Re: [ontolog-forum] Relevance of Aristotelian Logic

[Ali Hashemi <ali.hashemi+ontolog@xxxxxxxxxxx>]

On Fri, Feb 13, 2009 at 8:58 AM, John F. Sowa <sowa@xxxxxxxxxxx> wrote:

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
commitment.

John

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) 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.

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?

Thanks,

Ali

-- 
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