Although there is a consensus among philosophers of mathematics and mathematicians that mathematical explanations exist, only a few authors have proposed accounts of explanation in mathematics. These accounts fit into the unificationist or top-down approach to explanation. We argue that these models can be complemented by a bottom-up approach to explanation in mathematics. We introduce the mechanistic model of explanation in science and discuss the possibility of using this model in mathematics, arguing that using it does not presuppose a Platonist (...) view of mathematics and allows one to gain insight into why a theorem is true by answering what-if-things-had-been-different questions. (shrink)

Mathematics seems to have a special status when compared to other areas of human knowledge. This special status is linked with the role of proof. Mathematicians often believe that this type of argumentation leaves no room for errors and unclarity. Philosophers of mathematics have differentiated between absolutist and fallibilist views on mathematical knowledge, and argued that these views are related to whether one looks at mathematics-in-the-making or finished mathematics. In this paper we take a closer look at mathematical practice, more (...) precisely at the publication process in mathematics. We argue that the apparent view that mathematical literature, given the special status of mathematics, is highly reliable is too naive. We will discuss several problems in the publication process that threaten this view, and give several suggestions on how this could be countered.Las matemáticas parecen tener un estatuto especial cuando se las compara con otras áreas del conocimiento humano. Este estatuto especial está conectado con el papel de la demostración. Los matemáticos creen con frecuencia que este tipo de argumentos no deja margen para el error o la falta de claridad. Los filósofos de la matemática han distinguido entre una concepción absolutista y una falibilista del conocimiento matemático, argumentando que estas concepciones están relacionadas con una consideración de las matemáticas-en-proceso o en tanto que matemáticas ya hechas. En este artículo examinamos más de cerca la práctica matemática, más en concreto el proceso de publicación en matemáticas. Argumentaremos que la idea preconcebida de que la literatura matemática, dado el estatuto especial de las matemáticas, es altamente fiable, es demasiado ingenua. Discutiremos algunos problemas del proceso de edición que amenazan esta visión y haremos algunas sugerencias sobre cómo enfrentarlos. (shrink)

One of the central aims of the philosophical analysis of mathematical explanation is to determine how one can distinguish explanatory proofs from non-explanatory proofs. In this paper, I take a closer look at the current status of the debate, and what the challenges for the philosophical analysis of explanatory proofs are. In order to provide an answer to these challenges, I suggest we start from analysing the concept understanding. More precisely, I will defend four claims: understanding is a condition for (...) explanation, unificatory understanding is a type of explanatory understanding, unificatory understanding is valuable in mathematics, and mathematical proofs can contribute to unificatory understanding. As a result, in a context where the epistemic aim is to unify mathematical results, I argue it is fruitful to make a distinction between proofs based on their explanatory value. (shrink)

Mathematicians suggest that some proofs are valued for their explanatory value. This has led to a philosophical debate about the distinction between explanatory and non-explanatory proofs. In this paper, we explore whether contrasting views about the explanatory value of proof are possible and how to understand these diverging assessments. By considering an epistemic and contextual conception of explanation, we can make sense of disagreements about explanatoriness in mathematics by identifying differences in the background knowledge, skill corpus, or epistemic aims of (...) mathematicians or mathematical communities. We focus on the relation between explanation, epistemic aims and diverging explanatory assessments by looking at cases from mathematical practice. (shrink)

Mathematics seems to have a special status when compared to other areas of human knowledge. This special status is linked with the role of proof. Mathematicians all too often believe that this type of argumentation leaves no room for errors or unclarity. In this paper we take a closer look at mathematical practice, more precisely at the publication process in mathematics. We argue that the apparent view that mathematical literature is also more reliable is too naive. We will discuss several (...) problems in the publication process that threaten this view, and give several suggestions on how this could be countered. (shrink)

PurposeIn this article, we aim to present and defend a contextual approach to mathematical explanation.MethodTo do this, we introduce an epistemic reading of mathematical explanation.ResultsThe epistemic reading not only clarifies the link between mathematical explanation and mathematical understanding, but also allows us to explicate some contextual factors governing explanation. We then show how several accounts of mathematical explanation can be read in this approach.ConclusionThe contextual approach defended here clears up the notion of explanation and pushes us towards a pluralist vision (...) on mathematical explanation. (shrink)

In this paper we discuss three interrelated questions. First: is explanation in mathematics a topic that philosophers of mathematics can legitimately investigate? Second: are the specific aims that philosophers of mathematical explanation set themselves legitimate? Finally: are the models of explanation developed by philosophers of science useful tools for philosophers of mathematical explanation? We argue that the answer to all these questions is positive. Our views are completely opposite to the views that Mark Zelcer has put forward recently. Throughout this (...) paper, we show why Zelcer’s arguments fail. (shrink)

Leading scholars address the ethical and practical dimensions of Heidegger's thought.

