We present a formal system, E, which provides a faithful model of the proofs in Euclid's Elements, including the use of diagrammatic reasoning.

The concept of regulatory ‘checkpoints’ in the eukaryotic cycle has proved to be a fruitful one. Here, its applicability to the bacterial cell cycle is examined. A primitive DNA damage checkpoint operates in E. coli such that, after exposure to ultraviolet light, while excision repair occurs, chromosome replication continues very slowly with the production of discontinuous daughter strands. The slower the rate of excision of photoproducts, the greater the delay before the normal rate of DNA replication is restored, the additional (...) time for repair ensuring that normal survival is maintained. A model is proposed in which replication rate is controlled by the ratio of RecAcoated to uncoated single stranded regions of DNA in the replication fork. There are also two cell division inhibitors SulA (=SfiA) and SfiC under the control of the SOS system and sensitive to DNA damage, but they are irrelevant to the survival of wild‐type bacteria under normal conditions. In strains where SulA and SfiC do not operate, inhibition is not influenced by the rate of excision repair and so fails one of the criteria for a DNA damage checkpoint, namely the monitoring of the DNA for the level of residual damage. (shrink)

While there has been significant discussion in the health sciences and ethics literatures about problems associated with publication practices (e.g., ghost- and gift-authorship, conflicts of interest), there has been relatively little practical guidance developed to help researchers determine how they should fairly allocate credit for multi-authored publications. Fair allocation of credit requires that participating authors be acknowledged for their contribution and responsibilities, but it is not obvious what contributions should warrant authorship, nor who should be responsible for the quality and (...) content of the scientific research findings presented in a publication. In this paper, we review arguments presented in the ethics and health science literatures, and the policies or guidelines proposed by learned societies and journals, in order to explore the link between author contribution and responsibility in multi-author multidisciplinary health science publications. We then critically examine the various procedures used in the field to help researchers fairly allocate authorship. (shrink)

There is a widely acknowledged shortage of and an increasing demand for transplantable human organs and tissues (e.g., kidney, heart, lung, liver, cornea) in developed and developing countries around the world. In response to this need, Lott and Savulescu (2007) propose the creation of a human embryonic stem (hESC) bank to facilitate the equitable and efficient dissemination of human leukocyte anti- gen (HLA) matched tissues and organs to patients in need of replacement. Although not an unreasonable proposal, the authors go (...) on to make a much stronger claim. They argue that hESCs are such important tools for addressing the massive unmet global need for organs that it is ethically justified to require mandatory banking of spare embryos, and they argue for the use of financial (or other) inducements to procure embryos for the derivation of hESCs. (shrink)

In seeking to clarify the concept of conflict of interest (COI) in debates about physician–industry relationships, Howard Brody (2011) highlights the extent to which the prob- lem turns on a common pejorative understanding of COI. Whether it is the academic or public policy “pharmapologists” or “pharmascolds” talking about COI, there is often a straightforward and overly simplistic correlation made: that is, a conflict of interest—by definition—leads to fraudulent or corrupt behavior. The same type of reasoning is com- monly found in (...) discussions about COI outside the health sciences, most notably in news stories about the awarding of government contracts or the behaviour of corporate executives. The problem is that in focusing on dramatic failures to manage COI (e.g., around Vioxx), there is a tendency to strongly associate COI with extreme forms of financial and even criminal misconduct, leaving the public, policymakers, academics, and professionals with a skewed and limited understanding of the concept. (shrink)

: Decisions about funding health services are crucial to controlling costs in health care insurance plans, yet they encounter serious challenges from intellectual property protection—e.g., patents—of health care services. Using Myriad Genetics' commercial genetic susceptibility test for hereditary breast cancer (BRCA testing) in the context of the Canadian health insurance system as a case study, this paper applies concepts from social contract theory to help develop more just and rational approaches to health care decision making. Specifically, Daniels's and Sabin's "accountability (...) for reasonableness" is compared to broader notions of public consultation, demonstrating that expert assessments in specific decisions must be transparent and accountable and supplemented by public consultation. (shrink)

