Final answer:
The domain 'D' for a first-order sentence about a subject 'Z' does not always include all objects that fall under 'Z'; it depends on the context or intent. Bertrand Russell and Frege's logical theories aid in defining domains with descriptive specificity.
Step-by-step explanation:
When constructing a model for a first-order sentence in logic, say 'S' which refers to a subject 'Z', it's not necessarily assumed that the domain 'D' contains all objects that fall under 'Z'. Rather, the domain is often defined by the context of the discussion or the specific intent of the model. For the sentence 'All lizards like flies', 'S' is the sentence and 'Z' represents lizards. The domain 'D' could be all lizards in the world, or it could be a more restricted set, such as lizards in a particular zoo, depending on the purposes of the discourse or analysis.
Bertrand Russell's notion of descriptions suggests that every proper name or designator like 'lizards' in 'S' can be replaced by a set of descriptions that uniquely identifies the objects in question. Thus, the domain can be constructed with precision based on these identifying characteristics.
It is important to differentiate objects and concepts with proper predicate logic and to recognize that language often categorizes the world subjectively, not just reflectively. Frege's work emphasizes the formulation of sentences as functions relating objects to concepts, determining the structure of the domain 'D' which is vital for the model of 'S'.