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Re: [ontolog-forum] Ontological Assumptions of FOL

To: "John F. Sowa" <sowa@xxxxxxxxxxx>
Cc: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Sun, 18 Mar 2007 03:07:55 -0500
Message-id: <p06230907c222a25bcea7@[]>
>I agree with that point:
>  > If we go around saying the universe "is" a set, we are
>  > in danger of confusing a representation of the world with
>  > the world we are representing.
>Many people prefer to use mereology instead of set theory.    (01)

Use for what, John?    (02)

But in any case, if we go around saying that the 
universe "is" a mereological sum, we are in 
exactly the same danger. That is just as much of 
an abstraction as a set is.    (03)

>I won't argue with anyone about their preferences, but
>the fact that there are options implies that there are
>many ways of representing or talking about the world.
>Pat Hayes said that he doesn't like mereology -- perhaps
>because there are so many different axiomatizations for it.    (04)

There are of set theory also. No, for my reasons see below.    (05)

>Again, I won't argue about preferences, but I don't consider
>that an argument for preferring set theory.  I wouldn't
>consider any of them more fundamental than any other.    (06)

Its not a question of being more fundamental, but 
simply more useful. Mereology is a theory of 
parthood. Not all things have parts (what is a 
part of the number 17?) Set theory is a theory of 
collections. Anything at all can be treated as an 
element of a collection. And set theory does 
support virtually all of mathematics, whereas 
mereology supports virtually none. Mereology is 
fine in its place (Im giving a paper on mereology 
of contexts next week) but its utility is 
severely limited.    (07)

Pat    (08)

>Common Logic is completely neutral about that matter.  It has
>no built-in ontology of sets, mereology, or even numbers.  It
>does recognize the numerals as a special kind of names, but
>it doesn't assume any particular theory of numbers.
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>    (09)

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