This introductory chapter sets the stage for an engaging exploration of the multifaceted concept of proof in the philosophy of mathematical practice. As a fundamental pillar of mathematics, proof has long been a subject of intense scrutiny for mathematicians and philosophers alike. Traditionally, proofs have been perceived as rigorous and deductive arguments, and this analysis was directed towards the notion of formal proof. However, recent developments have challenged this traditional view, highlighting the dynamic and evolving nature of mathematical proofs. In (...) this section, we bring together diverse perspectives from leading scholars to delve into the philosophical significance and complexity of mathematical proof. (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)

In this article, we sketch a new approach to law and ethics. The traditional paradigm, exemplified in the debate on liberal moralism, becomes increasingly inadequate. Its basic assumptions are that there are clear moral norms of positive or critical morality, and that making statutory norms is an effective method to have citizens conform to those norms. However, for many ethical issues that are on the legislative agenda, e.g. with respect to bioethics and anti-discrimination law, the moral norms are controversial, vague (...) or still evolving. Moreover, law proves not to be a very effective instrument. Therefore, we need a new paradigm, both for descriptive and for normative analysis. This interactive paradigm, as a normative position, can be summarised in two theses. The process of legislation on ethical issues should be structured as a process of interaction between the legislature and society or relevant sectors of society, so that the development of new moral norms and the development of new legal norms may reinforce each other. And legislation on ethical issues should be designed in such a way that it is an effective form of communication which, moreover, facilitates an ongoing moral debate and an ongoing reflection on such issues, because this is the best method to ensure that the practice remains oriented to the ideals and values the law tries to realise. (shrink)

Is guidance by social norms compatible with rationality? Jon Elster has argued inThe Cement of Societythat there is a fundamental contrast between rationality and conformity to social norms. The context of study is the problem of collective action, with special emphasis on collective wage bargaining. In such negotiations, the appeal to social norms rather than to self-interest can block agreement. Suppose one union is committed to the norm of equal pay for equal work; another one appeals to the norm of (...) equal pay for everybody, regardless of the type of work. ‘In the presence of competing norms that favor different groups, the self-righteousness conferred by belief in a norm can lead to a bargaining impasse.'In confrontations between individuals, codes of honor can produce similar problems. It is in no one's interest to face a colleague over the barrel of a gun because one has made a nasty remark about his latest book, but if the code demands that one fight it out, the challenge must be accepted. (shrink)

Over the last few decades there have been several calls for a “big picture” of the history of science. There is a general need for a concise overview of the rise of modern science, with a clear structure allowing for a rough division into periods. This essay proposes such a scheme, one that is both elementary and comprehensive. It focuses on four machines, which can be seen to have mediated between science and society during successive periods of time: the clock, (...) the balance, the steam engine, and the computer. Following an extended developmental phase, each of these machines came to play a highly visible role in Western societies, both socially and economically. Each of these machines, moreover, was used as a powerful resource for the understanding of both inorganic and organic nature. More specifically, their metaphorical use helped to construe and refine some key concepts that would play a prominent role in such understanding. In each case the key concept would at some point be considered to represent the ultimate building block of reality. Finally, in a refined form, each of these machines would eventually make its entry in scientific research, thereby strengthening the ties between these machines and nature. (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)

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)

Medical research involving human subjects can be risky and burdensome. Therefore, such research must be reviewed and approved by a Research Ethics Committee (REC). To guarantee the safety of the subjects, it is very important that these studies be conducted in accordance with the approved protocol. An important issue in this respect is whether studies include the requisite number of subjects based on the research question. The research question is unlikely to be answered reliably if the requisite number of subjects (...) is not met. In such cases, subjects are exposed to unnecessary risks and burdens. In this descriptive study, the authors evaluated how frequently studies are completed with the required number of subjects. Moreover, the authors identified the characteristics of research that does and does not include the required number of subjects. The results of this study show that a considerable proportion of studies (41/107) were terminated although they failed to recruit a sufficient number of subjects. Furthermore, the authors found that investigator-initiated studies have significantly (p=0.028) more problems in recruiting the requisite number of subjects than studies initiated by pharmaceutical companies. Potential solutions are discussed to reduce the number of studies that do not include a sufficient number of subjects. (shrink)

How do Dutch people let each other know that they disagree? What do they say when they want to resolve their difference of opinion by way of an argumentative discussion? In what way do they convey that they are convinced by each other’s argumentation? How do they criticize each other’s argumentative moves? Which words and expressions do they use in these endeavors? By answering these questions this short essay provides a brief inventory of the language of argumentation in Dutch.

