Many thanks for taking the trouble to make such a full answer.
Like and agree with much of what you say, but a few points
Can I start with your last comment.
PH> Priority?? And aren't we, in this forum,
talking about logics (in a broad sense, ie formalisms for description) and KR,
rather than statistics or metaphysics?
I appreciate that this is your (and others) view.
However, there is another view (and another view of logic) which
I think John was espousing in an earlier set of emails (in relation to
Aristotelian syllogisms), which is that logic is a formalism for describing the
way the world is – or more grandly, what exists. And that in some way the
form of the logic reflects the structure/nature of the world.
A colleague pointed out to me something you may be familiar
with, “ARISTOTLE'S LOGIC: A COMPARISON OF LUKASIEWICZ'S AND
Though this is not exactly the point we are discussing, it
illustrates the kinds of tensions that can arise between the ‘formalisms
for description’ and ‘formalism for describing the way the world
However, I expect we will just have to agree to disagree.
With respect to the intended meaning of individual (a point you
raised), we were trying to find out what the OWL sense was. It is explicitly
mentioned several times in the specification. See some extracts below. We
definitely were not using it in its metaphysical sense.
1. Introduction (Informative)
document contains two formal semantics for OWL. One of these semantics, defined
3, is a direct, standard model-theoretic semantics for OWL ontologies
written in the abstract syntax. The other, defined in Section
5, is a vocabulary extension of the RDF semantics [RDF
Semantics] that provides semantics for OWL ontologies in the
form of RDF graphs. Two versions of this second semantics are provided, one
that corresponds more closely to the direct semantics (and is thus a semantics
for OWL DL) and one that can be used in cases where classes need to be treated
as individuals or
other situations that cannot be handled in the abstract syntax (and is thus a
semantics for OWL Full). These two versions are actually very close, only
differing in how they divide up the domain of discourse.
A contains a proof that the direct and RDFS-compatible semantics have the
same consequences on OWL ontologies that correspond to abstract OWL ontologies
that separate OWL individuals, OWL
classes, OWL properties, and the RDF, RDFS, and OWL structural vocabulary. Appendix
A also contains the sketch of a proof that the entailments in the
RDFS-compatible semantics for OWL Full include all the entailments in the
RDFS-compatible semantics for OWL DL. Finally a few examples of the various
concepts defined in the document are presented in Appendix
June 2003] Per a decision of the Web Ontology working group on 26 June
2003 to replace owl:sameIndividualAs
with owl:sameAs, recorded in http://lists.w3.org/Archives/Public/www-webont-wg/2003Jun/0364.html,
made changes to Section
5.2, and Appendix
June 2003] Fixed a bug in the semantic conditions for owl:hasValue
noticed by Jeremy Carroll, changing the conditions for the value from a
property to an individual or a
data value in Section
July 2003] In response to a substantive post-last-call change to the RDF
semantics, changing the if-and-only-if conditions for rdfs:subClassOf
and rdfs:subPropertyOf to only-if conditions,
added if-and-only-if conditions for rdfs:subClassOf,
over OWL classes, and rdfs:subPropertyOf, over
OWL individual-valued properties
and over OWL datatype properties, to Section
July 2003] In response to http://lists.w3.org/Archives/Public/public-webont-comments/2003Jul/0011.html
changed several uses of ``object'' to ``individual''
or ``individual-valued'' in Section
2 and Section
5.2 and made other editorial changes to Section
I agree that a logician may not like the term individual –
I prefer element – but in it what is intended in the ordinary language
sense. You may prefer ur-element.
PH> It is not a metaphysical classification: it does
not separate the ontic universe into two kinds of thing, one kind more 'individuated'
than the other. (Speaking personally, now, I have never understood what such a
distinction could possibly mean.)
I think, in logic, it may be the distinction between ur-elements
One of the things that continues to surprise me it that the
current ZF contain only sets. This seems to be the outcome of mathematicians
desire to avoid any contact with the real world at the beginning og the last
century. But “The Zermelo set theory of 1908 included urelements.
It was soon realized that in the context of this and closely related axiomatic
set theories, the urelements were not needed because they can easily be modeled
in a set theory without urelements. Thus standard expositions of the canonical
axiomatic set theories ZF and ZFC do not mention urelements.” http://en.wikipedia.org/wiki/Urelement
Have you come across NFU? http://en.wikipedia.org/wiki/New_Foundations
NFU has ur-elements and a universal set – which, from what you say, you
Could you live with an urelement / set distinction?