Imagine that you are part of the editorial board of a young bioethics journal committed to publishing open access (OA) and to ensuring accessibility to high quality and innovative scholarship. To support junior and interna- tional scholars who might not otherwise find places for their work in the leading Western bioethics journals, you do not charge author fees. Imagine also that you have no financial resources to pay for a professional website, auto- mated submissions manager, or even a part-time coordina- (...) tor: Your government has cut all grants for journals, you cannot go to industry for private funding because of the evident risk of apparent conflicts of interest, and your strapped-for-cash institution cannot afford to offer you any support. If one of the major publishers were to approach you to sign a deal, the temptation would be strong to accept. However, this would likely mean putting aside your ideals: It would be impossible to stay a “Green OA” publication (i.e., free of author publication charges) or supportive of junior and international scholars (because of pressures to “increase credibility” through artificially high rejection rates, for example). (shrink)

Objective Our study sought to (1) describe the practices and preferences of Colombian adolescents in accessing sexual and reproductive health services: accompanied versus alone; (2) compare actual practices with stated preferences; and (3) determine age and gender differences regarding the practice and these stated preferences. -/- Methods 812 participants aged 11–24 years old answered a survey in two Profamilia clinics in the cities of Medellin and Cali in Colombia. A cross-sectional analysis was performed to compare participants’ answers based on the (...) variables of gender and age. -/- Results A quarter of participants visited the clinic alone (25.4%). Females were more likely to go alone in comparison to males (26.3% vs 14.1%; p = 0.031), and older participants went alone more often than younger participants (p < 0.001). Most participants – 72.7% (95 %CI: 69.3–75.9) – expressed a preference in being accompanied to the clinic, and more than 90% had their preferences met. The preferences of older participants were, however, less likely to be met than those of younger participants (p < 0.001), notably, because they predominantly wanted to be accompanied. -/- Conclusion Contemporary public health and bioethics literature advocates in favor of developing health services that better meet the preferences of adolescents. The present research highlights an apparent blind spot related to the role that others (e.g., parents, friends, partners) can or should play in accompanying adolescent patients when they access sexual and reproductive health services. Respecting adolescents’ preferences, and hence their autonomy, is not simply a matter of ensuring freedom from constraints (e.g., their right and ability to go alone). Rather, it should also consider the liberty to choose whether to be accompanied when accessing SHRS and by whom. (shrink)

There are conceptual and ethical challenges to defining adolescents’ autonomy to access health care, and these can lead to health care norms and practices that could be maladjusted to the needs and preferences of adolescents. Particularly sensitive is access to sexual and reproductive health care services (SRHS). Yet, while there has been substantial conceptual work to conceptualize autonomy (e.g., as independence), there is a lack of empirical research that documents the perceptions of adolescents regarding on how they access or wish (...) to access health care services. The main objectives of this research were to (a) understand how adolescents in Colombia interpret the concept of “autonomy,” (b) describe how these adolescents articulate their autonomy (i.e., preferences) in accessing SRHS, and (c) analyze the ethical issues emerging from these data. Forty-five semi-structured interviews were conducted with participants aged 14 to 23 years old in the Departments of Antioquia and Valle del Cauca in Colombia. Our study showed that participants’ understanding of autonomy was context-based and highly dependent on personal experiences, and these influenced their choice in how to access SRHS. Seen through the ethical lens of a reproductive justice framework, our results highlight the unequal opportunities for adolescents in terms of autonomy to access SRHS. (shrink)

This paper explores the interface between users and producers of translational science through three case studies. It argues that effective TS requires a breakdown between user and producer roles: users become producers and producers become users. In making this claim, we challenge conventional understandings of TS as well as linear models of innovation. Policy-makers and funders increasingly expect TS and its associated socioeconomic benefits to occur when funding scientific research. We argue that a better understanding of the hybridity between users (...) and producers in TS is essential to encouraging effective TS activities. In arguing for broader understandings of the hybrid roles of user/producers in TS we rely on empirical observations made during our four-year study of three translational pathways here labeled clinical, commercial, and civic. These pathways were identified in a large-scale network of scientists investigating the pathogenomics of innate immunity (i.e. “the PI.2 network”.. (shrink)

