to suspect that the more natural features are the topic-specific features defined on
individual categories. Change of adicityconstitutes a fundamental difference of
behavior! Moreover, the behavior is “disjunctive”in character: it is either one
way or the other, but in a systematic way. So I say that, other things being equal,
if a feature is systematically variably polyadic, do not believe that it is a perfectly
natural feature.
Parthood is systematically variably polyadic. The specific parthood relations are
more fundamental than the generic relation of parthood. But note that it is clear to us
that the various kinds of parthood relations are all kinds of parthood relations! It is
not that we have simply decided to label each of the respective specific parthood
relations with a common term, but rather there is something that they all have in
common that makes it appropriate to introduce a common term to cover them all.
Parthood is not a merely disjunctive relation. However, we cannot account for its
non-disjunctive nature by articulating a common feature that makes each specifica-
tion of parthood appropriately lumped together. (What would that feature be?) And
none of the specifications of parthood seems clearly to be the central specification in
terms of which the others are defined. (Which one of the specifications is even a
good candidate for beingthecentral kind of parthood?) Rather, in some way that we
cannot explicate, the specifications are analogues of each other. In short, this is a case
of the third kind of metaphysical analogy: analogy without a focal point.
Let us now explore the other route to compositional pluralism. Let us say that the
“logic”of a feature consists in those necessary truths stateable using only some term,
such as a predicate or a name, standing for the feature along with purely logical
vocabulary. The principles constituting the logic of a feature are principles thatgovern
that feature: they apply to all possible situations in which that feature is exemplified,
but explicitly mention no other qualitative features obtaining in that situation. Let us
say that a feature issystematically variably axiomaticjust in case the principles
governing that feature differ systematically from one ontological category to the
next. If a feature is systematically variably polyadic, it will follow that the feature is
also systematically variably axiomatic. However, the converse need not hold.
Focus now on regions of space–time and facts. Both the parthood relation defined
on regions and the relation defined on facts is two-placed. Onecouldsay that there is
one perfectly natural relation that is exemplified by both regions and facts. However,
note that the logic of this relation is ugly. The principles of classical mereology govern
how parthood applies to regions: (i) whenever there are some regions, there is a
region composed of them (unrestricted composition); (ii) whenever regionr1and
regionr2are composed of the same regions, thenr1andr2are identical (extension-
ality); and (iii) ifr1is a part ofr2, andr2is a part ofr3, thenr1is a part ofr3
(transitivity).^22 However, the principles of classical mereology do not govern how
(^22) Unrestricted composition, extensionality, and transitivity are taken as the three axioms of classical
mereology in its formulation in Lewis (1991).