent bet, Ashton weaves tales of humanity's greatest creations to unpack the surprising true process of discovery. Drawing on the Amish and the iPhone, Kandinsky and cans of Coke, Lockheed, South Park, and the Wright brothers--who set out to "fly a horse"--he showcases the seemingly unremarkable individuals, gradual steps, multiple failures, and countless ordinary--and usually uncredited--acts that led to our most astounding breakthroughs. Creators, he shows, apply everyday, ordinary thinking that we are all capable of in particular ways, taking thousands of small steps, working in an endless loop of problem and solution. He explores why innovators meet resistance and how they overcome it, why most organizations stifle creative people, and how the most creative organizations work. In a passionate and profound narrative that amazes and inspires, Ashton's book sheds new light on how "new" comes to be. (shrink)

Cyprian’s appropriation of Scripture and his theological emphases are closely connected with the circumstances of his congregation. As a case study in Cyprian’s biblical interpretation, this article considers all his quotations of and allusions to Philippians through the lens of his pastoral concerns: the unity of the Church; care for the poor and captive; discipline and repentance; and divine truth and eternal glory. The reading strategies Cyprian uses can be categorized as contextual exegesis, model, image, direct application, and prophetic fulfilment. (...) The study provides a fresh perspective on patronage and almsgiving in Cyprian, deepens our understanding of the reception of Paul, and elucidates the interplay of text, context and theology in an important exponent of early Latin exegesis. (shrink)

In this short note, we discuss several aspectsof dimensions and the related constructof factors. We concentrate on those aspectsthat are relevant to articles in this specialissue, especially those dealing with the analysisof the wild animal cases discussed inBerman and Hafner's 1993 ICAIL article. We reviewthe basic ideas about dimensions,as used in HYPO, and point out differences withfactors, as used in subsequent systemslike CATO. Our goal is to correct certainmisconceptions that have arisen over the years.

In this short note, we discuss several aspectsof “dimensions” and the related constructof “factors”. We concentrate on those aspectsthat are relevant to articles in this specialissue, especially those dealing with the analysisof the wild animal cases discussed inBerman and Hafner's 1993 ICAIL article. We reviewthe basic ideas about dimensions,as used in HYPO, and point out differences withfactors, as used in subsequent systemslike CATO. Our goal is to correct certainmisconceptions that have arisen over the years.

This paper sets up a thought-experiment that examines the transformation of energy into codified mass. This transformation is understood as a semiosic action of interpretation. The semiosic action is analyzed within five “predicate” or “verbal modes” which establish different processes of transformation or interpretation. These “predicate modes”, which are sign processes, take place in different areas of reality, the external realm and the internal realm. The external realm is composed of discrete objects and their interactions. Its processes are examined within (...) classical mechanics and this paper posits a semiosic codification that is unique to these external processes. The internal realm is a holistic endoperspective with no recognition of discrete objects. Its processes are examined within quantum and field processes and this paper posits a semiosic codification that is unique to the internal processes. However, rather than promoting one or the other realm as a valid interpretation of reality, this paper suggests that both the external and internal energy-mass processes are necessary components of our universe. (shrink)

Volume 19, Issue 5, May 2019, Page 45-47.

Justifying involuntary psychiatric treatment on the basis of a judgment that a person lacks capacity is usually expressed in terms of a person’s ability to make a decision about his or her health and treatment. Typically, this relates to the ability to refuse treatment. Exactly what “capacity” means, however, and how one determines when another individual lacks capacity, or lacks sufficient capacity, in this context is particularly controversial, with the United Nations Committee on the Rights of Persons with Disabilities insisting (...) that involuntary treatment be abandoned altogether and capacity tests avoided.Capacity is a concept that has multiple meanings and applications across different disciplines and... (shrink)

The pluralism of methodologies and severe time constraints pose important challenges to pedagogy in clinical ethics. We designed a step-by-step student handbook to operate within such constraints and to respect the methodological pluralism of bioethics and clinical ethics. The handbook comprises six steps: Step 1: What are the facts of the case?; Step 2: What are your obligations to your patient?; Step 3: What are your obligations to third parties to your relationship with the patient?; Step 4: Do your obligations (...) converge or conflict?; Step 5: What is the strongest objection that could be made to the identification of convergence in step 4 or the arguments in step 4? How can this objection be effectively countered?; and Step 6: How could the ethical conflict, or perceived ethical conflict, have been prevented? (shrink)

Do people hold robots responsible for their actions? While Clark and Fischer present a useful framework for interpreting social robots, we argue that they fail to account for people's willingness to assign responsibility to robots in certain contexts, such as when a robot performs actions not predictable by its user or programmer.