While every health care system stakeholder would seem to be concerned with obtaining the greatest value from a given technology, there is often a disconnect in the perception of value between a technology’s promoters and those responsible for the ultimate decision as to whether or not to pay for it. Adopting an empirical ethics approach, this paper examines how five Canadian medical device manufacturers, via their websites, frame the corporate “value proposition” of their innovation and seek to respond to what (...) they consider the key expectations of their customers. Our analysis shows that the manufacturers’ framing strategies combine claims that relate to valuable socio-technical goals and features such as prevention, efficiency, sense of security, real-time feedback, ease of use and flexibility, all elements that likely resonate with a large spectrum of health care system stakeholders. The websites do not describe, however, how the innovations may impact health care delivery and tend to obfuscate the decisional trade-offs these innovations represent from a health care system perspective. Such framing strategies, we argue, tend to bolster physicians’ and patients’ expectations and provide a large set of stakeholders with powerful rhetorical tools that may influence the health policy arena. Because these strategies are difficult to counter given the paucity of evidence and its limited use in policymaking, establishing sound collective health care priorities will require solid critiques of how certain kinds of medical devices may provide a better (i.e., more valuable) response to health care needs when compared to others. (shrink)

Surveillance programs supporting the management of One Health issues such as antibiotic resistance are complex systems in themselves. Designing ethical surveillance systems is thus a complex task (retroactive and iterative), yet one that is also complicated to implement and evaluate (e.g., sharing, collaboration, and governance). The governance of health surveillance requires attention to ethical concerns about data and knowledge (e.g., performance, trust, accountability, and transparency) and empowerment ethics, also referred to as a form of responsible self-governance. Ethics in reflexive governance (...) operates as a systematic critical-thinking procedure that aims to define its value: What are the “right” criteria to justify how to govern “good” actions for a “better” future? The objective is to lay the foundations for a methodological framework in empirical bioethics, the rudiments of which have been applied to a case study to building reflexive governance in One Health. This ongoing critical thinking process involves “mapping, framing, and shaping” the dynamics of interests and perspectives that could jeopardize a “better” future. This paper proposes to hybridize methods to combine insights from collective deliberation and expert evaluation through a reflexive governance functioning as a community-based action-ethics methodology. The intention is to empower individuals and associations in a dialogue with society, which operation is carried out using a case study approach on data sharing systems. We based our reasoning on a feasibility study conducted in Québec, Canada (2018–2021), envisioning an antibiotic use surveillance program in animal health for 2023. Using the adaptive cycle and governance techniques and perspectives, we synthesize an alternative governance model rooted in the value of empowerment. The framework, depicted as a new “research and design (R&D)” practice, is linking operation and innovation by bridging the gap between Reflexive, Evaluative, and Deliberative reasonings and by intellectualizing the management of democratizing critical thinking locally (collective ethics) by recognizing its context (social ethics). Drawing on the literature in One Health and sustainable development studies, this article describes how a communitarian and pragmatic approach can broaden the vision of feasibility studies to ease collaboration through public-private-academic partnerships. The result is a process that “reassembles” the One Health paradigm under the perspective of global bioethics to create bridges between the person and the ecosystem through pragmatic ethics. (shrink)

Launched in 2007, the American Medical Students Association PharmFree Scorecard is an annual ranking of conflict of interest policies at American medical centres; it focuses on COIs that may occur when medical education seems likely to be influenced by university-industry relationships, especially those with the pharmaceutical and medical device industries. The PharmFree Scorecard has proven influential in stimulating changes in policy regarding the management of COI at American medical institutions, thus it provides a useful jumping off point for reflection on (...) how and why medical education institutions in other countries – and for our purposes, Canada – should pay more attention to the appropriate identification and management of COI. The PharmFree Scorecard methodology examines a diversity of factors and interests that could influence medical education; as such, it is an interesting approach to analysing the COI policies of medical schools. To test its utility or applicability outside the US, we decided to apply the PharmFree Scorecard to the COI policies of the 16 Canadian universities hosting medical schools. Overall, Canadian institutions rank very poorly, especially in ensuring that education and training tools are provided to staff, students and faculty members to enable the identification and management of COI. However, differences between the US and Canadian medical education contexts, e.g., with regards to the governance and funding of universities, limit to some extent the direct applicability of the AMSA ranking. Canadian medical schools – and their host universities – nonetheless have much to learn from insights provided by the AMSA PharmFree Scorecard ranking, although they can and should go further in developing their own COI policies and procedures. (shrink)

