In my dissertation, I make a case against the orthodoxy that identifies parthood with a relation. When I say that my finger is part of my hand, most people—including most philosophers—hear me saying that there are two objects (my hand and my finger) and a relation holding between them (parthood). I disagree. I think that, when I say that a finger is part of my hand, I am saying that our ontology (more technically, the domain of our quantifiers) has been expanded: it used to include one hand, and now it includes two things instead: one finger and the hand minus the finger. Like many philosophers, I think that the universe is itself an object and that, with some willingness for abstraction, every object can be said to be a part of at least one other object, the universe itself. Unlike most philosophers, however, I think that, when we say that every object is part of the universe, we are actually saying that the domain of quantification—which, when it is not expanded, includes one object only, the universe—can always be expanded so as to include, in place of the universe, any other object that might exist in it. In fact, I think that for any object to exist in the universe is for that object to be a part of the universe, which in turn is for it to exist in one of the infinitely many possible expansions of the quantification domain.

The takeaway is that parts are just new objects; to be a part is just to exist in an expansion of the quantification domain or, more technically, to be the value of a variable bound by a quantifier whose interpretation has been extended; parthood is not a relation but, rather, a quantificational notion, just like existence is for a Quinean. Just as a quantificational account of existence allows us to understand the fact that an object exists as the fact that the universe is the set of every object, which are one by one included in it, likewise a quantificational account of parthood allows us to understand the fact that an object is a part of another object (e.g this finger of this hand) as the fact that an object (the hand) can always be replaced, in the domain of quantification that has been expanded accordingly, by at least two new objects (the finger and the hand minus the finger). In this sense, to say that the universe is the set of every object really means that it is the set of every object that has been, so far, individuated or, in other words, that it is the totality of more and more things. Mereological complexity, then, is quantificational complexity and the possible sequences of expansions of the domain provide the ontology with a new dimension along which quantificational complexity unfolds.

As I said, most philosophers disagree with this picture, but I do not think that this has always been the case. In fact, if we look at the history of Western philosophy, and specifically at its ancient Greek origins, the notions of parts and whole were first introduced to articulate the following intuitions: that objects present an internal complexity that is not reducible to qualitative complexity; and that, as much as qualitative complexity comes with the associated problem of qualitative change, this other complexity, too, comes with its own kind of change, which, however, does not appear to unfold over time. Can something unchanging have parts? Parmenides’ answer is in the negative. If so, is everything-that-exists one or many? How do we reconcile the claim that there is one maximal object, or universe, with the claim that the universe is by definition a plurality of objects? One of the driving ideas motivating my project is that construing parthood as a relation between objects in the ontology trivializes the above questions and prevents parthood from carrying out its original function in metaphysical theorizing.

In this spirit, my dissertation falls at the intersection of contemporary and ancient metaphysics. I make my case against a relational account of parthood, and in favor of a quantificational turn, in three steps, corresponding to the three papers that together make up the dissertation. First, I show that the thesis known in the mereological literature as Composition as Identity—the claim that a whole is the same as its parts—is the old One-Many problem deadlocked and trivialized by the assumption that parthood is a relation between things. Then, I show that mereology—the formal theory of parthood relations—faces an antinomic result for which abandoning a relational account of parthood is the only way out. Finally, I show how a well-known interpretive challenge presented by the opening chapters of Aristotle’s Categories can be re-framed and addressed once we take seriously the textual evidence that Aristotle does not think of parthood as a relation or a property. In each paper, the most promising alternative to accounting for parthood relationally appears to be doing so quantificationally.

Composition as analysis: the meta-ontological origins (and future) of composition as identity. Synthese 198, 4545–4570 (2021)— a paper in which I present and defend some of the central intuitions that shape my dissertation project, including a preliminary account of metaphysically, as opposed to epistemic, informative statements.