It has been observed many times before that, as yet, there are no encompassing, integrated theories of mathematical practice available.To witness, as we currently do, a variety of schools in this field elaborating their philosophical frameworks, and trying to sort out their differences in the course of doing so, is also to be constantly reminded of the fact that a lot of epistemic aspects, extremely relevant to this task, remain dramatically underexamined. This volume wants to contribute to the stock of (...) studies filling this perceived lacuna. It contains papers by established, upcoming, as well as beginning scholars, covering general, metaphilosophical themes such as naturalism, semiotics, pragmaticism, or empiricism, next to more specific topics including the unity of mathematical theories, thruth-flow in mathematics, diagrammatic reasoning, erroneous argumentation, or numerical analysis. (shrink)

Medical research data is sensitive personal data that needs to be protected from unauthorized access and unintentional disclosure. In a research setting, sharing of data within the scientific community is necessary in order to make progress and maximize scientific benefits derived from valuable and costly data. At the same time, convincingly protecting the privacy of people participating in medical research is a prerequisite for maintaining trust and willingness to share. In this commentary, we will address this issue and the pitfalls (...) involved in the context of the PEP project1 that provides the infrastructure for the Personalized Parkinson’s Project,2 a large cohort study on Parkinson’s disease from Radboud University Medical Center, in cooperation with Verily life Sciences, an Alphabet subsidiary. (shrink)

Philosophy of mathematics today has transformed into a very complex network of diverse ideas, viewpoints, and theories. Sometimes the emphasis is on the "classical" foundational work (often connected with the use of formal logical methods), sometimes on the sociological dimension of the mathematical research community and the "products" it produces, then again on the education of future mathematicians and the problem of how knowledge is or should be transmitted from one generation to the next. The editors of this book felt (...) the urge, first of all, to bring together the widest variety of authors from these different domains and, secondly, to show that this diversity does not exclude a sufficient number of common elements to be present. In the eyes of the editors, this book will be considered a success if it can convince its readers of the following: that it is warranted to dream of a realistic and full-fledged theory of mathematical practices, in the plural. If such a theory is possible, it would mean that a number of presently existing fierce oppositions between philosophers, sociologists, educators, and other parties involved, are in fact illusory. (shrink)

Context: As one of the major approaches within the philosophy of mathematics, constructivism is to be contrasted with realist approaches such as Platonism in that it takes human mental activity as the basis of mathematical content. Problem: Mathematical constructivism is mostly identified as one of the so-called foundationalist accounts internal to mathematics. Other perspectives are possible, however. Results: The notion of “meaning finitism” is exploited to tie together internal and external directions within mathematical constructivism. The various contributions to this issue (...) support our case in different ways. Constructivist content: Further contributions from a multitude of constructivist directions are needed for the puzzle of an integrative, overarching theory of mathematical practice to be solved. (shrink)

In current philosophical research, there is a rather one-sided focus on the foundations of proof. A full picture of mathematical practice should however additionally involve considerations about various methodological aspects. A number of these is identified, from large-scale to small-scale ones. After that, naturalism, a philosophical school concerned with scientific practice, is looked at, as far as the translations of its epistemic principles to mathematics is concerned. Finally, we call for intensifying the interaction between both dimensions of practice and epistemology.

The Polymath Project is an online collaborative enterprise that was initiated in 2009, when Timothy Gowers asked whether and how groups could work together to solve mathematical problems that “do not naturally split up into a vast number of subtasks.” Gowers proposed to answer this question himself by actually trying to set up such a collaboration, based on interactions taking place in the comment-threads of a series of posts on a WordPress blog. Hence, the first project officially started in early (...) 2009, to be proclaimed successful only 6 weeks later (Gowers and Nielsen 2009). From its inception until April 2018, 15 more Polymath problems (and a handful of smaller or related ones) have been launched. These projects have attracted attention from different scholarly communities, including the philosophy of mathematical practices, from the perspective of which the Polymath Project can be seen as a vast repository of mathematics in action. This chapter continues previous work by its authors on the topic in question and topics related. More specifically, for the purposes of this volume, it is our aim to both summarize and expand upon these earlier contributions. The starting point is the above observation that in the past decade, the issue of “massively collaborative mathematics” (to be qualified below) has drawn quite some attention. However, does it also warrant intensive philosophical attention in particular? For, as exciting as these developments might be from mathematical and other points of view, the enhanced possibilities that have come with it do not per se give rise to any philosophical import. In Van Bendegem (2011), one of us has indeed tentatively argued for the philosophical relevance of these new dynamics of proof construction flowing from the wide availability and efficiency of Internet technology. We shall below briefly rehearse and update the argument given there. (shrink)

