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Dialectical Methods and the Stoicheia Paradigm in Plato's Trilogy And University of Kentucky UKnowledge Philosophy Graduate Research Philosophy 7-15-2019 Dialectical Methods and the Stoicheia Paradigm in Plato’s Trilogy and Philebus Colin C. Smith University of Kentucky Follow this and additional works at: https://uknowledge.uky.edu/philosophy_gradpub Part of the Philosophy Commons Right click to open a feedback form in a new tab to let us know how this document benefits ou.y Repository Citation Smith, Colin C., "Dialectical Methods and the Stoicheia Paradigm in Plato’s Trilogy and Philebus" (2019). Philosophy Graduate Research. 1. https://uknowledge.uky.edu/philosophy_gradpub/1 This Article is brought to you for free and open access by the Philosophy at UKnowledge. It has been accepted for inclusion in Philosophy Graduate Research by an authorized administrator of UKnowledge. For more information, please contact [email protected]. Dialectical Methods and the Stoicheia Paradigm in Plato’s Trilogy and Philebus Digital Object Identifier (DOI) https://doi.org/10.14195/2183-4105_19_1 Notes/Citation Information Published in Plato Journal, v. 19. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows sharing the work with recognition of authorship and initial publication in Plato Journal. This article is available at UKnowledge: https://uknowledge.uky.edu/philosophy_gradpub/1 COLIN C. SMITH | 9 Dialectical Methods and the Stoicheia Paradigm in Plato’s Trilogy and Philebus Colin C. Smith The University of Kentucky [email protected] 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. Keywords: method, metaphysics, epistemology, ontology https://doi.org/10.14195/2183-4105_19_1 10 | Dialectical Methods and the Stoicheia Paradigm in Plato’s Trilogy and Philebus I. INTRODUCTION ters, including in key moments in the Republic, and the speakers draw on this paradigm in the While Plato’s Theaetetus, Sophist, and States- dramatic moments in the near vicinity of each man dialogues bear clear narrative and dramatic methodological change in the trilogy.7 Thus the kinships, the relationship of the philosophical letter paradigm offers a fixed point of orienta- methods depicted in each is unclear.1 The two- tion for considering the nature of each of the day period of discussion in which the dialogues three methods.8 At issue in these changes are, are set begins with Socrates’ maieutic inquiry among other things, the notion of the element into the views of the young mathematician The- as part, its role in composing a whole, its rec- aetetus and concludes with the Eleatic Stranger’s ognizability as such, its appearances in given diairetic account of the statesman as a determi- contexts, its fitness for communing with other nate moment in the care for the human com- elements like it in kind, and its own nature as munity. This dramatic procession raises many defined by its relations to others like it in kind. questions, such as those of why Plato chose to Ultimately, I argue that the methodological link together dramatically these dialectical exer- changes in the trilogy map onto three senses of cises, whether and how one method or dialogue account (λόγος) through which knowledge is acts as a proleptic anticipation of another, and attained. These roughly correspond to the three what sense, if any, we can make of their unity.2 senses of account at issue late in the Theaetetus In what follows, I seek to offer the beginning (Theait. 206 d 1 - 208 d 9). In his final defini- of an answer to these by arguing that Plato’s tril- tion of knowledge, Theaetetus hypothesizes that ogy exhibits a series of related methods of inqui- knowledge is “true opinion with an account” ry into the sources of knowledge, representing a (Plat., Theait. 201 c 8.)9 Socrates then consid- set of dialectical exercises relevant to a Platonic ers three possible senses of ‘account,’ which, I education and the increasing philosophical ma- argue, correspond to the methodological moves turity of the student.3 These methods include made throughout the dialogues composing the the maieutic method depicted in the Theaetetus, trilogy. The first type of account Socrates con- the method of bifurcatory division initiated in siders is that in which one makes “one’s thought the Sophist and partially continued in the States- apparent vocally by means of words and verbal man, and the method of non-bifurcatory divi- expressions […] like reflections upon water sion employed by the Stranger in the second half or in a mirror” (Plat., Theait. 