This book contains 20 essays tracing the work of David Zarefsky, a leading North American scholar of argumentation from a rhetorical perspective. The essays cohere around 4 general themes: objectives for studying argumentation rhetorically, approaches to rhetorical study of argumentation, patterns and schemes of rhetorical argumentation, and case studies illustrating the potential of studying argumentation rhetorically. These articles are drawn from across Zarefsky’s 45-year career. Many of these articles originally appeared in publications that are difficult to access today, and this (...) collection brings the reader up to date on the topic. Zarefsky’s scholarship focuses on the role of language in political argumentation, the ways in which argumentation creates public knowledge and belief, the influence of framing and context on what is said and understood, the deployment of particular patterns and schemes of argumentation in public reasoning, and the influence of debate on politics and governance. All these topics are addressed in this book. Each of the conceptual essays includes brief application to specific cases, and five extended case studies are also presented in this volume. The case studies cover different themes: two explore famous political debates, the third focuses on presidential rhetoric across the course of United States history, the fourth on the arguments for liberalism at a time of political polarization, and the fifth on the contemporary effort to engage the United States with the Muslim world. This book is of interest to scholars in the fields of philosophy, logic, law, philosophy of law, and legal history. The range of topics and concepts addressed, the interplay of concepts and cases and the unifying perspective of rhetorical argumentation make this book a valuable read for students of argumentative practice, whether rhetorically or otherwise. (shrink)

In this paper, we will elaborate on a pronouncement that should be at the onset of any study in epistemology and ethnomathematics, namely, we will argue that learners do think mathematically and it is our responsibility as educators to recognize and appreciate their modes of mathematical reasoning. We will conduct our study in five parts. Following a brief introduction, in the second part, we will briefly discuss some of the critical tenets of epistemology especially as it applies to mathematics. The (...) third part will be devoted to elucidating the basic nomenclature and hypotheses associated with ethnomathematics. In the fourth part we will expound on the organic and intrinsic relationship between these two fields. Lastly, we will propose some changes in the way academic mathematicians regard philosophy and pedagogy of mathematics that, in our opinion, will facilitate students’ understanding of the cultural aspects of mathematics. (shrink)

Mathematicians frequently use aesthetic vocabulary and sometimes even describe themselves as engaged in producing art. Yet aestheticians, in so far as they have discussed this at all, have often downplayed the ascriptions of aesthetic properties as metaphorical. In this paper I argue firstly that the aesthetic talk should be taken literally, and secondly that it is at least reasonable to classify some mathematics as art.

The history of the continuous inclusion of mathematics in liberal education in the West, from ancient times through the modern period, is sketched in the first two sections of this chapter. Next, the heart of this essay (Sects. 3, 4, 5, 6, and 7) delineates the central role mathematics has played throughout the history of Western civilization: not just a tool for science and technology, mathematics continually illuminates, interacts with, and sometimes challenges fields like art, music, literature, and philosophy – (...) subjects now universally considered to be liberal arts. Section 8 adds an international perspective to the contemporary liberal arts story by describing some instructive mathematical achievements from many cultures and societies. Finally, Sect. 9 addresses how contemporary mathematics teaching can use the history of mathematics viewed as a liberal art to enhance the appreciation and understanding of mathematics for all students. (shrink)

The widespread and long-lived failings of academic economics are due to an over-reliance on largely inappropriate mathematical methods of analysis. This is an assessment I have long maintained. Many heterodox economists, however, appear to hold instead that the central problem is a form of political-economic ideology. Specifically, it is widely contended in heterodox circles that the discipline goes astray just because so many economists are committed to a portrayal of the market economy as a smoothly or efficiently functioning system or (...) some such, a portrayal that, whether sincerely held or otherwise, is inconsistent with the workings of social reality. Here I critically examine the contention that a form of political-economic ideology of this sort is the primary problem and assess its explanatory power. I conclude that the contention does not fare very well. I do not, though, deny that ideology of some sort has a major impact on the output of the modern economics academy. However it is of a different nature to the form typically discussed, and works in somewhat indirect and complex ways. Having raised the question of the impact of ideology I take the opportunity to explore its play in the economics academy more generally. (shrink)

