Abstract This paper offers a new reading of Heraclitus fragment B90 (Diels-Kranz). It argues that we can enrich our understanding of the fragment by reading it, not as a primitive analogy, but as a skillful simile grounded both in the poetic tradition and in the cultural context that would have conditioned its significance for Heraclitus and his audience. Read in this way, B90’s evocation of a cosmos whose common measure parallels the common measure of the polis’ marketplace is not simply a source of cosmological doctrine. It is also an epistemic challenge that threatens to undermine the very possibility of cosmology.
{"title":"Heraclitus on the Question of a Common Measure","authors":"S. Feldman","doi":"10.1515/rhiz-2023-0001","DOIUrl":"https://doi.org/10.1515/rhiz-2023-0001","url":null,"abstract":"Abstract This paper offers a new reading of Heraclitus fragment B90 (Diels-Kranz). It argues that we can enrich our understanding of the fragment by reading it, not as a primitive analogy, but as a skillful simile grounded both in the poetic tradition and in the cultural context that would have conditioned its significance for Heraclitus and his audience. Read in this way, B90’s evocation of a cosmos whose common measure parallels the common measure of the polis’ marketplace is not simply a source of cosmological doctrine. It is also an epistemic challenge that threatens to undermine the very possibility of cosmology.","PeriodicalId":40571,"journal":{"name":"Rhizomata-A Journal for Ancient Philosophy and Science","volume":"240 1","pages":"1 - 32"},"PeriodicalIF":0.0,"publicationDate":"2023-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75012077","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}
Abstract I have argued elsewhere that the idea that Aristotle aspired to improve the theories of the planetary motions of Eudoxus and Callippus by adding the ‘counteracting’ spheres (ἀνελίττουσαι) first emerged with the Peripatetic exegete Sosigenes in the second century CE. This paper supplements that argument by contrasting two major lines of interpretation of the astronomical system set out in Metaphysics Λ.8: Adrastus of Aphrodisias’ widely ahistorical account, and Sosigenes’ attempt to save Aristotle against later developments of astronomical science.
我曾在其他地方论述过，亚里士多德希望通过添加“抵消”球体(νελ到ττο ο σαι)来改进欧多克索斯和卡利普斯的行星运动理论，这种想法最早出现在公元2世纪的《逍遥经》注释者索西涅斯身上。本文通过对比《形而上学》Λ中对天文系统的两种主要解释来补充这一论点。8:阿德拉斯图斯的阿芙洛狄西亚的广泛的非历史的叙述，和索西涅斯试图拯救亚里士多德反对后来的天文科学的发展。
{"title":"Aristotle as an Astronomer? Sosigenes’ Account of Metaphysics Λ.8","authors":"Pantelis Golitsis","doi":"10.1515/rhiz-2023-0006","DOIUrl":"https://doi.org/10.1515/rhiz-2023-0006","url":null,"abstract":"Abstract I have argued elsewhere that the idea that Aristotle aspired to improve the theories of the planetary motions of Eudoxus and Callippus by adding the ‘counteracting’ spheres (ἀνελίττουσαι) first emerged with the Peripatetic exegete Sosigenes in the second century CE. This paper supplements that argument by contrasting two major lines of interpretation of the astronomical system set out in Metaphysics Λ.8: Adrastus of Aphrodisias’ widely ahistorical account, and Sosigenes’ attempt to save Aristotle against later developments of astronomical science.","PeriodicalId":40571,"journal":{"name":"Rhizomata-A Journal for Ancient Philosophy and Science","volume":"23 1","pages":"126 - 137"},"PeriodicalIF":0.0,"publicationDate":"2023-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87341772","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}
Abstract This paper considers some aspects of the early conception and use of the infinite in ancient Greece, in the spirit of recent results in the history of ancient mathematics. It follows aspects of the practice of reasoning ad infinitum from the extant corpus of and about Zeno of Elea up to early Hellenistic examples in Aristotle and Euclid. Starting with the idea of ‘reasoning from indefinite iteration’, based on the metalogical recognition of the unachievability of an inference process, it identifies several different classes of more or less sophisticated arguments that make use of this idea, and examines the logical devices and notions required for their acceptance in the philosophical practice. Those include ‘Infinite regress’ properly speaking, where Non-Contradiction is used in the formation of indirect infinitary arguments.
