We analyze the developments in mathematical rigor from the viewpoint of a Burgessian critique of nominalistic reconstructions. We apply such a critique to the reconstruction of infinitesimal analysis accomplished through the efforts of Cantor, Dedekind, and Weierstrass; to the reconstruction of Cauchy’s foundational work associated with the work of Boyer and Grabiner; and to Bishop’s constructivist reconstruction of classical analysis. We examine the effects of a nominalist disposition on historiography, teaching, and research.

We explore the potential of Simon Stevin’s numbers, obscured by shifting foundational biases and by 19th century developments in the arithmetisation of analysis.

One of the most influential scientific treatises in Cauchy's era was J.-L. Lagrange's Mécanique Analytique, the second edition of which came out in 1811, when Cauchy was barely out of his teens. Lagrange opens his treatise with an unequivocal endorsement of infinitesimals. Referring to the system of infinitesimal calculus, Lagrange writes:Lorsqu'on a bien conçu l'esprit de ce système, et qu'on s'est convaincu de l'exactitude de ses résultats par la méthode géométrique des premières et dernières raisons, ou par la méthode analytique (...) des fonctions dérivées, on peut employer les infiniment petits comme un instrument sûr et commode pour abréger et simplifier les demonstrations.Lagrange's renewed enthusiasm for .. (shrink)

The small, the tiny, and the infinitesimal have been the object of both fascination and vilification for millenia. One of the most vitriolic reviews in mathematics was that written by Errett Bishop about Keisler’s book Elementary Calculus: an Infinitesimal Approach. In this skit we investigate both the argument itself, and some of its roots in Bishop George Berkeley’s criticism of Leibnizian and Newtonian Calculus. We also explore some of the consequences to students for whom the infinitesimal approach is congenial. The (...) casual mathematical reader may be satisfied to read the text of the five act play, whereas the others may wish to delve into the 130 footnotes, some of which contain elucidation of the mathematics or comments on the history. (shrink)

We apply a framework developed by C. S. Peirce to analyze the concept of clarity, so as to examine a pair of rival mathematical approaches to a typical result in analysis. Namely, we compare an intuitionist and an infinitesimal approaches to the extreme value theorem. We argue that a given pre-mathematical phenomenon may have several aspects that are not necessarily captured by a single formalisation, pointing to a complementarity rather than a rivalry of the approaches.

We apply Benacerraf’s distinction between mathematical ontology and mathematical practice to examine contrasting interpretations of infinitesimal mathematics of the seventeenth and eighteenth century, in the work of Bos, Ferraro, Laugwitz, and others. We detect Weierstrass’s ghost behind some of the received historiography on Euler’s infinitesimal mathematics, as when Ferraro proposes to understand Euler in terms of a Weierstrassian notion of limit and Fraser declares classical analysis to be a “primary point of reference for understanding the eighteenth-century theories.” Meanwhile, scholars like (...) Bos and Laugwitz seek to explore Eulerian methodology, practice, and procedures in a way more faithful to Euler’s own. Euler’s use of infinite integers and the associated infinite products are analyzed in the context of his infinite product decomposition for the sine function. Euler’s principle of cancellation is compared to the Leibnizian transcendental law of homogeneity. The Leibnizian law of continuity similarly finds echoes in Euler. We argue that Ferraro’s assumption that Euler worked with a classical notion of quantity is symptomatic of a post-Weierstrassian placement of Euler in the Archimedean track for the development of analysis, as well as a blurring of the distinction between the dual tracks noted by Bos. Interpreting Euler in an Archimedean conceptual framework obscures important aspects of Euler’s work. Such a framework is profitably replaced by a syntactically more versatile modern infinitesimal framework that provides better proxies for his inferential moves. (shrink)

Did Leibniz exploit infinitesimals and infinities à la rigueur or only as shorthand for quantified propositions that refer to ordinary Archimedean magnitudes? Hidé Ishiguro defends the latter position, which she reformulates in terms of Russellian logical fictions. Ishiguro does not explain how to reconcile this interpretation with Leibniz’s repeated assertions that infinitesimals violate the Archimedean property (i.e., Euclid’s Elements, V.4). We present textual evidence from Leibniz, as well as historical evidence from the early decades of the calculus, to undermine Ishiguro’s (...) interpretation. Leibniz frequently writes that his infinitesimals are useful fictions, and we agree, but we show that it is best not to understand them as logical fictions; instead, they are better understood as pure fictions. (shrink)

