8.1. The mereology Dybkær implies🔗

The word mereology does not occur in Dybkær's text. The structure does, at two levels, and the levels never meet.

At the level of concepts, the vehicle is the partitive relation that ISO 704 and ISO 1087-1 provide and Fig. 2.1 (item 2) sets in notation: a comprehensive concept over its partitive concepts, beside the generic and associative relations. Dybkær puts it to work as a relation among universals. The quantity taxonomy itself is drawn with partitive rather than generic edges (Fig. 6.9); the representation of a unitary quantity value has the numerical value and the metrological unit as coordinate concepts in partitive relation to it (Fig. 9.25); a property-value scale stands in partitive relation to ⟨property value⟩ (§11.8). And he rules with it: ⟨property⟩ over ⟨property value⟩ cannot be comprehensive-over-partitive, because a property value is not a detachable piece of a property (§9.13.2).

At the level of systems, the vocabulary is plain part-talk, and it is load-bearing from the opening of Chapter 3. ⟨system⟩ was adopted "to accommodate any partition into components" (§3.2, where Bunge is quoted: "there are no simple structureless entities"). The definition itself is mereological — a system is a "demarcated arrangement of a set of elements and a set of relationships or processes between these elements" (§3.3), an element being "any definable part except a relationship or a process" (§3.3 Note 3) — and its worked examples are a six-deep chain of parts: a human being, the blood of that human being, the leukocytes of that blood, a single leukocyte among them, the DNA of that leukocyte, a given gene in that DNA. ⟨component⟩ is then defined as "part of a system" outright (§3.4), with the complementary part — the chemist's matrix — named beside it (§3.4 Note 2), and the improper case, system and component "designated identically", admitted (§3.4 Note 3). Fig. 3.5 splits ⟨object⟩ into composite and non-composite. The relation even carries definitional weight one level up: the minimal definition of ⟨property⟩ — "inherent feature of a system" — is available exactly because "a relevant component is a part of a system and therefore might not need special mention" (§5.5.1).

Two further facts fix how these two levels must be read, and both are Dybkær's own. First, they are genuinely two: the partitive relation holds between concepts — universals — while a component is part of a particular system, and nothing in the text identifies the two relations or maps one onto the other. Second, at the one point where the levels could have been collapsed, he refuses. Asked whether ⟨object⟩ stands in a partitive relation to its properties — whether properties are the parts objects are made of — §2.23.3 answers that "the description of a biological object by a set of all its properties hardly means that a duplicate instance can be created by putting the properties together", and the object–property relation is fixed as associative (§3.1, Fig. 2.25). That is a refusal of the bundle theory in one sentence: properties characterize objects, they do not compose them. What is needed, then, is a frame that keeps properties and their bearers in distinct categories related by characterization rather than parthood, distinguishes universals from particulars on both sides, and leaves room for a part–whole relation among the particulars and another among the universals without confusing either with instantiation. That frame exists, and it is Lowe's.