A hole exists as the space between boundaries not occupied by objects.

Assholes definitely exist. — 180 Proof

:rofl: Last I checked, you had a sense of humor. So...

Father Abraham had many sons
Many sons had Father Abraham
I am one of them and so are you
So let's just praise the Lord
Right arm — Father Abraham song

On a more serious note, can you have a look at what I think is going on with the "to be is to be the value of a variable" idea. It's rather simplistic I suppose but it's my best shot.

To be is the value of a variable

There is a big hole in Kimberly (Sounds dirty but that's a topic for another thread)

1. Non-mathematical interpretation

A hole = nothing in (surrounded by) something which I will simplify as hole = nothing and something. This can be treated as a general definition of a hole.

If I define a die as die = red and plastic and then say there is a die then what I mean is there is red and there is plastic.

Does this simple rule work for a hole?

There is a hole = There is nothing and there is something. I detect no issues with there is something but what about there is nothing?

Nothing, I'm told, is also nonexistence i.e. nonbeing as it were. So, to say there is nothing amounts to saying nonexistence exists. Contradiction!

In other words, there is a hole (in Kimberly) is nonsensical for it contains a contradiction viz. nonexistence exists!

2. Mathematical interpretation

I think this point of view is closer to the meaning of to be is to be the value of a variable.

Mathematical variables, most common symbol for them being x, can take on any value mathematically defined, including, this is key, zero which is the numerical version of nothing.

So, there is a hole in Kimberly simply means the variable x = 0 where x is a certain geological feature in Kimberly.

Make sense? Probably not! Well, you can't say I didn't try! :rofl:

On a more serious note, can you have a look at what I think is going on with the "to be is to be the value of a variable" idea. It's rather simplistic I suppose but it's my best shot.

To be is the value of a variable — TheMadFool

This Quinean criterion for
'ontological commitment' only refers to objects that 'exist' within given discourses (e.g. geometry, topology, etc) and does not refer to matters of fact (e.g. donut & sphincters)

No Heidegger yet? Cf "The Thing" and his discussion of just what a jug is.

I think I can group @hypericin , @Benkei , @unenlightened together a little with this one response, though I'll give some direct responses below too.

I would interpret you, within the idiom I'm attempting to phrase this in at the moment, as believing that there is no real hole in the ground. Rather, there is the ground, and we predicate of the ground a shape -- in this case a hole. So in ordinary language we say "the hole is deep", but through analysis we'd translate this as "the ground is shaped hole-wise" or something like that. It's clunky to read, but it fits within the framework between subject and predicate.

So in the first we'd formalize as ∃xL(x) ^ (x = "hole"), I think.
And in the second we'd formalize as ~∃(x)L(x) ^ (x = "hole"), and H(x) ^ (x = "ground")

Hopefully I'm doing that right. The important thing, from my perspective, is that you are asserting that there is no such thing as a hole unto itself, but rather, there are material things (the ground) which are placed into a hole-wise relation.


I'll follow up with individual responses, but I want to keep this post general for now just to share where my mind is moving.

Well, obviously different properties will be measured differently. Maybe I should've been clearer: why should we not treat the shape of an object as a property as we do for colour and texture? — Benkei

Well, because we can see the hole, and the hole has properties such as depth, width, and location -- and those properties differ from the properties of the ground, since the ground spreads out, and is certainly not shaped like a hole anywhere else. Would we call Africa a hole just because this one hole exists?

It's bloody ducks in a row all over again. 3 ducks exist and when you get them lined up, there's a row. Ducks in a row, not ducks and a row. Stuff exists and arrangements of stuff exist. a hole or a row is an arrangement. Or a relation, rather like a punch is a relation between a fist and a chin. If you're not sure that punches exist, get your wife or friend to do the experiment with their fist and your chin.

It might turn out that stuff is an arrangement of weirdness (another arrangement). Try not to panic. — unenlightened

I think there's a difference here... I agree that relation is important, but I'd say the relation is between the donut (a shape) and the hole. A donut can be represented, topologically, in a two dimensional space that wraps around -- if you imagine walking on a piece of paper, as you get to the top you immediately appear on the bottom. Were you in such a space -- which we don't empirically witness in our world, but is easily imaginable -- there would be no hole, but the shape would remain the same -- at least from a topological perspective.

But there be a hole I see, and I certainly don't deny its existence -- only noting that its existence is curious.

This Quinean criterion for
'ontological commitment' only refers to objects that 'exist' within given discourses (e.g. geometry, topology, etc) and does not refer to matters of fact (e.g. donut & sphincters) — 180 Proof

Now you're tempting me with my true bait -- exegesis.

But I'm going to use all of my willpower and not debate the meaning of Quine -- and just note that I'm using some of his words as a conceptual jumping off point, not exploring a consequence or a reductio of his philosophy.

To my understanding, at least, "to be is to be the value of a variable" is in reference to objects and predicates. Insofar that you can truthfully predicate of some object therein will you find what it means to exist.

