Constitutive of every fact :Rn(a1,a2,…,an), for n ≥ 1, is an ontic predicate, Rn(x1,x2,…,xn), that is the agent/cause of the characterizing predicable unity of itself with its relata, a1, a2,…, an, a unification whose type is to result in a fact, as opposed to a list, set, or mereological sum.
Every ontic predicate Rn(x1,x2,…,xn) has as a constituent an intension Rn whose ontic role is that of delimiting or determining non-arbitrarily the possible n-tuples of relata,
In addition to and distinct from intension Rn, there is constitutive of ontic predicate Rn(x1,x2,…,xn) its actual mode of union, its combinatorial or linking agency, among and to its subjects. The linking aspect of predicate Rn(x1,x2,…,xn) is itself not a further intension in addition to Rn, but a causal act of unification that is ‘joined’ with intension Rn that controls its effects. This joining is the unity of a continuous composite, i.e., a union of two distinct entities without the agency of a further interposing ontic predicate or act of unification. Moreover, the unifying act of an ontic predicate is unrepeatable and particular, rendering the containing predicate an individual, i.e., a unit attribute.
The analysis that yields these principles starts first in broadest terms with the fact that a given of our experience is the existence of a myriad of structured wholes—articulated composites—each as such having constituents in one or more types or kinds of inter-connectedness or organization, e.g., cognitive, physical/mechanical, and social structures. In such complexes, entities and their mutual qualitative connections (‘orderings’, relationships, arrangements) jointly contribute to the existence and nature (specific essence) of the whole. That is, the being of a structure, whether, say, as a dynamic physical system (e.g., an operating engine) or a static formal one (e.g., the Natural Number System), is a function of the mutual qualitative co-relevance of both the intension contents of the constituent unifying relationships and the compatible natures of their respective subjects, and as the former orders the latter. The simplest such or atomic structured whole would be one instance of one kind of intensioned connection or unification among one n-tuple of other constituents. This is a fact or state of affairs, :Rn(a1,a2,…,an), e.g., :Red1(a), :Contiguous-with2(b,c), :Owes3(d,e,f) (as in ‘d owes e to f’), whose arrangement-kind is intension Rn, in the examples, respectively, Red1, Contiguous2, Owe3. Here the subjects, a1, a2,…, an, are linked and ordered (if any) into a resultant fact :Rn(a1,a2,…,an) according to intension Rn, though, on the analysis below, not by the intension Rn.
We now have Principles I and II, and from them follows important and particularly relevant Principle III. With I and II we know that ontic predicates are agent-unifiers among n-tuples of subjects and so jointly generate facts, but that the predicates’ subsumed/constituent intensions that specify and delimit their linkings have no such agency. This implies that for each ontic predicate there is, in addition to its constituent intension, a non-identical remainder of constituent and intensionless unifying or combinatorial act. The combinatorial acts of ontic predicates are the ‘ontoglial’ (Greek: ‘glue of being’) essential to the unity of and marking the diversity in a plural universe. Like an intension relative to its ontic predicate, and indeed the predicate relative to its fact, the unifying act of an ontic predicate is recognized via a process of abstraction, but does not otherwise exist separated. Recall there are no ‘bare linkings’ without intensions, nor are there ontic predicates without subjects to unify. This now brings us to the principle thesis of the essay: The union between the combinatorial aspect, say unifying act U, and the ontically distinct intension aspect Rn of an ontic predicate Rn(x1,x2,…,xn), the latter providing the intensional unity of some fact :Rn(a1,a2,…,an), is not a function of an agency of act U, or any other constituent unifier U´, whether U´ is itself an intensionless unifying act or an intensioned ontic predicate. When this is established we will have a composite—ontic predicate Rn(x1,x2,…,xn)— consisting of act U and intension Rn but without a constituent unifier, and in particular without a constituent unifier interposing and thus registering an internal differentiation between and so a discreteness of U and Rn. Hence, an ontic predicate is a composite but one ‘tighter’ than an articulated complex.