Re: SUO: Re: The lattice of theories + language-games
----- Original Message -----
From: "Chris Menzel" <firstname.lastname@example.org>
To: "Robert E. Kent" <email@example.com>
Cc: "SUO" <firstname.lastname@example.org>
Sent: Friday, June 14, 2002 3:11 PM
Subject: Re: SUO: Re: The lattice of theories + language-games
> > Hi Chris,
> > > Robert Kent wrote:
> > > > A 1st-order language L consists of
> > > >
> > > > * a set of entity types (sorts) ent(L), where examples of entity
> > > > might be Person, Organization, Emotion, etc;
> > >
> > > So a language for you comes pre-packaged with a particular semantics?
> > No. How so? Person and Organization are intended to be just type names,
> > whereas "Chris Menzel" and "Texas A&M University" would be instances of
> > those types.
> Ah, OK, your entity types are sets, or types, of names. Then it would
> be a lot less misleading if you would use the moniker "Person-name"
> instead of "Person" and that you'd call these things "entity-name types"
> rather than "entity names". "Robert Kent" is an instance of entity-name
> type Person-name, whereas Robert Kent is an instance of entity type
> Person. Seems to me you are reinforcing deep and all too pervasive
> confusions between syntax and semantics with your current terminology.
No that is not what I mean. The entity types (as well as relation types) are
just abstract objects. They are elements of the type set component of a
classification. They indirectly represent sets via the extent function of
their classification. There are no names explicitly involved here. Types
could be name types or object types. It just depends on what the specifier
wants to do.
Robert E. Kent
> > > > * a set of variables var(L) that is often of the form var(L) =
> > > > ent(L) x natno the binary Cartesian product of entity types and
> > > > natural numbers;
> > >
> > > Hm, so if ent(L) = Person, then an example of a variable might be the
> > > ordered pair <Robert Kent, 17>? Is that really what you mean?
> OK, I see now what you mean; you are just creating sorted variables. My
> misunderstanding here (in addition to not grokking the bit about entity
> types) was in choosing a *member* of ent(L) as an example of ent(L)
> > No, two problems here. First, Person might be an element of ent(L), but
> > would not be the whole set. And second, a variable might be <Person,
> > which might be abbreviated person_17, but <Robert Kent, 17> would not
> > normally be a variable, since "Robert Kent" is an instance, not a type.
> Yes, but let's at least be clear about the confusion here. My ordered
> pair consisted of you, Robert Kent, and the number 17, not the name
> "Robert Kent" and the number 17. The problem with the example is simply
> that the entity Robert Kent (as well as entity-name "Robert Kent", for
> that matter) is not an entity-name *type*.
> > The variable <Person, 17> would reference (have sort) the entity type
> > refer(L)(<Person, 17>) = Person.
> I think it is a Real Bad Idea to use the heretofore completely semantic
> term "reference" to talk about a completely nonsemantic relationship.
> > > It's difficult to distinguish syntax and semantics here, as
> > > traditionally understood, anyway.
> > I apologize for the terseness and abstraction. The terseness is my
> > problem, the abstraction is in the nature of the thing.
> Abstraction good; abstruseness bad.