abstract:

This paper examines Aristotle's discussion of the priority of actuality to potentiality in geometry at Metaphysics Θ9, 1051a21–33. Many scholars have assumed what I call the "geometrical construction" interpretation, according to which his point here concerns the relation between an inquirer's thinking and a geometrical figure. In contrast, I defend what I call the "geometrical analysis" interpretation, according to which it concerns the asymmetrical relation between geometrical propositions in which one is proved by means of the other. His argument as so construed is ultimately based on the asymmetrical relation between the corresponding geometrical facts. Then I explore this ontological priority in geometry by drawing attention to a parallel passage, Posterior Analytics II.11, 94a24–35, where Aristotle explains the relation between the same geometrical propositions in connection to material causation.

摘要：

本文考察了亚里士多德在Metaphysics Θ9, 1051a21-33中关于几何中现实性优先于潜在性的讨论。许多学者采取了我所谓的“几何构造”解释，据此他的观点涉及探究者的思维与几何图形之间的关系。相比之下，我为我所谓的“几何分析”解释辩护，根据该解释，它涉及几何命题之间的不对称关系，其中一个被另一个证明。他这样解释的论证最终是基于相应几何事实之间的不对称关系。然后我通过将注意力引向平行段落后验分析来探索几何学中的这种本体论优先级 II.11, 94a24-35，其中亚里士多德解释了与物质因果关系相关的相同几何命题之间的关系。