Plato’s Theaetetus, Sophist, and Statesman exhibit several related dialectical methods relevant to Platonic education: maieutic in Theaetetus, bifurcatory division in Sophist and Statesman, and non-bifurcatory division in Statesman, related to the ‘god-given’ method in Philebus. I consider the nature of each method through the letter or element (στοιχεῖον) paradigm, used to reflect on each method. At issue are the element’s appearances in given contexts, its fitness for communing with other elements like it in kind, and its own nature defined through its relations to others. These represent stages of inquiry for the Platonic student inquiring into the sources of knowledge.
{"title":"Dialectical Methods and the Stoicheia Paradigm in Plato’s Trilogy and Philebus","authors":"Colin C. Smith","doi":"10.14195/2183-4105_19_1","DOIUrl":"https://doi.org/10.14195/2183-4105_19_1","url":null,"abstract":"Plato’s Theaetetus, Sophist, and Statesman exhibit several related dialectical methods relevant to Platonic education: maieutic in Theaetetus, bifurcatory division in Sophist and Statesman, and non-bifurcatory division in Statesman, related to the ‘god-given’ method in Philebus. I consider the nature of each method through the letter or element (στοιχεῖον) paradigm, used to reflect on each method. At issue are the element’s appearances in given contexts, its fitness for communing with other elements like it in kind, and its own nature defined through its relations to others. These represent stages of inquiry for the Platonic student inquiring into the sources of knowledge.","PeriodicalId":53756,"journal":{"name":"Plato Journal","volume":"1 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2019-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66679675","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}
{"title":"[Recensão a] Plato and the Power of Images. By Pierre Destrée and Radcliffe G. Edmonds III (ed.). Leiden: Brill 2017. Pp. 243.","authors":"Jana Schultz","doi":"10.14195/2183-4105_19_5","DOIUrl":"https://doi.org/10.14195/2183-4105_19_5","url":null,"abstract":"https://doi.org/10.14195/2183-4105_19_5","PeriodicalId":53756,"journal":{"name":"Plato Journal","volume":" ","pages":""},"PeriodicalIF":0.1,"publicationDate":"2019-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43971237","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}
In the final scene of the Euthydemus, Socrates argues that because the art of speechwriting merely partakes of the two good arts philosophy and politics, it places third in the contest for wisdom. I argue that this curious speech is a reverse eikos argument, directed at the speechwriters own eikos argument for the preeminence of their art. A careful analysis of the partaking relation reveals that it is rather Socratic dialectic which occupies this intermediate position between philosophy and politics. This result entails that Socrates’ peculiar art is only a part of philosophy, and its practitioner only partially wise.
{"title":"Socratic Dialectic between Philosophy and Politics in Euthydemus 305e5-306d1","authors":"Carrie Swanson","doi":"10.14195/2183-4105_19_3","DOIUrl":"https://doi.org/10.14195/2183-4105_19_3","url":null,"abstract":"In the final scene of the Euthydemus, Socrates argues that because the art of speechwriting merely partakes of the two good arts philosophy and politics, it places third in the contest for wisdom. I argue that this curious speech is a reverse eikos argument, directed at the speechwriters own eikos argument for the preeminence of their art. A careful analysis of the partaking relation reveals that it is rather Socratic dialectic which occupies this intermediate position between philosophy and politics. This result entails that Socrates’ peculiar art is only a part of philosophy, and its practitioner only partially wise.","PeriodicalId":53756,"journal":{"name":"Plato Journal","volume":" ","pages":""},"PeriodicalIF":0.1,"publicationDate":"2019-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48471810","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}
The paper analyzes the final proof with Greek mathematics and the possibility of intermediates in the Phaedo. The final proof in Plato’s Phaedo depends on a claim at 105c6, that μονάς, ‘unit’, generates περιττός ‘odd’ in number. So, ψυχή ‘soul’ generates ζωή ‘life’ in a body, at 105c10-11. Yet commentators disagree how to understand these mathematical terms and their relation to the soul in Plato’s arguments. The Greek mathematicians understood odd numbers in one of two ways: either that which is not divisible into two equal parts, or that which differs from an even number by a unit. (Euclid VII.7) Plato uses the second way in the final proof. This paper argues that a proper understanding of these mathematical terms within Greek mathematics shows that the argument for the final proof is better than previously thought. Such an interpretation of the final proof lends credence to Platonic intermediates.