Purpose This study aims to explore how health informatics can underpin the successful delivery of recovery-orientated healthcare, in rural and remote regions, to achieve better mental health outcomes. Recovery is an extremely social process that involves being with others and reconnecting with the world. Design/methodology/approach An interpretivist study involving 27 clinicians and 13 clients sought to determine how future expenditure on ehealth could improve mental health treatment and service provision in the western Murray Darling Basin of New South Wales, Australia. (...) Findings Through the use of targeted ehealth strategies, it is possible to increase both the accessibility of information and the quality of service provision. In small communities, the challenges of distance, access to healthcare and the ease of isolating oneself are best overcome through a combination of technology and communal social responsibility. Technology supplements but cannot completely replace face-to-face interaction in the mental health recovery process. Originality/value The recovery model provides a conceptual framework for health informatics in rural and remote regions that is socially responsible. Service providers can affect better recovery for clients through infrastructure that enables timely and responsive remote access whilst driving between appointments. This could include interactive referral services, telehealth access to specialist clinicians, GPS for locating clients in remote areas and mobile coverage for counselling sessions in “real time”. Thus, the technology not only provides better connections but also adds to the responsiveness of any treatment available. (shrink)

It is widely accepted that public discourse as we know it is less than ideal from an epistemological point of view. In this paper, we develop an underappreciated aspect of the trouble with public discourse: what we call the Listening Problem. The listening problem is the problem that public discourse has in giving appropriate uptake and reception to ideas and concepts from oppressed groups. Drawing on the work of Jürgen Habermas and Nancy Fraser, we develop an institutional response to the (...) listening problem: the establishment of what we call Receptive Publics, discursive spaces designed to improve listening skills and to give space for counterhegemonic ideas. (shrink)

Legal reasoning is an engaging field for cognitive science, since it raises so many fundamental questions, such as the representation and evolution of complex concepts. This article focuses on aspects of legal reasoning that require reasoning with cases, often in concert with other modes of reasoning.

Equilibrium explanations use an equilibrium to represent and explain a system’s dynamic behavior. They provide a system with the property of global stability: a system will converge towards and remain in equilibrium regardless of its initial conditions and dynamic process. Thus, equilibrium explanations are generally treated as non-causal explanations. There are two claims subsumed under that comprehensive thesis. The first claim is that equilibrium explanations do not identify any causes because a system with global stability resists manipulation. The second claim (...) is that even if equilibrium explanations do identify causes by manipulation, those causes are embedded in a system’s deeper, underlying structural relationships, and those causes are irrelevant to explaining a system’s behavior. Only the system’s structural relationships are relevant. But equilibrium explanations are not monolithic. I compare dynamic systems with multiple, competing equilibria to systems with a globally stable equilibrium. Equilibrium explanations of the former use intervention on a system’s initial conditions and dynamic process to manipulate equilibria, which identifies causes. Furthermore, a system’s initial conditions and dynamic process are relevant to explaining why one equilibrium is selected instead of another. I then apply these lessons to systems with a globally stable equilibrium and discuss when their corresponding equilibrium explanations have a proper role in the parent sciences. (shrink)

The BankXX system models the process of perusing and gathering information for argument as a heuristic best-first search for relevant cases, theories, and other domain-specific information. As BankXX searches its heterogeneous and highly interconnected network of domain knowledge, information is incrementally analyzed and amalgamated into a dozen desirable ingredients for argument (called argument pieces), such as citations to cases, applications of legal theories, and references to prototypical factual scenarios. At the conclusion of the search, BankXX outputs the set of argument (...) pieces filled with harvested material relevant to the input problem situation.This research explores the appropriateness of the search paradigm as a framework for harvesting and mining information needed to make legal arguments. In this article, we describe how legal research fits the heuristic search framework and detail how this model is used in BankXX. We describe the BankXX program with emphasis on its representation of legal knowledge and legal argument. We describe the heuristic search mechanism and evaluation functions that drive the program. We give an extended example of the processing of BankXX on the facts of an actual legal case in BankXX's application domain — the good faith question of Chapter 13 personal bankruptcy law. We discuss closely related research on legal knowledge representation and retrieval and the use of search for case retrieval or tasks related to argument creation. Finally we review what we believe are the contributions of this research to the understanding of the diverse disciplines it addresses. (shrink)

Feminist epistemologies hold that differences in the social locations of inquirers make for epistemic differences, for instance, in the sorts of things that inquirers are justified in believing. In this paper we situate this core idea in feminist epistemologies with respect to debates about social constructivism. We address three questions. First, are feminist epistemologies committed to a form of social constructivism about knowledge? Second, to what extent are they incompatible with traditional epistemological thinking? Third, do the answers to these questions (...) raise serious problems for feminist epistemologies? We argue that some versions of two of the main strands in feminist epistemology – feminist standpoint theory and feminist empiricism – are committed to a form of social constructivism, which requires certain departures from traditional epistemological thinking. But we argue that these departures are less problematic than one might think. Thus, (some) feminist epistemologies provide a plausible way of understanding how (some) knowledge might be socially constructed. (shrink)