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Re: [ontolog-forum] Universal and categories in BFO & DOLCE

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Mon, 05 Sep 2011 08:40:55 -0400
Message-id: <4E64C357.6010000@xxxxxxxxxxx>
Dear Matthew,    (01)

I believe that set theory is great, and a 4D ontology is very useful.    (02)

In fact, I also believe that the only difference between your position
and mine is in the choice of words.    (03)

> MW: You can also postulate facts that will be true in a particular possible
> world. I would consider it disingenuous to construe those as definitions of
> the world. This principle is central to the way that possible worlds are
> used in practice for e.g. planning.    (04)

I certainly agree.    (05)

But there's a simpler and more accurate term for "postulated facts"
about the future:  *assumptions*.    (06)

Please note that many of the most useful sets in mathematics
are generated by *intensional* assumptions (AKA axioms).    (07)

The set of natural numbers, for example, is infinite.  The only
way to specify an infinite set is by some axioms (AKA assumptions)
that generate it -- or by some operations such as intersections
and unions of other infinite sets that had previously been specified
by assumptions.    (08)

>> But I would add that you can have possible worlds with non-null sets
>> of unicorns.    (09)

> MW: Of course. That is why the use of possible worlds permits you
> a system that does not depend on types.    (010)

It's irrelevant whether you use the term 'type' for the assumption
that specifies unicorns or 'monadic predicate' is-unicorn(x) for
specifying the identity conditions of those entities in your
possible world that happen to be unicorns.    (011)

The point I was trying to make is that the only information you
can get by contemplating or proving theorems about those worlds
comes from whatever assumptions you put into the specification
of predicates such as is-unicorn(x).    (012)

>> However, any data you get about unicorns in those worlds
>> are just implications of your starting assumptions about them.    (013)

> MW: No they are not. They can also be facts that you stipulate to be
> the case in that particular possible world. Facts are not assumptions.    (014)

Facts are obtained by observation or from reports of observations
by reliable sources; 'stipulation' is a legal term for a proposition
agreed by two or more parties as a basis for further argument, as in
a court of law.  In other words, a stipulation is not an observed fact,
but it is accepted by all parties *only* for the purpose of argument.    (015)

Summary:  No information about the future or about any possible world
can be obtained by observation.  It is only derived from specification,
stipulation, hypothesis, postulate, axiom, or definition.  The general
term that includes all those sources is 'assumption'.    (016)

John    (017)

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