ABSTRACT

According to an influential line of argument, the past must be finite because no infinite series can be formed by successive addition. The present paper pinpoints the non sequitur at the heart of this argument, disentangles the ambiguities that disguise it, and dismantles the misleading picture of ‘traversing the infinite’ that gives the argument so much of its allure. Finally, the paper critically explores the related argument that a beginningless series of past events is impossible because there could be no explanation of its having been ‘completed’ at one time rather than another.

中文翻译：

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无穷大、时间和连续加法

摘要

根据一个有影响力的论点，过去一定是有限的，因为连续相加不能形成无限级数。本论文指出了这一论点的核心不合逻辑，解开了掩盖它的模棱两可，并消除了“穿越无限”的误导性画面，它赋予了该论点如此多的吸引力。最后，本文批判性地探讨了相关论点，即一系列无始的过去事件是不可能的，因为无法解释它是在某个时间而不是另一个时间“完成”的。