Anna Marmodoro’s Forms and Structure in Plato’s Metaphysics has several important features. First, the volume claims a deep connection between Plato’s and Anaxagoras’s metaphysics that reveals unresearched aspects of Plato’s philosophy. The novelty in Marmodoro’s account is that she claims that both philosophers posit constitutional overlap at the core of their metaphysics. What this means is that objects would be qualified by an Opposite (Anaxagoras) or by a Form (Plato) by coming to have within its constitution shares or parts of that Opposite or Form. Thus, objects of this world would overlap constitutionally with that which causes them. This is also the volume’s assumed overarching argument. Second, Marmodoro provides a coherent story of the development of Plato’s metaphysics, from its initial Anaxagorean influences and Anaxagorean inherited problems to the perspective and answer that Plato offers to these problems in the Timaeus. Her thorough analysis of the connections between Anaxagoras and Plato deserves further discussion. Third, ancient metaphysics is explained with the tools of current day metaphysical work. The first two aspects are fresh and provocative. The third aspect—the use of contemporary metaphysical notions for explaining ancient metaphysics—deserves a debate in its own right. In this connection, Plato’s deliberate vagueness regarding certain notions—as, for example, that of participation—may be richer than reducing it to only one explanation, even one as attractive as constitutional overlap.
The first chapter begins with a depiction of Anaxagoras’s metaphysical system. The four kinds of things in his cosmos are the Opposites, which are irreducible to anything else; Stuffs, composed from Opposites; Seeds, also composed from Opposites; and Nous, which is not reducible to anything else. The focus becomes the status of the Opposites. Marmodoro sides with Vlastos, who believes that they have to be understood in terms of causal powers. The way in which Anaxagoras’s Opposites are causally efficacious is the question to which Marmodoro offers the solution provided by constitutional change.
In the same first chapter, Marmodoro offers an attractive account of Anaxagoras’s system by applying contemporary metaphysical concepts. She describes Anaxagoras as the first gunk lover in the history of metaphysics (31). This idea introduces a gentle discussion about the opportunity of using contemporary metaphysical language to explain ancient metaphysical positions. The debate is ongoing, and people who study ancient philosophy may take diverse positions on this, between the two extremes: rejecting it completely or applying it extensively. This description of qualitative gunk applicable to Anaxagoras’s philosophy shows that sometimes the approach is beneficial because it succeeds in bringing clarity. In contemporary metaphysics, a “particular physical property […]is gunky if and only if every part of it has a proper part that is a particular physical property […] of that kind” (31). In the case of Anaxagoras, this explanation is appropriate because it uses clear language to express something that is supposedly clear in Anaxagoras’s mind. The criterium of clarity should not be applied exhaustively, though. In some cases, bringing clarity does not mean being faithful to the ancient author, as in Plato’s theory of participation. Giving it a clear path and a clear explanation by applying to it contemporary metaphysical theories is, perhaps, charitable to Plato, because it shows how his theories make sense in a logical totality; but it can also harm one’s appreciation of his views if this approach eliminates Plato’s genuine attempt at clarifying his own position without being committed to a clear version of participation.
In the second chapter, Marmodoro plans to do two things. First, focus on Anaxagoras’s account of what makes things qualitatively differentiated. Second, focus on Anaxagoras’s account of how things are made up, examining the role of the seeds and nous. It is here that she offers the explanation that constitutional overlap between what has the property and the property itself is at work in property possession in Anaxagoras. Constitutional overlap will become significant later, in her treatment of Platonic philosophy.
These ideas develop in chapter 3, where she argues that Plato’s Forms are causal powers that have constitutional causal efficacy, just as Anaxagoras’s Opposites do. There is, of course, an important difference: Plato’s Forms are non-physical, transcendent powers, whilst Anaxagoras’s Opposites are physical.
This is precisely the problem one has to surmount. For if the Forms are transcendental powers, then it is difficult to offer an account of their presence in a sensible object—this translates to the problem of how to clarify participation in Plato. Marmodoro’s answer relies on the notion of constitutional causation attributed to the Forms. They do not change the entities that belong to the world of becoming efficiently, Marmodoro says. Plato does have elements of efficient causation, but this is only for the interaction between these latter entities among themselves. Thus, Marmodoro argues, Platonic causation is difference-making, not efficient. And, she says, “Neither Anaxagoras, nor Plato (pre-Timaeus) had developed an account of efficient causation, by which I mean that they had not developed the conception of causation by interaction” (77).
Returning to the idea mentioned above, I believe Marmodoro correctly points out that Plato “elevates” the Opposites from their physical status to “the transcendent domain of the intelligible” (81). Being transcendent and, at the same time, constitutionally causing things in the physical world is difficult to explain. A further problem has to do with the instantiation of properties. If there are parts of the Form of Heat, which is transcendent, that make a sensible object hot, how are these parts to be understood? Are they parts in a mereological sense and, as such, divide the Form? Are they to be understood as copies of the Forms that somehow participate in the composition of sensible objects? The following chapters attempt to bring an answer to these questions.