Despite having essential health needs regarding sexual and reproductive health services (SRHS), young people (e.g., adolescents) in many countries show low use of such services. The World Health Organization advocates fostering young people’s autonomy to access health services to address this global health problem. However, there are gaps in the literature to understand how young people’s autonomy can be fostered to access SRHS. In 2019–2020, we conducted semi-structured interviews with 45 young people aged 14–23 years old in Colombia to explore (...) how they might wish to have their autonomy fostered in accessing SRHS. Research in different cultural contexts has shown that young people generally do not wish to discuss sex with their parents. By contrast, most of our participants expressed a strong wish for the ability to talk openly with their parents about their sexual and reproductive health. One of the main complaints of these young people was that their parents lacked the necessary knowledge to help them make informed decisions related to their sexual and reproductive health (e.g., choosing a contraceptive option). As a potential solution, participants were enthusiastic about initiatives that could provide parents with comprehensive sex education to assist young people in making informed choices for their sexual and reproductive health, including how to access SRHS. (shrink)

Health care providers (HCPs) are routinely placed into morally challenging situations that have the potential to cause moral distress. This is especially true for HCPs working in the military, whether they are on deployment outside their typical contexts of practice such as in disaster relief (e.g., Haiti and the Ebola missions in West Africa), or in more typically military settings such as peace keeping or armed conflicts (e.g., Afghanistan, Syria). Moral distress refers to “painful feelings and/or psychological disequilibrium” (Nilsson, Sjöberg, (...) Kallenberg, & Larsson, 2011, p. 50) that occur when an individual is aware of a morally appropriate action in a moral dilemma but obstruction prevents them from carrying it out, or when in a situation where they must choose between upholding equally treasured but conflicting moral values. Similarly, moral distress can occur when faced with a ‘tragic choice’ where all available courses of action require something of moral significance to be given up, such as surgical triage in a mass casualty event (Hunt, Sinding, & Schwartz, 2012). In the literature, moral distress has been connected to negative psychological effects and even stress related mental health issues including compassion fatigue, burnout, and post-traumatic stress disorder (Owen & Wanzer, 2014; Gustafsson, Eriksson, Strandberg, & Norberg, 2010; Litz, et al., 2009). (shrink)

This translation of the two books that make up Against the Logicians is a valuable addition to the ever increasing literature on Pyrrhonism. The only previous complete English version of these two books is that of R. G. Bury, which appeared in 1935 in the Loeb Classical Library as the second volume of..

Particularly during the past twenty five years, there has been an outstanding advance in the study of ancient skepticism, both in its Pyrrhonian and Academic varieties. This is reflected in the publication of a considerable number of works about the nature and consistency of those philosophical outlooks, as well as about their influence on the development of early modern philosophy and their relevance to present day epistemological discussions. Most of these works concern Pyrrhonian skepticism. This predominance of interest in Pyrrhonism (...) over Academic skepticism also manifests itself in the fact that, whereas in recent years several new translations of Sextus Empiricus' writings (our principal source for Pyrrhonism) have appeared in the most important European languages, the same has not happened with Cicero's Academica, which is our main source of information about the philosophy of the skeptical Academy. Even though Sextus'. (shrink)

This work is the latest contribution to the Clarendon Later Ancient Philosophers series edited by Jonathan Barnes and A. A. Long. As with the earlier volumes (John Dillon's Alcinous, The Handbook of Platonism , R. J. Hankinson's Galen, On the Therapeutic Method Books I and II, Richard Bett's Sextus Empiricus, Against the Ethicists, and D. L. Blank's Sextus Empiricus, Against the Grammarians), D(obbin) provides an introduction, an English translation, and a critical commentary predominantly focused on the philosophical content of the (...) text of an author from the period ranging from the first century BC to the fifth century AD. A bibliography of a dozen earlier editions of E(pictetus), a painstaking bibliography of secondary literature, an index nominum, a generous index locorum, and a brief subject index are also included. Overall this edition maintains the high standards characteristic of the CLAP series. (shrink)

Up to now scholars have not approached E[pictetus] as author, stylist, educator, and thinker, according to the eminent scholar of Stoicism Tony L[ong]. The aim of this book is to fill precisely this gap. L wants "to provide an accessible guide to reading E, both as a remarkable historical figure and as a thinker whose recipe for a free and satisfying life can engage our modern selves, in spite of our cultural distance from him" (2). This goal is met admirably. (...) Not only does L succeed in presenting E on his own terms, but in the process, he fairly demolishes the view, held by many since Adolf Bonhöffer,1 that E is a sturdy but unoriginal moralist who basically rehashed the same ideas, with an emphasis on practical application, that were articulated in a more sophisticated, theoretically fastidious form by Chrysippus and the early Stoics. (shrink)