Except in very poor mathematical contexts, mathematical arguments do not stand in isolation of other mathematical arguments. Rather, they form trains of formal and informal arguments, adding up to interconnected theorems, theories and eventually entire fields. This paper critically comments on some common views on the relation between formal and informal mathematical arguments, most particularly applications of Toulmin’s argumentation model, and launches a number of alternative ideas of presentation inviting the contextualization of pieces of mathematical reasoning within encompassing bodies of (...) explicit and implicit, formal and informal background knowledge. (shrink)

In current philosophical research, there is a rather one-sided focus on the foundations of proof. A full picture of mathematical practice should however additionally involve considerations about various methodological aspects. A number of these is identified, from large-scale to small-scale ones. After that, naturalism, a philosophical school concerned with scientific practice, is looked at, as far as the translations of its epistemic principles to mathematics is concerned. Finally, we call for intensifying the interaction between both dimensions of practice and epistemology.

We explore aspects of an experimental approach to mathematical proof, most notably number crunching, or the verification of subsequent particular cases of universal propositions. Since the rise of the computer age, this technique has indeed conquered practice, although it implies the abandonment of the ideal of absolute certainty. It seems that also in mathematical research, the qualitative criterion of effectiveness, i.e. to reach one’s goals, gets increasingly balanced against the quantitative one of efficiency, i.e. to minimize one’s means/ends ratio. Our (...) story will lead to the consideration of some limit cases, opening up the possibility of proofs of infinite length being surveyed in a finite time. By means of example, this should show that mathematical practice in vital aspects depends upon what the actual world is like. (shrink)

Except in very poor mathematical contexts, mathematical arguments do not stand in isolation of other mathematical arguments. Rather, they form trains of formal and informal arguments, adding up to interconnected theorems, theories and eventually entire fields. This paper critically comments on some common views on the relation between formal and informal mathematical arguments, most particularly applications of Toulmin’s argumentation model, and launches a number of alternative ideas of presentation inviting the contextualization of pieces of mathematical reasoning within encompassing bodies of (...) explicit and implicit, formal and informal background knowledge. (shrink)

The paper gives an impression of the multi-dimensionality of mathematics as a human activity. This 'phenomenological' exercise is performed within an analytic framework that is both an expansion and a refinement of the one proposed by Kitcher. Such a particular tool enables one to retain an integrated picture while nevertheless welcoming an ample diversity of perspectives on mathematical practices, that is, from different disciplines, with different scopes, and at different levels. Its functioning is clarified by fitting in illustrations based on (...) actual research. (shrink)

