Let us agree that material things must have one of the predicates of the motion catena, that is, that they must either be at rest or in motion, either in some (quasi-)absolute sense, or with respect to a certain frame of reference. Consequently they can have a negative velocity, a positive velocity, or a neutral one called "rest". But the predicate of positive velocity itself does not have a positive velocity because a set cannot be identical to one of its elements. As a matter of fact, it does not have any of the predicates of the motion catena, because a primary predicate cannot have a primary predicate as an element. Nevertheless, as a simplex, primary thing a primary predicate like positive velocity has attributes and relations of its own: it is positive, for instance. This is an attribute it has in common with other positive predicates such as electropositivity, happiness and increase. The secondary attribute of positivity itself, however, cannot be predicated to objects, or even not to immaterial or abstract, primary things. It can only be predicated of primary attributes and relations in the second domain of discourse. As secondary attributes positivity, neutrality and negativity do not constitute a catena, because the component parts of a catena are primary predicates like heaviness and happiness. Even as secondary attributes they are not (the intensional) whole-attributes of any catena either, for the catena itself is as a whole not positive, neutral or negative. At the most it might be said that positivity, neutrality and negativity are its part-attributes, or that they are the common denominators of all positive, neutral and negative predicates of the catena as common denominator of all catenas.

What belongs to the predicaments of catenas is in the first place their relations with other catenas, like that between the heaviness catena and the catena of heavier than, as heavy as and lighter than. In general this relation is a relation between a catena and another complex, secondary thing. But also a relation with a simplex, secondary thing, or a secondary attribute, may be conceived of. The abstract world of catenas and related things in the second domain of discourse is structurally an exact copy of a concrete or abstract world of first- and higher-type things in the first domain of discourse. This parallelism is depicted in figure I.2.1.3.1. The attribute- or relation-catena is shown here to have three component parts. As we will see, this is the minimum number of parts it must have. To be a catena, a third-type, second-order thing must have at least one negative, one neutral and one positive attribute or relation.