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TL;DR

This paper provides a mathematical framework for universalism in mereology, extending models to include all collections of parts, and demonstrates the uniqueness of such extensions under certain principles.

Contribution

It offers a formal account of extending core mereology models to universalism, analyzing the conditions for unique and economical completions.

Findings

Any model can be extended to satisfy universalism.

Under Strong Supplementation, the extension is unique up to isomorphism.

The paper characterizes the most economical ways to extend models.

Abstract

The aim of this paper is to give mathematical account of an argument of David Lewis in Parts of Classes in defense of universalism in mereology. Specifically we study how to extend models of Core Mereology (following Achille Varzi's terminology) to models in which every collection of parts can be composed into another part. We focus on the two main definitions for mereological compositions and show that any model can be extended to satisfy universalism. We explore which are the "most economical" ways of extending models under various conditions. Remarkably, we show that if the principle of Strong Supplementation is assumed, there is a unique mereological completion, up to isomorphism.