So if "The hole is 3/4 of an inch in diameter" is true, then we can certainly conclude that there exists such a hole.

No Heidegger yet? Cf "The Thing" and his discussion of just what a jug is. — tim wood

Welllll... did he ever really propose what it means to be? He kind of got stuck in his own interpretative circle looking for how one could possibly understand the very question "what is the meaning of being?" -- how on Earth would he know if a hole exists? ;)

But by all means, you can be the one to bring in the ontology of Heidegger, rather than Quine, and bring us illumination on the topic. I'd love to read it! That is why I started the thread.

This seems like a non-issue. Materialists are willing to accept that there is such a thing as space between two objects. It's an uncharitable interpretation of materialism to argue that they must commit to the space between two objects itself being some third material object. — Michael

Whoops! I missed you in my responses.

I don't think I'm arguing that. What I'm arguing is that the materialist is committed to the hole not existing -- it's the ground that exists arranged hole-wise.

Well, because we can see the hole, and the hole has properties such as depth, width, and location -- and those properties differ from the properties of the ground, since the ground spreads out, and is certainly not shaped like a hole anywhere else. Would we call Africa a hole just because this one hole exists? — Moliere

Is Africa yellow just because the sand in the Sahara is? I really have trouble finding what your argument is so far. The immediate matter surrounding a hole is clearly not a hole.

I think the question is, do properties exist? If so, then holes exist. I'm not committed one way or another because it depends on language use and definitions. Holes are a specific topographic feature such that an area without solid matter is surrounded by solid matter. If defined that way, the question arises do circles and squares exist? It's not particular to holes unless you insist holes ought to be defined by the absence of something. I don't like such a definition though, because I can't take a hole out of the context of the matter defining it because if I remove that matter I'm left with nothing. And this is the same with a square, if you take away the matter, I'm not left with a square but if I remove the square, I still have (amorphous) matter.

I would interpret you, within the idiom I'm attempting to phrase this in at the moment, as believing that there is no real hole in the ground. — Moliere

Not at all. Fall down the hole to discover its reality. The confusion of reality with materiality is where we're at here. Space (and/or time) is real and it is the relation that material has to itself. Stuff and structure - not two things, but the dual aspects of reality. If you want me to deny something it would be stuff, not structure - the ground, not the hole. The ground is nothing but a stubborn refusal to let you fall.

Cool.

I think we're closer in belief, then, actually -- and I misgrouped you.

I am of the belief that holes exist. It seems less queer to me than the alternative.

Keeping with my idiom, you'd simply agree that the hole exists, and that relations have a reality.

One thing that's queer about relations is that I wonder what can be predicated of them?

At least, this is where I'd be stuck in how I started...

Also, I want to know -- what is the relationship involved?


The difference between us, right now at least, is that I think there is a hole and some background material, and there is a relationship between these two entities -- and I posit an entity because shape is not adequate to address the hole in a donut, as a donut shape can be represented without a hole.

So I would say "The hole is in the ground", where the relationship is indicated by "in" -- not that this indicates being, since we're talking about relationships here, and I am not quantifying over a predicate here.


EDIT: Also, I want to note that I'm open to other approaches with respect to "to be" -- while I'm using a notion of Quine, I'd like other notions put forward and used to analyze or have a better understanding of holes. If you have such a notion aside from quantification I'm all ears.

Is Africa yellow just because the sand in the Sahara is? I really have trouble finding what your argument is so far. The immediate matter surrounding a hole is clearly not a hole. — Benkei

Hrrm, probably just misreading you. I'll try and restate in a different way to see if it clicks:


The hole is in Kimberley, South Africa.

Kimberley is 164.3 km2

The big hole is 0.17 km2


Let's just say that "Kimberley" designates the matter surrounding the hole. So Kimberley is clearly not the hole. And we can truthfully predicate of Kimberley that it is 164.3 km square, whereas we can truthfully predicate of the big hole -- its surface -- that it is 0.17 km2.

So, there are two different properties between the surrounding matter and the hole. We might go so far as to say that Kimberley is enholed, thereby indicating that there is a property of Kimberley, but that wouldn't change the fact that we can truthfully predicate of the hole a size different from Kimberley -- thereby indicating that they have different properties, and are separate from one another.

This all follows from the notion of "to be" I opened with.

If we can quantify over a predicate and create a true statement from said quantification, then whatever said statement uses to bound the variable exists -- in this case, the hole.

I think the question is, do properties exist? If so, then holes exist. I'm not committed one way or another because it depends on language use and definitions. Holes are a specific topographic feature such that an area without solid matter is surrounded by solid matter. If defined that way, the question arises do circles and squares exist? It's not particular to holes unless you insist holes ought to be defined by the absence of something. I don't like such a definition though, because I can't take a hole out of the context of the matter defining it because if I remove that matter I'm left with nothing. And this is the same with a square, if you take away the matter, I'm not left with a square but if I remove the square, I still have (amorphous) matter. — Benkei

I agree that if you take away the matter the hole does not exist -- were an asteroid to smash the Earth apart then, within the reference frame of the sun, the hole in Kimberley, South Africa will not be floating there in space without Kimberley being there.