The study of argumentation is prospering. After its brilliant start in Antiquity, highlighted in the classical works of Aristotle, after an alternation of ups and downs during the following millennia, in the post-Renaissance period its gradual decline set in. Revitalization took place only after Toulmin and Perelman published in the same year their landmark works The Uses of Argument and La nouvelle rhétorique. The model of argumentation presented by Toulmin and Perelman’s inventory of argumentation techniques inspired a great many scholars (...) in various ways to take up the study of argumentation in a serious manner. Nowadays there are well-established logical approaches to argumentation, but also social and socio-psychological, linguistic, juridical and other approaches. In most of these approaches traces can be found of the influence of the classical and neo-classical argumentation theories just mentioned. (shrink)

Some conspicuous characteristics of argumentation as we all know this phenomenon from our shared everyday experiences are in my view vital to its theoretical treatment because they should have methodological consequences for the way in which argumentation research is conducted. To start with, argumentation is in the first place a communicative act complex, which is realized by making functional verbal communicative moves.

This paper describes the development of pragma-dialectics as a theory of argumentative discourse. First the development of the pragma-dialectical model of a critical discussion is explained, with the rules that are to be complied with in order to avoid fallacies from occurring. Then the integration is discussed of rhetorical insight in the dialectical framework. In this endeavour, the concept of strategic manoeuvring is explained that allows for a more refined and more profoundly justified analysis of argumentative discourse and a better (...) identification of fallacies. The paper ends with a brief overview of current research projects. (shrink)

This article reacts against the undesirable ideological separation between dialectical and rhetorical approaches to argumentative discourse. It argues that a sound evaluation of argumentation requires an analysis that reveals all aspects of the discourse pertinent to critical testing. To explain the rationale of the various moves made in the discourse and the strategic patterns behind them, not only the interlocutors' dialectical goals must be taken into account, but also their rhetorical goals. After explaining how rhetorical insight can be instrumental in (...) deepening and justifying a dialectical analysis, an integrated analysis is made of the rhetorical strategies that are brought to bear in an advertorial published by the oil company Shell. (shrink)

How do Dutch people let each other know that they disagree? What do they say when they want to resolve their difference of opinion by way of an argumentative discussion? In what way do they convey that they are convinced by each other’s argumentation? How do they criticize each other’s argumentative moves? Which words and expressions do they use in these endeavors? By answering these questions this short essay provides a brief inventory of the language of argumentation in Dutch.

Suppose “chicken” eggs could be produced by quasi‐chickens—genetically engineered humps of living chicken‐flesh that do nothing but lay eggs. Would there be anything amiss with that? Animal ethicists invoke the notion of animal integrity in order to give intellectual content to the intuition that there would be. On inspection, ‘integrity’ isn't everything its proponents want it to be. Yet there's enough in it to make reasoned argument possible.

During the past thirty years the pragma-dialectical theorizing has developed in various steps from designing an abstract ideal model for critical discussion to examining strategic manoeuvring in the various argumentative activity types in which argumentative discourse manifests itself in argumentative reality. The response to the theoretical proposals that have been made includes, next to approval, also various kinds of criticisms. This paper explores the nature and thrust of these criticisms. In doing so, a distinction is made between criticisms concerning the (...) dialectical and the pragmatic dimensions of pragma-dialectics, the scope of the theory, the rhetorical dimension and moral quality, the treatment of the fallacies, and the epistemic dimension. (shrink)

Pragmatics and dialectics are two disciplines which have been amongst the first and most important partners for argument studies in the exploration of the complex realm of communication. Treating argumentation as a construct consisting of premises and conclusion allows for investigating some interesting properties of the phenomenon of reasoning, but does not capture a variety of aspects related to the usage of natural language and dialogical context in which real-life argumentation is typically embedded. This special issue explores some of the (...) fascinating research questions which emerge when we move beyond logic into the territory of the pragmatics and dialectics of argument. (shrink)

The study of argumentation is prospering. After its brilliant start in Antiquity, highlighted in the classical works of Aristotle, after an alternation of ups and downs during the following millennia, in the post-Renaissance period its gradual decline set in. Revitalization took place only after Toulmin and Perelman published in the same year their landmark works The Uses of Argument and La nouvelle rhétorique. The model of argumentation presented by Toulmin and Perelman’s inventory of argumentation techniques inspired a great many scholars (...) in various ways to take up the study of argumentation in a serious manner. Nowadays there are well-established logical approaches to argumentation, but also social and socio-psychological, linguistic, juridical and other approaches. In most of these approaches traces can be found of the influence of the classical and neo-classical argumentation theories just mentioned. (shrink)