Though pictures are often used to present mathematical arguments, they are not typically thought to be an acceptable means for presenting mathematical arguments rigorously. With respect to the proofs in the Elements in particular, the received view is that Euclid's reliance on geometric diagrams undermines his efforts to develop a gap-free deductive theory. The central difficulty concerns the generality of the theory. How can inferences made from a particular diagrams license general mathematical results? After surveying the history behind the received (...) view, this essay provides a contrary analysis by introducing a formal account of Euclid's proofs, termed Eu. Eu solves the puzzle of generality surrounding Euclid's arguments. It specifies what diagrams Euclid's diagrams are, in a precise formal sense, and defines generality-preserving proof rules in terms of them. After the central principles behind the formalization are laid out, its implications with respect to the question of what does and does not constitute a genuine picture proof are explored. (shrink)

Diagrams are ubiquitous in mathematics. From the most elementary class to the most advanced seminar, in both introductory textbooks and professional journals, diagrams are present, to introduce concepts, increase understanding, and prove results. They thus fulfill a variety of important roles in mathematical practice. Long overlooked by philosophers focused on foundational and ontological issues, these roles have come to receive attention in the past two decades, a trend in line with the growing philosophical interest in actual mathematical practice.

Modern formal accounts of the constructive nature of elementary geometry do not aim to capture the intuitive or concrete character of geometrical construction. In line with the general abstract approach of modern axiomatics, nothing is presumed of the objects that a geometric construction produces. This study explores the possibility of a formal account of geometric construction where the basic geometric objects are understood from the outset to possess certain spatial properties. The discussion is centered around Eu , a recently developed (...) formal system of proof (presented in Mumma (Synthese 175:255–287, 2010 )) within which Euclid’s diagrammatic proofs can be represented. (shrink)

In line with Ken Manders’s seminal account of Euclid’s diagrammatic method in the “The Euclidean Diagram,” two proof systems with a diagrammatic syntax have been advanced as formalizations of the method FG and Eu. In a paper examining Eu, Nathaniel Miller, the creator of FG, has identified a variety of technical problems with the formal details of Eu. This response shows how the problems are remedied.

It is commonplace to view the rigor of the mathematics in Euclid's Elements in the way an experienced teacher views the work of an earnest beginner: respectable relative to an early stage of development, but ultimately flawed. Given the close connection in content between Euclid's Elements and high-school geometry classes, this is understandable. Euclid, it seems, never realized what everyone who moves beyond elementary geometry into more advanced mathematics is now customarily taught: a fully rigorous proof cannot rely on geometric (...) intuition. In his arguments he seems to call illicitly upon our understanding of how objects like triangles and circles behave rather than grounding everything rigorously in axioms.Though widespread, the attitude is in a historical sense puzzling. For over two millenia, mathematicians of all levels studied the arguments in Elements and found nothing substantial missing. The book, on the contrary, represented the limit of mathematical explicitness. It served as the paradigm for careful and exact reasoning. How it could enjoy this reputation for so long is mysterious if careful and exact reasoning demands that all inferences be grounded in a modern axiomatic theory in the way Hilbert did in his famous Foundations of Geometry. By these standards, Euclid's work is deeply flawed. The holes in his arguments are not minor and excusable, but massive and cryptic.With his book Euclid and His Twentieth Century Rivals, Nathaniel Miller makes substantial progress in clearing this mystery up. The book is an explication of FG , a formal system of proof developed by Miller which reconstructs Euclid's deductions as essentially diagrammatic. The holes in Euclid's arguments are taken to appear precisely at those steps which are unintelligible without an accompanying geometric diagram. Interpreting the reasoning in the Elements in terms of a modern axiomatization , …. (shrink)