Given its non-invasive nature, there is increasing interest in the use of transcutaneous vagus nerve stimulation across basic, translational and clinical research. Contemporaneously, tVNS can be achieved by stimulating either the auricular branch or the cervical bundle of the vagus nerve, referred to as transcutaneous auricular vagus nerve stimulation and transcutaneous cervical VNS, respectively. In order to advance the field in a systematic manner, studies using these technologies need to adequately report sufficient methodological detail to enable comparison of results between (...) studies, replication of studies, as well as enhancing study participant safety. We systematically reviewed the existing tVNS literature to evaluate current reporting practices. Based on this review, and consensus among participating authors, we propose a set of minimal reporting items to guide future tVNS studies. The suggested items address specific technical aspects of the device and stimulation parameters. We also cover general recommendations including inclusion and exclusion criteria for participants, outcome parameters and the detailed reporting of side effects. Furthermore, we review strategies used to identify the optimal stimulation parameters for a given research setting and summarize ongoing developments in animal research with potential implications for the application of tVNS in humans. Finally, we discuss the potential of tVNS in future research as well as the associated challenges across several disciplines in research and clinical practice. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Journal of Aesthetic Education 37.1 (2003) 90-106 [Access article in PDF] Schopenhauer, Nietzsche, and the Aesthetically Sublime Bart Vandenabeele Much has been written on the relationship between Arthur Schopenhauer and Friedrich Nietzsche. Much remains to be said, however, concerning their respective theories of the sublime. First, I shall argue against the traditional, dialectical view of Schopenhauer's theory of the sublime that stresses the crucial role the sublime (...) plays in bridging the wide gap between aesthetics and ethics. Although this traditional interpretation is definitely influenced by Nietzsche, I do not maintain it is exclusively Nietzschean as such. Second, I would like to offer some points of contention concerning their accounts of the feeling of the sublime. I will try and show that, although Nietzsche's account of the Apollonian and the Dionysian is highly influenced by Schopenhauer's analysis of the sublime feeling, his analysis of Dionysian intoxication cannot be taken to simply develop out of Schopenhauer's philosophy. Moreover, by way of (a not so innocent) example, it is shown that Nietzsche's philosophy of music — although highly influenced by Schopenhauer's — cannot as easily be reconciled with Schopenhauer'stheory as is commonly believed, due to their differing accounts of the nature of the feeling of the sublime. Schopenhauer on the Feeling of the Sublime: Pleasure and Pain When one tries to describe the exact relationship between the aesthetic feelings of the beautiful and the sublime in the philosophy of "Nietzsche's educator," many interpretation problems arise. 2 The main problem can be compared to a similar issue in Kant: if one agrees with Kant that the theory of the sublime is "a mere appendix to our aesthetic judging," then it is possible to restrict the Kantian critique of the aesthetic appreciation to the Analytic of the judgment of taste 2 — that is, if one neglects the subtle displacements and gaps in Kant's text. In this way, as one can read in its introduction, the [End Page 90] Critique of Judgement serves as the sought-after "bridge" between the theoretical and the practical, spanning the gulf previously created between the knowledge of objects according to the conditions of possible experience and the realization of freedom under the unconditional of moral law. Moreover, if one notices that Schopenhauer too, in his aesthetics, stresses the fact that "in the main" the feeling of the sublime "is identical with the feeling of the beautiful" and "is distinguished from that of the beautiful only by the addition, namely the exaltation beyond the known hostile relation of the contemplated object to the will in general,then the option for a similar unifying and pacifying reading seems evident. 3 I shall argue that things are far more complicated and that such a "dialectical" interpretation is far from evident.In the appendix to his The World as Will and Representation, Schopenhauer had stressed — long before Jean-François Lyotard — the enormous importance of Kant's analysis of the sublime, when he wrote that "the theory of the sublime" is "by far the most excellent thing in the Critique of Aesthetic Judgment" (WWR, I, 532). That theory, Schopenhauer says, is even "incomparably more successful than that of the beautiful" and "gives not only, as that does, the general method of investigation, but also a part of the right way to it, so much so that, although it does not provide the real solution to the problem, it nevertheless touches on it very closely" (WWR, I, 532).According to Schopenhauer, the main difference between the sublime and the beautiful is that, while in the case of the latter, pure knowledge has gained the upper hand without a struggle...and not even a recollection of the will remains [with the sublime] that state of pure knowing is obtained first of all by a conscious and violent tearing away from the relations of the same object to the will which are recognized as unfavorable, by a free exaltation, accompanied by consciousness, beyond the will and the knowledge related to it (WWR, I, 202). The objects can be hostile to the human... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Aesthetic Solidarity "after" Kant and LyotardBart Vandenabeele (bio)Whatever view we hold, it must be shown / Why every lover has a wish to make / Some other kind of otherness his own: / Perhaps in fact we never are alone.—W. H. AudenIntroductionUndoubtedly one of the most fascinating aspects of Kant's aesthetics is the link that the Königsberg philosopher establishes between aesthetic judging and the idea of being-together and being-in-community. (...) This connection is developed through a subtle analysis of aesthetic communicability or shareability (Mitteilbarkeit). A judgment of beauty, what Kant terms "a pure judgment of taste,"—that is, a judgment "that is not influenced by charm or emotion (though these may be connected with a liking for the beautiful), and whose determining basis is therefore merely the purposiveness of the form" (CJ, §13, 223)1—does not postulate everyone's agreement. Yet Kant claims that it does require this agreement from everyone.The judgment of the sublime, on the other hand—which is not based on pure pleasure but on a "mixture" of pleasure and displeasure, on a rapid alternation of repulsion from, and attraction to, the same object" (CJ, §27, 258), or, as Kant writes, on "a displeasure that we present at the same time as purposive" (CJ, §27, 259)—also "demands" universal validity. But this "demand" (or "call," as Kant sometimes writes) is not as immediate (or unmediated) as in the pure judgment of taste. The universal shareability that is proper to the judgment of the sublime passes through the moral law. According to Jean-François Lyotard, this implies that "the sublime feeling is [End Page 17] neither moral universality nor aesthetic universalization, but is, rather, the destruction of one by the other in the violence of their differend. This differend cannot demand, even subjectively, to be communicated to all thought."2 Whatever the exact meaning of these words may be, the gist seems to be that Kant's analysis of the judgment of the sublime implies the impossibility of any sort of genuine togetherness.I shall argue that this is too rash a conclusion and that a more "plastic" and pragmatic conception of "being-in-community" can be deduced from Kant's idea of the universal shareability of the judgment of the sublime—a conception lacking in Lyotard's characterizations of togetherness. In this article I merely hint at possible ways to connect the possibility of the communicability of the sublime and this more pragmatic conception of togetherness. I will try to show why Lyotard is wrong to suppose that Kant's analysis of the judgment of the sublime testifies to a crisis of being-together. If Kant's account really pertains to some sort of crisis, it may well be to the crisis of the highly contentious idea that being-together ought to be based on some harmony of feeling(s) or shared essence(s). To understand the gist and scope of Kant's complex analysis, however, we shall have to study first how pure aesthetic judgments that are grounded in the subject's pure feeling of pleasure and/or displeasure (Lust oder Unlust) can establish universally valid norms or an Idea of aesthetic solidarity without appeal to conceptual rules or rational laws. Only afterwards can we get a better view of Lyotard's misinterpretation of Kant's ideas on togetherness.The Feeling of the Beautiful: Solidarity in statu nascendiAdmiring a still life by Cézanne, one could say, "Look, that's an apple," which is a determinant judgment employing concepts. However, judging that the painting is beautiful occurs without the employment of any concepts and is completely disinterested; it reflects on the pure feeling of pleasure, which surges on the occasion of a particular empirical sensation. Our judgment is a pure judgment of taste only if the following conditions are true:1. The pleasure grounding it is not motivated by any (empirical, ethical, theoretical, or practical) interest.2. The subjective purposiveness of the pleasure we experience is not known (in contrast to the agreeable that we experience when we satisfy a desire or need).3. The judgment is singular—"this sunset in Urbana is beautiful" is an... (shrink)