{"title":"Μονάς and ψυχή in the Phaedo","authors":"Sophia A. Stone","doi":"10.14195/2183-4105_18_5","DOIUrl":"https://doi.org/10.14195/2183-4105_18_5","url":null,"abstract":"The paper analyzes the final proof with Greek mathematics and the possibility of intermediates in the Phaedo. The final proof in Plato’s Phaedo depends on a claim at 105c6, that μονάς, ‘unit’, generates περιττός ‘odd’ in number. So, ψυχή ‘soul’ generates ζωή ‘life’ in a body, at 105c10-11. Yet commentators disagree how to understand these mathematical terms and their relation to the soul in Plato’s arguments. The Greek mathematicians understood odd numbers in one of two ways: either that which is not divisible into two equal parts, or that which differs from an even number by a unit. (Euclid VII.7) Plato uses the second way in the final proof. This paper argues that a proper understanding of these mathematical terms within Greek mathematics shows that the argument for the final proof is better than previously thought. Such an interpretation of the final proof lends credence to Platonic intermediates.","PeriodicalId":53756,"journal":{"name":"Plato Journal","volume":" ","pages":""},"PeriodicalIF":0.1,"publicationDate":"2018-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48704032","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}
Broadly speaking, something can be called intermediate for Plato insofar as it occupies a place between two objects, poles, places, time, or principles. But this broad meaning of the intermediate has been eclipsed by the Aristotelian critique of the intermediate objects of the dianoia, so that it has become more difficult to think of the intermediates as functions of the soul. The aim of this paper is to show how, in the Republic, thumos is analogously treated as an intermediate with other kinds of intermediate objects, and tentatively to relate this psychological intermediate in a broader theory with doxa, as its epistemological ground in the course of action.
{"title":"Thumos and doxa as intermediates in the Republic","authors":"O. Renaut","doi":"10.14195/2183-4105_18_6","DOIUrl":"https://doi.org/10.14195/2183-4105_18_6","url":null,"abstract":"Broadly speaking, something can be called intermediate for Plato insofar as it occupies a place between two objects, poles, places, time, or principles. But this broad meaning of the intermediate has been eclipsed by the Aristotelian critique of the intermediate objects of the dianoia, so that it has become more difficult to think of the intermediates as functions of the soul. The aim of this paper is to show how, in the Republic, thumos is analogously treated as an intermediate with other kinds of intermediate objects, and tentatively to relate this psychological intermediate in a broader theory with doxa, as its epistemological ground in the course of action.","PeriodicalId":53756,"journal":{"name":"Plato Journal","volume":" ","pages":""},"PeriodicalIF":0.1,"publicationDate":"2018-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49606995","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}
{"title":"The Problem of Intermediates, an Introduction","authors":"N. Baima","doi":"10.14195/2183-4105_18_3","DOIUrl":"https://doi.org/10.14195/2183-4105_18_3","url":null,"abstract":"https://doi.org/10.14195/2183-4105_18_3","PeriodicalId":53756,"journal":{"name":"Plato Journal","volume":" ","pages":""},"PeriodicalIF":0.1,"publicationDate":"2018-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49452624","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}
In Metaphysics B.2 and M.2, Aristotle gives a series of arguments against Platonic mathematical objects. On the view he targets, mathematicals are substances somehow intermediate between Platonic forms and sensible substances. I consider two closely related passages in B2 and M.2 in which he argues that Platonists will need intermediates not only for geometry and arithmetic, but also for the so-called mixed mathematical sciences (mechanics, harmonics, optics, and astronomy), and ultimately for all sciences of sensibles. While this has been dismissed as mere polemics, I show that the argument is given in earnest, as Aristotle is committed to its key premises. Further, the argument reveals that Annas’ uniqueness problem (1975, 151) is not the only reason a Platonic ontology needs intermediates (according to Aristotle). Finally, since Aristotle’s objection to intermediates for the mixed mathematical sciences is one he takes seriously, so that it is unlikely that his own account of mathematical objects would fall prey to it, the argument casts doubt on a common interpretation of his philosophy of mathematics.
