Sorry to be a little late to the party here…
I would like to clarify on some remarks recently made about Common Logic.
On 5/14/13 12:00 PM, John F Sowa wrote:
5. Common Logic has only one domain of quantification,
...
In addition a CL interpretation allows for reference to entities that
are outside of the domain of quantification.
A little more carefully, it is only CL itself that allows this; a given interpretation either has entities outside the domain of quantification or it doesn't.
This larger set of entities is called the universe of reference.
I think this is a bit misleading. For one thing, the universe of reference (UoR) needn't be larger than the domain of quantification, or, in CL-speak, the universe of discourse (UoD), as I'm sure you know. For another, every interpretation has a UoR. More exactly, every interpretation contains a UoD and a UoR; the UoD is the domain over which the quantifiers range, and the UoR is designated to be the set that contains the denotations of the names of the language (a.k.a. dialect) being interpreted. The UoD of an interpretation is stipulated to be a subset of the UoR. For non-segregated dialects — i.e., those in which no names have been set aside to play only predicative or functional roles — the UoR is (for all intents and purposes anyway) identical with the UoD. The UoD must be a proper subset of the UoR only in interpretations of segregated dialects.
In that sense,
one could say that CL has an implicit one-category ontology.
I would say that CL has an implicit five-category ontology. There are
the three categories of entity, function and relation.
I'm with John on this one; at root, CL's is a one-category ontology. There is just one kind of thing in CL's ontology — things, or entities — but those things can play three different roles: a relation role, a function role, and the role (roughly put) of a subject to the predication of a relation or application of a function.
The category of
entity is further divided into the domain of discourse and the
complement of the domain of discourse within the universe of reference.
I definitely do not see this as a categorical division. There are just entities. Any entities in the UoR are simply ones that, for whatever reasons, are to play relation and function roles only.
The functions and relations can also be partitioned into discourse and non-discourse.
But again, nothing is intrinsically a function or relation in a CL interpretation. Even the entities in UoR \ UoD play both relation and function roles.
While it is possible to have the same function/relation
Important to note that you are talking about function/relation extensions here.
associated with a discourse entity and also with a non-discourse entity,
any function/relation associated with some entity in the domain of
discourse could be considered a discourse function/relation, due to it
being "reachable" by a quantification such as
(exists (x) (= x(a) b) )
You lost me here. So let f_e be the function extension of e, where e ∈ UoD. I'm sure what "could be considered" amounts to here. Things aren't "considered" one way or another in an interpretation, they just are one thing or another. And I don't in particular see how f_e is "reachable" in any significant sense; suppose e is the value of "x" in "(= x(a) b)". "x(a)" does not refer to f_e; f_e is simply used in the calculation of the denotation of "x(a)".
This gives six categories ( discourse and nondiscourse relations, functions and entities).
Again, I think you are mistaking divisions within (some) CL interpretations for significant ontological distinctions; I don't think that is the right way to think about CL. I've laid out my thoughts on this in more detail in
this article. A preprint is
available here.
-chris