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Re: [ontolog-forum] Visual Complexity

To: "John F. Sowa" <sowa@xxxxxxxxxxx>
Cc: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Thu, 8 Feb 2007 11:59:24 -0600
Message-id: <p0623091bc1f113f1b715@[]>
>Sergei and Bill,
>That is the distinction between set theory and mereology:
>  > If sets are there in the world, then no - there's nothing
>  > abstract going on.  I'm real.  Chuck is real.  And the set
>  > of me and Chuck is real.
>In mereology, Bill and Chuck are each parts of the collection    (01)

"sum" is the correct term I believe. Whether or not collections are 
sums is a matter of active debate.    (02)

>that consists of Bill and Chuck.  You can call that pair C,
>but C is not a new entity.  It is just Bill and Chuck.    (03)

It has them as parts, but it's not the same as them. There are (at 
least) three mereological sums in this story so far.    (04)

>But in set theory, if Bill and Chuck are members of the set S,
>then S is a third entity that is different from each of them.    (05)

Same in mereology.    (06)

>You have three things:  Bill, Chuck, and {Bill,Chuck}.  You
>can also construct a fourth thing, which is the set whose only
>member is the set whose members are Bill and Chuck: {{Bill,Chuck}}.    (07)

Right, therein lies the difference. Better example is to stick with 
Bill. Then in mereology that is all we have (until we decide to carve 
him up) but in set theory we also have {Bill}, {{Bill}}, {{Bill}, 
Bill}, etc.. ad infinitum.    (08)

Pat    (09)

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