The Nature and Purpose of Relative Terms in Plato Matthew Duncombe Peterhouse Submitted for the degree of Doctor of Philosophy The Nature and Purpose of Relative Terms in Plato Matthew Duncombe Dissertation Summary Relative terms are those such as ‘larger’, ‘smaller’, ‘parent’ and ‘offspring’. Questions concerning the nature of this type of term in Plato fall under three themes. First, logic: what is the syntax and semantics of relative terms? Second, metaphysics: what structures in the world constitute relative properties? Third, taxonomy: do relative terms form a distinguishable class? Questions concerning purpose ask what role these terms have in the wider economy of Plato’s thought. Only one existing approach addresses all of these themes and questions: it was put forward by G.E.L. Owen in 1957, although it was subsequently developed by others. The Owenian view holds that relatives are syntactically or semantically incomplete, that they are identical to metaphysically dyadic relations and that they do form a taxonomic class. According to Owen, Plato introduces relative terms to bolster a certain argument for the separation of forms and participants. Therefore, they have an ontological purpose. This thesis aims to offer a plausible, non–anachronistic alternative to the Owenian view. To give such an account I have to argue for a radically different logic, metaphysics and purpose for relatives in Plato. I call the view that I defend ‘conjunctivism’. I begin by characterising the logic of conjunctivism. Plato holds that relative terms have formal objects. These are exceptionlessly correct objects of the relative in question. A parent is always and only parent of offspring, so ‘offspring’ is the formal object of ‘parent’. I then demonstrate that the metaphysical problems for relatives which are not dyadic relations are avoided by Plato’s version of conjunctivism. Looking at Sophist 255c–d and Parmenides 133c– 134e, I discuss the taxonomy of relative terms. I show that, under the conjunctive reading, they form a distinguishable class and, in contrast to Owenian relatives, each reciprocates with its correlative. So, just as a parent is relative to offspring, so offspring are relative to a parent. With the nature of relative terms established, I proceed to refute Owen’s account of their purpose, and give my own explanation. By looking at passages from the Euthydemus and Charmides, I argue that Plato introduced relative terms to articulate why some arguments are fallacies and others not. That is, relative terms have a dialectical purpose. iii Table of Contents Dissertation Summary iii Table of Contents iv Declaration and Acknowledgements vi Introduction 1 Mignucci 5 Castañeda 8 Chapter 1 14 1.1 The Owenian Reading 14 1.2 The Conjunctive Reading 17 1.3 An objection to the conjunctive reading 36 1.4 Passages where relatives are discussed 42 Conclusion 43 Chapter 2 45 2.1 Relatives in the partition argument 45 2.2 The role of relatives in the validity of the partition argument 55 2.3 Relatives and the denial of a Socratic paradox 60 Conclusion 66 Chapter 3 68 3.1 Terms or Predications? 68 3.2 An alternative term–based reading 74 3.3 Parmenides 133c–134e 78 3.4 The Classes as Reciprocal Relatives and Absolute Terms 88 3.5 The nature of reciprocation 92 Conclusion 95 Chapter 4 97 iv 4.1 Owen and the ‘Argument from Relativity’ 98 4.2 The Equals Argument 100 4.3 Context–sensitivity and relative terms 110 4.4 The Scope Objection 115 Conclusion 118 Chapter 5 121 5.1 Sophisms in the Euthydemus 122 5.2 Relatives in the Charmides 132 5.3 The Neutrality of the Relative/Non–relative distinction 139 5.4 Taxonomy and Categories 142 Conclusion 151 Conclusion 152 Relatives in Plato and Categories 7 156 Appendix 163 Bibliography 164 v Declaration and Acknowledgements This dissertation is the result of my own work and includes nothing which is the outcome of work done in collaboration except where specifically indicated in the text. It falls within the Faculty of Classics word limit of 80,000 words, including footnotes and appendices, but excluding the bibliography. Although required by the university’s regulations to state that this dissertation is the result of my own work, I am compelled by gratitude to acknowledge the help and support of many individuals and organisations over the last three and a half years. First and foremost is David Sedley, who not only suggested the topic of the dissertation, but who has provided enthusiastic support and encouragement for my academic endeavours as a graduate student. His penetrating understanding of ancient philosophy has, of course, improved almost every aspect of this dissertation and his assistance has gone far beyond the call of duty. But more importantly, through intellectual and practical guidance, David has opened up for me a whole world