It has been pointed out (in 1.2.1) that for every relation there are one or more derelativized one-place predicates. If A looks at B, there is a relation of looking between A and B, directed from A towards B. Thing A, then, has the property of looking-at-something, or simply looking, and B has the property of being-looked-at. A is at the fundament of the relation and performs the act of looking. (Looking is something else than receiving reflected beams of light.) We shall assume that the active form looking(-at-something) represents a real attribute. B, which is at the terminus of the relation, does not perform anything, and there is no need to assume that it has any real attribute because of its being looked at. Being-looked-at and other passive forms stand as such for pseudo-attributes. In diagrams where we show nonprimitive relations between things as lines connecting these things, there is no need to show the corresponding, existing one-place predicate(s) separately (inside the closed curve): altho not wrong, it would be superfluous.

It has also been pointed out that a relation between basic things is a relation between attributes in the attributive interpretation of formal systems. If there is such a relation, then at least one of these related attributes must have a derelativized one-place predicate itself. But in the first domain of discourse such an attribute has no elements because it is a basic thing in this domain. Therefore it cannot be at the fundament of a relation with something else at all. It could be at the terminus of a relation tho as this does not require the attribute to have a real one-place predicate itself. When an attribute is said to have attributes itself, and when an attribute is said to have relations in which it is not just at the terminus, it is treated as a nonbasic thing, a thing with several elements itself, in another domain of discourse. The relations between those attributes belong to that domain of discourse too, that is, not to the domain in which one speaks of relations between nonattributive objects. Whereas the latter relations are primary, the former are secondary. And whereas attributes which are not attributes of any other (kind of) attribute are primary, the attributes of those attributes are secondary attributes. All of them are primary and secondary predicates.

Just like in the objectualist interpretation, a predicate of a predicate of order n is itself a predicate of order n+1. This does not apply to the primitive having(-as-an-element), because this is a 'relation' inherent in the hierarchical structure itself. Like being and existing it is of all orders, or rather of no order in particular. The same applies to the primitive 'relation' of identity, which is purely conceptual and neither ontic nor of any particular order either. Identity solely plays a role in the description of reality, not in nonpropositional reality itself. Identity statements cannot express a relation between different things in reality, because, trivially, everything is identical to itself and to nothing else.

Predicates have only higher-order (nonprimitive) predicates. They do not have component parts, of whatever order they might be. So every predicate of order n is an ontic set of predicates of order n+1. In the same way as a 'really elementary', that is, simplicial, particle is a set of primary attributes, a primary attribute is itself a set of secondary attributes, a secondary attribute a set of tertiary attributes, and so on. And like in the objectualist interpretation there is in principle no end to this hierarchy. Those who despise infinity should bear in mind that this hierarchy is an abstract, conceptual structure and in no way forces us to accept the existence of infinite sets of concrete things.

As a basic thing a predicate belongs to one domain of discourse, and as a set of predicates to another one, that is, the next domain. Thus there are (basic) things in the one domain which are identical to (nonbasic) things in the next domain. This identity of things across the border of domains can be represented by means of a line interrupted by a special identity symbol (=), as indicated in figure I.

It is now clear why it may seem that a relation between primary attributes exists in the first domain of discourse. The explanation is that the relation exists between two nonbasic things of the second domain which are both found as basic things in the first domain as well. The relation itself is secondary, however, and corresponds to a secondary one-place predicate found inside at least one of the primary attributes in the second domain of discourse. Figure I. gives some examples of primary, pseudoprimary and secondary relations between and with primary attributes. (By way of clarity the relational attributes are shown extra as a separate attribute besides the relations themselves.)

In the attributivist terminology a universe of discourse is the totality of all hierarchically ordered domains involved in a particular communication. The ultimate constituents of the first domain of this universe are primary attributes, those of primary attributes and all other things of the second domain secondary attributes, those of secondary attributes and all other things of the third domain tertiary attributes, and so on. Hence, the ultimate constituents of all domains are attributes, and those of a particular universe of discourse the attributes of the highest domain in the hierarchy.

The simplex particles and the predicates in a universe of discourse are all simplex things, that is, things which have no extensional elements and which cannot present themselves by means of component parts. They are sets of predicates which exist in reality as a thing -- according to our typification in section 1.3.2 as a thing of type 2. All things of a higher type we shall call "complex things". Simplex and complex things belong to the same domain as the attributes of the highest order they have belong to. (Attributes of a lower order are components.) Hence, a simplicial particle belongs to the first domain, altho it could be represented as a set of sets of secondary attributes in a universe of discourse which would include the second domain too. If we allowed this, however, only its 'parts' would have attributes and relations, not the thing itself. Since a simplicial particle must have attributes and relations of itself, it does not belong to the domain of secondary attributes. On the other hand, a complex thing with a primary attribute does belong to the second domain, if it contains one or more secondary attributes as well. Its primary attribute is, then, not an attribute in the sense of a basic thing, but a component part.

Some might have expected that our distinction between parts (as nonpredicative elements) and attributes (as basic, predicative elements) is a distinction only to be found in the physical world. They might have believed such a distinction to be inappropriate to the general framework of an ontology. But our example of a complex thing in the domain of secondary attributes proves that this objection is wrong, for complexity of this sort exists as much in the abstract world as it exists in the concrete or physical world. The very recognition of this complexity is an absolute prerequisite to understanding the structures in both these worlds. It is of paramount importance to realize at this stage that the universe does not only encompass material things, with or without related things and attributes, but that it also encompasses complex systems of nonprimary attributes. The development of one of the two paradigmatic components of our weltanschauung itself will depend on this insight.

©MVVM, 41-57 ASWW

Model of Neutral-Inclusivity
Book of Instruments
Having and Thingness
Attributes as Ultimate Constituents