At 07:52 PM 1/18/2006, you wrote:
>Chris and Barry,
>
>I was following Church's definition of a function as rule
>(see the excerpt in http://www.jfsowa.com/logic/alonzo.htm ).
>I consider a type to be of the same nature as a function,
>since one could consider a type to be a function from
>entities to truth values.
>
>JS>> A _type_ t is a rule or specification for classifying entities,
> >> concrete or abstract. Any entity that has the characteristics
> >> specified by the type t is called an _instance_ of t. (01)
A dog is an instance of function from entities to truth values (02)
Still does not sound right to me. (03)
>I admit that my definition is as loosely stated as Church's,
>but I consider that at worst a venial sin, and it's certainly
>no disgrace to be lumped into the same group with Alonzo C. (04)
Good to follow common sense, too, I think. (05)
>BS> However, I think it wrong to coin a term 'relation type'. This
> > is because most of the relations which interest us here, e.g. is_a
> > (meaning: is subtype of), instance_of, part_of, etc., DO NOT HAVE
> > INSTANCES.
>
>Actually, they do. If you consider the extension of a type to be
>a set of instances, the extension of a relation is a set of n-tuples,
>each of which may be called an instance of the relation. (06)
You yourself have correctly been arguing that a type and its
extension are two different entities. And now here too we see that
there is a disanalogy between types and relations. The extension of a
type is a set of instances of that type. Thus Fido instance_of the type dog. (07)
The extension of a relation is a set of (ordered pairs of) instances
of other quite different types. (08)
We do not have instances of is_a, part_of. (09)
For suppose that we did, e.g. the ordered pair <dog, animal> is an
instance of the relation is_a. (010)
Then this would mean that we would have to accept not merely the statement (011)
dog is_a animal (012)
but also the instantiation statemeno (013)
dog <dog, animal> animal. (014)
Put that in your pipe and smoke it. (015)
BS (016)
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