of philosophy, the pleasures of which I never imagined as a callow logician in training! For this and more, my warmest thanks. I must also acknowledge the support and assistance of my ancillary supervisors, Nick Denyer and Robert Wardy. Nick has been an inexhaustible source of humour, philosophical acumen and practical help throughout my PhD, and I owe him a great deal, as many of my footnotes attest. Early discussions with Robert profoundly shaped my thinking on this topic and on how to write a dissertation. He also gave me the invaluable advice to ‘read everything Gwil Owen ever wrote’. This dissertation was kindly funded by an AHRC studentship. I spent the academic year 2009–10 as a visiting student at the École Normale Supérieure in Paris, where the bulk of the research for Chapters 2 and 3 was carried out. I would like to thank the ENS and the Master and Fellows of Peterhouse, Cambridge for financial support during my stay and , of the ENS, and Dmitri El–Murr, of L'Université Paris I: Panthéon–Sorbonne, for their personal hospitality. I must also thank Philip Pattenden, Ted Buttrey, Nick Denyer (again) and Barrie Fleet, who gave up their time to read Greek with me over the last four years. The community of graduates in the B Caucus has been astonishingly welcoming and conducive to learning about ancient philosophy. It seems invidious to pick out individuals, but I must acknowledge Carol Atack, Ben Harriman, Christina Hoenig, Ailsa Hunt, Naoya Iwata, Dhananjay Jaganathan, Tamer Nawar, Maria Kilby, –Schluderer, Shaul Tor and Michael Withey, vi who helped the process of writing this dissertation in various ways: reading drafts; commenting on papers that contained key ideas; patiently listening while I reiterated the arguments of my dissertation and, in general, forcing me to try to keep up with their talent and intelligence! I owe my family and friends the most gratitude. My mum and dad supported my interest in philosophy far beyond the point where most parents would have insisted that I find a proper job, and this undertaking would not even have started, let alone been finished, without them. Anna Cant, Ramin Hassan and Jen Rouse have always been much better friends than I deserve, and especially so during the last few months. Finally, to Mabel Wale, my confidante, co– conspirator and comrade: thank you. vii viii Introduction Russell was famously pessimistic about Plato on relatives: ‘Plato is perpetually getting into trouble through not understanding relative terms. He thinks that if A is greater than B and less than C, that A is at once great and small, which seems to him a contradiction. Such troubles are among the infantile diseases of philosophy’.1 The view that Plato suffers from a logical colic was widespread. The ailment in question is the failure to grasp relative terms correctly, and those who diagnose it include, alongside Russell, some of the most serious scholars of Plato.2 The diagnosis deserves scrutiny; Russell implies not that Plato has a poor understanding of relative terms, but rather that he has no understanding of them at all. I aim to show that this claim is false: Plato does have an understanding of relative terms and it is quite developed. As it turns out, understanding Plato’s attitude towards relative terms is important for understanding his reasons for introducing the Forms, his attitude towards relativism and his relationship to the category ontologies that proliferated in the Academy after his lifetime. The quotation from Russell already suggests two areas for investigation. The first is the nature of relative terms in Plato. Russell implies that Plato does not have any clear understanding of them, since he gets into trouble through his failure to understand them. So does Plato even have a conception of relative terms? If so, how does he think of them? Indeed, what is supposed to be the relative term in Russell’s example: the individual, A, or the relation, being greater than? Could it be the property, being large? Or does Plato characterise relatives in a way that differs from all of these options? The second theme suggested by Russell’s quotation is the purpose of using relative terms: are they introduced simply to articulate a contradiction, as Russell seems to imply, or could they be used to avoid such contradictions? Maybe they have very little to do with contradiction and the idea that they have is an anachronistic retrojection of a conception of relations as dyadic properties. What other purposes could there be for Plato to introduce the concept of relative terms? This thesis takes up the two themes of the nature and purpose of relative terms in Plato. First, I will begin to map the intellectual territory concerning the nature of relatives, before going on to discuss how we might approach questions regarding their purpose.