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Re: [ontolog-forum] Universal Basic Semantic Structures

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Chris Menzel <chris.menzel@xxxxxxxxx>
Date: Sat, 29 Sep 2012 18:03:29 -0500
Message-id: <CAO_JD6Mx0EpLPMsgh2Z4fGqobnRrTz6QX99tDC7R245Gn+xGwg@xxxxxxxxxxxxxx>
On Fri, Sep 28, 2012 at 11:54 AM, John F Sowa <sowa@xxxxxxxxxxx> wrote:
> I do not see set theory and mereology as alternatives that you choose
> one from for your ontology, rather I see them as being appropriate
> in different circumstances. One of the tests I use to determine which
> is appropriate is whether I am or could be interested in the weight
> of the collection. Sets are abstract and so do not have a weight.
> A mereological sum on the other hand does.

That's a very good, one-paragraph summary of the difference.  Formally,
I would emphasize that set theory has two operators (subset and isIn),
but mereology has only one operator (partOf).

John, virtually every text on set theory presents the axioms with just a single binary predicate "∈" for membership. The subset relation is always defined; using "isin" instead of "∈":

  (iff (subset x y) (forall z) (if (isin z x) (isin z y))).
I agree that you can use set theory for those purposes.  And set
theory can be used in conjunction with continuous math in physics.
Furthermore, the method of partitioning and projection by Bittner
et al. can be adapted just as easily to set theory as to mereology.

I doubt that is true except in the sense that one can model mereology in set theory (e.g., as a certain type of algebra, depending on the mereological theory in question).


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