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Dear Avril,
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.
For example, if I am looking at the collection of cars sold under a particular brand and model, then I would see that as a set, because the weight I want to associate with the collection is the nominal weight of each member of the model. On the other hand if I am looking at a collection of cars on a scrap heap, then I am interested in the mereological sum, because I want to know about the weight of the whole collection.
Regards
Matthew
On Sep 28, 2012 11:04 AM, "Avril Styrman" < Avril.Styrman@xxxxxxxxxxx> wrote:
Lainaus "John F Sowa" <sowa@xxxxxxxxxxx>:
> Before criticizing mereology, I want to say that I consider it
> a useful alternative to set theory for many aspects of ontology.
I fully agree that e.g. as a definition of a flat part, mereology does
all that is required, in a simpler way than set theory, and thus is
better than set theory. Also, as a definition of what is continuous,
continuous mereology is a lot simpler than set theory which can be
used as a foundation continuous point-sets, and thus mereology is
better. A better question is that why do we need 'continuity' in the
first place in modeling finite and discrete phenomena?
Apart from all this, set theory is not all bad. When we take
transfinities and the empty set away, the empirically applicable
'structural' features are revealed: set theory can be used in modeling
granular structures that are found all around in nature. If mereology
is used in modeling granular structures, then mereology will in any
case have to be complemented with the epsilon/memberOf relation, or
with some corresponding relation that does the job of epsilon.
-Avril
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