## Tuesday, December 3, 2019

### Holes and substantivalism

Suppose substantivalism about space is correct. Imagine now that the following happens to a slice of swiss cheese: the space where the holes were suddenly disappears. I don’t mean that the holes close up. I mean that the space disappears: all the points and regions that used to be in the hole are no longer there (and any air that used to be there is annihilated). The surfaces of the cheese that faced the hole now are at an edge of space itself.

The puzzle now is that in this story we have an inconsistent triad:
1. There is no intrinsic change in the cheese.
2. The slice of cheese no longer has holes.
3. Changing with respect to whether you have holes is intrinsic.
Here are my arguments for the three claims. There is no intrinsic change in the slice of cheese as something outside the cheese has changed—space has been annihilated. The slice of cheese no longer has holes, as it makes sense to talk of the size or shape or volume of a hole, but there is no size or shape or volume where there is no space. And changing with respect to whether you have holes is change of shape, and changes of shape are intrinsic.
It seems that the above story forces you to reject one of the following:
2. Intrinsicness of shape.
But there is another way out. Deny (3). Whether you have holes is not intrinsic. What is intrinsic is your topological genus with respect to your internal space and similar topological properties.

Note, also, a lesson relevant to the famous Lewis and Lewis paper on holes: the counting of holes should not involve the counting of regions, but the computation of a numerical invariant, namely the genus.

Philip Rand said...

There is no intrinsic change in the slice of cheese as something outside the cheese has changed—space has been annihilated.

Incorrect.

The boundary conditions have changed.

Philip Rand said...

THOUGHT EXPERIMENT:
Imagine the following happens to a slice of swiss cheese: the space where the holes were suddenly disappears. I don’t mean that the holes close up. I mean that the space disappears: all the points and regions that used to be in the hole are no longer there (and any air that used to be there is annihilated). The surfaces of the cheese that faced the hole now are at an edge of space itself.

WHAT NEXT HAPPENS TO THE CHEESE?

Philip Rand said...

You see, the problem you have is that an Aristotle/Aquinas approach cannot give you a perspicuous view...

For example you will be unable to give the reasion why topological genus is an intrinsic feature... what is required is the method used in solving the Seven Bridges of Königsberg...

Philip Rand said...

By the way... topological genus is not an intrinsic feature of the cheese.