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Drawing on the material culture of the Ancient Near East as interpreted through Material Engagement Theory, the journey of how material number becomes a conceptual number is traced to address questions of how a particular material form might generate a concept and how concepts might ultimately encompass multiple material forms so that they include but are irreducible to all of them together. Material forms incorporated into the cognitive system affect the content and structure of concepts through their agency and affordances, (...) |
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A traditional problem of ethics in mathematics is the denial of social responsibility. Pure mathematics is viewed as neutral and value free, and therefore free of ethical responsibility. Applications of mathematics are seen as employing a neutral set of tools which, of themselves, are free from social responsibility. However, mathematicians are convinced they know what constitutes good mathematics. Furthermore many pure mathematicians are committed to purism, the ideology that values purity above applications in mathematics, and some historical reasons for this (...) |
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This paper offers a caution that emphasis upon the importance of mathematics in recent historiography is in danger of obscuring the historical fact that, for the most part, mathematics was not seen as important in the pre-modern period. The paper proceeds by following a single case study, and in so doing offers the first account of the mathematical writings of Jean Fernel (1497–1558), better known as a leading medical innovator of the 16th century. After establishing Fernel's early commitment to mathematics, (...) |
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This inaugural handbook documents the distinctive research field that utilizes history and philosophy in investigation of theoretical, curricular and pedagogical issues in the teaching of science and mathematics. It is contributed to by 130 researchers from 30 countries; it provides a logically structured, fully referenced guide to the ways in which science and mathematics education is, informed by the history and philosophy of these disciplines, as well as by the philosophy of education more generally. The first handbook to cover the (...) |
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By the end of the twelfth century in the south of Europe, new methods of calculating with Hindu-Arabic numerals developed. This tradition of sub-scientific mathematical practices is known as the abbaco period and flourished during 1280–1500. This paper investigates the methods of justification for the new calculating procedures and algorithms. It addresses in particular graphical schemes for the justification of operations on fractions and the multiplication of binomial structures. It is argued that these schemes provided the validation of mathematical practices (...) |
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The purpose of this article is to analyse the mathematical practices leading to Rafael Bombelli’s L’algebra (1572). The context for the analysis is the Italian algebra practiced by abbacus masters and Renaissance mathematicians of the fourteenth to sixteenth centuries. We will focus here on the semiotic aspects of algebraic practices and on the organisation of knowledge. Our purpose is to show how symbols that stand for underdetermined meanings combine with shifting principles of organisation to change the character of algebra. |
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La recherche historique dans le cours du dernier demi-siècle a amélioré notre connaissance des mathématiques de I 'Antiquité. Les textes en provenance d'Égypte et de Mésopotamie ont été mieux compris et leur interprétation a dépassé l'alternative sommaire entre empirisme et rationalisme. Le panorama offert par la science grecque s'est enrichi et diversifié: il n'est plus possible de le réduire à la seule théorie géométrique. Les principaux problèmes que posait son histoire ont été l'objet de discussions approfondies. À partir de là (...) |
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What is early modern philosophy? Two interpretative trends have predominated in the related literature. One, with roots in the work of Hegel and Heidegger, sees early modern thinking either as the outcome of a process of gradual rationalization (leading to the principle of sufficient reason, and to "ontology" as distinct from metaphysics), or as a reflection of an inherent subjectivity or representational semantics. The other sees it as reformulations of medieval versions of substance and cause, suggested by, or leading to, (...) |
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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 – (...) |
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This essay shows that comparable notions of humanism emerged independently in two twentieth-century scholars, Yuen Ren Chao (1892–1982) and George Sarton (1884–1956). They met as young men at Harvard University and found themselves to be compatible thinkers. They both respected the so-called facts of science, perhaps more than theories in science. They saw their task as assembling these facts for a future synthesis. They recognized the diversity of the world’s civilizations, and they actively participated in trying to unite scholars of (...) |
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