|From:||Gary Berg-Cross <gbergcross@xxxxxxxxx>|
|Date:||Mon, 1 Mar 2010 22:27:22 -0500|
I have a small question to wedge into this discussion on whether the meaning of Primitives in a Foundation Ontology change (or may change) as we add axionms.
Patrick Cassidy describd this as a
>disconnect between PatH's view of "meaning" and mine is that he is
>content to believe that the meanings of the elements used in programs,
>databases, ontologies (e.g. time, distance, physical object, dollar, person)
>all change every time we add a new assertion about unicorns, and I am not.
>IMNSHO, this is not a useful interpretation of "meaning" for practical
Eearlier John Sowa expressed his objection to using 'primitives' as a foundation is that
"the meaning of a primitive changes with each theory in which it occurs.
For example, the term 'point' is a 'primitive' in cand
various non-Euclidean geometries. But the meaning of the term 'point' is
specified by axioms that are different in each of those theories."
(and in another note) "As soon as you add more axioms to a theory, the "meaning" of the
so-called "primitives" changes.'
Since Euclidean geometry, an axiomitized systems, was mentioned it reminded me of Euclid's first 4 postulates (axioms) which involve primitives like point. When a 5th axioms is added it didn't seem like the primitives changed and that any conclusion just using the first 4 axioms would be the same. If the 5ht axioms is involved then new conclusions are reached. On the face of it this seems to be the an intuition that supports (in part) what Pat C was saying.
Can our formalists help out on this question?
SOCoP Executive Secretary
On Thu, Feb 25, 2010 at 12:18 PM, Patrick Cassidy <pat@xxxxxxxxx> wrote:
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