What sorts of epistemic virtues are required for effective mathematical practice? Should these be virtues of individual or collective agents? What sorts of corresponding epistemic vices might interfere with mathematical practice? How do these virtues and vices of mathematics relate to the virtue-theoretic terminology used by philosophers? We engage in these foundational questions, and explore how the richness of mathematical practices is enhanced by thinking in terms of virtues and vices, and how the philosophical picture is challenged by the complexity (...) of the case of mathematics. For example, within different social and interpersonal conditions, a trait often classified as a vice might be epistemically productive and vice versa. We illustrate that this occurs in mathematics by discussing Gerovitch’s historical study of the aggressive adversarialism of the Gelfand seminar in post-war Moscow. From this we conclude that virtue epistemologies of mathematics should avoid pre-emptive judgments about the sorts of epistemic character traits that ought to be promoted and criticised. (shrink)

ABSTRACTIn this paper I investigate how conceptual engineering applies to mathematical concepts in particular. I begin with a discussion of Waismann’s notion of open texture, and compare it to Shapiro’s modern usage of the term. Next I set out the position taken by Lakatos which sees mathematical concepts as dynamic and open to improvement and development, arguing that Waismann’s open texture applies to mathematical concepts too. With the perspective of mathematics as open-textured, I make the case that this allows us (...) to deploy the tools of conceptual engineering in mathematics. I will examine Cappelen’s recent argument that there are no conceptual safe spaces and consider whether mathematics constitutes a counterexample. I argue that it does not, drawing on Haslanger’s distinction between manifest and operative concepts, and applying this in a novel way to set-theoretic foundations. I then set out some of the questions that need to be engaged with to establish mathematics as involving a kind of conceptual engineering. I finish with a case study of how the tools of conceptual engineering will give us a way to progress in the debate between advocates of the Universe view and the Multiverse view in set theory. (shrink)

Derivationists, those wishing to explain the correctness and rigour of informal proofs in terms of associated formal proofs, are generally held to be supported by the success of the project of translating informal proofs into computer-checkable formal counterparts. I argue, however, that this project is a false friend for the derivationists because there are too many different associated formal proofs for each informal proof, leading to a serious worry of overgeneration. I press this worry primarily against Azzouni's derivation-indicator account, but (...) conclude that overgeneration is a major obstacle to a successful account of informal proofs in this direction. (shrink)

In this paper I shall consider two related avenues of argument that have been used to make the case for the inconsistency of mathematics: firstly, Gödel’s paradox which leads to a contradiction within mathematics and, secondly, the incompatibility of completeness and consistency established by Gödel’s incompleteness theorems. By bringing in considerations from the philosophy of mathematical practice on informal proofs, I suggest that we should add to the two axes of completeness and consistency a third axis of formality and informality. (...) I use this perspective to respond to the arguments for the inconsistency of mathematics made by Beall and Priest, presenting problems with the assumptions needed concerning formalisation, the unity of informal mathematics and the relation between the formal and informal. (shrink)

Maximilian Bergengruen analysiert den Zusammenhang von Naturwissenschaft und Theologie bei Paracelsus sowie die Übernahme zentraler Theoreme im Paracelsismus und in der Literatur des Barock.

In this paper, I explore some parallels and dissimilarities between aesthetic appreciation that takes as its focus art objects and that which focuses on natural objects. I cover three areas. The first deals with general approach, whether a paradigm of engagement is more appropriate to environmental aesthetics than one of detachment and disinterest. The second theme is about preservation and whether the appropriate model is static or dynamic. The final theme is about environmental criticism and the application of aesthetic theory (...) to arguments for preservation. (shrink)

Adult number representations can belong to either of two types. One is discrete, language-specific, and culturally-derived; the other is analog and language-independent. Quantitative evidence is presented to demonstrate that analog number representations are adult-like in young children. Five- to 7-year-olds accurately estimated rapidly presented groups of 5--11 items. Groups were presented in random order and random arrangements controlling for overall area. Children's data were qualitatively, and to some degree quantitatively, similar to adult data with one exception: the ratio of the (...) standard deviation of estimates to mean estimates decreased with age. (shrink)

Extinction is a concept of rapidly growing importance, with the world currently in the sixth mass extinction event and a biodiversity crisis. However, the concept of extinction has itself received surprisingly little attention from philosophers. I will first argue that in practice there is no single unified concept of extinction, but instead that its usage divides between descriptive, epistemic, and declarative concepts. I will then consider the epistemic challenges that arise in ascertaining whether a species has gone extinct, and how (...) these lead to serious limitations on responsibility and accountability for preventing extinctions. I will propose two conceptual engineering changes to our understanding of extinction. Firstly, to use twin epistemic concepts of extinction, corresponding to high and low epistemic demands. Secondly, to explicitly recognize that in many contexts extinction is a thick concept that contains an evaluative component, which therefore motivates explicit ethical considerations such as the use of precautionary principles. (shrink)

