ONTOLOGICAL AND EPISTEMOLOGICAL INTERPRETATION OF THE CONCEPTS OF NUMBER AND QUANTITY IN THE WORKS OF AL-KHWARIZMI

Abstract

This article examines the ontological and gnoseological interpretation of the concepts of number and quantity in the scientific heritage of Muhammad ibn Musa al-Khwarizmi. The relevance of the study is determined by the growing interest in the philosophical foundations of mathematical knowledge and the need to reconsider classical scientific thought within contemporary epistemological frameworks. The paper explores how al-Khwarizmi conceptualizes number not merely as a technical or computational tool, but as a fundamental category reflecting the structure of reality and the process of human cognition. Particular attention is devoted to the analysis of his seminal work Al-Kitab al-mukhtasar fi hisab al-jabr wal-muqabala, where numerical relations and quantitative structures are systematically organized and interpreted through logical operations. The study demonstrates that al-Khwarizmi’s approach integrates ontological assumptions about the objective existence of quantitative relations with gnoseological principles concerning their cognition, representation, and application. His treatment of number reveals a synthesis of abstraction, generalization, and practical orientation, bridging the gap between empirical reality and theoretical reasoning.