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Infinitesimal Gunk
Journal of Philosophical Logic ( IF 0.7 ) Pub Date : 2020-01-22 , DOI: 10.1007/s10992-020-09544-x
Lu Chen

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:

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。
更新日期:2020-01-22
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