Because of its reliance on a basically Aristotelian conception of virtue, contemporary virtue ethics is often criticised for being inherently elitist. I argue that this objection is mistaken. The core of my argument is that we need to take seriously that virtue, according to Aristotle, is something that we acquire gradually, via a developmental process. People are not just stuck with their characters once and for all, but can always aspire to become better (more virtuous). And that is plausibly the (...) basic normative requirement of virtue ethics. Philosophical Papers Vol. 37 (1) 2008: pp. 131-155. (shrink)

The issues addressed in philosophical papers on quotation generally concern only a particular type of quotation, which I call 'closed quotation'. The other main type, 'open quotation', is ignored, and this neglect leads to bad theorizing. Not only is a general theory of quotation out of reach: the specific phenomenon of closed quotation itself cannot be properly understood if it is not appropriately situated within the kind to which it belongs. Once the distinction between open and closed quotation has been (...) drawn and properly appreciated, it is tempting to consider that only closed quotation is relevant to semantics. Open quotation is more a matter of pragmatics: it is a matter of what people do with words, rather than a matter of content and truth-conditions. In this way one can provide the beginning of a justification for the neglect of open quotation in current semantic theorizing. There is some truth in this view, yet the phenomenon of 'mixed quotation', investigated at length in this paper, is interesting precisely because it shows that things are not so simple. Important issues concerning the interface between semantics and pragmatics will thus be raised. (shrink)

'Philosophische Anthropologie' meint in dieser Studie nicht eine philosophische Subdisziplin, sondern eine besondere Theorierichtung in der deutschsprachigen Philosophie des 20. Jahrhunderts, die mit den Namen Max Scheler, Helmuth Plessner, Erich Rothacker, Arnold Gehlen, Adolf Portmann u.v.a. mehr verbunden ist. Der erste Teil erzählt die verwickelte, teils abenteuerliche Entstehungs-, Aufstiegs- und Entfaltungsgeschichte dieser Denkergruppe von 1919 bis 1975 - einschließlich ihrer beachtlichen Wirkungsgeschichte in verschiedenen Disziplinen wie der Soziologie, Psychologie, Biologie und der Philosophie selbst. Im zweiten Teil wird der philosophische Identitätskern (...) dieser Philosophischen Anthropologie als Denkansatz präzisiert. (shrink)

'Philosophische Anthropologie' meint in dieser Studie nicht eine philosophische Subdisziplin, sondern eine besondere Theorierichtung in der deutschsprachigen Philosophie des 20. Jahrhunderts, die mit den Namen Max Scheler, Helmuth Plessner, Erich Rothacker, Arnold Gehlen, Adolf Portmann u.v.a. mehr verbunden ist. Der erste Teil erzählt die verwickelte, teils abenteuerliche Entstehungs-, Aufstiegs- und Entfaltungsgeschichte dieser Denkergruppe von 1919 bis 1975 - einschließlich ihrer beachtlichen Wirkungsgeschichte in verschiedenen Disziplinen wie der Soziologie, Psychologie, Biologie und der Philosophie selbst. Im zweiten Teil wird der philosophische Identitätskern (...) dieser Philosophischen Anthropologie als Denkansatz präzisiert. (shrink)

In this book two of the leading figures in argumentation theory present a view of argumentation as a means of resolving differences of opinion by testing the acceptability of the disputed positions. Their model of a 'critical discussion' serves as a theoretical tool for analysing, evaluating and producing argumentative discourse. They develop a method for the reconstruction of argumentative discourse that takes into account all aspects that are relevant to a critical assessment. They also propose a practical code of behaviour (...) for discussants who want to resolve their differences in a reasonable way. This is a major contribution to the study of argumentation and will be of particular value to professionals and graduate students in speech communication, informal logic, rhetoric, critical thinking, linguistics, and philosophy. (shrink)