Abraham Robinson’s framework for modern infinitesimals was developed half a century ago. It enables a re-evaluation of the procedures of the pioneers of mathematical analysis. Their procedures have been often viewed through the lens of the success of the Weierstrassian foundations. We propose a view without passing through the lens, by means of proxies for such procedures in the modern theory of infinitesimals. The real accomplishments of calculus and analysis had been based primarily on the elaboration of novel techniques for (...) solving problems rather than a quest for ultimate foundations. It may be hopeless to interpret historical foundations in terms of a punctiform continuum, but arguably it is possible to interpret historical techniques and procedures in terms of modern ones. Our proposed formalisations do not mean that Fermat, Gregory, Leibniz, Euler, and Cauchy were pre-Robinsonians, but rather indicate that Robinson’s framework is more helpful in understanding their procedures than a Weierstrassian framework. (shrink)

In relation to a thesis put forward by Marx Wartofsky, we seek to show that a historiography of mathematics requires an analysis of the ontology of the part of mathematics under scrutiny. Following Ian Hacking, we point out that in the history of mathematics the amount of contingency is larger than is usually thought. As a case study, we analyze the historians’ approach to interpreting James Gregory’s expression ultimate terms in his paper attempting to prove the irrationality of \. Here (...) Gregory referred to the last or ultimate terms of a series. More broadly, we analyze the following questions: which modern framework is more appropriate for interpreting the procedures at work in texts from the early history of infinitesimal analysis? As well as the related question: what is a logical theory that is close to something early modern mathematicians could have used when studying infinite series and quadrature problems? We argue that what has been routinely viewed from the viewpoint of classical analysis as an example of an “unrigorous” practice, in fact finds close procedural proxies in modern infinitesimal theories. We analyze a mix of social and religious reasons that had led to the suppression of both the religious order of Gregory’s teacher degli Angeli, and Gregory’s books at Venice, in the late 1660s. (shrink)

To explore the extent of embeddability of Leibnizian infinitesimal calculus in first-order logic (FOL) and modern frameworks, we propose to set aside ontological issues and focus on pro- cedural questions. This would enable an account of Leibnizian procedures in a framework limited to FOL with a small number of additional ingredients such as the relation of infinite proximity. If, as we argue here, first order logic is indeed suitable for developing modern proxies for the inferential moves found in Leibnizian infinitesimal (...) calculus, then modern infinitesimal frameworks are more appropriate to interpreting Leibnizian infinitesimal calculus than modern Weierstrassian ones. (shrink)

Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy’s proof, and discuss the related epistemological questions involved in comparing distinct interpretive paradigms. Cauchy’s proof is often interpreted in the modern framework of a Weierstrassian paradigm. We analyze Cauchy’s proof closely and show that it finds closer proxies in a different modern framework.

Philosophy with children (P4C) 1 presents significant positive challenges for educators. Its 'community of enquiry' pedagogy assumes not only an epistemological shift in the role of the educator, but also a different ontology of 'child' and balance of power between educator and learner. After a brief historical sketch and an outline of the diversity among P4C practitioners, epistemological uncertainty in teaching P4C is crystallised in a succinct overview of theoretical and practical tensions that are a direct result of the implementation (...) of P4C in mainstream education. These recurring pedagogical tensions in my practice as P4C teacher, teacher educator and mentor of teacher educators cause disequilibrium that opens up rich opportunities for philosophy of education in supporting novice P4Cers. Disequilibrium is a positive force that opens up a space in which educators need to reflect upon their values, their beliefs about learning and teaching, and ultimately encourages educators to rethink their own role. Plato's metaphor of the stingray highlights the role of the P4C teacher educator as model of the P4C teacher in any setting: 'to numb and to be numbed'. The P4C community and its institutions need to address the questions arising from these pedagogical tensions; and this needs to be done with integrity, that is, in communities of enquiry that include children. If not, in the long term, a more instrumental version of P4C may prevail. (shrink)

The Posthuman Child combats institutionalised ageist practices in primary, early childhood and teacher education. Grounded in a critical posthumanist perspective on the purpose of education, it provides a genealogy of psychology, sociology and philosophy of childhood in which dominant figurations of child and childhood are exposed as positioning child as epistemically and ontologically inferior. Entangled throughout this book are practical and theorised examples of philosophical work with student teachers, teachers, other practitioners and children (aged 3-11) from South Africa and Britain. (...) These engage arguments about how children are routinely marginalised, discriminated against and denied, especially when the child is also female, black, lives in poverty and whose home language is not English. The book makes a distinctive contribution to the decolonisation of childhood discourses. Underpinned by good quality picturebooks and other striking images, the book's radical proposal for transformation is to reconfigure the child as rich, resourceful and resilient through relationships with (non) human others, and explores the implications for literary and literacy education, teacher education, curriculum construction, implementation and assessment. It is essential reading for all who research, work and live with children. (shrink)

