# Question Regarding Holes

What even are holes? Are they something or nothing? Do they even exist? Sure, you might think me saying that holes do not exist is idiotic but think about it. The existence of holes doesn't make sense in of themselves. I’ll quote an example, say I get a donut and I ate it. Did I eat the hole too? If no, where did it go? Can I go to a restaurant and ask them to give me a donut without the hole?

• See eg SEP article on holes plato.stanford.edu/entries/holes Commented Oct 21, 2023 at 10:05
• Advice for happiness: "Keep your eye on the donut, and not on the hole." Commented Oct 21, 2023 at 12:54
• In electronics, hole refers to an electron going the other way. It is something, just moving away instead of toward. "The sun rises, and the sun goes down. And hastens to the place it arises." - Ecclesiastes Commented Oct 21, 2023 at 12:57
• Quine's pragmatic proposal is to say that holes do not exist and we should say rather that some things have the property of being perforated. Commented Oct 21, 2023 at 21:14
• @Bumble What does ‘perforated’ mean, in a philosophical Quine-type usage? Commented Oct 22, 2023 at 17:09

In mathematics a hole in a closed surface is an obstruction to contract a loop to a single point on the surface without removing the loop from the surface. The number of independent non-contractible loops is an important number to distinguish different surfaces.

Examples: On the sphere S, e.g. on the surface of the earth, each loop can be contracted to the northpole and hence to any arbitrary point. Therefore there are no obstruction, and S has no holes.

On the donought T there exist two independent loops which cannot be contracted to a point. Hence T has 1 hole.

On a pretzel P there exist more than two independent non-contractible loops. Depending on the form of the pretzel there are 4,6,8,... independent non-contractible loops, hence P has 2,3,4,... holes.

The importance of the mathematical result is the fact that one can formalize the concept of a hole of a surface without looking to the exterior of the surface, into the ambient space. Instead one counts independent non-contractible loops on the surface.

• This excellent answer shows the problem with @Marco's. Commented Oct 21, 2023 at 22:57
• @Araucaria-Nothereanymore.But is doesn't seem to address the question about whether you eat the hole. Commented Oct 23, 2023 at 6:11

No, when you eat a donut you eat the donut. The hole is no different to the rest of the space outside the volume occupied by the body of the donut, none of which do you eat. A hole is a term that effectively refers to the shape of whatever surrounds it. When you say the hole 'exists' what you really mean is that the surrounding object definitely has a surface that bounds a cylindrical portion of space.

The problem underlying your question, like many other topics debated in philosophy, is a tendency to take words at their face value rather than thinking through what they are really signifying. We say bricks exist and we say holes exist, but we are using the language in different ways in the two cases.

• "Eat your words, but don't go hungry. Words have nearly always hung me." Commented Oct 21, 2023 at 12:56
• @MichaelHall in UK you certainly can. Doughuts are sold both with and without holes. Commented Oct 21, 2023 at 20:34
• @Araucaria-Nothereanymore. Good point. Given your legendary skill with devising crossword clues, and the fact that being dead gives you lots of free time, perhaps you might like to work on an improvement. I agree holes being circular is a cliché, and the hole in a donut could be filled with jam, say, but the task of crafting a succinct expression to cover all the possible circumstances was beyond me. Commented Oct 22, 2023 at 5:49
• @Araucaria-Nothereanymore. Is it your belief that describing the hole in terms of the mix of atmospheric gasses present would enhance the OP's understanding? Commented Oct 22, 2023 at 15:56
• @Araucaria-Nothereanymore., so what is your confusion with this answer? Commented Oct 22, 2023 at 16:25

A hole cannot exist independently of something else. We cannot have a universe where the only denizen is a hole. It is always a hole in something -- it is a feature of an object, not an object itself.

Other examples are "dimples", "bumps", "ripples" or any other topological quality (riffing off of Jo's answer). These are things whose existence depends on something else.

In a different vein, "waves" don't exist in the same way that water does either, they are things "water does" or "about water".

• I would be careful with your appeals to mathematics. The hole in a circle exists in an absolute sense. It doesn't depend on the circle being anything other than a circle. It doesn't even depend on how the circle sits in some higher dimensional space. The same goes for the whole in a donut (which is just a fattened circle). Commented Oct 22, 2023 at 14:17
• @CharlesHudgins What hole in a circle are you referring to? Commented Oct 22, 2023 at 17:06
• The hole that can be detected by the existence of a one-form on the circle (e.g. $d\theta$) that cannot be expressed as the derivative of a function. This is a fact about the circle that intrinsically (i.e. without needing reference to an embedding space) distinguishes it from a line segment (for which no such one-form exists). Mathematicians say that the circle has a hole because of this intrinsic difference. Commented Oct 22, 2023 at 18:16
• Rereading your post I understand your meaning better. I would still quibble that the existence of the hole doesn't depend on the circle but is rather (almost precisely) constitutive of the circle in the mathematical sense. But you are right, there is no reason we have to take the mathematicians' word for it. I (wrongly it seems) assumed you were interested in the mathematician's perspective because you mentioned topology. Commented Oct 22, 2023 at 18:32
• @MichaelHall Circle is the mathematical term for any space homeomorphic to $[0,1]$ with the endpoints identified. We call a solid disc... a disc. The point is that the circle is somehow the simplest example of a space in which not every loop is contractible. When a loop is not contractible, we say there is a hole in the way of that loop contracting. That is the sense in which I meant that the hole is constitutive of the circle. A circle is special to mathematicians because it's the simplest example of a space with a hole. Commented Oct 23, 2023 at 21:24

"... say i get a donut and ate it. Did i eat the hole too? If no, where did it go?"

The same place your lap goes when you stand up.

• Answering the question without answering the question :-) both are concepts that rely on certain physical conditions; when the conditions change the concepts are no longer fulfilled.
– Frog
Commented Oct 27, 2023 at 9:40
• @Frog - I enjoy giving a reply that points out that the questioner knew the answer all along. Commented Oct 27, 2023 at 15:07
• Are you suggesting the OP bend over and take a look?
– J D
Commented Oct 27, 2023 at 16:45

I prefer the Eastern philosophical insight (which dovetails well with Wittgenstein's later work), which is that a 'hole' is defined by use-value. In other words — straight from the Daodejing — the form of a cup may be determined by solid clay, but the use of a cup is determined by the empty space (the hole) that the clay surrounds. Without that empty space, we don't have a cup.

Analytically then, a 'hole' would be defined as as a volume of space reserved through some material boundary for some human purpose (or contrarily, a similarly bounded volume of space that must be filled or avoided for some human purpose).

A cup has a basin (an open-topped hole) to contain loose materials. A funnel has a basin with a smaller hole at the bottom, to contain and concentrate loose materials into a stream. Donuts and bagels have holes to increase the surface-area-to-volume ratio, ensuring even cooking. Streets have potholes that are a risk to motorists and must be dealt with. If we have a volume of space that we have no particular use for or interest in, or that isn't contained by some material boundary, we don't generally label it a hole.

A hole is nothing that exists within something. A black hole is a good example.

• Your comment is correct. But it doesn't answer the question(s) Commented Oct 29, 2023 at 11:39