Discussions on the Anthropocene as the geology of mankind imply the question whether globalized technology such as energy technologies or A.I. ought to be first and foremost conceptualized as a strategy of the human in relation to nature or as a strategy of some humans over others. I argue that both positions are mirrored in the philosophy and sociology of technology through the concepts of technology as an extension and as a fetish. The extension concept understands technology as an extension (...) of the human body and its capabilities, resulting in a local ‘inward’ perspective. The fetish concept offers a contrary ‘outward’ perspective by drawing attention to the global socio-material context of modern technology. Despite their differences, I argue that both concepts share an underlying operation principle of technology as functional simplification. Technology always involves a functional simplification of physical as well as social causality. Sociologists and philosophers of technology would do well not to give primacy to the former as it leads to the belief in technology as a universal tool that neglects how technology is not embedded in but consists of (unequal) social arrangements. (shrink)

Immanuel Kant and his work occupied a space at the crossroads of several important movements in philosophy. In this essay, I look at two important crossroads in aesthetics. First, the subjective turn in aesthetics, when the focus on aesthetic objects was rebalanced with the focus on the subject’s experience of such objects, the weight shifting from the objective to the subjective. Second, after many years and many theories advancing the view that universality of judgment could be achieved, at least in (...) part, through adoption of the appropriate perspective – or attitude – when considering a particular aesthetic object, Kant offers us perhaps the most sophisticated view of disinterestedness of any, and as he does so he solidifies that tradition, bringing it to its culmination, and ushers in the beginning of its end. (shrink)

Nick Zangwill has done more than any person recently to resuscitate aesthetic formalism. I say "resuscitate" because formalism has not been in favor for several decades. Zangwill writes that "Aesthetic Formalism has fallen on hard times. At best it receives unsympathetic discussion and swift rejection. At worse it is the object of abuse and derision." The reasons many today believe aesthetic formalism is not viable have been the subject of discussion since the pendulum swing away from New Criticism, via the (...) work of William Wimsatt, Cleanth Brooks, Clement Greenberg, André Levinson, and Heinrich Wolfflin. Most of these reasons have been discussed thoroughly, and those that I will review here that have been discussed I will spend little time reconsidering. I believe, though, that there are a few more reasons why formalism has fallen on hard times, reasons that have not been much discussed, or at least not directly. They are the subject of this article. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Why Was There So Much Ugly Art in the Twentieth Century?David E.W. Fenner (bio)Two of the most common challenges that teachers of aesthetics have to face in their classrooms today are, first, the presumption that since "beauty is in the eye of the beholder" and "there's no disputing taste," every aesthetic judgment is as good as every other one. The second is that the content from which aesthetics (...) courses commonly draw for examples and for the impetus for contemporary philosophy of art theory — and by this I mean art from Post-Impressionism to the present — is made up of "stuff I could have done when I was four years old." The substance behind these two challenges — that aesthetic judgment is highly or perhaps exclusively subjective and that twentieth-century art does not demonstrate care of technique, or that it is simply ugly1 — are intimately connected. This connection is the focus of this essay. The answer to the question, "why was there so much ugly art in the twentieth century?" may be that the tradition of showing beauty to be a highly or purely subjective phenomenon renders beauty apparently less valuable than if it were objective in character, and so we have, in the twentieth century, a move away from the production in art of beauty to that which is simply "artistic" or "artistically important." I want to come at this thesis not through a discussion about either the location or the reality of aesthetic properties. Instead, I want to focus on the "ugly art."Students in aesthetics courses tend to take one of three positions regarding modern art, and by "modern art," I mean art from Post-Impressionism to the present, including Pop Art, Dada, Surrealism, Abstract Expressionism, and the rest: 1. They deny the value of it, together with claims about their artistic abilities during their kindergarten years. 2. Because they know something of the history and progression of twentieth-century art, or because they have an experiential basis for approaching modern art conceptually, they actually appreciate and value it. 3. They think they ought to value it (the way so many of us feel when buying our very first tickets to the [End Page 13] opera), and they do their level best to act in accord with what they see as their aesthetic obligation. Those of the first camp will probably voice their positions early in aesthetics courses, and at that point the challenge for the teacher is raised.Teachers in aesthetics courses, when faced with this challenge, tend, I think, to take one of three positions in response: 1. They use the authority of their office to stifle the discussion, hoping that students of the first camp will over the course of time and exposure at least move to being students of the third camp. 2. They embrace the complaint, discuss it, give it due regard (after all, those teachers probably read Tom Wolfe's The Painted Word themselves), but leave the final decision about the merit of modern art open and unsettled. I presume this is the majority position, at least in philosophical courses of aesthetics. 3. They seek to impart to students — through exposure, discussion, and the eloquence they can muster of descriptions of their own positive, valuable experiences with modern art — some sense of its merit. In this essay, I will sketch out yet another way to deal with the challenge, one that focuses on the history of aesthetics itself.The HistoryThe history of aesthetic judgment — that is, with the correctness of particular aesthetic judgments — begins with Aristotle.2 He said that an object is aesthetically good — or, actually, beautiful — if it is ordered, symmetrical, and definite, and if it demonstrates each of these virtues to a high degree.3 This analysis we call "formal," because it focuses on the presence in the object of certain aesthetic properties, ones that have to do with the form (as distinguished from the content) of the object. The more basic the cited aesthetic properties, the better, because the strength of the power of one's judgment, along with the power of evidence that can be cited in support of that judgment... (shrink)