The philosophy for children curriculum was specially written by Matthew Lipman and colleagues for the teaching of philosophy by non-philosophically educated teachers from foundation phase to further education colleges. In this article I argue that such a curriculum is neither a necessary, not a sufficient condition for the teaching of philosophical thinking. The philosophical knowledge and pedagogical tact of the teacher remains salient, in that the open-ended and unpredictable nature of philosophical enquiry demands of teachers to think in the moment (...) and draw on their own knowledge and experience of academic philosophy. Providing specialist training or induction in the P4C curriculum cannot and should not replace undergraduate and postgraduate degrees in academic philosophy at universities. However, although for academic philosophers the use of the P4C curriculum could be beneficial, I will argue that its use poses the risk of wanting to form children into the ideal ‘abnormal’ child, the thinking child—the adult philosopher’s child positioned as such by the Lipman novels. The notion of narrativity is central in my argument. With the help of two picturebooks—The Three Pigs by David Weisner and Voices in the Park by Anthony Browne—I illustrate my claim that philosophy as ‘side-shadowing’ or meta-thinking can only be generated in the space ‘in between’ text, child and educator, thereby foregrounding a ‘pedagogy of exposure’ rather than ‘teacher proof’ texts. (shrink)

BackgroundOur human societies and certainly also (bio) medicine are more and more permeated with technology. There seems to be an increasing awareness among bioethicists that an effective and comprehensive approach to ethically guide these emerging biomedical innovations into society is needed. Such an approach has not been spelled out yet for bioethics, while there are frequent calls for ethical guidance of biomedical innovation, also by biomedical researchers themselves. New and emerging biotechnologies require anticipation of possible effects and implications, meaning the (...) scope is not evaluative after a technology has been fully developed or about hypothetical technologies, but real-time for a real biotechnology.Main textIn this paper we aim to substantiate and discuss six ingredients that we increasingly see adopted by ethicists and that together constitute “ethics parallel research”. This approach allows to fulfil two aims: guiding the development process of technologies in biomedicine and providing input for the normative evaluation of such technologies. The six ingredients of ethics parallel research are: (1) disentangling wicked problems, (2) upstream or midstream ethical analysis, (3) ethics from within, (4) inclusion of empirical research, (5) public participation and (6) mapping societal impacts, including hard and soft impacts. We will draw on gene editing, organoid technology and artificial intelligence as examples to illustrate these six ingredients.ConclusionEthics parallel research brings together these ingredients to ethically analyse and proactively or parallel guide technological development. It widens the roles and judgements from the ethicist to a more anticipatory and constructively guiding role. Ethics parallel research is characterised by a constructive, rather than a purely critical perspective, it focusses on developing best-practices rather than outlining worst practice, and draws on insights from social sciences and philosophy of technology. (shrink)

This book argues that the development of German philosophy from Kant, through post-Kantian German Idealism, to the thought of Franz Rosenzweig, was largely driven by the perceived promise of Kant's philosophy for solving the conflict of reason, but also by its perceived shortcomings in solving this conflict.

Dementia is highly prevalent and incurable. The participation of dementia patients in clinical research is indispensable if we want to find an effective treatment for dementia. However, one of the primary challenges in dementia research is the patients’ gradual loss of the capacity to consent. Patients with dementia are characterized by the fact that, at an earlier stage of their life, they were able to give their consent to participation in research. Therefore, the phase when patients are still competent to (...) decide offers a valuable opportunity to authorize research, by using an advance research directive. Yet, the use of ARDs as an authorization for research participation remains controversial. In this paper we discuss the role of autonomous decision-making and the protection of incompetent research subjects. We will show why ARDs are a morally defensible basis for the inclusion of this population in biomedical research and that the use of ARDs is compatible with the protection of incompetent research subjects. (shrink)

