[sc34wg3] New SAM PSIs

[Murray Altheim]

Lars Marius Garshol wrote:
> * Mary Nishikawa
> | 
> | [subtype loops]
> |
> | Can you give an example of this? 
> 
> I don't know of any, admittedly.
 >
 > | I do not think that this works. You can create a loop, but does it
 > | have any bearing to reality?

It is impossible unless you conflate "set" and "class", or believe
that a superclass and subclass could have the same definition (I agree
that this is nonsense, as Mary says, it has no bearing to reality).

> Well, what you are saying with the loop is basically this: "these
> classes have different definitions, but they all have the same set of
> instances". There's nothing unreasonable about that.

Actually, there is, and this has been the most important point,
that it's not just a fluffy equivalency mechanism, it could lead
to erroneous conclusions.

To say that because two sets have the same instances, they are
the same class, is an error in logic. Two sets could very well
have the same instances and not have the same class definition.

One paradox is that all sets with no members would equate
to having the same class definition. Another error would
occur on any coincidental set, equating the class definitions
when the definitions are *not* equivalent. Eg., at some point
all passengers on a bus are male. You can't then equate "male"
and "passengers" as being the same class just because of this
coincidence.

I thought I'd said this already.

Murray

......................................................................
Murray Altheim                  <http://kmi.open.ac.uk/people/murray/>
Knowledge Media Institute
The Open University, Milton Keynes, Bucks, MK7 6AA, UK

     "In Las Vegas Mr Gates also demonstrated a prototype
      fridge magnet which can be programmed to receive traffic
      reports, sports results and advertisements from local
      restaurants using the same FM signal as the wristwatch."
                                  -- The Guardian, 10 Jan 2003.