The Mereology of Groups

Abstract

An interpretation of LP (without “w” and “PA”) can be formulated which verifies the axioms AP1 — AP6 (including AP5) and in which all entities in the universe of discourse — with the exception of a single one — are time-free material individuals. The concept of parthood “P” on this interpretation is not time-dependent (and, therefore, it cannot be spatial parthood between time-free material individuals). In order to state this interpretation we select appropriate time-free material individuals (we cannot choose arbitrary ones; see for this section (e) below) — the Xs — as elements (they are precisely the entities to which the predicate “EL” as defined by DP20 — and further by DP5, DP6 — can be truthfully applied in our interpretation) and declare that the entities that are spoken about in LP are all groups of Xs, all Xs, and Nothing. (The choice of the word “group” for what is meant is not entirely arbitrary; nevertheless, its appropriateness will be felt to vary with the choice of the Xs — depending on whether they are rather heterogeneous or have a natural affinity; the specific meaning in which “group” is used here is further described below. Concerning “Nothing,” we will see below what this notoriously dark metaphysical notion is good for; see, in particular, comment [*5].)