This book investigates the extensive and growing economic inequalities that characterize the affluent market societies in which we currently live. It uses insights both from political philosophy and the new science of happiness to make the case for more just alternatives. We diagnose the damaging impact that existing inequalities have on our well-being. We draw on philosophical, psychological, social scientific and other insights to diagnose what has gone wrong in our highly unequal and frequently unhappy societies. Combining the approaches both (...) of philosophers such as Jean-Jacques Rousseau, Adam Smith, Georg Wilhem Friedrich Hegel, John Rawls and Philip Pettit and analyses from political economists, we uncover the economic, social and political mechanisms that create and perpetuate income and wealth inequality. The key claim is that wealthy elites engage in rent seeking and opportunity hoarding and shape our social, economic and political structures in ways that benefit them and harm the rest. We assess important insights from the new science of happiness to assess the impact of inequality on the well-being of the poor, the middle class and the rich. We specifically examine the role of key emotions, such as shame (amongst the poor), envy and admiration (towards and for the rich). We discuss which emotional narratives serve to justify and entrench excessive inequalities in income and wealth. The result is an explanation of the emotional regime that characterizes our capitalist societies and that perpetuates the unfair gap between the extravagance of the rich and the misery of the poor. We conclude with policies and proposals to re-shape this emotional regime in the interests of justice and solidarity. (shrink)

The recent claiming of Simone de Beauvoir's legacy by French feminists for a policy of assimilation of Muslim women to Western models of self and society reduces the complexity and richness of Beauvoir's views in inacceptable ways. This article explores to what extent a politics of difference that challenges the ideals and political strategies of abstract liberalism can be extracted from and legitimized by the philosophies of Simone de Beauvoir and Jean-Paul Sartre. Without assuming their thought is identical, we (...) can read them as elucidating each other and as implicitly exposing weak and strong points in their respective philosophies on ethnocultural relations and social identities. (shrink)

