Logicians do it with Models

When the ontological status of a property or attribute is in question, the central issue is the ontological status of an object’s possessing or exemplifying a property.  When the ideological status of a property or attribute is in question, the central issue are the kinds of predicates that express the property.  The following example brings this out starkly:  A property can be mental, but not physical (ideologically), but can be ontologically physical, but not mental.

If a mental predicate is not lawlike coextensive with a physical predicate , where and are appropriate vocabularies, the attribute expressed by is mental, but not physical.  Nevertheless, by the principle of physical exhaustion (PE), the attribute is physical, but not mental (ontologically), as it is possessed solely by physical objects.

Entity-wise, every attribute is mathematical-physical, but only those attributes are mathematical-physical that are expressible by mathematical-physical predicates.  So, if physical reductionism is false (which is likely the case), there are attributes which are mathematical-physical entities, but are not mathematical physical attributes.

The confusion arises when terms like “mental” or “material” are used to call out properties or attributes without clearly setting out whether one is talking about the ontological or ideological status of the attribute.  This is an important point by Hellman, and we will see how this distinction and physicalist materialism in general are useful in clarifying questions of reductionism and materialism in the philosophy of mind when we turn to an analysis of Chalmers’ anti-materialist claims.

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.