On May 20, 2013, at 10:22 AM, doug foxvog wrote: (01)
> On 19 May 2013 07:26, Hassan Aït-Kaci wrote:
>> On 5/19/2013 1:43 AM, jmcclure@xxxxxxxxxxxxxx wrote:
>
>>> Could you provide example of a nontransitive part relation
>
>> A sport team is part of a sport club. A club is part of a sport federation
>> if it has at least one team all of whose members are professional players.
>> So a sport team may be part of a club, but not part of a federation.
>
>> --
>> -hak
>
> On Sun, May 19, 2013 06:26, Matthew West wrote:
>
>> This is conflating two things:
>>
>> a) Membership of a club to a sports federation, and of a player to a
>> sports club
>
>> b) Whole-part.
>
>> I would argue that it is the membership relation that is not transitive
>
> So subOrganizationOf is a specialization of partOf which is not transitive.
> (subOrganizationOf GaithersburgMD StateOfMaryland)
> (subOrganizationOf StateOfMaryland UnitedStatesOfAmerica)
> (subOrganizationOf UnitedStatesOfAmerica UnitedNations)
> (not (subOrganizationOf GaithersburgMD UnitedNations)
>
>> but that it is quite reasonable to create a mereological sum
>> of the players of the clubs that are members of a sports club
>> and of a sports federation, and that this is transitive.
>
> OK, one can create a transitive partanomic relation that has something
> to do with the non-transitive partanomic relation suggested. But the
> meaning of such a relation seems like it might be tricky to describe
> since the relationship between individual team members to their
> teams is different from their relationship to the club that their team
> is a member of and still different from the relationship that they have
> to the federation of clubs. (02)
Matthew is quite correct, and mereology is not particularly tricky to describe.
But you do have to actually learn what it is that it is talking about.
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. (03)
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. (04)
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. (05)
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.) 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? (06)
Pat Hayes
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