Dear John, (01)
I think this is an important point. (02)
> MW> For example, you could have a Linnean structure of living things
> > that did not know about 3D or 4D, but could take on either flavour
> > when incorporated into those theories.
> My guess is that a conjunction of the Linnean theory with either
> a 3D or 4D theory of space & time would not cause any inconsistency.
> But you can test the consistency by a variation of the method above:
> 1. Start with a model for which one of the theories is true.
> Store the data that represent that model in a relational DB.
> 2. Take the axioms of the theory that you want to combine it
> with, convert each one to an SQL query, and check them
> one at a time by executing the query.
> Note that the WHERE clause of an SQL query can express full FOL.
> Therefore, any axiom stated in first-order logic (or any subset
> of FOL) can be tested just by translating it to SQL.
> MW> This could have considerable value in achieving interoperability,
> > and might well be the useful thing that arises from Pat C's vision
> > of a common defining vocabulary, though I don't think there is any
> > such vocabulary that is finite, but if we have extensibility, that
> > does not matter too much, we just add what we need when we need it.
> Actually, the likelihood of inconsistency *increases* when you have
> a great deal of common vocabulary. If two theories have nothing
> in common, it's unlikely that they disagree about anything. But
> if they have a lot of terms defined in a common vocabulary,
> the likelihood of an inconsistency is greater.
MW: I think it is more than just a vocabulary, but I agree that great care
would need to be taken not to introduce into what I am calling abstract
theories axioms that did not contradict say the 3D and 4D axioms that would
be introduced when they were combined with those theories. However, having
such a theory would greatly simplify mapping between say 3D and 4D
ontologies. These would I think need to be carefully designed rather than
just picking something up, since it is casually almost certainly made some
upper ontology assumptions. (03)
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