Pub Date : 2023-11-10DOI: 10.1515/apeiron-2023-0006
Robby Finley
Abstract There are two distinct but interrelated questions concerning Aristotle’s account of infinity that have been the subject of recurring debate. The first of these, what I call here the interpretative question, asks for a charitable and internally coherent interpretation of the limited pieces of text where Aristotle outlines his view of the ‘potential’ (and not ‘actual’) infinite. The second, what I call here the philosophical question, asks whether there is a way to make Aristotle’s notion of the potential infinite coherent and rigorous with modern tools that can stand as a rival to the widely-accepted view of the infinite as characterized in a mathematical theory of sets. In this paper, I argue that the theoretical roles that Aristotle intends his account of the potential infinite to fulfill lead to a deep and irresoluble tension that can help explain the persistence of debates on both of these questions. I do so by turning to the places where Aristotle attempts to argue for or against the existence of particular infinite processes to show that he slides between different underlying notions of when changes are possible. Making these underlying notions clear can help us better understand the role of Aristotle’s account in the history of philosophy, the possible pitfalls for a contemporary theory of the potential infinite, and what each of these debates might learn from each other.
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Pub Date : 2023-11-10DOI: 10.1515/apeiron-2023-0030
Sarale Ben-Asher
Abstract The paper offers a new reading of the argument against poetry in Republic 10. I argue that Socrates’ corruption charges rely on the tripartite theory of the soul, and that metaphysical doctrines play a role only in the first charge, which demonstrates that the poets are not qualified to teach by reducing tragic poetry to mimetic skill. This accusation clears the way for two corruption charges: the strengthening of appetite, and the softening of spirit (i.e., ‘the greatest charge’). The former focuses on the dangerous association between the poets and the largest appetitive class in the city ( hoi polloi ), while the latter focuses on the corruption of the educated elite ( hoi epieikeis ).
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Pub Date : 2023-11-06DOI: 10.1515/apeiron-2023-0049
Nena Bobovnik
Abstract In the Timaeus, Plato famously acknowledges the receptacle as extremely difficult to comprehend. It is neither intelligible (which is reserved exclusively for the Forms) nor sense-perceptible (as it is a principle far too basic). Instead, as Plato proposes, the receptacle can only be apprehended through a “bastard” sort of “reasoning” (νόθος λογισμός, Tim. 52b1-2.). This paper explores an exegesis of Plato’s claim as offered by Calcidius, the 4th century translator of and commentator on the Timaeus. I identify two distinctive methods Calcidius advances when grappling with the knowability of the material substratum that underpins our world. The first method – analysis (resolutio) – traces its intellectual lineage to earlier philosophical tradition, and Calcidius primarily uses it to uncover the proper nature and ontological characteristics of matter. Conversely, the second method corresponds to the only cognitive grasp of matter Calcidius believes humans are capable of. In his view, we can neither sense-perceive nor rationally understand matter. Instead, matter yields itself only to the cognitive mode of suspicion (suspicio). The paper provides a detailed analysis of Calcidius’ suspicio, delving into its intricacies and exploring the interrelationships between suspicio and resolutio. As such it offers a pioneering and comprehensive exploration of Calcidius’ account of the knowability of matter.
在《蒂迈奥篇》中，柏拉图著名地承认容器极其难以理解。它既不是可理解的(这是专门为形式保留的)，也不是可感觉的(因为它是一个太基本的原则)。相反，正如柏拉图所提出的，容器只能通过一种“杂种”的“推理”来理解(ν ο θος λογισμός， Tim. 52b1-2)。这篇论文探讨了由卡尔迪乌斯(caldius)提供的柏拉图主张的注释，卡尔迪乌斯是公元4世纪《蒂麦乌斯》的翻译家和评论员。我认为，在探究支撑我们世界的物质基础的可知性时，卡尔迪乌斯提出了两种不同的方法。第一种方法——分析(分解)——可以追溯到早期的哲学传统，卡尔迪乌斯主要用它来揭示物质的固有性质和本体论特征。相反，第二种方法对应于卡尔迪乌斯认为人类有能力的对物质的唯一认知把握。在他看来，我们既不能感知物质，也不能理性地理解物质。相反，物质只屈服于怀疑的认知模式(猜疑)。本文对卡尔迪乌斯的怀疑进行了详细的分析，深入探讨了其复杂性，并探讨了怀疑与解决之间的相互关系。因此，它提供了一个开创性的和全面的探索卡尔迪乌斯的可知性的物质的叙述。
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Pub Date : 2023-10-01DOI: 10.1515/apeiron-2023-frontmatter4
{"title":"Frontmatter","authors":"","doi":"10.1515/apeiron-2023-frontmatter4","DOIUrl":"https://doi.org/10.1515/apeiron-2023-frontmatter4","url":null,"abstract":"","PeriodicalId":42543,"journal":{"name":"Apeiron-A Journal for Ancient Philosophy and Science","volume":"122 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135656210","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-01DOI: 10.1515/apeiron-2023-frontmatter3
{"title":"Frontmatter","authors":"","doi":"10.1515/apeiron-2023-frontmatter3","DOIUrl":"https://doi.org/10.1515/apeiron-2023-frontmatter3","url":null,"abstract":"","PeriodicalId":42543,"journal":{"name":"Apeiron-A Journal for Ancient Philosophy and Science","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135453893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-29DOI: 10.1515/apeiron-2023-frontmatter2
{"title":"Frontmatter","authors":"","doi":"10.1515/apeiron-2023-frontmatter2","DOIUrl":"https://doi.org/10.1515/apeiron-2023-frontmatter2","url":null,"abstract":"","PeriodicalId":42543,"journal":{"name":"Apeiron-A Journal for Ancient Philosophy and Science","volume":"329 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135469339","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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