Paola, (01)
That is the point of the discussion: (02)
> the one questrion that I am left with is whether
> holes are entities as such, or non entities (03)
That article on the Stanford philosophy site gives a brief
summary of the issues, and the book by Casati and Varzi goes
into more detail. (04)
My preference is to adopt something like an Aristotelian
form-matter combination. According to that principle, holes
definitely have a form, but the matter is something external
to them -- namely some part of the boundary of an object that
delimits their form. (05)
For typical physical objects, a boundary has a finite thickness.
But in the limit (which is only attainable by an abstract
mathematical object) the boundary would have zero thickness
and hence no material content. (06)
In summary, my recommendation would be to define a hole as
an object that has a location in space-time and a 3-dimensional
volume, which is determined by some part of the boundary of
an ordinary physical object. (07)
This definition accommodates some of the issues, such as
a hole that remains in a fixed location with a stable shape
while the matter that surrounds it may be changing (for
example, a hole formed by the space between two branches
of a waterfall). (08)
This does not imply that a hole is nothing. It is more like
a boundary than like a pure nothingness. (09)
John (010)
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