Dear Matthew, Bart, Ed, Barry, and Joel, (01)
I generally agree with your points. (02)
I would just like to state some general principles that hold
for any discussion about extended matter of any kind. (03)
Two important cases are fluids (like water) and solids (like rock).
With rock, there is a linguistic ambiguity, since we can talk about
"a rock" as a detached piece or just "rock" as the stuff that makes up
a rock. With water, there is no ambiguity, since we can't talk about
"pieces" of water without specifying some shape (such as "a drop")
or some container (such as a cup). (04)
Barry Smith pointed to articles about fiat vs. natural boundaries. (05)
An example would be some rock that broke away from the mountain
and crumbled into multiple detached pieces. Most of those pieces
would have a clear, natural boundary that separated it from other
rocks on which it happened to be resting. (06)
But there would also be some very fine-grained pieces that would
merge with the soil at the foot of the rock slide. That raises
another issue about the treatment of "stuff" made of detachable
grains. Depending on your scale of measurement, there could
be disputes about what is a "natural" boundary. (07)
But you might have a "fiat" boundary that separates two or more
regions of the mountain. For example, part of the mountain
might belong to a protected national park, but another part
could be part of a privately owned ski resort. In that case,
the boundary between them would be an invisible line established
"by fiat". (08)
These are all well-known cases for which people have established
conventions for talking about in ordinary language. And any of
those conventions could also be expressed in logic. (09)
However, there are many problematical cases, such as the boundary
between the ocean and the land. That boundary shifts with the tides
and with every wave. There are many practical and legal issues for
dealing with such cases. But any convention that anybody can state
in any natural language can be mapped to a statement in logic. (010)
John Sowa (011)
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