Philosophy of Mathematics Relevance.docx

The present doldrums position and state of decadence, internal differences, external aggression (geographical and ideological), lack of self-confidence and dependence, illiteracy, political instability, economic disaster, lack of knowledge and wisdom, back benchers in science and technology, education, medicine, trade and business, banking system and defensive incapability of Muslim World prompted me to look at our principal sources of inspiration, which are, the Qur’an, Sunnah of the Prophet (SAW), and examples of the “enlightened Caliphs” and see what is Islam’s view about seeking knowledge, technology and inventions in general and mathematics’ education in particular. We will discuss the nature of mathematics and its scientific status. We will highlight the position of mathematics in Islamic classification of knowledge. We will also discuss the current state of mathematics and future suggestions. We have gathered together some of these impressions; these are all tentative, nothin...

Studies in History and Philosophy of Science, vol. 44 (2013), pp. 32-42., 2013

The paper distinguishes between two kinds of mathematics, natural mathematics which is a result of biological evolution and artificial mathematics which is a result of cultural evolution. On this basis, it outlines an approach to the philosophy of mathematics which involves a new treatment of the method of mathematics, the notion of demonstration, the questions of discovery and justification, the nature of mathematical objects, the character of mathematical definition, the role of intuition, the role of diagrams in mathematics, and the effectiveness of mathematics in natural science.

2015

Humankind has been able to explore from within him most of his potentials through his creative prowess. The benefits of such exploratory potentials are found in various artistic and scientific innovations and development. The work is an attempt at evaluating the value of mathematics and culture to human development. Mathematics is a rational outgrowth of cultural knowledge. There are views that put mathematics in human perspective as a cultural phenomenon. Mathematics as a department of culture is a product of human intellectualism, while culture abides as social requirement for mathematics. The relation between culture and mathematics is enabled by man as the instrumental constructor. Thus, mathematics becomes a cultural discipline that gives an intelligible picture about reality to mankind. To that extent, the mathematician cannot be isolated from the particular society in which he locates his operation. Moreover, the way of organizing information is a mathematical precedent of presenting nature's reality in a calculative format. Culture therefore is that civilization that brought about the mathematization of the world for the enhancement of human and environmental security. Mathematics as a cultural concept remains the basic postulate of the descriptive order of the world.

Archimedes Series 66, 2023

This colective book, edited by Karine Chemla, J Ferreirós, Lizhen Ji, Erhard Scholz & Chang Wang, is a unique introduction to historiographical questions concerning the history of mathematics, with essays by many leading scholars, aimed at guiding newcomers to the field. It provides multiple perspectives on mathematics, its role in culture, development, connections with other sciences, with philosophy, etc.

Semiotic Review, 2020

Starting from the profound impact of Kenneth Arrow's Impossibility Theorem on the social sciences of the postwar twentieth century, this essay engages with the ways in which mathematics can be seen as a language-ideologically inflated notational system. In the mid-twentieth century, a profound belief in mathematics as a purely objective and non-ideological organization of knowledge took hold, and mathematical proof became the most authoritative type of statement on reality. When something was ruled 'logically impossible', real-world occurences could be seen as transgressions and exceptions. Hidden inside this belief is a set of irrational, metaphysical assumptions about humans and social behavior that can be laid bare by means of linguistic-anthropological analysis.

2007

This paper explores the philosophical significance of the Keralese and Indian subcontinent contribution to history of mathematics. Identifying the most accurate genesis and trajectory of mathematical ideas in history that current knowledge allows should be the goal of every history of mathematics, and is consistent with any philosophy of mathematics. I argue for the need of a broader conceptualization of philosophy of than the traditional emphasis on scholastic enquiries into epistemology and ontology. For such an emphasis has been associated, though I add need not necessarily be so, with an ideological position that devalues non-European contributions to history of mathematics. The philosophy of mathematics needs to be broad enough to recognise the salient features of the discipline it reflects upon, namely mathematics.

2015

The paper discusses the question "what is mathematics" from a point of view inspired by anthropology. In this perspective, the character of mathematical thinking and argument is strongly affected-almost essentially determined, indeed-by the dynamics of the specific social, mostly professional environments by which it is carried. Environments where future practitioners are taught as apprentices produce an approach different from that resulting from teaching in a school-the latter inviting to intra-mathematical explanation in a way the former does not. Moreover, once the interaction with the early classical Greek philosophical quest for causes and general explanations had caused mathematical explanation to become an autonomous endeavour in the shape of explicit proof and deductivity, proof and deductivity presented themselves as optionssometimes exploited, sometimes not-even in the teaching of mathematics for practitioners.

I. Prologue: Scientific and Cultural Bases of Mathematics ORIGINS AND HISTORICAL PERSPECTIVE The present account is largely based on the principle that mathematics is a scientific activity with social-historical roots, in opposition to a static view that takes it as existent per se, quite independent from human culture. The first stand, on whose side one counts famous forerunners, sees mathematics in a position similar to that of other sciences, to wit, both a function and agent of society and of the scientifically explainable universe. The precise language of mathematics and the beauty of its universal formulas, apparently conceived to perfection, would seemingly be responsible for the platonic-like vision of the discipline as a pure manifestation of the human or divine spirit, which exists independently of a given cultural state of mankind or of its social development. The nature of the present document moves away from the above vision and tries to convey the idea that the mathema...

Handbook of research on mathematics teaching and …, 1992