Cory points below to a problem related to the Peanut Butter Sandwich
problem I addressed earlier. (01)
There is a class of all people with 874 hairs on their left arm at
midnight on 14 January 2006.
This is because there is an extension of the predicate 'has 874 hairs
on their left arm at midnight on 14 January 2006'.
But there is no such type (aka 'natural kind').
This is because there is nothing in reality which all the members of
this extension share in common and whose identification would assist
science in understanding the causal structure of the universe.
Rather, the class in question is an arbitrary class.
BS (02)
At 09:18 PM 1/20/2006, you wrote:
>Ok, logical gurus, help me out here.
>The asserted "difference", between type and class is extensional. The
>statements below say that if the instances satisfying the types are the same
>then types are the same.
>Another statement would be if the instances satisfying the types must be the
>same the types must be the same.
>The <are> and <must be> are very important.
>
>The first statement would only work for predicates that assume a very closed
>and very static world. E.G. the type of people on this list and the type of
>people with 874 hairs on their left arm are the same so these types must be
>the same - a very bad inference, particularly after I pluck a hair. It
>assumes global knowledge and a static world. While I have no problem that
>predicates or even logics may choose to make those assumptions, it should
>not be part of the definition of type (or class).
>If, on the other hand there is a logical necessity for the extensions to be
>the same, the class and type concepts are the same - this works and I don't
>see the issue. This also works in OWL. This is what I thought the concept
>of extensional classes entailed - but I am still learning.
>As Chris says, you can ADD those assumptions to an ontology or context
>without constraining core concepts like type/class/isKindOf.
>
>
>-----Original Message-----
>From: ontac-dev-bounces@xxxxxxxxxxxxxx
>[mailto:ontac-dev-bounces@xxxxxxxxxxxxxx] On Behalf Of Chris Menzel
>Sent: Friday, January 20, 2006 12:33 PM
>To: ONTAC Taxonomy-Ontology Development Discussion
>Subject: Re: [ontac-dev] Type vs. Class -- Please vote
>
>On Fri, Jan 20, 2006 at 06:27:49PM +0200, Christopher Spottiswoode wrote:
> > ...
>
>Hello, Christopher, it's been a while.
>
> > Pat, my own vote goes strongly to "type" (if I may emerge albeit
> > perhaps incongruously from my lurking state on this list).
> > Im my own work, which I hope to release to this list and the widest
> > user community at a more appropriate time, I have for many years
> > consistently and insistently used "type" to denote the intensional
> > sense. "Class", it seems to me (as to John Sowa), invites confusion
> > with the extensional sense.
>
>I continue to be utterly flummoxed by this argument. Do we, or do we
>not, believe ontologies can avert exactly these sorts of confusions?
>If not, just what do we think we are doing? Looky here:
>
>(forall (C1 C2)
> (if (and (Class C1)
> (Class C2)
> (forall (x)
> (iff (instanceOf x C1)
> (instanceOf x C2))))
> (= C1 C2)))
>
>Add that axiom to your ontology, you get extensional classes. Leave it
>out, you don't. Simple, eh? :-) What *is* the controversy here?
>
> > Having said that, I would however agree with Cory that we should try
> > to conform as far as possible with what seems like colloquial use.
> > But I think that that rather argues in favour of "type", as it is (to
> > me at least...) more colloquially intensional than "class"!
>
>Well, at the risk of furthering the impression that this red herring of
>an argument is to the point :-) , I respectfully disagree. Indeed, I
>can't even think of a colloquial use of the term "class" that is
>extensional. Not even "set" is extensional in colloquial usage.
>
> > I mention that because both Chris Menzel and Leo Obrst have warned us
> > against using "type" because of all the uses of that word in various
> > formal systems.
>
>That skews my point badly. It is not simply the fact that "class" is
>the term of choice in the formal system OWL that we should use it; it is
>the fact that it is in OWL AND the fact that OWL and its kin are the
>primary W3C languages for publishing ontologies on the web. We're
>swimming unnecessarily, indeed perversely, upstream if we choose
>otherwise. Seems to me that the only thing that could justify the
>choice of "type" would some definite semantic incompatibility between
>the desired ONTAC notion and the W3C notion of class. But there isn't.
>So if we go with "type", we force EVERY user of OWL out there who wants
>to interact with an ONTAC-based ontology needlessly to worry about
>translating every occurrence of "type" into "class". Similarly for
>every user of any ONTAC-based ontology. Isn't the point here to
>*enhance* interoperability? Why throw up this completely unnecessary
>stumblingblock, folks?
>
> > I would strongly urge us, however, not to be so influenced by such
> > perhaps confusing formal uses:
>
>It is the informal uses that are confused. We have axioms to prevent
>that sort of confusion.
>
>-chris
>
>
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