This thesis is about the nature of proofs in mathematics as it is practiced, contrasting the informal proofs found in practice with formal proofs in formal systems. In the first chapter I present a new argument against the Formalist-Reductionist view that informal proofs are justified as rigorous and correct by corresponding to formal counterparts. The second chapter builds on this to reject arguments from Gödel's paradox and incompleteness theorems to the claim that mathematics is inherently inconsistent, basing my objections on (...) the complexities of the process of formalisation. Chapter 3 looks into the relationship between proofs and the development of the mathematical concepts that feature in them. I deploy Waismann's notion of open texture in the case of mathematical concepts, and discuss both Lakatos and Kneebone's dialectical philosophies of mathematics. I then argue that we can apply work from conceptual engineering to the relationship between formal and informal mathematics. The fourth chapter argues for the importance of mathematical knowledge-how and emphasises the primary role of the activity of proving in securing mathematical knowledge. In the final chapter I develop an account of mathematical knowledge based on virtue epistemology, which I argue provides a better view of proofs and mathematical rigour. (shrink)

This paper focuses on the use of ‘black box’ AI in medicine and asks whether the physician needs to disclose to patients that even the best AI comes with the risks of cyberattacks, systematic bias, and a particular type of mismatch between AI’s implicit assumptions and an individual patient’s background situation.Pacecurrent clinical practice, I argue that, under certain circumstances, these risks do need to be disclosed. Otherwise, the physician either vitiates a patient’s informed consent or violates a more general obligation (...) to warn him about potentially harmful consequences. To support this view, I argue, first, that the already widely accepted conditions in the evaluation of risks, i.e. the ‘nature’ and ‘likelihood’ of risks, speak in favour of disclosure and, second, that principled objections against the disclosure of these risks do not withstand scrutiny. Moreover, I also explain that these risks are exacerbated by pandemics like the COVID-19 crisis, which further emphasises their significance. (shrink)

We investigate how epistemic injustice can manifest itself in mathematical practices. We do this as both a social epistemological and virtue-theoretic investigation of mathematical practices. We delineate the concept both positively—we show that a certain type of folk theorem can be a source of epistemic injustice in mathematics—and negatively by exploring cases where the obstacles to participation in a mathematical practice do not amount to epistemic injustice. Having explored what epistemic injustice in mathematics can amount to, we use the concept (...) to highlight a potential danger of intellectual enculturation. (shrink)

The attribution of perceptually based aesthetic properties to a garden should be indexed to whether that attribution is (1) to the ever-changing dynamic garden or (2) to some phenomenal capture of the garden in one’s experience, frozen like a photograph. Perceptually based aesthetic properties are used to identify objects, to compare them to others, to evaluate them, and to describe them as we seek to interpret or find meaning in them. This set of activities requires aesthetic properties that do not (...) change, or at least not much, if any degree of normativity is to be maintained. But those aesthetic properties that are derived from our immediate sensations of a garden only describe a garden at a certain time, under certain conditions, in certain states—all of which change constantly. Both descriptions are useful, and perhaps necessary, for appreciating gardens. (shrink)

Once a group of physicists at my university invited me to a physics colloquium. They were certain that I would get a great deal out of it. I love theoretical physics, although my preparation for understanding the "real stuff" is extremely modest. After the first ten minutes of the lecture, I realized I was in way over my head; though I understood the topic and the trajectory, I was not able to follow the path. But I stayed and continued to (...) enjoy the lecture. No longer was I understanding the lecture as a physics lecture—that is, as a lecture the contents of which was the articulation of a case for understanding a physical phenomenon or the application of a physical theory for understanding a physical phenomenon.... (shrink)

