>Kathy,
>
>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.
>
>John
>
>
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