The two sermons edited and translated here for the first time are primary material from the years before the establishment of the Fatimid caliphate in 297/909. The authors have been identified as Abu 'Abd Allah al-Shi'i and Abu'l-'Abbas Muhammad, two brothers who were central to the success of the Ismaili da'wa in North Africa. Da'wa, a term used to describe how Muslims teach others about the beliefs and practices of their Islamic faith, therefore provide a unique view of the nature (...) and development of Islam throughout history. In this case, the primary texts shed light on the development of Islam among the Berbers of the Maghreb. The first text by Abu 'Abd Allah al-Shi'i shows how the arguments for belief in the 'imamate' of the family of the Prophet, that is, the Shi'a belief that all imams should be spiritual descendants of the Prophet Muhammad and his household, were developed and presented to bring new adherents to the cause. The Book of the Keys to Grace by his elder brother Abu'l-'Abbas, too, concerns not only the centrality of the imam in the faith but also sheds light on the hierarchy of the da'wa in this early period and its organisational sophistication. Both texts also reveal the contemporary theology propagated by the Ismaili da'wa, including for instance, the powerful analogy of Moses/Aaron and Muhammad/'Ali, the awareness of a variety of religious traditions and the use of detailed Qur'anic quotations and a wide range of hadith. As such they constitute primary source material of interest not only for Ismaili history but for this early period of Islam in general.". (shrink)

The Ismailis, among whom are the followers of the Aga Khan, rose to prominence during the fourth Islamic/tenth Christian century. They developed a remarkably successful intellectual programme to sustain and support their political activities, promoting demands of Islamic doctrine together with the then newly imported sciences from abroad. The high watermark of this intellectual movement is best illustrated in the writings of the Ismaili theoretician Abu Ya´qub al-Sijistani. Using both published and manuscript writings of al-Sijistani that have hitherto been largely (...) hidden, forgotten or ignored, Dr Paul Walker reveals the scholar's major contribution to the development of philosophical Shiism. He analyses his role in the Ismaili mission of that time and critically assesses the major themes in his combination of philosophy and religious doctrine. (shrink)

The first book-length study of a leading tenth-century Ismaili theoretician Abu Ya'qub al-Sijistani.

Extends the ideas of social constructivism to the philosophy of mathematics, developing a powerful critique of traditional absolutist conceptions of mathematics, and proposing a reconceptualization of the philosophy of mathematics.

Although many agree that all teaching rests on a theory of knowledge, this is an in-depth exploration of the philosophy of mathematics for education, building on the work of Lakatos and Wittgenstein.

Kitcher and Aspray distinguish a mainstream tradition in the philosophy of mathematics concerned with foundationalist epistemology, and a ‘maverick’ or naturalistic tradition, originating with Lakatos. My claim is that if the consequences of Lakatos's contribution are fully worked out, no less than a radical reconceptualization of the philosophy of mathematics is necessitated, including history, methodology and a fallibilist epistemology as central to the field. In the paper an interpretation of Lakatos's philosophy of mathematics is offered, followed by some critical discussion, (...) and an extension to a social constructivist position (which might well have been unacceptable to Lakatos). (shrink)

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 (...) are discussed. MacIntyre’s virtue ethics accommodates both the good mathematician and the ethics of the social practice of mathematics. It demonstrates that purism is compatible with acknowledging the social responsibility of mathematics. Four aspects of this responsibility are mentioned, two concerning the impact of mathematics via education, and two concerning explicit and implicit applications of mathematics. The last of these opens up the performativity of mathematical and measurement applications in society, which change the very processes they are supposed to measure. Although these applications are not explored in detail, they illustrate the importance of considering the ethics and social responsibility of mathematics in society. MacIntyre’s virtue theory opens a broad approach to the controversial topic of the ethics of mathematics encompassing purism, and absolutist and social constructivist philosophies of mathematics, but still enabling ethical critiques of the impact of mathematics on society. (shrink)

This book offers an up-to-date overview of the research on philosophy of mathematics education, one of the most important and relevant areas of theory. The contributions analyse, question, challenge, and critique the claims of mathematics education practice, policy, theory and research, offering ways forward for new and better solutions. The book poses basic questions, including: What are our aims of teaching and learning mathematics? What is mathematics anyway? How is mathematics related to society in the 21st century? How do students (...) learn mathematics? What have we learnt about mathematics teaching? Applied philosophy can help to answer these and other fundamental questions, and only through an in-depth analysis can the practice of the teaching and learning of mathematics be improved. The book addresses important themes, such as critical mathematics education, the traditional role of mathematics in schools during the current unprecedented political, social, and environmental crises, and the way in which the teaching and learning of mathematics can better serve social justice and make the world a better place for the future. (shrink)

The concept of infinity has a long and troubled history. Thus it is a promising concept with which to explore rejection, disagreement, controversy and acceptance in mathematical practice. This paper briefly considers four cases from the history of infinity, drawing on social constructionism as the background social theory. The unit of analysis of social constructionism is conversation. This is the social mechanism whereby new mathematical claims are proposed, scrutinised and critiqued. Minimally, conversation is based on the two roles of proponent (...) and critic. The proponent puts forward a proposal, which is reacted to and evaluated by those in the role of critic. There is a continuum of contexts in which such conversations take place from inner conversations the mathematician has within themselves, and casual face-to face interactions between mathematicians at the chalkboard, all the way to the formal responses of referees and editors to submitted journal papers. Such responses vary from unconditional acceptance, partial acceptance through to outright rejection. There may be disagreements between proponents and critics, among those in the joint role of critic, and broader, community-wide disagreements and controversies, according to specific mathematical proposal and the critical judgements of it. (shrink)

Mathematicians and physical scientists depend heavily on the formal symbolism of mathematics in order to express and develop their theories. For this and other reasons the last hundred years has seen a growing interest in the nature of formal language and the way it expresses meaning; particularly the objective, shared aspect of meaning as opposed to subjective, personal aspects. This dichotomy suggests the question: do the objective philosophical theories of meaning offer concepts which can be applied in psychological theories of (...) meaning? In recent years cognitive scientists such as Chomsky [1980], Fodor [1981] and MacNamara [1982] have used philosophical approaches to the meaning of formal language expressions as the basis for their psychological theories. Following this lead it seems appropriate to review some of the main treatments of meaning with a view to their transferability. (shrink)