The book offers a compact but comprehensive introductory overview of the crucial components of argumentation theory. In presenting this overview, argumentation is consistently approached from a pragma-dialectical perspective by viewing it pragmatically as a goal-directed communicative activity and dialectically as part of a regulated critical exchange aimed at resolving a difference of opinion. As a result, the book also systematically explains how the constitutive parts of the pragma-dialectical theory of argumentation, which are discussed in a number of separate publications, hang (...) together. The following crucial topics are discussed: argumentation theory as a discipline; the meta-theoretical principles of pragma-dialectics; the model of a critical discussion aimed at resolving a difference of opinion; fallacies as violations of a code of conduct for reasonable argumentative discourse; descriptive research of argumentative reality; analysis as theoretically-motivated reconstruction; strategic manoeuvring aimed at combining achieving effectiveness with maintaining reasonableness; the conventionalization of argumentative practices; prototypical argumentative patterns; pragma-dialectics amidst other approaches. Argumentation Theory: A Pragma-Dialectical Perspective is clearly written and makes argumentation theory understandable to all scholars and advanced students interested in argumentation research. (shrink)

It is now—at least loosely—acknowledged that most health and clinical outcomes are influenced by different interacting causes. Surprisingly, medical research studies are nearly universally designed to study—usually in a binary way—the effect of a single cause. Recent experiences during the coronavirus disease 2019 pandemic brought to the forefront that most of our challenges in medicine and healthcare deal with systemic, that is, interdependent and interconnected problems. Understanding these problems defy simplistic dichotomous research methodologies. These insights demand a shift in our (...) thinking from ‘cause and effect’ to ‘causes and effects’ since this transcends the classical way of Cartesian reductionist thinking. We require a shift to a ‘causes and effects’ frame so we can choose the research methodology that reflects the relationships between variables of interest—one-to-one, one-to-many, many-to-one or many-to-many. One-to-one (or cause and effect) relationships are amenable to the traditional randomized control trial design, while all others require systemic designs to understand ‘causes and effects’. Researchers urgently need to re-evaluate their science models and embrace research designs that allow an exploration of the clinically obvious multiple ‘causes and effects’ on health and disease. Clinical examples highlight the application of various systemic research methodologies and demonstrate how ‘causes and effects’ explain the heterogeneity of clinical outcomes. This shift in scientific thinking will allow us to find the necessary personalized or precise clinical interventions that address the underlying reasons for the variability of clinical outcomes and will contribute to greater health equity. (shrink)

The ethics of care, developed in early 1980s within feminism as a critique on the biases of neokantian ethics, is 40 years old. This book presents its key insights, the developments and debates over the years and the challenges care ethics faces. Internationally renown scholars from various continents have contributed, a clear sign that care ethics has spread over the globe. The key insights regard issues close by, care from person to person, but also at an institutional level and questions (...) of global impact. Vulnerability and relationality are examples of these insights. What can caring practices, ranging from social welfare to palliative care, learn from care ethics? Has care ethics had an impact on ethics at large and what is its future? (shrink)

The Historical Dictionary of Philosophy, the _Historisches Wörterbuch der Philosophie,_ is distinguished by its particular presentation of philosophical terms, ideas and concepts. Rather than providing mere defintions or descriptive and analytical explanantions the _HWPh_ strictly applies the critical method of history of concepts developed by the eminent German scholar and philosopher Joachim Ritter. By means of precise and detailed references it documents the origin, first occurrence, the historical evolution and the changes of meaning of each concept, from Ancient Greek (...) to contemporary philosophy. For the reader this presentation is of unique value: it makes traceable the importance of terms and concepts at certain periods or for a particular philosopher, as well as its changes and development of meaning. Voulmes 1–12 of the _HWPh_ comprises more than 17.000 text columns on 3.670 philosophical terms. The dictionary does not include articles on persons. Volume 13 includes, besides of a comprehensive introductory essay, three different indexes: - the Subject Index classifies the articles by disciplinary and systematic categories - the Main Index includes all philosophical keywords with more than 30.000 references to their occurrences in other articles and contexts - the Author Index lists all authors and their contributions The included CD-ROM allows full text research of the _HWPh's_ entire content. (shrink)

What are consequential world problems? As “grand societal challenges”, one might define them as problems that affect a large number of people, perhaps even the entire planet, including problems such as climate change, distributive justice, world peace, world nutrition, clean air and clean water, access to education, and many more. The “Sustainable Development Goals”, compiled by the United Nations, represent a collection of such global problems. From my point of view, these problems can be seen as complex. Such complex problems (...) are characterized by the complexity, connectivity, dynamics, intransparency, and polytely of their underlying systems. These attributes require special competencies for dealing with the uncertainties of the given domains, e.g., critical thinking. My position is that it is not IQ, but complex problem-solving competencies for dealing with complex and dynamic situations, that is important for handling consequential global problems. These problems require system competencies, i.e., competencies that go beyond analytical intelligence, and comprise systems understanding as well as systems control. Complex problem-solving is more than analytic intelligence. (shrink)

This chapter contains sections titled: Introduction What is Chemistry about? Is Chemistry Reducible to Physics? Are There Fundamental Limits to Chemical Knowledge? Is Chemical Research Ethically Neutral? Conclusion References.

