## Tuesday, December 3, 2019

### Shapes of holes

The ordinary notion of a hole is kind of dubious. Consider the hole in the thin wavy sheet of rubber on the right. What is the shape of that hole? How thick is it? Is it exactly as thick as the rubber sheet? But the rubber sheet varies in thickness, actually. How does it stretch from its wavy edges to the middle? Does it have a sinewave bump in the middle, to correspond to where there are sinewave bumps in the sheet elsewhere? Or does that depend on the history of its formation (e.g., maybe if the sheet used to have a bump there but then a hole was made--that's how my code generating this picture works--then the hole has a bump, but if the sheet was pre-made with a hole, then the hole is flatter)? I think there really are no good answers to these questions, and hence holes don't exist.

Martin Cooke said...

Great question! It sounds like a classic analytic puzzle, but I have never heard of it before. I think that holes obviously exist. Perhaps I could defend my position by posing similar questions of other things that obviously exist.

The thickness of a hole is perhaps not an important property of it. So perhaps it is like the loveliness of your sheet of rubber. Loveliness is an important property of people and pets and views and works of art and many other things. And while it is a matter of opinion, that does not mean that there are not good answers to questions of loveliness. Hitler was clearly not lovely, for example. But, while you probably like your sheet of rubber, even you might doubt its loveliness. It is kind of dubious. Still, the sheet exists (so to speak). And similarly, although I have no idea how thick the hole in it is, still that hole exists.

Philip Rand said...

PROPOSITION: I think there really are no good answers to these questions, and hence holes don't exist.

CONCLUSION: It is impossible to fall down a hole because holes don't exist.

Alexander R Pruss said...

The shape of a hole does seem to be an important property of it.

Alexander R Pruss said...

It's also odd that for a hole in a thin wavy sheet, there may be no point in space such that it's definitely the case that the point is in the hole. Maybe that's an ok amount of vagueness.

Martin Cooke said...

While the shape of a hole is an important property of it, that is not its three-dimensional shape but its two-dimensional shape. The thickness is not so important, just so long as it goes all the way through, just so long as it is a hole.

If it was very thick, then it would be less of a hole and more of a tunnel. There is probably a grey area between a hole and a tunnel. And I guess you could think of string as a tunnel in space.

A hole in an unusual substance could be very odd indeed, but that is less about the existence of holes in general. And while points in a hole are odd, so are, for example, atoms in our bodies, so I think that such vagueness might just be par for the course.

Martin Cooke said...

A hole through a wall, for a very thick wall, would also be a tunnel.

But if the ends of the hole were filled in, the wall would have no hole in it, only a cavity. Whereas if the ends of the tunnel were filled in, the tunnel would still be there.

That is not too odd though.

Philip Rand said...

Martin Cooke

There is probably a grey area between a hole and a tunnel.

There is probably a grey area between a hole and an arse-hole.

What is the difference?

Philip Rand said...

Martin Cooke

Think of holes and tunnels as porosity. This should remove the grey area between a hole and a tunnel for you.

Michael Gonzalez said...

I think the fundamental issue is much deeper, and it is a linguistic/conceptual issue. We can say of something that it "exists", even if there is no object in the world corresponding to the grammatical object in the sentence "X's exist". Easy example: "There exist grounds for impeachment". No one thinks that there is any such object (except, maybe, some Platonists). And we certainly aren't logically or linguistically required to think so. Which is to say, we can deploy such sentences at the highest levels of competency with the English language and with the subject matter being discussed, without holding that there are any such objects in the world... indeed, I think we would be quite hampered and would cloud the issue if we added the consideration that there were real objects in the world corresponding to "grounds for impeachment".

Having made that general point (I could have given any number of examples proving it), I think the one thing we must NOT say is that holes don't exist. It is clearly possible to fall into one, to dig one, etc. However, that doesn't meant that there are any objects in the world corresponding to that grammatical object in the sentence "holes exist".

Michael Gonzalez said...

I realize, after posting, that a person will ask "can we not determine the size and shape of holes, and therefore there must be some object that has those properties?" Again, no. We can determine the position of a "center of gravity" without there actually being anything at all in that location. When one gives the dimensions of a hole, one is actually giving the dimensions of the walls, the edge, etc, of the object which certainly does exist: namely: the thing which has a hole in it. It's like how we describe an "edge". There is no such separate object as an "edge". The physical object that really exists "has" an edge, just in so much as it does not extend beyond certain points. And the "dimension of the edge" are really descriptions of the extension of the thing which "has" the edge.

There is so much that can be elucidated by dealing very carefully with the English use of "have" in various tricky situations; and I do think this is one of them.

Philip Rand said...

Michael Gonzalez

I suggest you apply the concept count-noun... it will reduce your confusions by providing you with a rule...

Michael Gonzalez said...

Sorry, Philip, but no such magic solution. "Relationship" is a count-noun, but there is no such object in the world. And it's precisely looking for such "rules" of ontological commitment that leads the Quineans and the Platonists astray.

Philip Rand said...

Michael Gonzalez

There is so much that can be elucidated by dealing very carefully with the English use of "have" in various tricky situations; and I do think this is one of them.

And count-noun is a rule of English use: a noun indicating a kind that can be counted

So, it is very interesting that you are now contradicting yourself... interesting...

Philip Rand said...

Michael Gonzalez

What becomes clear using the rule is that it shows that the proposition:

An hole cannot be counted.

Is equivalent to: (p & (p->q)) & ¬q

Philip Rand said...

What Pruss is doing is this (though he isn't aware of it)...

Proposition: An hole can be counted.

Rather than considering this proposition he first considers it's negation:

Proposition: An hole cannot be counted.

The negation is a contradiction. Pruss, then concludes that since the negation of the proposition is a contradiction (i.e. the negation is neither true or false) then the assertion must also be a contradiction.

Therefore, he comes to the conclusion that an hole cannot be counted.

In simplistic terms this amounts to his argument...can you observe the hole in his inference?

Michael Gonzalez said...

Philip:
1) Count-nouns just have to have singular and plural forms and be modifiable by am indefinite article. But, even if we go with the more face value meaning of "able to be counted", relationships, marriages, grounds for impeachment, criteria, etc would still qualify. They can be ennumerated. That doesn't mean they are objects.

2) Holes do exist and they can be counted. Likewise for gaps in my teeth. And for all the examples I gave above (e.g. marriages). Nevertheless, these are not objects in the world, just because they exist and are grammatical "objects" in a sentence.