On May 20, 2013, at 4:33 PM, doug foxvog wrote: (01)
> On Mon, May 20, 2013 13:36, Pat Hayes wrote:
>
>> Mereology - the ontology of parthood - is concerned with the
>> relation being-a-part-of, which is a rather particular relation, and
>> cannot be understood by just making vague analogies to how people might
>> express themselves in casual English conversation.
>
>> Mereology (which was originally conceived as an alternative to set theory,
>> a foundational theory for mathematics) thinks of the world as made up of
>> lumps of anonymous stuff, and the basic relation between these lumps is
>> parthood. A is part of B when, if you "take" all of B, you must "take" all
>> of A with it. (It does NOT mean, you would say "A is part of B" in normal
>> idiomatic English.) If we are talking about physical objects (the usual
>> case) then it can be described as: if you were to draw a tight
>> spatiotemporal boundary around B, A would be wholly included inside that
>> boundary. So if a lock is part-of a door, and a door is part-of a house,
>> then yes, that lock is part-of that house, because the door is inside the
>> house-boundary and the lock is inside the door-boundary.
>
> The lock is certainly not within the house's spatiotemporal boundary.
> In almost all cases, the lock was made outside the house, so the
> spatiotemporal boundary of the house would intersect the lock (and
> the nails, boards, and most other primary components of the house),
> not encompass it. If you mean an instantaneous spatial boundary, (02)
I was thinking of a cotemporal spatial boundary, yes. (03)
> then the lock is within the boundary and thus included as part of the
> house, but so is every piece of furniture, person, pet, insect, liter of
> air and water that happens to be within the confines of the house at
> the time. (04)
No, the spatial boundary of the house can be limited from within the contained
space. Boundaries do not have to be convex. (05)
There are certainly tricky edge cases. Carry a can of paint into a room of a
house, paint the walls, let the paint dry. The dried paint is then, arguably,
part-of the house. When did that happen? I honestly don't know, but it was
somewhen in the above scenario. (06)
>
> It seems that you would have to define interior boundaries to the
> house so that you can exclude the contents of the house as not
> being "part of" the house. (07)
Yes, exactly. I was presuming a topological notion of 'boundary'. (08)
>
>> One might object, but the world is not made of lumps of anonymous stuff:
>> there are other kinds of things, and in any case the lumps have
>> properties, and roles and names, etc.. But mereology does not deny this,
>> of course: it simply ignores it when describing parthood. Or, one might
>> object, but that is not what *I* mean by 'part of'. Fine: your notion is
>> one relation, and mereological parthood is, apparently, a different
>> relation.
>
> Yes, there are many types of parthood.
>
>> Take the team/club example.
>> It seems obvious to me that a team member is
>> indeed a mereological part-of the team, at least if we ignore temporal
>> extents (We might have to say, the temporal part of the member during the
>> time interval that the team exists, is part-of the team.)
>
> Why do you consider the team to have a spatial extent? (09)
Yes. Assuming that membership in the team is well defined, of course. (010)
> I'd resist
> such a model. (011)
Why? On what grounds? (012)
> Does the team have a mass and a volume? (013)
I don't see why not. If I were to ask for the total weight of the team, the
question seems to have a clear and determinate answer. Its not a very usual
question to ask, but I'm sure you can make up a scenario which might require
it. (014)
Pat (015)
>
> -- doug foxvog
>
>> It is far less
>> obvious that the team is part-of the club; indeed, that seems like a
>> category mistake. (Does a club have a spatiotemporal extent?) And it is
>> surly not true to say that a club is part-of a federation. I don't see a
>> federation as being a mereological whole. So, part-of is indeed
>> transitive, its is easy to describe, and it has nothing much to do with
>> federations. That all seems pretty obvious to me. Next question?
>>
>> Pat Hayes
>> ------------------------------------------------------------
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>>
>>
>>
>>
>>
>>
>
>
>
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