The authors of the paper ‘Advance euthanasia directives: a controversial case and its ethical implications’ articulate concerns and reasons with regard to the conduct of euthanasia in persons with dementia based on advance directives. While we agree on the conclusion that there needs to be more attention for such directives in the preparation phase, we disagree with the reasons provided by the authors to support their conclusions. We will outline two concerns with their reasoning by drawing on empirical research and (...) by providing reasons that contradict their assumptions about competence of people with dementia and the importance of happiness in reasoning about advance directives of people with dementia. We will draw attention to the important normative questions that have been overstepped in their paper, and we will outline why further research is required. (shrink)

Historians and philosophers of twentieth-century life sciences have demonstrated that the choice of experimental organism can profoundly influence research fields, in ways that sometimes undermined the scientists’ original intentions. The present paper aims to enrich and broaden the scope of this literature by analysing the career of unicellular green algae of the genus Chlorella. They were introduced for the study of photosynthesis in 1919 by the German cell physiologist Otto H. Warburg, and they became the favourite research objects in this (...) field up to the 1960s. The paper argues that dealing with Chlorella’s high metabolic flexibility was crucial for the emergence of a new conception of photosynthesis, as a plastic, integrated system of pathways. At the same time, it led to new collaborations between physiologists and phycologists, both of whom started to re-orient their studies in ecologically informed directions. Following Chlorella’s trail, hence, not only elucidates how experimental organisms forced scientists to change their conceptual approaches and techniques, but also provides insight into the interaction of different lines of research of mid-twentieth century plant sciences. (shrink)

This article analyses the relationship between the concept of single aspect similarity and proposed measures of similarity. More precisely, it compares eleven measures of similarity in terms of how well they satisfy a list of desiderata, chosen to capture common intuitions concerning the properties of similarity and the relations between similarity and dissimilarity. Three types of measures are discussed: similarity as commonality, similarity as a function of dissimilarity, and similarity as a joint function of commonality and difference. Relative to the (...) desiderata, it is found that a measure of the second type fares the best. However, rather than recommend this measure alone as a measure of similarity, it is suggested that there are at least three separate concepts of single aspect similarity, corresponding to the three types of measures. In light of this proposal, three of the eleven measures (and variants of these) are deemed acceptable. (shrink)

In teaching statistics in secondary schools and at university, two visualizations are primarily used when situations with two dichotomous characteristics are represented: 2×2 tables and tree diagrams. Both visualizations can be depicted either with probabilities or with frequencies. Visualizations with frequencies have been shown to help students significantly more in Bayesian reasoning problems than probability visualizations do. Because tree diagrams or double-trees (which are largely unknown in school) are node-branch-structures, these two visualizations (compared to the 2×2 table) can even simultaneously (...) display probabilities on branches and frequencies inside the nodes. This is a teaching advantage as it allows the frequency concept to be used to better understand probabilities. However, 2×2 tables and (double-) trees have a decisive disadvantage: While joint probabilities (e.g., P(AB)) are represented in 2×2 tables but no conditional probabilities (e.g., P(A|B)), it is exactly the other way around with (double-) trees. Therefore, a visualization that is equally suitable for the representation of joint probabilities and conditional probabilities is desirable. In this article, we present a new visualization—the frequency net—in which all absolute frequencies and all types of probabilities can be depicted. In addition to a detailed theoretical analysis of the frequency net, we report the results of a study with 249 university students that shows that “net diagrams” can improve reasoning without previous instruction to a similar extent as 2×2 tables and double-trees. Regarding questions about conditional probabilities, frequency visualizations (2×2 table, double-tree, or net diagram with natural frequencies) are consistently superior to probability visualizations. The frequency net performs as well as the frequency double-tree. Only the 2×2 table with frequencies—the only visualization that participants were already familiar with —led to higher performance rates. If, on the other hand, a question about a joint probability had to be answered, all implemented visualizations clearly supported participants’ performance, and no uniform format effect becomes visible. Participants reached the highest performance in the versions with probability 2×2 tables and probability net diagrams. Furthermore, after conducting a detailed error analysis, we report interesting error shifts between the two information formats and the different visualizations and give recommendations for teaching probability. (shrink)

This article focuses upon the construction of wants and the embodying of the market in the work routines of workers on the Swiss foreign exchange market. The authors are particularly concerned with the role of the computer screen within the establishment of postsocial relations around a sense of embodied lack. The screen does not provide access to the market but is the market as an exteriorized assemblage of practices brought together in one place. The screen is the (ontologically liquid) market (...) rather than its representation into which traders immerse themselves. Traders engage with this market in their daily work practices through a constructed sense of lack that requires them to act passionately within the market in order to satisfy the self understood as a structure of wanting. While Knorr Cetina and Bruegger draw on a Lacanian understanding of the self as lack, rather than focus on the formation of direct human social relations around this issue, they look instead at the materiality of lack and its position within the postsocial relations constituted through trading online in the foreign exchange market. Desire is constituted and realized here through the object of the computer screen rather than with other people directly. In this way relations between persons are mediated by real objects that constitute persons virtually. (shrink)

