Hi Pat, (01)
May I check out one of your claims? I know we may well be going over old
ground. (02)
PH>This is because the *only*, repeat ONLY, assumption that FOL makes about
its universe is that is is a nonempty set (03)
If we take the old early 20th century philosopher's view of logic as the
language to express an ontology (strictly speaking - the language in which
to describe an ontology). This assumes some sort of link between predicates
and properties - where there may be more predicates than properties. Then I
think we find (at least two) awkward constraints. (04)
The first, we have discussed before. The world seems (to me at least) to
have what I will call second order universals - i.e. universals of
universals (I am not trying here to make a commitment to universals, call
them classes, sets, types or whatever is your poison). This can be difficult
(impossible?) to describe properly in FOL. (05)
The second is that the predication relation is not really accessible - and I
have found that it is useful to have this. In Barry Smith's terms - if you
start with Fa - you have nothing explicit in your notation for the link
between F and a. I am sure you can dig up papers on the varieties of
predication, exemplification etc. which give a more theoretical position on
this. (06)
I also find it odd to think of the subsumption (subtype/subclass) relation
as a kind of material implication (Fa -> Fb) - as seems to happen with some
FOL ontologies. (07)
I realise that one can regard properties and universals as the range of the
FOL variables (see Andrew Newman's The Physical Basis of Predication - as
well as Barry's Fantology paper). I have been told that there are problems
with this in terms of the categoricity of models (I'll let you or ChrisM
explain this). (08)
So, I suppose that if you drop the predicate-property assumption, then FOL
becomes ontologically bland. But I am not sure that is the way people want
to go. It seems to me that a number of the inference engines have this
assumption built in. (09)
BTW my concerns are not down to theoretical ontological squeamishness - I
find this has serious practical problems. In my 'reverse-engineering' of
ontologies from legacy systems, I find large tracts of the reference data
are irredeemably higher-order (universals). If that is what the empirical
data tells us, we should listen. (010)
If I may put this another way (and bring it back to the title of the post),
if you are making claims about FOL in terms of logic/inference, I do not
disagree. If you are making claims about ontology/existence - through the
structure of FOL - then it seems to me that there are examples where FOL is
not neutral. (011)
And, I think it would make things a lot easier if we had a better
explanation of the links between inference/logic and ontology (in the
philosophical sense). (012)
Regards,
Chris (013)
-----Original Message-----
From: Pat Hayes [mailto:phayes@xxxxxxx]
Sent: 16 March 2007 15:37
To: Chris Partridge
Cc: [ontolog-forum]
Subject: Re: [ontolog-forum] The Relation Between Logic and Ontology in
Metaphysics (014)
>Chris, John,
>
>The topic itself seems to me interesting.
>
>You may be able to shed some light on this.
>
>>From what little I know, it seems as if at the beginning of the 20th
>century, philosophical opinion tended towards regarding logic as a
potential
>candidate for ontology. By the end of the century, ontology is about what
>exists and logic about what can be inferred.
>
>It seems to be the case, as noted below, that "ontological considerations
>might play a role in the choice of an appropriate formalism" and
presumably
>that a formalism (such as FOL) might have implicit ontological
implications. (015)
Hmm. I wish ChrisM has not agreed to this quite
so readily. I think this dictum, while of course
defensible, can be very misleading if understood
too strongly, as a kind of Whorfian view of
logic. All the formal and I would suggest
informal evidence seems to point to FOL, in some
incarnation, as the single best 'ontologically
neutral' logic. This is because the *only*,
repeat ONLY, assumption that FOL makes about its
universe is that is is a nonempty set (and if you
are willing to live with a free logic, which Im
not, you can even allow it to be empty). And,
moreover, it is the ONLY logic which does make
only this minimal assumption. All other logics
seem to impose extra conditions on their
universes: HOL requires it to be closed under
relational comprehension, modal and context
logics require it to support some kind of
neo-Kripkean structure, etc.. Now, it is hard for
me to image what could possibly be *less* of an
ontological commitment than that the elements of
the universe can be viewed as members of a set:
this is almost a prerequisite for *any* kind of
thing that can possibly be describe
mathematically, i.e. using the apparatus of a
modern precise semantic theory. So FOL - again,
understood model-theoretically, so the term can
encompass quite a wide variety of actual logics -
seems to me to be as ontologically bland, as
ontologically un-Whorfian, as it is possible for
a logical framework to get. MOreover, virtually
all the various alternative formalisms that have
been suggested for serious ontology use can be
easily transliterated back into FOL or a suitable
FOL theory (eg for modalities one needs to
introduce possible worlds, aka states, aka
situations, aka contexts, and quantify over them
in an appropriate way.) Can we all simply agree
on this, and move forward? We have serious
engineering points to get solved, and it is very
discouraging to find ourselves debating and
re-debating issues that were interesting in
technical philosophy a century ago but which have
been laid to rest in every practical sense for
about 30 years now. (016)
>I wonder whether either of you (or anyone else on the list) could point to
>philosophical research on the links between the two.
>
>One thing that puzzles me, for example, is whether something like an axiom
>that states the whole-part relation is transitive is implying that there is
>some kind of ontological dependence between the parental and ancestral
>whole-part relations. (017)
Say what you mean by 'ontological dependence'.
That axiom certain asserts that there is an
inferential connection between them: it allows
you to infer statements involving one of them
from statements involving the other. Is this an
'ontological dependence'? (018)
>And if so, why? And under what conditions does
>inference imply ontological dependence? (019)
I have no idea, because I don't know what the second phrase means. (020)
>Why is this interesting? Well, understanding it may help us in choosing our
>formalisms. (021)
Lets just choose (your favorite subset of) FOL,
and move forward. Everyone else does, whether
they admit it or not. (022)
Pat (023)
>
>Regards,
>Chris
>
>-----Original Message-----
>From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
>[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F. Sowa
>Sent: 16 March 2007 13:44
>To: [ontolog-forum]
>Subject: Re: [ontolog-forum] The Relation Between Logic andOntology in
>Metaphysics
>
>Chris,
>
>Fine. We can all agree on that:
>
> > I certainly agree that ontological considerations might
> > play a role in the choice of an appropriate formalism.
>
>And the converse is also true: the formalism can affect
>or bias the choice of ontological categories and the
>way they are developed, studied, and used.
>
>John
>
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