Rare earth elements have become increasingly important because of their relative scarcity and worldwide increasing demand, as well as China’s quasi-monopoly of this market. REEs are virtually not substitutable, and they are essential for a variety of high-tech products and modern key technologies. This has raised serious concerns that China will misuse its dominant position to set export quotas in order to maximize its own profits at the expense of other rare earth user industries. In fact, export restrictions on REEs (...) were the catalyst for the U.S. to lodge a formal complaint against China in 2012 at the World Trade Organization. This paper analyzes possible wealth transfer effects by focusing on export quota announcements by China, and the share price reactions of Chinese REE suppliers, the U.S. REE users, and the rest of the world REE refiners. Overall, we find limited support for the view of a wealth transfer in connection with MOFCOM announcements only when disentangling events prior to and post the initiation of the WTO trial, consistent with the trial triggering changes to China’s REE policy and recent announcement to abolish quotas. We do find, however, that extreme REE price movements have a first-order effect on all companies in the REE industry consistent with recent market trends to enable hedging against REE price volatility. (shrink)

The world is experiencing a cataclysmically increasing burden from chronic illnesses. Chronic diseases are on the advance worldwide and treatment strategies to counter this development are dominated by symptom control and polypharmacy. Thus, chronic conditions are often considered irreversible, implying a slow progression of disease that can only be hampered but not stopped. The current plant-based movement is attempting to alter this way of thinking. Applying a nutrition-first approach, the ultimate goal is either disease remission or reversal. Hereby, ethical questions (...) arise as to whether physicians’ current understanding of chronic illness is outdated and morally reprehensible. In this case, physicians may need to recommend plant-based diets to every patient suffering from chronic conditions, while determining what other socioecological factors and environmental aspects play a role in the chronic disease process. This article provides insights to aspects of diet and chronic illness and discusses how the plant-based movement could redefine current understanding of chronic disease. The ethical justifications for recommending of a plant-based diet are analyzed. The article concludes that not advocating for plant-based nutrition is unethical and harms the planet and patients alike. (shrink)

In Art in Context: Understanding Aesthetic Value, philosopher David Fenner presents a straightforward, accessible overview of the arguments about the importance of considering the relevant context in determining the true merit of a work of ...

Angesichts der unter der Führungsrolle der natur- und sozial-technologisch relevanten Wissenschaften vollzogenen extremen Spezialisierung und Ausdifferenzierung des Wissens-systems in immer engere Disziplinen mit spezialistischem Fachwissen scheint das Bemühen um ,,Weisheit", das in der Bezeichnung unserer Arbeitsbereiche steckt, gänzlich obsolet geworden zu sein. Zunächst soll die Verdrängung der Weisheitsliebe bzw. -suche anhand einiger historisch-kultureller Etappen der veränderten Bedingungen der Wissensinstitutionen und Gesellschaftsstrukturen nachgezeichnet werden . Danach wird das neuzeitliche Wissenschaftsideal mit dem antiken Weisheitsideal kontrastiert, und die Philosophie in diesem Spannungsfeld geortet (...) . Schließlich wird mit Blick auf die aktuelle Weisheitsrenaissance in verschiedenen Wissenschaften ein integrativer Ansatz eines gegenwartsfähigen Weisheitskonzeptes entworfen. (shrink)

It has become commonplace to consider start-ups originating from the science field usually referred to as academic spin-offs as drivers of innovation, productivity, and employment. However, only little is known about the process of spin-off creation (e.g., Goethner et al., 2009) and development (e.g., Mustar et al., 2006; Vohora et al., 2004). Specifically, there has not been sufficient empirical research directly comparing equivalently matched groups of academic spin-offs and non-academic start-ups in order to draw definitive conclusions on whether there are (...) specific growth paths of firms spun off from scientific research (Ensley & Hmieleski, 2005). We aim to fill this gap in the literature and provide unique empirical evidence on the economic and innovative performance of academic spin-offs within the first three business years. (shrink)

Philosophical inquiry into the theory and practice of responsibility is a major and fast-growing area of study. It spans perennial philosophical, political, and legal questions about free will and agency as well as more recent, controversial topics such as coercion, ignorance, and responsibility for historical injustices. The Routledge Handbook of Philosophy of Responsibility is an outstanding survey and exploration of these issues and more. Comprised of forty-one chapters by an international team of contributors, the Handbook is divided into three clear (...) parts - on the history, theory, and practice of responsibility - within which the following key areas are examined: responsibility and wrongdoing responsibility and determinism the scope of responsibility individuals and society the concepts of responsibility the conditions and challenges of responsibility being and holding responsible the ethics and politics of responsibility responsibility in the law. Including suggestions for further reading at the end of each chapter, The Routledge Handbook of Philosophy of Responsibility provides an extremely useful guide to the topic. It will be valuable reading for students and researchers in philosophy and applied ethics, as well as for those in related disciplines such as politics, law, and policymaking. (shrink)