In this article I aim to clarify the nature of Kant’s transformation of rationalist metaphysics into a science by focusing on his conception of transcendental reflection. The aim of Kant’s Critique of Pure Reason, it is argued, consists primarily in liberating the productive strand of former general metaphysics - its reflection on the a priori elements of all knowledge - from the uncritical application of these elements to all things and to things that can only be thought. After considering Kant’s (...) conception of metaphysics and his various uses of the term ‘transcendental’ I closely examine his account of logical and transcendental reflection in the section entitled ‘On the Amphiboly of the Concepts of Reflection’. Whereas commentators generally attribute the activity called transcendental reflection to Kant alone, I contend, first, that Kant regarded philosophy as such to rely on a mode of transcendental reflection and, second, that the critical mode of transcendental reflection enacted in the Critique itself yields insight into the reason why our a priori knowledge is limited to the realm of possible objects. This is illustrated by outlining the difference between Kant’s and Leibniz’ employment of the concepts of reflection. (shrink)

Human science researchers tend to be targeted for critique on the grounds that their approach is too individualistic to take due cognisance of societal and political influences. What is accordingly advocated is that the phenomenological and so-called romantic theories should be abandoned in favour of analytic or continental theories that have as their main focus the system, the group, the society, and the various influences of the social world on the existential reality of the individual.

It will be shown in this article that an ontological approach for some problems related to the interpretation of Quantum Mechanics could emerge from a re-evaluation of the main paradox of early Greek thought: the paradox of Being and non-Being, and the solutions presented to it by Plato and Aristotle. More well known are the derivative paradoxes of Zeno: the paradox of motion and the paradox of the One and the Many. They stem from what was perceived by classical philosophy (...) to be the fundamental enigma for thinking about the world: the seemingly contradictory results that followed from the co-incidence of being and non-being in the world of change and motion as we experience it, and the experience of absolute existence here and now. The most clear expression of both stances can be found, again following classical thought, in the thinking of Heraclitus of Ephesus and Parmenides of Elea. The problem put forward by these paradoxes reduces for both Plato and Aristotle to the possibility of the existence of stable objects as a necessary condition for knowledge. Hence the primarily ontological nature of the solutions they proposed: Plato's Theory of Forms and Aristotle's metaphysics and logic. Plato's and Aristotle's systems are argued here to do on the ontological level essentially the same: to introduce stability in the world by introducing the notion of a separable, stable object, for which a principle of contradiction is valid: an object cannot be and not-be at the same place at the same time. So it becomes possible to forbid contradiction on an epistemological level, and thus to guarantee the certainty of knowledge that seemed to be threatened before. After leaving Aristotelian metaphysics, early modern science had to cope with these problems: it did so by introducing "space" as the seat of stability, and "time" as the theater of motion. But the ontological structure present in this solution remained the same. Therefore the fundamental notion `separable system', related to the notions observation and measurement, themselves related to the modern concepts of space and time, appears to be intrinsically problematic, because it is inextricably connected to classical logic on the ontological level. We see therefore the problems dealt with by quantum logic not as merely formal, and the problem of `non-locality' as related to it, indicating the need to re-think the notions `system', `entity', as well as the implications of the operation `measurement', which is seen here as an application of classical logic on the material world. (shrink)

Background: Clinical group supervision has existed for over 20 years in nursing. However, there is a lack of studies about the role of supervision in nursing students’ education and especially the focus on ethical reasoning. Aim: The aim of this study was to explore and describe nursing students’ ethical reasoning and their supervisors’ experiences related to participation in clinical group supervision. Research design: The study is a qualitative interview study with interpretative description as an analysis approach. Participants and research context: (...) A total of 17 interviews were conducted with nursing students (n = 12) who had participated in clinical group supervision in their first year of nursing education, and with their supervisors (n = 5). Ethical considerations: The study was based on the ethical principles outlined in the Declaration of Helsinki, and permission was obtained from the Regional Ethical Review Board in Sweden. Findings: The analysis revealed that both the form and content of clinical group supervision stimulated reflection and discussion of handling of situations with ethical aspects. Unethical situations were identified, and the process uncovered underlying caring actions. Discussion and conclusion: Clinical group supervision is a model that can be used in nursing education to train ethical reflection and to develop an ethical competence among nursing students. Outcomes from the model could also improve nursing education itself, as well as healthcare organizations, in terms of reducing moral blindness and unethical nursing practice. (shrink)

Volume 20, Issue 8, August 2020, Page 90-92.

