Collection and division in Plato’s Dialogues
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Date
28/11/2016Author
Pasqualoni, Anthony Michael
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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.
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