"Bill Page" <[EMAIL PROTECTED]> writes:
| On Fri, Jul 4, 2008 at 6:32 PM, Gabriel Dos Reis wrote:
| > Bill Page writes:
| > ...
| > | But
| > |
| > | Integer has Type
| > |
| > | is well-formed and yields true. Does that mean that Integer is a
| > | subtype of Type,
| >
| > Yes.
| >
|
| Ok, I will consider this. I would have said (with Stephen Watt and
| Aldor) that Integer is a Domain-valued object (an object of the domain
| Domain).
Do you think there is a contradiction between
Integer is a subtype of Type
and
Integer is a Domain-valued object
?
| But you have domains as subtypes of the category Type.
| Therefore everything besides objects are subtypes of Type?
This is no easy question, because while we are trying to define
category and domain, we have thrown in `object', and now we are
wondering whether everything besides objects are subtypes of Type.
| > | i.e. a category?
| >
| > Is your definition that a `subtype of Type is a category'?
| >
|
| I considered that since Type is a category that it's subtypes would
| also be categories, but I guess that is an unjustified assumption.
then we are back to what is meant by `subtype'. I proposed the
predicate
S has T
but you did not like it. Could you propose something?
| > | Of course not!
| >
| > `not!' to which part exactly?
| >
|
| I withdraw my exclamation.
|
| > | Axiom has two different uses of 'has'. One of them represents the subtype
| > | (inclusion) relation, the other is the membership relation.
| >
| > Now, I have two undefined terms (subtype and inclusion) precisely when
| > I'm trying to get you define just one (subtype). We are not progressing.
| >
|
| You are right. I fear that I have reached the limit of my cognition at
| this point and it might be best to let this subject rest again for
| awhile...
This certainly is no easy subject.
>From my part, more experimentation is needed to guide and nuture the
abstractions.
-- Gaby
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