Offering aesthetic judgments of gardens is common. These judgments follow an evidentiary structure that is common to the evaluation of other aesthetic objects: summary judgments evidenced by the attribution of narrow formal aesthetic properties, “formal-adjacent” aesthetic properties, and relevant contextual relations. Yet, in a garden, these evidencing properties and relations take on forms that are different from those of other aesthetic and/or art objects. In this article, I consider these differences and consider whether aesthetic analyses of gardens rest on one (...) or more conceptual mistakes. In the end, I conclude that we can meet all challenges. (shrink)

In this paper we apply social epistemology to mathematical proofs and their role in mathematical knowledge. The most famous modern collaborative mathematical proof effort is the Classification of Finite Simple Groups. The history and sociology of this proof have been well-documented by Alma Steingart (2012), who highlights a number of surprising and unusual features of this collaborative endeavour that set it apart from smaller-scale pieces of mathematics. These features raise a number of interesting philosophical issues, but have received very little (...) attention. In this paper, we will consider the philosophical tensions that Steingart uncovers, and use them to argue that the best account of the epistemic status of the Classification Theorem will be essentially and ineliminably social. This forms part of the broader argument that in order to understand mathematical proofs, we must appreciate their social aspects. (shrink)

A common description of a mathematical proof is as a logically structured sequence of assertions, beginning from accepted premises and proceeding by standard inference rules to a conclusion. Does this description match the language of proofs as mathematicians write them in their research articles? In this chapter, we use methods from corpus linguistics to look at the prevalence of imperatives and instructions in mathematical preprints from the arXiv repository. We find thirteen verbs that are used most often to form imperatives (...) in proofs, and that these show up significantly more often within proofs than in the surrounding mathematical writing. We also show that there are many more verbs used to form a diverse selection of instructions in proofs. These findings are at odds with the view of proofs as sequences of assertions. Instead, we argue in favour of the recipe model of proofs: that proofs are like recipes, giving instructions for mathematical actions to be carried out. (shrink)

Artificial intelligence increasingly executes tasks that previously only humans could do, such as drive a car, fight in war, or perform a medical operation. However, as the very best AI systems tend to be the least controllable and the least transparent, some scholars argued that humans can no longer be morally responsible for some of the AI-caused outcomes, which would then result in a responsibility gap. In this paper, I assume, for the sake of argument, that at least some of (...) the most sophisticated AI systems do indeed create responsibility gaps, and I ask whether we can bridge these gaps at will, viz. whether certain people could take responsibility for AI-caused harm simply by performing a certain speech act, just as people can give permission for something simply by performing the act of consent. So understood, taking responsibility would be a genuine normative power. I first discuss and reject the view of Champagne and Tonkens, who advocate a view of taking liability. According to this view, a military commander can and must, ahead of time, accept liability to blame and punishment for any harm caused by autonomous weapon systems under her command. I then defend my own proposal of taking answerability, viz. the view that people can makes themselves morally answerable for the harm caused by AI systems, not only ahead of time but also when harm has already been caused. (shrink)

In 2017, the German ethics commission for automated and connected driving released 20 ethical guidelines for autonomous vehicles. It is now up to the research and industrial sectors to enhance the development of autonomous vehicles based on such guidelines. In the current state of the art, we find studies on how ethical theories can be integrated. To the best of the authors’ knowledge, no framework for motion planning has yet been published which allows for the true implementation of any practical (...) ethical policies. This paper makes four contributions: Firstly, we briefly present the state of the art based on recent works concerning unavoidable accidents of autonomous vehicles (AVs) and identify further need for research. While most of the research focuses on decision strategies in moral dilemmas or crash optimization, we aim to develop an ethical trajectory planning for all situations on public roads. Secondly, we discuss several ethical theories and argue for the adoption of the theory “ethics of risk.” Thirdly, we propose a new framework for trajectory planning, with uncertainties and an assessment of risks. In this framework, we transform ethical specifications into mathematical equations and thus create the basis for the programming of an ethical trajectory. We present a risk cost function for trajectory planning that considers minimization of the overall risk, priority for the worst-off and equal treatment of people. Finally, we build a connection between the widely discussed trolley problem and our proposed framework. (shrink)