یکی از مهم‌ترین ویژگی‌های علم نوین روش کمّی و ریاضیاتی آن است. باور رایج این است که این مبنای علم نوین در قرن شانزدهم و در انقلاب علمی به همراه خود علم نوین به وجود آمده است، لکن بررسی‌های تاریخی حاکی از آن است که روش کمّی علم نه در بحبوحه ظهور علم نوین در انقلاب علمی، بلکه در منازعات الهیاتی قرون وسطای متأخر متولد شد. این نکته از جهت روشن کردن رابطه‌ای که علم و دین در طول تاریخ مغرب‌زمین (...) داشته‌اند حائز اهمیت است. شواهدی حاکی از آن است که متألهان مسیحی، با انگیزه‌های الهیاتی، مسائلی را مطرح کردند که بستر مناسبی را برای پیدایش تجربه‌گرایی به وجود آورد. در نوشتار حاضر عوامل پیدایش روش کمّی را در قرون وسطای متأخر و در میان متألهان مسیحی مورد بررسی قرار خواهیم داد. از خلال این بررسی آشکار خواهد شد که در این عصر سه عامل مهم که با انگیزه‌های الهیاتی همراه بودند در به وجود آمدن روش کمّی موثر واقع شدند: توجه به نورشناسی با انگیزه‌های الهیاتی، افلاطون‌گرایی در الهیات، و وجود انگیزۀ الهیاتی در استفاده از ریاضیات. در ضمنِ این تحلیل، رابطۀ تجربه‌گرایی و الهیات مسیحی در قرون وسطای متأخر روشن خواهد شد. (shrink)

The paper contends that neoclassical ideology stems, to a great extent, from mathematical analysis. It is suggested that mainstream economic thought can be comprehensively revisited if both histories of mathematical and economic thought are to be taken collaboratively into account. Ideology is understood as a 'social construction of reality' that prevents us from evaluating our own standpoint, and impedes us from realising our value judgments as well as our theories of society and nature. However, the mid-19th century's intellectual controversies about (...) the validity of mathematical thought, truth and knowledge can procure new interesting insights concerning the ideological stance of the first marginalists. In this respect, the methodological categories of analysis and synthesis serve as the basis for the crucial distinction between old geometry and mathematical analysis, indicating that the discipline of mathematics has its own history of fundamentally unresolved disputes. Lastly, this may also shed some light on Alfred Marshall's peculiarly reluctant attitude towards the use of mathematical analysis in his work. (shrink)

Ordinary mathematical proofs—to be distinguished from formal derivations—are the locus of mathematical knowledge. Their epistemic content goes way beyond what is summarised in the form of theorems. Objections are raised against the formalist thesis that every mainstream informal proof can be formalised in some first-order formal system. Foundationalism is at the heart of Hilbert's program and calls for methods of formal logic to prove consistency. On the other hand, ‘systemic cohesiveness’, as proposed here, seeks to explicate why mathematical knowledge is (...) coherent (in an informal sense) and places the problem of reliability within the province of the philosophy of mathematics. (shrink)

It is tempting to consider Girard Desagues’ mathematical work, more precisely his Brouillon project on conics, as a work of mathematics applied to perspective. We would like to show in this text that it is probably more pertinent to consider that Desargues does mathematics as a practitionner of the art of perspective. We shall analyse a few extracts of Desargues’ work with this point of view in mind so as to shed light on his innovative ideas that could be hard (...) to understand in his sometimes obscure style. We shall show how this way of doing geometry can be also be found in the works Philippe de la Hire and Jacques-Francois le Poîvre, leading them to consider a transformation of the plane into itself as an explicited mathematical object. (shrink)