This paper studies John Buridan's octagons of opposition for the de re modal propositions and the propositions of unusual construction. Both Buridan himself and the secondary literature have emphasized the strong similarities between these two octagons (as well as a third one, for propositions with oblique terms). In this paper, I argue that the interconnection between both octagons is more subtle than has previously been thought: if we move beyond the Aristotelian relations, and also take Boolean considerations into account, then the strong analogy between Buridan's octagons starts to break down. These differences in Boolean structure can already be discerned within the octagons themselves; on a more abstract level, they lead to these two octagons having different degrees of Boolean complexity (i.e. Boolean closures of different sizes). These results are obtained by means of bitstring analysis, which is one of the key tools from contemporary logical geometry. Finally, I argue that this historical investigation is directly relevant for the theoretical framework of logical geometry, and discuss how it helps us to address certain open questions in this framework.

中文翻译：

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对约翰布里丹八边形对立的布尔考量

本文研究了约翰·布里丹 (John Buridan) 对 de re modal 命题和不寻常构造命题的对立八边形。布里丹本人和二级文献都强调了这两个八边形（以及第三个八边形，用于带有斜项的命题）之间的强烈相似性。在本文中，我认为两个八边形之间的相互联系比以前认为的更微妙：如果我们超越亚里士多德的关系，同时考虑布尔因素，那么布里丹八边形之间的强类比就开始失效。布尔结构的这些差异已经可以在八边形本身中辨别出来；在更抽象的层面上，它们导致这两个八边形具有不同程度的布尔复杂性（即不同大小的布尔闭包）。这些结果是通过位串分析获得的，位串分析是当代逻辑几何的关键工具之一。最后，我认为这项历史调查与逻辑几何的理论框架直接相关，并讨论它如何帮助我们解决该框架中的某些开放性问题。