{"title":"From Zeno ad infinitum: Iterative Reasonings in Early Greek Philosophy","authors":"Pierrot Seban","doi":"10.1515/rhiz-2023-0002","DOIUrl":"https://doi.org/10.1515/rhiz-2023-0002","url":null,"abstract":"Abstract This paper considers some aspects of the early conception and use of the infinite in ancient Greece, in the spirit of recent results in the history of ancient mathematics. It follows aspects of the practice of reasoning ad infinitum from the extant corpus of and about Zeno of Elea up to early Hellenistic examples in Aristotle and Euclid. Starting with the idea of ‘reasoning from indefinite iteration’, based on the metalogical recognition of the unachievability of an inference process, it identifies several different classes of more or less sophisticated arguments that make use of this idea, and examines the logical devices and notions required for their acceptance in the philosophical practice. Those include ‘Infinite regress’ properly speaking, where Non-Contradiction is used in the formation of indirect infinitary arguments.","PeriodicalId":40571,"journal":{"name":"Rhizomata-A Journal for Ancient Philosophy and Science","volume":"10 1","pages":"33 - 54"},"PeriodicalIF":0.0,"publicationDate":"2023-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82842886","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}
Abstract This paper offers a fresh examination of a salient distinction located at the beginning of the Affinity Argument between the composite (τὸ σύνθετον) and the incomposite (τὸ ἀσύνθετον). I offer reasons for why Plato may have intended for us to assume that the soul is an incomposite unity in its essential nature. I then substantiate this claim by reviving an ancient interpretation to the Affinity Argument according to which the soul is of the same metaphysical kind as the Forms. I thus suggest that the argument may be seen as supporting the basic indestructibility cum immortality of all souls.
{"title":"Reconsidering the Essential Nature and Indestructibility of the Soul in the Affinity Argument of the Phaedo","authors":"Stephanos Stephanides","doi":"10.1515/rhiz-2023-0004","DOIUrl":"https://doi.org/10.1515/rhiz-2023-0004","url":null,"abstract":"Abstract This paper offers a fresh examination of a salient distinction located at the beginning of the Affinity Argument between the composite (τὸ σύνθετον) and the incomposite (τὸ ἀσύνθετον). I offer reasons for why Plato may have intended for us to assume that the soul is an incomposite unity in its essential nature. I then substantiate this claim by reviving an ancient interpretation to the Affinity Argument according to which the soul is of the same metaphysical kind as the Forms. I thus suggest that the argument may be seen as supporting the basic indestructibility cum immortality of all souls.","PeriodicalId":40571,"journal":{"name":"Rhizomata-A Journal for Ancient Philosophy and Science","volume":"16 1","pages":"77 - 104"},"PeriodicalIF":0.0,"publicationDate":"2023-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83172870","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}
Abstract In Plato’s Gorgias, Socrates says to Callicles that “your love of the people, existing in your soul, stands against me, but if we closely examine these same matters often and in a better way, you will be persuaded” (513c7–d1). I argue for an interpretation that explains how Socrates understands Callicles’s love of the people to stand against him and why he believes examination often and in a better way will persuade Callicles.
{"title":"Believing for Practical Reasons in Plato’s Gorgias","authors":"Thomas A. Blackson","doi":"10.1515/rhiz-2023-0005","DOIUrl":"https://doi.org/10.1515/rhiz-2023-0005","url":null,"abstract":"Abstract In Plato’s Gorgias, Socrates says to Callicles that “your love of the people, existing in your soul, stands against me, but if we closely examine these same matters often and in a better way, you will be persuaded” (513c7–d1). I argue for an interpretation that explains how Socrates understands Callicles’s love of the people to stand against him and why he believes examination often and in a better way will persuade Callicles.","PeriodicalId":40571,"journal":{"name":"Rhizomata-A Journal for Ancient Philosophy and Science","volume":"1 1","pages":"105 - 125"},"PeriodicalIF":0.0,"publicationDate":"2023-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91284539","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 : 2023-08-14DOI: 10.1515/rhiz-2023-frontmatter1
{"title":"Titelseiten","authors":"","doi":"10.1515/rhiz-2023-frontmatter1","DOIUrl":"https://doi.org/10.1515/rhiz-2023-frontmatter1","url":null,"abstract":"","PeriodicalId":40571,"journal":{"name":"Rhizomata-A Journal for Ancient Philosophy and Science","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135265490","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}
Abstract The paper explores the interrelations between Pindar, Heraclitus and the Hippocratic author with regard to ideas of the body, the soul and dreams. I shall consider Pindar’s fr.131b as an overlooked testimony of the poet’s interest in a non-Homeric conceptualization of the soul. I will suggest reading Heraclitus’ fragments B26 and B21 together and offer a new interpretation of the latter. Furthermore, I will compare Pindar’s fr. 131b with the Hippocratic On Regimen (4. 86, 87) and Pindar’s fr. 133 with On Regimen (4. 92) respectively, in order to highlight unnoticed similarities.
