The place of mathematical sciences in Fârâbî's logic-An analysis through mathematical examples-

Al-Fârâbî's conception of logic is grounded in the profound relationship between the structural features of language and the principles of rational thought. According to him, the accurate expression and comprehension of intellectual forms are only possible through a systematic investigation of the structural rules of language. Hence, in his work Enumeration of the Sciences, he places the linguistic sciences at the forefront of his classification, followed by logic. Al-Fârâbî positions logic not only as an independent discipline but also as the methodological foundation and criterion for all other sciences. This functional role of logic is largely rooted in the principles derived from mathematical modes of thinking. By employing mathematical examples to elucidate logical topics, he establishes a theoretical bridge between logic and mathematics. Al-Fārābī classifies knowledge into two primary categories: conceptualization (taṣawwur) and assertion (taṣdīq). This division laid the foundation for the later Islamic logical tradition, in which the discipline of logic was systematically organized into two main sections: tasawwurāt (concepts) and taṣdīqāt (judgments). Within the realm of tasawwurāt, he focuses on concepts and definitions, while the domain of taṣdīqāt encompasses propositions, syllogisms, and the five arts—rhetoric, poetry, dialectic, sophistry, and demonstration. In addressing these topics, al-Fārābī frequently draws upon mathematical examples to concretize abstract logical ideas. In conclusion, al-Fārābī views logic and mathematics as mutually reinforcing disciplines. While logic serves as a tool for organizing language and shaping thought, its foundation is grounded in the precision and clarity characteristic of mathematical reasoning. In this regard, al-Fārābī's approach to logic represents an early and significant example of an interdisciplinary methodology.