2025 Theses Doctoral

Parthood without Mereology

Botti, Martina

Objects have, and themselves are, parts. If we endorse a sufficiently liberal notion of object, anything is an object and anything, excluding the universe, is a part of some larger one. If we think that the universe, too, is an object, then any object is a part of it. What is it, then, for an object to be a part? Contra the orthodoxy, in my dissertation I argue that to be a part is no more a relation than to exist is a property. In fact, to be a part is just to be the value of a variable in the range of a quantifier whose interpretation has been extended. When I say that, for instance, my hand is a part of my body, I am not making the claim that two objects in the domain of quantification—my hand and my body—stand in a certain relation of ordering—being a part of—to one another. Rather, I am making the claim that the domain of quantification, which used to include my body but not my hand, has been expanded and now includes my hand. For the hand to be a part (of my body, but most importantly of the universe) is for it to exist in an expansion of the quantification domain.

As I construe it, the operation of re-interpreting the quantifiers—and, so, of individuating parts of objects—is both modal (the interpretations of the quantifiers are indefinitely extensible) and actuality-bound (the modality at play operates across interpretations, rather than across possible worlds). In the resulting ontology, the universe itself (i.e. effectively, the actual world) is the only object that exists before we start individuating its parts—that is to say, before we start expanding our domain. As such, individuating parts is an operation that is generative (with each re-interpretation, the domain includes new objects, which replace the previous ones, and its cardinality is higher than that of the domains associated with previous, less extended interpretations); maximally general (any new object is a part); and world-bound (every new object is a part of the universe). Insofar as it is indefinitely extensible, the interpretation of our quantifiers can always be extended, but does not need to be. Insofar as individuating the parts of any object is expanding the domain of quantification, the universe, which is the only object that exists in the non-expanded domain, is itself part-less, albeit extended. Similarly, the objects existing at further levels of expansions are, too, themselves part-less, for individuating their parts is, once again, expanding the domain. Mereological complexity is, strictly speaking, quantificational complexity.

The dissertation is written as three papers. In the first paper, “Composition as Analysis: The Meta-Ontological Origins and Future of Composition as Identity” I argue that a non-trivial formulation of the claim that a composite object is the same as its parts requires that we construe parthood quantificationally. I then suggest that we construe the system of domain expansions as an information ordering and interpret the corresponding many-one identity statements as metaphysically informative. In the second paper, “Parthood Without Mereology,” I present an antinomic result for parthood: that we cannot both construe coincident objects as numerically distinct and mereologically indiscernible while also claiming that absolutely every object coincides with at least one other object. I blame a relational account of parthood for this result and argue that switching to a quantificational account is needed both to make sense of the problem and to find a solution. In the third and last paper, “To be said of as a quantifier: quantity, parts, and the invention of ontology in Aristotle’s Categories,” I take on an interpretive challenge from Aristotle’s Categories and show that the challenge could be met by appreciating that Aristotle has a non-relational notion of parthood and re-thinking his account of quantity on that basis.