A mereological sum (or fusion) is the single whole object that consists of all the given parts taken together, regardless of their spatial or conceptual distance from one another. [1]

Key Characteristics

Composition: According to the principle of unrestricted mereological composition (universalism), whenever you have any collection of distinct objects, there exists another object that is their exact mereological sum. [1, 2]
Difference from Sets: Unlike a mathematical set, a mereological sum is composed of its parts literally and materially (or structurally), rather than as an abstract list or collection of elements. For example, the mereological sum of your left shoe and the moon is a single composite object in this framework, whereas a set is just a container of two abstract items. [1, 2]
Overlap and Unity: The parts within a sum can overlap, and the resulting whole maintains the identity of those combined components. [1, 2]

You can read more about the formal framework in the Stanford Encyclopedia of Philosophy entry on Mereology or explore the foundational definitions on Wikipedia. [1, 2]

Would you like to explore how mereological sums differ from sets in mathematical logic, or dive into theories like mereological universalism and nihilism?