On Feb 14, 2009, at 7:40 AM, Ali Hashemi wrote:
On Fri, Feb 13, 2009 at 8:58 AM, John F. Sowa <sowa@xxxxxxxxxxx>
I agree that FOL is the most neutral notation that we know how
to formalize. (I'll leave open the question of whether there
might be something even more primitive.)
But given that FOL is neutral, the first time we add an axiom
with a named predicate or relation, we are making a metaphysical
I'd love to get some opinions here about the degree (if that's an appropriate word) of ontological commitment. And particularly, how one choice might set off a slew of unintended consequences if one is not careful.
For example, take the notion of linesegment in (or extending) Hilbert's geometry formalization. One might be tempted to implement it is as strictly a relation between 2 (or 3)
Or indeed any number. One widely used geomorphology model defines an area as something bounded by a closed line, a closed line as any contiguous sequence of linesegments, and a linesegment as a pair of points.
points say in ontology O1 - i.e. (linsegment x y z) where (x,y,z) are all points. Another, might in ontology O2, be tempted to define a new entity "linesegment" which consists of points -i.e. (linesegment XY x y). Is one making a stronger ontological commitment than the other?
An incidence relation connecting linesegments to points would have the same extension as the linesegment relation in O1.
i.e. relI(on1) = relI(on2) where in O1: (on1 (lineseg x y z) a) and in O2: (on2 linseg a).
Clearly O2 is commiting to the existence of some thing called a linesegment, whereas it is only implied in O1, so in some sense, it is making a greater ontological commitment.
Yes, exactly. Though in CL, there is less to choose between them as the first is also committing to the existence of the linesegment relation itself.
What are advantages / disadvantages to the different formalization choices? It seems O2 would allow more things to be said, but might it be over committing?
It does enable more to be said. And what does OVER commitment mean, here? Philosophers are often leery of admitting to the existence of things because they have a philosophical agenda to reduce everything to some small subclass of entities (for example, nominalists like Chris Partridge tend to think that only actual concrete physical things are really real), but when writing ontologies for practical use, we should not be guided by merely philosophical agendas. I see very few practical problems arising from having ontologies commit to the existence of things fairly freely, and having the relevant things in ones ontology tends to make it a lot easier to say what you need to say. For example, once you have linesegments, you can speak of their being parallel, orthogonal, etc., and of lying on other useful lines, such as legislatively defined boundary lines.
If one tended to seek evidence in language, the fact that English can take almost any word and nominalize it seems to suggest that English native speakers, at least, have little trouble thinking of a wide variety of things as nameable entities that exist.
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