On May 30, 2009, at 3:28 PM, Ian Bailey wrote:
> Hi All,
>
> Felt the need to poke my nose in on this one, and I'm sure I'll
> regret it. (01)
Hope not! (02)
> I think it *is* possible to have a small set of primitives (I've
> heard them
> called "ontic categories"), provided everyone using them has the same
> ground-rules (I've heard Chris Partridge call these "metaphysical
> choices").
> Without an agreement on those metaphysical choices, there cannot be an
> agreed set of primitives that are realistically usable. Here are some
> (purely fictitious) examples:
>
> * I decide first-order ontologies are plain nonsense, dreamt up by
> flat-earther computer scientists in a vain attempt to retro-fit the
> real
> world to their ideas about inference (obviously, I would never do
> such a
> thing). Let's call this metaphysical choice "world of warcraft". I
> want my
> ontology to be higher-order, let's call this "hairy-arsed engineer".
> The
> computer scientist grunts twice from beneath his beard to indicate
> he wishes
> the primitive "class" to be first order. Immediately here, we have a
> problem
> - the extent of what I call "class" is different to what he calls
> "class";
> mine can have classes as members, his can't. (03)
The idea of a "primitive" being first- or second-order or not doesn't
make a lot of sense to me on the face of it. Do you mean, e.g., you
want to use second-order set theory and your engineer first-order set
theory? Or you want to use full second-order logic and the engineer
wants to use a second-order language with so-called general semantics
(which is expressively first-order)? I'm not sure what you're saying
here. (04)
> My higher-order class can't be
> used by the flat-earthers, as they might have to wait an infinite
> amount of
> time for their computer (probably called "Gandalf") to come up with an
> answer. (05)
But first-order reasoning is also intractable (indeed, undecidable). (06)
> I can't use their class, as it's too restrictive. (07)
I'd be interested in seeing an example that is relevant to the goals
of ontological engineering. There is no complete proof theory for
second-order logic so it's pretty useless as a foundation for a
project whose goal, in large part, at least, involves automated
reasoning. (08)
> OWL tried to get
> round this by having different language conformance classes - full,
> DL, etc.
> But...if one person uses OWL:Class in the full sense and another in
> the lite
> sense, they have a different extent, and so really shouldn't use the
> same
> OWL keyword, (09)
That is not exactly true. The difference is only that, in the
semantics of OWL Full, the class of OWL classes is *required* to be
exactly the class of RDF classes instead of a subset. But this means
that there are interpretations of OWL DL (not sure about OWL Lite)
that are also interpretations of OWL Full and hence in which OWL:Class
has the same extent for both. The big difference between the two,
from the perspective of ontological engineering, is that validity is
provably decidable in OWL DL and provably undecidable in OWL Full.
It's not at all clear that this warrants using different OWL keywords
in the two frameworks. (010)
> * If I decide to be an extensional fundamentalist (a la Partridge /
> West
> flavour of ontology), and someone else decides intensional is the
> way, then
> again we have a problem. My classes are defined by the extent of their
> members. And, I need to ground my thinking in physical reality, so I
> have
> these things called individuals (or elements in BORO) which have
> spatio-temporal extent. The extent of the intensional classes will be
> different to that of the extensional ones - I'd have one class with
> two
> names "Equiangular Triangles" and "Equilateral Triangles", they'd
> have two
> classes. (011)
That depends on the theory. (012)
> Similarly, if they bother to have individuals, the intensional
> folks might have more than one referring to the same spatio-temporal
> extent.
> This would be a no-no to an extensional Jihadi like Chris Partridge.
> Again,
> we're unable to re-use each other's primitives. (013)
Isn't the obvious solution here to look at the axioms for the two
notions of class and subsequently to conclude they are simply
different (but related concepts) and hence need different names? Then
one can simply articulate the differences in terms of logical
principles that characterize the two, e.g., "If x is an instance of I-
Class A and not an instance of I-Class B, then the extension of A
(i.e., the E-Class consisting of its instances) is distinct from the
extension of B." (014)
> There are plenty of other choices too - modal logic vs possible
> worlds, 3D
> vs 4D, etc. (015)
In both cases the logical connections between the two are quite well
understood (not to say entirely unproblematic). But even still I
think your conclusions are largely warranted: (016)
> So, in my view, you can't have a common set of ontic categories
> unless you
> all agree on the ground-rules (metaphysical choices). If you really
> want to
> go down the road of developing a common set of primitives, you need
> to get
> an understanding of what everyone's ground-rules are, and how they all
> differ. Philosophers and logicians must have lots of ways to
> categorise this
> kind of stuff. Let's face it, what else have they got to do with
> their time? (017)
You don't know many logicians or philosophers, I guess. (018)
> They've had 3000 years to work on all this, albeit 2999 of them seem
> to
> have been spent arguing the existence/non-existence of God/gods. (019)
Haven't studied much philosophy, eh? But you do get back to the point: (020)
> So, I think the idea of one set of primitives to rule them all is
> impractical at least, and probably impossible. Based just on the
> range of
> opinion on ontolog alone, you can bloody well forget it. If you're
> talking
> about going beyond ontic categories, to produce what is sometimes
> called an
> "upper ontology" then the problem becomes an order of magnitude worse.
> (021)
> There. I think I've insulted just about everyone. A fine evening's
> work, I
> think.
>
> No computer scientists were harmed in the making of this e-mail. (022)
:-) (023)
Chris Menzel (024)
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