206 d 1-4). This of the Statesman.4 Since the Stranger does not type of account is closely related to the maieutic make the aim of this final method clear, I will method in the Theaetetus, insofar as the task in here consider it with reference to the method of maieutic is to externalize the internal by reflect- inquiry described in the Philebus and referred to ing thought in an account, exposing it in its na- in the literature as the ‘god-given method.’5 ture and presenting it for scrutiny. At issue in It is difficult to track these large shifts in lim- the Sophist and Statesman will be the latter two ited space. To understand these methods and types of account that Socrates identifies. The their relation to one another, we will here follow second is the account that entails “being able, the guidance offered by the paradigm of letters when questioned about what a thing is, to give or elements (στοιχεῖα) in each instance.6 Plato an answer by reference to its elements” (Plat., frequently has his primary interlocutors make Theait.206 e 10 – 207 d 2), which will be at stake epistemological moves with reference to let- in the non-bifurcatory divisions of the States- COLIN C. SMITH | 11 man. The third, “being able to tell some mark packing the entailments of each hypothesis. In by which the object you are asked about differs other words, Socrates uses the maieutic method from all other things” (Plat., Theait. 208 c 8-9), as a means of assisting the interlocutor in the anticipates the aim of the Stranger in practic- production of the account already implicit in ing bifurcatory division in the Sophist and early the interlocutor’s own thinking. Statesman.10 I suggest that these three types of The maieutic method used in the dialogue account represent three stages of inquiry for the contrasts with a discussion of mathematical student of Platonic philosophy inquiring into knowledge early in the text. This discussion the sources of knowledge and her means of no- points beyond itself to the next step necessary etically grasping them with reference to parts after maieutic, although the interlocutors will constitutive of wholes and co-constituted by not take it up until the dramatically later dia- other parts like them in kind. logues. In his discussion of mathematical pow- ers (Plat., Theait. 147 d 3 – 148 b 4), Theaetetus describes his goal of understanding the oneness II. MAIEUTIC IN THE inherent in many mathematical objects and ac- THEAETETUS counting for the objects with reference to this oneness. This is what he calls the attempt to In the Theaetetus, the interlocutors seek “gather together [the powers in question] into a satisfying account of knowledge through some one [term], [to] which we could address Socrates’ familiar question and answer process. our speech”.13 In other words, Theaetetus’ goal Socrates here acts in the role of the midwife, and in this mathematical study is to understand he reflects on the maieutic method (Plat., Theait. many in terms of their sameness, or to account 149 a 1 – 151 d 5) by describing it as helping for the one inherent in many. But Theaetetus the interlocutor to make progress by “discover- ultimately fails to find a way to turn this math- ing and bringing forth many beautiful things ematical method of gathering and sorting into themselves out of themselves” (Plat., Theait. an account of the means by which knowledge 150 d 5-9).11 This corresponds to Socrates’ later is attained. consideration of one sense of account as making The maieutic method is useful insofar as “thought apparent vocally by means of words it acts as a propaedeutic to more systematic and verbal expressions […] like reflections upon studies. The seeming aporia inherent in the water or in a mirror” (Plat., Theait. 206 d 1-4). dialogue’s conclusion is in fact provocative of He describes the ‘birthing’ process as leading to further considerations, and suggests ways in the subsequent test of the result in terms of its which Socrates’ three conceptions of ‘account’ truth or falsity (Plat., Theait 150 c 1-5). In these anticipate the turns taken the next day in the ways, the maieutic method entails externalizing Sophist and Statesman.14 The key to allowing the the internal by submitting the internal to an ac- aporia to provoke further studies lies in con- count, and hence to scrutiny. With these goals sidering the moves that Socrates and Theaete- in mind, Socrates limits his involvement to tus make after hypothesizing that knowledge helping to give birth to the ideas of Theaetetus, is “true opinion with an account”.
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