With the principle of Physical Exhaustion (PE: where is a rank in the hierarchy of the physical), which allows us to say that everything is exhausted by the physical, every attribute is mathematical-physical (i.e., existing somewhere (possibly high-up) on the set-theoretic hierarchy; see this and this). Thus the ontological status of attributes is mathematical-physical. Now, for a given vocabulary , and for any attribute that expressed by a predicate that makes essential use of members of , call that attribute a -attribute. So, for example, attributes expressed by physical predicates are physical attributes and those expressed by psychological predicates are psychological. This is their ideological status.
The ontological status of a thing has to do with which extensions of predicates (of ontological kind) under which the thing falls. The most encompassing of such predicates is “is mathematical physical’. But there are other, narrower ways to distinguish the ontological status of things. For example, some metaphysical predicates, “is abstract”, “is concrete”, or some scientific ones, “is an elementary particle”, “is an event”, “is a person”, “is a social process”, “is a physical magnitude”, etc. Some other ontological kind predicates have empty extensions: “is a soul”, “is a phenomenally raw feel not identifiable with any entity in the hierarchy of the physical”. But if something were to satisfy these predicates, the predicates would indicate the ontological kind of these things. So the important semantic relationship here is satisfaction of ontological kind predicates.
This is different than in the case of the ideological status of attributes, where the important semantic relationship is expression of an attribute by a predicate –i.e., the relationship between the argument and value of a universalizing function. Every entity has an ontological status, but only universals have ideological status determined by the types of predicates for which the universal under consideration is the value of the universalizing function.
So the ideological status of an attribute, is given by the predicates that express it. These predicates themselves can be classified, for instance, according to scientific discipline, psychological-predicates, physical-predicates, Economic/Sociological-predicates, etc. These classifications are historical and are subject to change due to a variety of factors –not all of them scientific. Hellman explains that attributes themselves may have more than one ideological status: for the predicate ‘is in pain at t‘ is coextensive in a law-like fashion with a complex physical predicate then ‘being in pain’ is both a psychological and a physical attribute since it is expressed by both psychological and physical predicates.
In the next update I’ll go into Hellman’s discussion of the confusion that results when the ideological and ideological status of attributes is not clearly stated in debates concerning materialism and the mental.