Unextended Complexes

Abstract

Extended simples are fruitfully discussed in metaphysics. They are entities which are located in a complex region of space but do not themselves have parts. In this paper, I will discuss unextended complexes: entities which are not located at a complex region of space but do themselves have parts. In particular, I focus on one type of unextended complex: pointy complexes (entities that have parts but are located at a single point of space). Four areas are indicated where pointy complexes might prove philosophically useful. Unextended complexes are therefore philosophically fruitful, in much the same way as extended simples.

Extended Simples, Unextended Complexes

“…In the absence of Exactness one might formulate a weaker version of Expansivity, WEAK EXPANSIVITY as follows: x y ∧y@ • r → ∃r 2 (x@ • r 2 ∧r 2 r 1 ). Note that the scenario described by Pickup [39] does not violate Weak Expansivity. I owe this suggestion to an anonymous referee for this journal.…”

“…[O]ne natural way to understand what it is to be an extended region is as being composed of more than one point (Pickup [39]: 263). 21 Strictly speaking there is a sense in which colocation occurs every time a material object x is exactly located at region r. For, x and r are indeed colocated at r in all such cases.…”

“…McDaniel [34] argues they are ruled out by reductive accounts of mereology. 25 Pickup [39] focuses exclusively on them. Both McDaniel and Pickup characterize them similarly:…”

“…38 The superscript " * " will become important later on. 39 As I will discuss later, another limitation of the mereological notion of extension is that it seems impossible to define an extended simple region. I want to briefly sketch an argument to the point that, broadly speaking, a metrical notion does not suffer from the same limitation.…”

“…This already rules out unextended complex regions for Functionality entails Non-Colocation for regions. Pickup [39] discusses co-location as well, but he also adds a new interesting spin:…”