Children and adults with dementia are vulnerable populations. Both groups are also relatively seldom included in biomedical research. However, including them in clinical trials is necessary, since both groups are in need of scientific innovation and new therapies. Their dependence and limited decision-making capacities increase their vulnerability, necessitating extra precautions when including them in clinical trials. Beside these similarities there are also many differences between the groups. The most obvious one is that children have an entire life ahead of them (...) and will become persons with certain ideals and preferences, while adults with dementia have lived a life in which they have expressed their ideals and preferences. Some of the available research guidelines recognize these differences, setting one list of specific requirements for groups of incapacitated adults and another list for children. Other documents, however, do not differentiate and only set requirements for subjects unable to consent as a single category of subjects. In this article we analyse to what extent the similarities and differences between the two groups are represented in legal documents and ethical guidelines. The article presents an overview and an analysis of the requirements for doing research with children and dementia patients. We conclude with suggestions about how to better incorporate the morally relevant aspects of these two groups in legislation and ethical guidelines. (shrink)

In this essay I argue that even though egalitarianism and prioritarianism are different theories of social welfare, they can use the same social welfare measures. I present six different arguments for this thesis. The first argument is that conceptual connections between egalitarianism and prioritarianism ensure that any measure that works for either theory works for both. The second argument is that conditions necessary and sufficient to identify egalitarian and prioritarian measures, respectively, are equivalent. The third argument is that both egalitarianism (...) and prioritarianism can use two standard measures, typically proposed for only one theory. The fourth to sixth arguments contend that four properties that have been proposed as distinctive of either egalitarian or prioritarian measures cannot distinguish between them. I conclude that any egalitarian measure is also a prioritarian measure, and vice versa. (shrink)

Dementia is highly prevalent and up until now, still incurable. If we may believe the narrative that is currently dominant in dementia research, in the future we will not have to suffer from dementia anymore, as there will be a simple techno-fix solution. It is just a matter of time before we can solve the growing public health problem of dementia. In this paper we take a critical stance towards overly positive narratives of techno-fixes by placing our empirical analysis of (...) dementia research protocols and political statements in a framework of technology assessment. From this perspective, it becomes obvious that a techno-fix is just one of many ways to approach societal problems and more importantly that technologies are way less perfect than they are presented. We will argue that this narrow scope, which focusses on the usual suspects for solving illnesses, reduces dementia to organismic aspects, and may be counterproductive in finding a cure for dementia. We conclude with outlining how the narrow scope can be balanced with other narratives and why we should have a reasonable scepticism towards the usual suspects. (shrink)

In their paper ‘Responsibility, second opinions and peer-disagreement: ethical and epistemological challenges of using AI in clinical diagnostic contexts’, Kempt and Nagel discuss the use of medical AI systems and the resulting need for second opinions by human physicians, when physicians and AI disagree, which they call the rule of disagreement.1 The authors defend RoD based on three premises: First, they argue that in cases of disagreement in medical practice, there is an increased burden of proof for the physician in (...) charge, to defend why the opposing view is adopted or overridden. This burden for justification can be understood as an increased responsibility. In contrast, such burden does allegedly not arise, when physicians agree in their judgement. Second, in those medical contexts where humans collaborate with humans such justification can be provided, since human experts can discuss the evidence and reasons that have led them to their judgement, through which the sources of disagreement can be found and a justified decision can be made by the physician in charge. Third, unlike human-to-human collaboration, such communicative exchange is not possible with an AI system. Due to AI’s opacity, the physician in charge has no means of illuminating why the AI disagrees. Conclusively, the authors propose RoD as a solution. RoD suggests that a second human expert should be consulted for advise in cases of human–AI disagreement. Once AI systems become more widespread in clinical practice, it can be expected that such type of disagreement occurs more frequently. AI, after all, is being implemented, because it promises, among others, higher accuracy, which implies that some abnormalities will be detected that the physician would have missed.2 Hence, it is laudable to discuss the moral implications of …. (shrink)