Labelling schemes are practical arrangements aimed at making 'ethical' products widely available and visible. They are crucial to expanded development of ethical markets and hence to the addition of moral dimensions to the normally amoral behaviour linking consumers and retail and production businesses. The study reported here attempts to assess the contribution of UK ethical, social and environmental certification and labelling initiatives to 'sustainable' consumption and production. The research sought to assess the overall potential of initiatives to inject human values (...) into the supply-distribution chains, through a qualitative survey of 15 of the 26 main UK initiatives: in social justice, animal welfare and environmental sustainability from the agriculture, food processing, timber, aquaculture, textiles and personal care sectors. By analysing the basic characteristics and concepts of these labels and investigating the emergence of labelling initiatives, we assess whether labels help add an ethical dimension, or whether, in some respects, they also reduce such missions to the technical management of adding only another 'utility' to a product. The analysis assesses whether the gradual 'mainstreaming' of ethical initiatives such as 'Fairtrade' risks subsuming ethical goals within business participants' competitive and profit-oriented logics. However, the contrasting perspectives revealed between rival labelling initiatives show that the scope and functions of labelling projects go beyond the manifest ones of information communication between consumers and producer and actually introduce elements of socio-political regulation. These are essential for more sustainable and ethical business practices and are an integral part of any humanisation of business involvement. (shrink)

Developing novices’ proficiency in skilful activities is central to the reproduction of human societies. The interactional practices through which instruction is accomplished have provided a rich focus for ethnomethodological and conversation analytic studies examining classroom settings, and, more recently, non-classroom environments of instruction in practical and manual skills. This paper examines the work of instruction in basketball training and in particular the correction of player performances, which are a ubiquitous and central feature of instruction in basketball training sessions. A central (...) part of this instructional action relies on the coach observing training activities to determine players’ competencies and to extract relevant correctables from the players’ embodied displays, which are in turn embedded within complex arrangements of rapidly moving bodies situated in material environments. In this paper we examine the visual-analytic work involved in both organizing and observing a basketball training activity, demonstrating the sequential layering of multiple membership categorization devices drawn upon in producing and recognizing actions in this setting. We argue that the coach deploys spatial orientations which function analogously to membership categorization devices, with players’ bodily positions relative to one another and the material structure of the surround generating category-like sets of rights, responsibilities, and sequential relevancies. As we demonstrate, these orientations provide crucial resources for the identification of players’ errors and thereby for the organization of instruction in interaction in this setting. (shrink)

This article explores how researchers in a scientific research lab co-operate with each other and value these co-operations, using a case study of a life sciences lab as an illustrative example. It explores how researchers within the lab co-operate in three main ways: through their ideas, methods and resources. A core contention of this article is that the values researchers attach to these different ways of co-operating can be assessed on two dimensions: goals and ways of understanding. The goals dimension (...) moves from group goals, manifested in the vision of the lab defined by its principal investigator, to the goals of individual researchers within the lab, often achieved through work on individual projects. Individual goals were more highly valued by researchers in this case study. The ways of understanding dimension moves from theory-based and theory-building research activities, to craft-based activities related to the research lab’s experiments. Theoretical ways of understanding are more highly valued by researchers in this case study. Combined, these two dimensions mean that researchers will value co-operations that support individual goals and theoretical ways of understanding more highly. Idea-based collaborations, individualistic and theoretical in nature, were the most highly valued. Collaborations based on resources, communal and craft-centered, were the least valued in this case study. (shrink)

Topological relations such as inside, outside, or intersection are ubiquitous to our spatial thinking. Here, we examined how people reason deductively with topological relations between points, lines, and circles in geometric diagrams. We hypothesized in particular that a counterexample search generally underlies this type of reasoning. We first verified that educated adults without specific math training were able to produce correct diagrammatic representations contained in the premisses of an inference. Our first experiment then revealed that subjects who correctly judged an (...) inference as invalid almost always produced a counterexample to support their answer. Noticeably, even if the counterexample always bore a certain level of similarity to the initial diagram, we observed that an object was more likely to be varied between the two drawings if it was present in the conclusion of the inference. Experiments 2 and 3 then directly probed counterexample search. While participants were asked to evaluate a conclusion on the basis of a given diagram and some premisses, we modulated the difficulty of reaching a counterexample from the diagram. Our results indicate that both decreasing the counterexample density and increasing the counterexample distance impaired reasoning performance. Taken together, our results suggest that a search procedure for counterexamples, which proceeds object‐wise, could underlie diagram‐based geometric reasoning. Transposing points, lines, and circles to our spatial environment, the present study may ultimately provide insights on how humans reason about topological relations between positions, paths, and regions. (shrink)