Plato on Parts and Wholes: The Metaphysics of Structure (review)

In this book, Verity Harte seeks to provide an account of Plato's view of mereology. According to Harte, Plato presents two distinct models about the relation of part to whole, but actually only ever accepts one of these two models. Plato presents one model in the Parmenides, Theaetetus, and one passage in the Sophist. In this model, which Harte compares to a conception of part and whole recently advanced by David Lewis, the whole is simply identical to its collective parts and Plato attends to this model only to call attention to its problems. Harte explicates Plato's presentation of this model in the last section of Chapter 1 and in Chapter 2 of her book. The second model—the only one Plato actually accepts, according to Harte—Plato initially outlines in the Parmenides, but then explicates in finer detail in the Sophist, Philebus, and Timaeus. In this conception, wholes are now understood as "structures, the identity of whose parts is determined only in the context of the whole they compose" (3). Harte presents her evidence for Plato's endorsement of this model in Chapters 3 and 4, and then draws conclusions in Chapter 5.

The book has several significant virtues, including especially clarity of exposition, and care and thoroughness in the review of the relevant texts from Plato's later dialogues. But this same care and attention to detail does not at all extend to any of Plato's discussions of part and whole in earlier works, and Harte's peremptory refusal to consider the relevant passages in these other works is puzzling, at best.

Indeed, Harte bothers to identify only two such passages from earlier works, and then only to explain why they and other passages like them do not merit further attention: the Republic's famous division of the soul into three parts in Book IV and the consideration of virtue as a whole and the several virtues as parts of that whole in the Protagoras. Harte acknowledges that Plato explicitly supplies, in the Protagoras discussion, two different sorts of relations of part and whole, in distinguishing the way in which parts of gold form a larger whole, and the way the parts of the face are related to the whole face (349d4-8), but seems oblivious to the clear implication that—at least when he wrote the Protagoras, and contrary to Harte's primary thesis—Plato recognized more than one way in which wholes could be composed of parts. But Harte dismisses the significance of both discussions by noting, first, that the "principle of opposition" given in the Republic by which Plato divides the soul provides "at most, a sufficient, and not necessary, condition on something having parts" and concludes that it thus "cannot be used to establish general claims about parts" (2). Harte never mentions that this same view of the partitioned soul seems to reappear in the Phaedrus and Timaeus—a dialogue in which the allegedly preferred conception of mereology is presented—and also passes over the Republic's representation of the tripartition of the kallipolis, and Plato's conception of the citizen as a part of a state. As for the Protagoras's discussion of the relationships between the virtues, Harte says only that "there is here no discussion of the nature of parts or of the relation between parts and whole" (2). She concludes that "in both works the focus of discussion is the examples themselves (the soul, the virtues) and not wholes of parts as such" (2). Harte fails to notice, however, that the arrangement of virtues into parts and wholes may also be found in the Laches (190a1-199e7), Meno (78d7-e2), and especially the Euthyphro (12c2-d2), in which the relation of piety to justice as part to whole is likened to the relationships between reverence and fear and odd numbers and numbers, which are plainly not examples of part-whole relationships between virtues.

Harte is well...