The main problem discussed in chapter 4 is the challenge that faces Plato to explain how the Forms account for the being of each individual thing that partakes in the Form, while not being divided in parts. Marmodoro proposes a notion of partitioning which she calls Cambridge Partitioning, based on the notion of Cambridge change. In Cambridge change, a thing changes if it satisfies a description at one time that it does not satisfy at another. This can take place even in the absence of an intrinsic change: if someone outgrows me, I can no longer satisfy the description of being as tall as he even if nothing changed in my height. Marmodoro believes that the partitioning of a Form in all the sensible objects that partake of it works the same way. She proposes that sensible objects overlap with the Forms, and in doing so they divide the Forms extrinsically, which Marmodoro calls Cambridge Partitioning. There are two arguments that she proposes for this view. The first, the Principle of Charity: Cambridge Partitioning resolves difficulties stemming from the Affinity Argument in the Phaedo, where Plato states that Forms are not composite in the sense of being composed out of parts. The second: Plato provides two examples/analogies in the Parmenides that would support Marmodoro’s interpretation.
The two examples from the Parmenides belong, apparently, to a more complicated situation. While the two examples are suggested by Socrates as if he indeed understood partaking in Forms as partitioning by overlap (what Marmodoro calls Cambridge partitioning), they are immediately rejected by Parmenides, who shows that this type of partitioning would not work in the case of Forms. The sail example shows that it is a part of the sail as such that covers certain people, and not the sail in its totality. It is possible, of course, that the example is rejected not because Cambridge partitioning does not work in the case of Forms, but rather because this analogy does not give full justice to the real status of Forms. Still, Parmenides’s rejection of the two examples raised by Socrates casts doubt on the claim that, prior to the Timaeus, Plato believed that partaking in Forms is partitioning by overlap. If this were the case, then one requirement may be that the Forms and the sensible objects share a common existence. How would the Form of Justice, for example, overlap with various just acts that happen at different moments in different places? The two examples of the day and of the sail presuppose a continuity of the Form, while any partaking of sensible objects in the form does not presuppose this continuity.
Of course, this difficulty can be merely a manifestation of the complexity and, to some, even the impossibility of explaining how sensible objects partake of the Forms in Plato’s theory. While one may say that his theory can be solved by Cambridge partitioning, I suspect that Plato himself might not agree with that.
The fifth chapter starts from the claim that the Forms’ parts are only extrinsically individuated parts by Cambridge Partitioning. Their existence as, let’s say, Cambridge parts still manages to undermine a presupposition of Plato’s theory, incompositeness. Using the notion of Cambridge parts, Marmodoro argues that Plato’s Forms can be conceived as logical fusions of all the parts of the Forms. Of course, this works only as long as that which makes sensible objects have a certain quality is their possession of parts of forms.
Marmodoro sees the difficulty of her account and asks the right question: “In what sense are a transcendent Form and its physically distributed parts (in the sensible world) a logical fusion?” (133). An even more basic question is: in what sense does a transcendent Form have physically distributed parts?
In 5.3. Marmodoro discusses two qualities of Plato’s Forms. The first, monoeides, is stated as such in Plato’s text. The second, homoeomer, is, according to Marmodoro, implied in Plato’s other metaphysical commitments. It is difficult to make this claim work in Plato’s context, unless one is talking about what the author calls Cambridge parts. This approach allows her to construct a theory of a so-called Platonic hylomorphism. Assuming that Aristotle’s hylomorphism is non-mereological since the hylomorphic whole is partless for Aristotle, we can also speak, Marmodoro says, of Plato’s Forms as non-mereological compounds. The first problem here, though, is that the compounds in non-mereological entities are of the same kind, which raises the question why we need separation. It also remains problematic why one would call a composition of parts of Forms hylomorphism, unless one would assume that the parts participating in sensible objects are material.
Chapter 6 begins by restating that Plato’s model of participation—one of the most sought after explanations in Platonic scholarship—is based on Anaxagorean metaphysics and is “constitutional overlap between the sensible objects and the properties the Forms stand for” (156). The job of this chapter, though, is an exploration of two different types of partaking in the Forms: individually and plurally. The latter is indeed hardly explored in scholarship, and Marmodoro’s contribution is substantial. She distinguishes two types of plural partaking. First, joint partaking, when two or more individuals partake jointly in one and the same Form. Second, parallel partaking, when two or more individuals partake of a Form each, in parallel to each other (e.g. Socrates in Largeness and Simmias in Smallness, in parallel to each other). Marmodoro argues that both of them are types of constitutional overlap.
The final chapter is dedicated to Plato’s metaphysical innovations from the Timaeus. It includes a discussion about a solution to the Third Man Argument and ends by describing Plato in the Timaeus as Plato-successor.
One attractive line of research which Marmodoro mentions in a footnote, for example, concerns the causal power over nature of Anaxagoras’s nous, Plato’s form of the good, and Aristotle’s unmoved mover (19). This is just one interesting idea in a volume rich in fresh analyses that can lead to many fruitful philosophical discussions.