{"title":"The Mixed Mathematical Intermediates","authors":"E. Katz","doi":"10.14195/2183-4105_18_7","DOIUrl":"https://doi.org/10.14195/2183-4105_18_7","url":null,"abstract":"In Metaphysics B.2 and M.2, Aristotle gives a series of arguments against Platonic mathematical objects. On the view he targets, mathematicals are substances somehow intermediate between Platonic forms and sensible substances. I consider two closely related passages in B2 and M.2 in which he argues that Platonists will need intermediates not only for geometry and arithmetic, but also for the so-called mixed mathematical sciences (mechanics, harmonics, optics, and astronomy), and ultimately for all sciences of sensibles. While this has been dismissed as mere polemics, I show that the argument is given in earnest, as Aristotle is committed to its key premises. Further, the argument reveals that Annas’ uniqueness problem (1975, 151) is not the only reason a Platonic ontology needs intermediates (according to Aristotle). Finally, since Aristotle’s objection to intermediates for the mixed mathematical sciences is one he takes seriously, so that it is unlikely that his own account of mathematical objects would fall prey to it, the argument casts doubt on a common interpretation of his philosophy of mathematics.","PeriodicalId":53756,"journal":{"name":"Plato Journal","volume":" ","pages":""},"PeriodicalIF":0.1,"publicationDate":"2018-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43355364","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}
In this paper, I examine the problem of the so-called Mathematical Objects within the context of the Divided Line. I argue that Plato believes that there are such objects but their distinctness and the mode of cognition relative to them can only be understood in relation to the superordinate, unhypothetical first principle of all, the Idea of the Good. The objects of mathematics or διάνοια are, unlike the objects of intellection or νόησις, cognized independently of the Good.
{"title":"What are the Objects of Dianoia?","authors":"L. Gerson","doi":"10.14195/2183-4105_18_4","DOIUrl":"https://doi.org/10.14195/2183-4105_18_4","url":null,"abstract":"In this paper, I examine the problem of the so-called Mathematical Objects within the context of the Divided Line. I argue that Plato believes that there are such objects but their distinctness and the mode of cognition relative to them can only be understood in relation to the superordinate, unhypothetical first principle of all, the Idea of the Good. The objects of mathematics or διάνοια are, unlike the objects of intellection or νόησις, cognized independently of the Good.","PeriodicalId":53756,"journal":{"name":"Plato Journal","volume":" ","pages":""},"PeriodicalIF":0.1,"publicationDate":"2018-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47933449","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}
Many have argued that Plato’s intermediates are not independent entities. Rather, they exemplify the incapacity of discursive thought (διάνοια) to cognizing Forms. But just what does this incapacity consist in? Any successful answer will require going beyond the intermediates themselves to another aspect of Plato’s mathematical thought - his attribution of a quasi-numerical structure to Forms (the ‘eidetic numbers’). For our purposes, the most penetrating account of eidetic numbers is Jacob Klein’s, who saw clearly that eidetic numbers are part of Plato’s inquiry into the ontological basis for all counting: the existence of a plurality of formal elements, distinct yet combinable into internally articulate unities. However, Klein’s study of the Sophist reveals such articulate unities as imperfectly countable and therefore opaque to διάνοια. And only this opacity, I argue, successfully explains the relationship of intermediates to Forms.
{"title":"From Intermediates through Eidetic Numbers: Plato on the Limits of Counting","authors":"Andy R. German","doi":"10.14195/2183-4105_18_9","DOIUrl":"https://doi.org/10.14195/2183-4105_18_9","url":null,"abstract":"Many have argued that Plato’s intermediates are not independent entities. Rather, they exemplify the incapacity of discursive thought (διάνοια) to cognizing Forms. But just what does this incapacity consist in? Any successful answer will require going beyond the intermediates themselves to another aspect of Plato’s mathematical thought - his attribution of a quasi-numerical structure to Forms (the ‘eidetic numbers’). For our purposes, the most penetrating account of eidetic numbers is Jacob Klein’s, who saw clearly that eidetic numbers are part of Plato’s inquiry into the ontological basis for all counting: the existence of a plurality of formal elements, distinct yet combinable into internally articulate unities. However, Klein’s study of the Sophist reveals such articulate unities as imperfectly countable and therefore opaque to διάνοια. And only this opacity, I argue, successfully explains the relationship of intermediates to Forms.","PeriodicalId":53756,"journal":{"name":"Plato Journal","volume":" ","pages":""},"PeriodicalIF":0.1,"publicationDate":"2018-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47825178","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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