Spacetime gaps and the persistence of objects through time

When we begin to investigate the persistence of objects through time, we find immediately that the sort of concerns embodied in Leibniz's Law cause philosophers to divide themselves into the two major camps of Purdurantists and Endurantists. What is required according to each for a given object at a given time to be identified with a given object at another time is held to be dramatically different, even while both often look to the same general sort of indicators for their answers to identity questions: identity or similarity of physical properties, including relational properties like spatial location. I believe, however, that logically prior to the problem of the persistence of objects through time will be questions regarding the composition of objects--we must have coherent notions of what an object is, what it means for parts to compose an object, and what is required for an object to be considered to exist at a single time before we can discuss the continued existence of objects at other times. I believe that posing the problem of temporal gaps for both the Perdurantist and Endurantist to solve can help us uncover reasonable answers to these more basic questions, and thereby help us judge the comparative coherence of the parent theories. Towards this goal, we investigate here some of the assumptions of persistence theories--that Perdurantists are four-dimensionalists and Endurantists are Presentists, for example--before moving on to find reasonable explanations of the composition of objects from within each theory. Important at this stage is clarifying such concepts as parthood and the present. When we at length turn our attention to the problem of gaps, it becomes useful to distinguish two sorts of gaps, each with their own difficulties: a 'gap' as a length of time during which the proper parts of an object are scattered through space, and a 'gap' as a length of time during which the proper parts of an object do not exist in space at all. My contention here is that Perdurantism, paired with four-dimensional spacetime, provides the most coherent answers to the challenges presented throughout.
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