In this paper, I advance an original view of the structure of space called Infinitesimal Gunk . This view says that every region of space can be further divided and some regions have infinitesimal size, where infinitesimals are understood in the framework of Robinson’s ( 1966 ) nonstandard analysis. This view, I argue, provides a novel reply to the inconsistency arguments proposed by Arntzenius ( 2008 ) and Russell ( 2008 ), which have troubled a more familiar gunky approach. Moreover, it has important advantages over the alternative views these authors suggested. Unlike Arntzenius’s proposal, it does not introduce regions with no interior. It also has a much richer measure theory than Russell’s proposal and does not retreat to mere finite additivity.

中文翻译：

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无限小黏性

在这篇论文中，我提出了一个名为 Infinitesimal Gunk 的空间结构的原始观点。这种观点认为，空间的每个区域都可以进一步划分，有些区域的尺寸是无穷小的，在罗宾逊 (1966) 非标准分析的框架中可以理解无穷小。我认为，这种观点为 Arntzenius (2008) 和 Russell (2008) 提出的不一致论点提供了一个新颖的回答，这些论点困扰了更熟悉的笨拙方法。此外，与这些作者建议的替代观点相比，它具有重要的优势。与 Arntzenius 的提议不同，它没有引入没有内部的区域。它还有比罗素的提议更丰富的测度理论，并且不会退回到单纯的有限可加性。