The discussion in Perspectives on Psychological Science about criteria for scholarly merit shows a potential bias of quantitative measurements compared with informed judgments of scholarly merits. This comment argues for a selection procedure that is open for qualitative arguments.

This article presents and discusses different kinds of data documents, including data sets, data studies, data papers and data journals. It provides descriptive and bibliometric data on different kinds of data documents and discusses the theoretical and philosophical problems by classifying documents according to the DIKW model (data documents, information documents, knowl­edge documents and wisdom documents). Data documents are, on the one hand, an established category today, even with its own data citation index (DCI). On the other hand, data documents (...) have blurred boundaries in relation to other kinds of documents and seem sometimes to be understood from the problematic philosophical assumption that a datum can be understood as “a single, fixed truth, valid for everyone, everywhere, at all times”. (shrink)

ABSTRACT We outline a number of ethical objections to genetic technologies aimed at enhancing human capacities and traits. We then argue that, despite the persuasiveness of some of these objections, they are insufficient to stop the development and use of genetic enhancement technologies. We contend that the inevitability of the technologies results from a particular guiding worldview of humans as masters of the human evolutionary future, and conclude that recognising this worldview points to new directions for ethical thinking about genetic (...) enhancement technologies. (shrink)

Complex problem solving (CPS) emerged in the last 30 years in Europe as a new part of the psychology of thinking and problem solving. This paper introduces into the field and provides a personal view. Also, related concepts like macrocognition or operative intelligence will be explained in this context. Two examples for the assessment of CPS, Tailorshop and MicroDYN, are presented to illustrate the concept by means of their measurement devices. Also, the relation of complex cognition and emotion in the (...) CPS context is discussed. The question if CPS requires complex cognition is answered with a tentative “yes.”. (shrink)

In the pragma-dialectical approach, fallacies are considered incorrect moves in a discussion for which the goal is successful resolution of a dispute. Ten rules are given for effective conduct at the various stages of such a critical discussion (confrontation, opening, argumentation, concluding). Fallacies are discussed as violations of these rules, taking into account all speech acts which are traditionally recognized as fallacies. Special attention is paid to the role played by implicitness in fallacies in everyday language use. It is stressed (...) that identifying and acknowledging fallacies in ordinary discussions always has a conditional character. Differences between the pragma-dialectical perspective, the Standard Treatment, and the formal logic approach to fallacy analysis are discussed. (shrink)

This theoretical expose explores the complex notion of argumentative style, which has so far been largely neglected in argumentation theory. After an introduction of the problems involved, the theoretical tools for identifying the properties of the discourse in which an argumentative style manifests itself are explained from a pragma-dialectical perspective and a theoretical definition of argumentative style is provided that does full justice to its role in argumentative discourse. The article concludes with a short reflection upon the next steps that (...) need to be taken in argumentation theory in further substantiating the notion of argumentative style. (shrink)

In "Literary Forms of Argument in Early China," Gentz and Meyer explore a new analytical approach to the study of written thinking by focusing on the argumentative function of literary patterns in early Chinese texts.

In dieser Aufsatzsammlung wird Johann Georg Hamanns Grundthese von Gott als Schriftsteller interpretiert und in weitest reichende literarische Zusammenhange gestellt. Der Zusammenhang von Reden, Horen und Sehen wird theologisch und eschatologisch untersucht. Hamanns Gedanken zum Abendmahl und Sacrament der Sprache werden mit der Rolle des Essens und Trinkens in Beziehung gebracht. Die Narziss-Episode der Metamorphosen des Ovid deutete der Schriftsteller christologisch und als Kenner des Hebraerbriefs verfasste er eine kritische Rezension des Kommentars von J. D. Michaelis (Gottingen). Der Autor arbeitet (...) die Bedeutung Hamanns als der massgebliche theologische Sprachdenker nach Luther heraus, dessen Worttheologie u. a. Kierkegaard gepragt hat. (shrink)