This is an attempt at reviving Kneale's version of the description theory of names, which says that a proper name is synonymous with a definite description of the form ‘the individual named so-and-so’. To begin with, I adduce a wide range of observations to show that names and overt definites are alike in all relevant respects. I then turn to Kripke's main objection against Kneale's proposal, and endeavour to refute it. In the remainder of the paper I elaborate on Kneale's (...) analysis, adopting a theory of presupposition proposed by van der Sandt. (shrink)

This latest offering from one of the founding figures of postmodernism is a collection of fifteen "fables" that ask, in the words of Jean-Francois Lyotard, "how to live, and why?

The phenomenological origins of the concept of givenness -- Remarks on the origins of Gegebenheit in Heidegger's thought -- Substitution and solicitude: how Levinas re-reads Heidegger -- Sketch of a phenomenological concept of sacrifice.

The chapter begins by establishing the absence of organizations in the organization of philosophy as a specialist academic discipline. The second section highlights the reasons why this gap is detrimental to philosophical inquiries. The third section seeks to clarify how philosophy, as a type of theoretical inquiry, can contribute to the study of organizations. Three basic features are proposed as underpinning the philosophical method. Hegel’s social theory is then put forward as an exemplary model of what a philosophical account of (...) organizations might achieve. The fourth and final section shifts the perspective to focus on the life of individuals in organizations. Following a recent book combining post-Hegelian critical theory and Christophe Dejours’ psychodynamic approach, the paper highlights important aspects of individual and collective work that lead to a cooperative conception of management. (shrink)

Contractarianism in some form has been at the center of recent debates in moral and political philosophy. Jean Hampton was one of the most gifted philosophers involved in these debates and provided both important criticisms of prominent contractarian theories plus powerful defenses and applications of the core ideas of contractarianism. In these essays, she brought her distinctive approach, animated by concern for the intrinsic worth of persons, to bear on topics such as guilt, punishment, self-respect, family relations, and the (...) maintenance and justification of the state. Edited by Daniel Farnham, this collection is an essential contribution to understanding the problems and prospectus of contractarianism in moral, legal and political philosophy. (shrink)

In this paper, we look for the relevance of chaos in the well-known Hicks-Samuelson's oscillator model investigating the endogenous fluctuations of the national income between two limits: full employment income and under-employment income. We compute the Lyapunov exponent, via Monte- Carlo simulations, to detect chaos in the evolution of the income between both limits. In the case of positive Lyapunov exponent and large values of the parameter (i.e. marginal propensity to consume and technical coefficient for capital), the evolution of income (...) is seen to be chaotic. The model also may contain a quasi-periodic attractor that can be chaotic or not. (shrink)

Baudrillard's unsettling coda: previously unpublished texts written just before the visionary theorist's death in 2007. History that repeats itself turns to farce. But a farce that repeats itself ends up making a history.—from The Agony of Power In these previously unpublished manuscripts written just before his death in 2007, Jean Baudrillard takes a last crack at the bewildering situation currently facing us as we exit the system of “domination” and enter a world of generalized “hegemony” in which everyone becomes (...) both hostage and accomplice of the global market. But in the free-form market of political and sexual liberation, as the possibility of revolution dissipates, Baudrillard sees the hegemonic process as only beginning. Once expelled, negativity returns from within ourselves as an antagonistic force—most vividly in the phenomenon of terrorism, but also as irony, mockery, and the symbolic liquidation of all human values. This is the dimension of hegemony marked by an unbridled circulation—of capital, goods, information, or manufactured history—that is bringing the very concept of exchange to an end and pushing capital beyond its limits: to the point at which it destroys the conditions of its own existence. In the system of hegemony, the alienated, the oppressed, and the colonized find themselves on the side of the system that holds them hostage. In this paradoxical moment in which history has turned to farce, domination itself may appear to have been a lesser evil.This book gathers together three essays—“From Domination to Hegemony,” "The White Terror of World Order," and "Where Good Grows"—and a 2005 interview with Baudrillard by Sylvère Lotringer. Semiotext launched Baudrillard into English back in the early 1980s; now, as our media and information infested “ultra-reality” finally catches up with his theory, Semiotext offers The Agony of Power, Baudrillard's unsettling coda. (shrink)