{"title":"Between Poetry, Philosophy and Medicine: Body, Soul and Dreams in Pindar, Heraclitus and the Hippocratic On Regimen.","authors":"C. R. Ciampa","doi":"10.1515/rhiz-2023-0003","DOIUrl":"https://doi.org/10.1515/rhiz-2023-0003","url":null,"abstract":"Abstract The paper explores the interrelations between Pindar, Heraclitus and the Hippocratic author with regard to ideas of the body, the soul and dreams. I shall consider Pindar’s fr.131b as an overlooked testimony of the poet’s interest in a non-Homeric conceptualization of the soul. I will suggest reading Heraclitus’ fragments B26 and B21 together and offer a new interpretation of the latter. Furthermore, I will compare Pindar’s fr. 131b with the Hippocratic On Regimen (4. 86, 87) and Pindar’s fr. 133 with On Regimen (4. 92) respectively, in order to highlight unnoticed similarities.","PeriodicalId":40571,"journal":{"name":"Rhizomata-A Journal for Ancient Philosophy and Science","volume":"11 1","pages":"55 - 76"},"PeriodicalIF":0.0,"publicationDate":"2023-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73647137","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}
Infinite regress arguments are a powerful tool in Aristotle, but this style of argument has received relatively little attention. Improving our understanding of infinite regress arguments has become pressing since recent scholars have pointed out that it is not clear whether Aristotle’s infinite regress arguments are, in general, effective or indeed what the logical structure of these arguments is. One obvious approach would be to hold that Aristotle takes infinite regress arguments to be per impossibile arguments, which derive an infinite sequence. Due to his finitism, Aristotle then rejects such a sequence as impossible. This paper argues that this obvious approach does not work, even for its most amenable cases. The paper argues instead that infinite regress arguments involve domain-specific infinities, and so there is not a general finitism which underpins infinite regress arguments in Aristotle, but rather domain-specific reasons that there cannot be an infinite number of entities in each domain in which Aristotle invokes an infinite regress argument.
{"title":"Infinite Regress Arguments as <b>\u0000 <i>per impossibile</i>\u0000 </b> Arguments in Aristotle: <b>\u0000 <i>De Caelo</i>\u0000 </b> 300<b>\u0000 <sup>a</sup>\u0000 </b>30–<b>\u0000 <sup>b</sup>\u0000 ","authors":"M. Duncombe","doi":"10.1515/rhiz-2022-0015","DOIUrl":"https://doi.org/10.1515/rhiz-2022-0015","url":null,"abstract":"\u0000 Infinite regress arguments are a powerful tool in Aristotle, but this style of argument has received relatively little attention. Improving our understanding of infinite regress arguments has become pressing since recent scholars have pointed out that it is not clear whether Aristotle’s infinite regress arguments are, in general, effective or indeed what the logical structure of these arguments is. One obvious approach would be to hold that Aristotle takes infinite regress arguments to be per impossibile arguments, which derive an infinite sequence. Due to his finitism, Aristotle then rejects such a sequence as impossible. This paper argues that this obvious approach does not work, even for its most amenable cases. The paper argues instead that infinite regress arguments involve domain-specific infinities, and so there is not a general finitism which underpins infinite regress arguments in Aristotle, but rather domain-specific reasons that there cannot be an infinite number of entities in each domain in which Aristotle invokes an infinite regress argument.","PeriodicalId":40571,"journal":{"name":"Rhizomata-A Journal for Ancient Philosophy and Science","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77315911","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}
Abstract On Malcolm Schofield’s highly influential reading of the Similarity Regress in Part I of the Parmenides, the problem that the Regress poses is explanatory. Socrates posited the Similarity Form in order to explain why similar things are similar: similar things are similar because they participate in the Form Similarity as copies of the same original. Yet, the Similarity Regress generates an infinite series of Similarity Forms such that explanation is deferred ad infinitum. Schofield provides a philosophical incentive for adopting his reading. He argues that the treatment of similarity in Part II of the dialogue yields a complete explanation of similarity. If we adopt this account, we can avoid the Similarity Regress altogether since a Form of Similarity is not needed in order to explain why similar things are similar. Thus, his interpretation has a hugely important philosophical pay-off. However, there is a different way to read the argument. Socrates claims that each Form is only one. Yet, the Similarity Regress is an argument that generates an infinite series of Similarity Forms. This results in a violation of the principle of non-contradiction: there is both only one Similarity Form and infinitely many Similarity Forms. Yet, anything that is incompatible with the principle of non-contradiction is surely absurd. Nobody, as far as I am aware, has explored whether this reading also has philosophical pay-off if we look at it together with similarity in Part II. However, should this interpretation pay off, it would be a viable alternative to Schofield’s. In this paper, I explore both views in the context of the treatment of similarity in Part II of the Parmenides. I argue for an account of similarity that differs from Schofield’s. Although my account is not wholly dismissive of Schofield’s, it renders the pay-off of Schofield’s account less appealing than he suggests. Furthermore, I show that the account of similarity in Part II also yields important lessons for the proponent of the alternative reading of the Similarity Regress: similarity as treated in Part II simply leads to further infinite regresses, thereby pushing us to consider rejecting the account of similarity in Part II too and to look for some other account intead.
