It is widely assumed that a geometric model of boundaries, which prescribes a tripartite topological characterisation of the boundaries for material objects – fully open, fully closed, or partially open/closed – can be unproblematically extended from regions to material objects. Drawing on a disanalogy between regions and material objects – that only the latter move – I demonstrate the incoherence of (fully or partially) open material objects through two arguments relating to the ability for such objects to freely move. The first is a dilemma considering separately open material objects occupying their location directly or indirectly (located in virtue of their proper parts occupying locations). It is argued that movement in the former case would involve a miraculous topological transformation; whilst in the latter case, would involve miraculous reorganising movements in the object's proper parts. The second argument reignites a problem regarding the moment of change specifically for the movement of such objects.

中文翻译：

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运动的新悖论：反对开放边界的物质对象

人们普遍认为，边界几何模型规定了物质对象边界的三方拓扑特征——完全开放、完全封闭或部分开放/封闭——可以毫无问题地从区域扩展到物质对象。借鉴区域和物质对象之间的不相似——只有后者会移动——我通过两个与此类对象自由移动能力有关的论点来证明（完全或部分）开放的物质对象的不连贯性。第一个是考虑单独打开的物质对象直接或间接占据它们的位置（根据它们的适当部分占据位置而定位）的困境。有人认为，前一种情况下的运动将涉及神奇的拓扑变换；而在后一种情况下，将涉及到对象适当部分的奇迹般的重组运动。第二个论点重新引发了一个关于专门针对此类物体运动的变化时刻的问题。