Holes

In Holes and Their Mode of Being from August 2012 Bill says,
Consider a particular hole H in a piece of swiss cheese. H is not nothing. It has properties. It has, for example, a shape: it is circular. The circular hole has a definite radius, diameter, and circumference. It has a definite area equal to pi times the radius squared. If the piece of cheese is 1/16th of an inch thick, then the hole is a disk having a definite volume. H has a definite location relative to the edges of the piece of cheese and relative to the other holes. H has causal properties: it affects the texture and flexibility of the cheese and its resistance to the tooth. H is perceivable by the senses: you can see it and touch it. You touch a hole by putting a finger or other appendage into it and experiencing no resistance.
Hmmm.  There is something wrong with this, surely?  But what?  Bill then says,
Now if anything has properties, then it exists. H has properties; so H exists. 
But wait. What about r, the rational square root of two?  It's rational, and it squares to two.  So it has properties.  Does it exist?

Here is an earlier unpublished response to Bill's piece.  It was to be titled The metaphysics of absence.

Much of this is contestable, I think.  If there is a spade in my bucket then it seems I have two things.  If there is a hole in my bucket then it seems I have one thing with a certain geometry that probably makes it useless for carrying water. An incomplete bucket, perhaps, or a leaky bucket, or a holed bucket.
H is not nothing. It has properties. It has, for example, a shape: it is circular.
Alternatively, it's the local boundary of the cheese that's circular.
The circular hole has a definite radius, diameter, and circumference. It has a definite area equal to pi times the radius squared. If the piece of cheese is 1/16th of an inch thick, then the hole is a disk having a definite volume. H has a definite location relative to the edges of the piece of cheese and relative to the other holes.
This describes the geometry of some material that we can readily imagine being present but whose absence 'constitutes' the hole.  It's a little harder to describe the geometry of the hole in a torus or quoit.  Easier to say where the material is rather than where it isn't.  And if something is absent how do we measure its size?
H has causal properties: it affects the texture and flexibility of the cheese and its resistance to the tooth. 
Of course,  we find it convenient to talk of absences in the language of presences.  But this isn't really good enough.  It's a little like saying that if I weld three rods of steel into a triangle then the strength and rigidity of the triangle is somehow due to the empty space around it.
H is perceivable by the senses: you can see it and touch it. You touch a hole by putting a finger or other appendage into it and experiencing no resistance.  
A good criterion for there being nothing rather than something.
Now if anything has properties, then it exists. H has properties; so H exists. 
This looks like a metaphysical 'bridging' principle between language and reality.  It seems to be saying that there may be 'things' that have properties.  If so, these are the things that exist.  In contrast, presumably, there may be 'things' that do not have properties, and these won't exist.  This is a strange notion of thing.  'Imaginings' might be better.

Despite my title I don't want to think of holes as absences.  That way lie paradox and confusion.  This puzzle is part of the much bigger problem of how geometrical features and 'accidents' in general can be thought of as things or said to exist or depend.

Bill goes on to argue that the holes in his slice of Emmental have a different 'mode of existence' from the slice of cheese.  This seems to be building a metaphysical structure on a spongy foundation of decidedly debatable substantive commitments, but Bill says he has other examples besides holes, so we will have to wait and see.

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