{"title":"Regress? I’ve Had a Few?","authors":"Saloni de Souza","doi":"10.1515/rhiz-2022-0014","DOIUrl":"https://doi.org/10.1515/rhiz-2022-0014","url":null,"abstract":"Abstract On Malcolm Schofield’s highly influential reading of the Similarity Regress in Part I of the Parmenides, the problem that the Regress poses is explanatory. Socrates posited the Similarity Form in order to explain why similar things are similar: similar things are similar because they participate in the Form Similarity as copies of the same original. Yet, the Similarity Regress generates an infinite series of Similarity Forms such that explanation is deferred ad infinitum. Schofield provides a philosophical incentive for adopting his reading. He argues that the treatment of similarity in Part II of the dialogue yields a complete explanation of similarity. If we adopt this account, we can avoid the Similarity Regress altogether since a Form of Similarity is not needed in order to explain why similar things are similar. Thus, his interpretation has a hugely important philosophical pay-off. However, there is a different way to read the argument. Socrates claims that each Form is only one. Yet, the Similarity Regress is an argument that generates an infinite series of Similarity Forms. This results in a violation of the principle of non-contradiction: there is both only one Similarity Form and infinitely many Similarity Forms. Yet, anything that is incompatible with the principle of non-contradiction is surely absurd. Nobody, as far as I am aware, has explored whether this reading also has philosophical pay-off if we look at it together with similarity in Part II. However, should this interpretation pay off, it would be a viable alternative to Schofield’s. In this paper, I explore both views in the context of the treatment of similarity in Part II of the Parmenides. I argue for an account of similarity that differs from Schofield’s. Although my account is not wholly dismissive of Schofield’s, it renders the pay-off of Schofield’s account less appealing than he suggests. Furthermore, I show that the account of similarity in Part II also yields important lessons for the proponent of the alternative reading of the Similarity Regress: similarity as treated in Part II simply leads to further infinite regresses, thereby pushing us to consider rejecting the account of similarity in Part II too and to look for some other account intead.","PeriodicalId":40571,"journal":{"name":"Rhizomata-A Journal for Ancient Philosophy and Science","volume":"19 1","pages":"238 - 261"},"PeriodicalIF":0.0,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73866512","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}
Abstract This paper discusses two broadly logical issues related to Protagoras’ measure doctrine (M) and the self-refutation argument (SRA). First, I argue that the relevant interpretation of (M) has it that every individual human being determines all her own truths, including the truth of (M) itself. I then turn to what I take to be the most important move in the SRA: that Protagoras recognises not only that his opponents disagree with him about the truth of (M), but also that they hold that (M) is false simpliciter. By recognising that his opponents do not make the relativising concession he makes for them, he is forced to accept that (M) is false. I go on to argue that several other defenders of the SRA end up with a regress which is difficult to end and might not favour anti-Protagoreans. On my reading, by recognising what his opponents believe, Protagoras is barred from adding qualifiers, and the possible regress doesn’t get off the ground. I conclude with brief discussions of how Protagoras might try to avoid the result of the SRA and the argument’s role in this part of the Theaetetus.
{"title":"Logical Oddities in Protagorean Relativism","authors":"Evan Keeling","doi":"10.1515/rhiz-2022-0013","DOIUrl":"https://doi.org/10.1515/rhiz-2022-0013","url":null,"abstract":"Abstract This paper discusses two broadly logical issues related to Protagoras’ measure doctrine (M) and the self-refutation argument (SRA). First, I argue that the relevant interpretation of (M) has it that every individual human being determines all her own truths, including the truth of (M) itself. I then turn to what I take to be the most important move in the SRA: that Protagoras recognises not only that his opponents disagree with him about the truth of (M), but also that they hold that (M) is false simpliciter. By recognising that his opponents do not make the relativising concession he makes for them, he is forced to accept that (M) is false. I go on to argue that several other defenders of the SRA end up with a regress which is difficult to end and might not favour anti-Protagoreans. On my reading, by recognising what his opponents believe, Protagoras is barred from adding qualifiers, and the possible regress doesn’t get off the ground. I conclude with brief discussions of how Protagoras might try to avoid the result of the SRA and the argument’s role in this part of the Theaetetus.","PeriodicalId":40571,"journal":{"name":"Rhizomata-A Journal for Ancient Philosophy and Science","volume":"16 1","pages":"215 - 237"},"PeriodicalIF":0.0,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89630499","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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