Abstract

Plato describes a way of reasoning that comprises two complementary operations, collection and division. Collection unifies many into one while division divides one into many. In other words, while collection brings together many parts into a whole, division divides a whole into many parts. While Plato goes into some detail in his observations on collection and division, several questions remain unanswered. More specifically, the means by which collection and division operate, their product, and their relation to deductive and non-deductive reasoning are uncertain. The purpose of this study is to shed light on collection and division by defending the following thesis: collection and division define logical frameworks that underlie both deductive and non-deductive reasoning. Chapter 1 will introduce collection and division by reviewing recent literature, defining key terms, and discussing illustrations of collection and division in the dialogues. Chapter 2 will explain how collection and division define logical frameworks through three operations: seeing, naming, and placing. These operations will be discussed in terms of their relations to reasoning about wholes and parts. Chapter 3 will present four models for interpreting the logical structures that are produced by collection and division. It will present the argument that collection and division define non-hierarchical structures of overlapping parts. Chapter 4 will present the argument that collection and division define whole-part relations that underlie deductive reasoning on the one hand, and the formulation of definitions in dialogues such as the Sophist and the Statesman on the other. Chapter 5 will explore the relation between collection and division and non-deductive reasoning. It will present the argument that Meno’s definition of virtue and Euthyphro’s definition of piety are formulated using collection and division. Chapter 6 will provide a summary of key points from the preceding chapters and discuss unanswered questions and avenues for future research.