On 27 April 2014 12:10, Terence Love <[log in to unmask]> wrote:
> The difference is that 'sets' comprise collections of distinctly defined
> objects. Some sets may overlap and an object may be in more than one set.
> Set theory is relatively straightforward as the relationships between
> different sets are straightforward. In contrast, 'mereology' refers to the
> way that some things are 'parts' of a 'whole'. This is a complex issue and
> very different from 'sets'. For more detail see
> http://plato.stanford.edu/entries/mereology/
>
Quick followup on mereology.
Turns out one of my research projects in design deals with using
mereotopology (MT) (the combination of mereology and topology) to devise a
formal system (logical, not computational) for product models. I even
managed to get a reasonable paper out on the preliminaries -
http://digitalcommons.ryerson.ca/islandora/object/RULA%3A310 - but it's
been a tough row to hoe because that kind of research is not appreciated in
Canada's industry-driven research strategy (if you detect bitterness there,
then you'd be right).
A "classic" (if somewhat macabre) question that MT tries to handle is "Is a
cat that loses its tail in some accident still the same cat?" Even from an
engineering POV, it's an important question. If a bridge loses a
structural element, is it still the same bridge? If a kettle loses its
handle, it is still the same kettle?
Unfortunately, I've fallen behind in keeping up with the MT lit because I
was trying to keep myself funded. Now that that's basically over with, I
would like to try to return to my real interests, including MT.
My doctorate used rather conventional set theory, but I had a helluva time
trying to formalize product models with it. MT made that much easier. One
of the things I noticed when I first fell upon MT was that set theory had,
over time, become foundational to mathematics, to do things like prove the
logical existence of integers. As a result, ST had drifted away from
Cantorian "collections" and toward more esoteric number theoretic features.
Important stuff, but beyond the scope of my (design) interests. MT had
always been, and remains today as far as I know, intended to address
questions of parts and wholes (and how they connect together). Because of
this, I still believe quite strongly that MT is a better way to go than ST.
/fas
\V/_
Prof. Filippo A. Salustri, Ph.D., P.Eng.
Email: [log in to unmask]
http://deseng.ryerson.ca/~fil/
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