从三段论到学科分离：亚里士多德逻辑体系的构建与古希腊数学–逻辑关系的再考察

From Syllogism to Disciplinary Separation: The Construction of Aristotle’s Logical System and a Re-Examination of the Relationship between Ancient Greek Mathematics and Logic

摘要: 本文系统探讨了亚里士多德逻辑体系的构建及其历史局限性，并分析了古希腊数学与逻辑之间未能深度融合的复杂原因。亚里士多德通过《工具论》确立了以三段论为核心的演绎逻辑框架，但其体系因缺乏量化表达和形式化不足，难以处理复杂推理。泰奥弗拉斯托斯虽扩展了假言三段论，但仍受限于亚里士多德框架。希腊数学以几何学证明著称，其依赖直观图示与定性描述，与逻辑学追求的抽象普遍性存在根本差异；同时，学科发展的地理分隔及历史偶然性进一步加剧了两者的分离。古代逻辑与数学的分离是特定历史条件与学科特性的产物，由此为理解现代逻辑–数学融合提供了历史镜鉴。

Abstract: This paper systematically explores the construction of Aristotle’s logical system and its historical limitations, while analyzing the complex reasons for the lack of deep integration between ancient Greek mathematics and logic. Aristotle, through his Organon, established a deductive logical framework centered on the syllogism; however, his system struggled to handle complex reasoning due to its lack of quantificational expression and insufficient formalization. Although Theophrastus expanded the theory of hypothetical syllogisms, he remained constrained by the Aristotelian framework. Greek mathematics, renowned for its geometric proofs, relied on intuitive diagrams and qualitative descriptions, which fundamentally differed from the abstract universality pursued by logic. Meanwhile, geographical separation in disciplinary development and historical contingencies further exacerbated their divergence. The separation between ancient logic and mathematics was thus a product of specific historical conditions and disciplinary characteristics, offering a historical lens through which to understand the modern integration of logic and mathematics.