I am not defining holes or arguing from definition in the sense of providing necessary and sufficient conditions -- I am using an ostensive definition, instead. This is a hole! So in your case we'll have to talk about pipes and 3/4" holes, or indentations in place of holes ;).

I am skeptical of holes being a typographic feature, however, given the ability to represent a donut on a plane without a hole in a topologically identical manner.

I am skeptical of holes being a typographic feature, however, given the ability to represent a donut on a plane without a hole in a topologically identical manner. — Moliere

Do you have a picture of a donut without a hole for me?

Imagine you're in the middle of the page of this graph paper. Choose any direction to go in, and go straight. When you reach the edge of the paper, place yourself on the opposite side of the page. Continue walking.

This, topologically, is identical to a donut. It's not too hard to imagine either -- just think about what a donut looks like, and then mentally cut through exactly once so that you don't split it in half -- you'll have a cylindrical shape. Then cut down one edge of the cylinder and spread out the cylinder -- you'll have a plane.


A donut is a plane which is connected in the manner I'm describing. Were space donut shaped, rather than what we happen to experience, then this would just be common sense -- to get back to where you started all you need to do is keep walking.

In a way our Earth isn't so far off, it's just so large that we don't notice that it's actually spherical.

Now, if we lived on a donut within the space with which we were familiar -- empirical space as we know it -- we'd be able to look up, sometimes, and see the other side of the donut. But that's a donut in space as we know it, rather than a donut shaped space without a hole.


(EDIT: Just to avoid confusion, the holes in the paper are not what I'm talking about here)

Ahh, here we go -- an example of a donut without a hole that is less abstract:

One thing that's queer about relations is that I wonder what can be predicated of them?

At least, this is where I'd be stuck in how I started...

Also, I want to know -- what is the relationship involved? — Moliere

A hole is the surroundingness of a doughnut; a row is the alignment of ducks; a marriage is the joining of two matched parts. If you treat the doughnut as single material object, then the hole is the way the nut relates to itself. Or the way Pacman's world joins up. Or the way the ground of Kimberly relates to itself.
I don't know where predicates and variables sit though they seem like linguistic affairs...

Incidentally, the topology of Pacman's world is rather odd, the corners all join together as if they were all bent round as in a sphere, but the way they join up is backwards, as if one were on the inside of the sphere. Hence the hole/no hole that doesn't know whether it runs one way or the other.

EDIT: Also, I want to note that I'm open to other approaches with respect to "to be" -- while I'm using a notion of Quine, I'd like other notions put forward and used to analyze or have a better understanding of holes. If you have such a notion aside from quantification I'm all ears. — Moliere

Interesting. Not 100% on this, but what about: that which is is that which stands out as a whole, and thereby stands out as an entirety which is other than its context, else other relating to that which is in relation to it, such as its parts. A hole stands out as an entirety which is other than its ground, and thereby is. There are parts to a hole (e.g. its left or right boundary or quadrant) but it nevertheless is cognized as an entirety and thereby stands out. Fairly confident there will be drawbacks to this approach - which, acknowledgedly, assimilates being with existence - but its an idea.

Edit: Maybe obviously, this approach to a hole's being does not however preclude quantification. The quantity of "one" would abstractly represent that which stands out as an entirety.

'Materiality' is full of holes (wholly holey). Atomic structures are 99.99% empty. Some ancients say 'atoms swerving in void'. Yes, :ok: is an aspect of reality.

I take the position that holes do not exist. There is no difference between the Grand Canyon and the Great Plains other than location, although I am not committed to location existing because, while we all talk about it, no one can tell me where it is.

Without valleys there would be no mountains.

Without valleys there would be no mountains. — frank

My head just literally exploded.

My head just literally exploded. — Hanover

But you just kept typing and then you went to work and stood around at the water cooler with no head.

Then you said screw this and you got in the car and drove to Mexico and rented a boat with six other people and it crashed into a deserted island and everyone was calling you "Skipper"

Except of course that's not a donut. It's a picture of a representation of one in two-dimensional space, while we know a donut is a three-dimensional object with a hole. I can draw you a two-dimensional graph with a line representing the acceleration of a donut falling to the ground. The line itself is static. What happened to the acceleration of the donut? Did it disappear thanks to my drawing?

Except of course that's not a donut. It's a picture of a representation of one in two-dimensional space, while we know a donut is a three-dimensional object with a hole — Benkei

Do we? How's that?

If we know it by definition, then we're simply defining what we mean -- it's a stipulation. Which can work if we have something else we're arguing about, but when that's the very assertion under dispute I dare say we are begging the question.

A hole is the surroundingness of a doughnut; a row is the alignment of ducks; a marriage is the joining of two matched parts. If you treat the doughnut as single material object, then the hole is the way the nut relates to itself. Or the way Pacman's world joins up. Or the way the ground of Kimberly relates to itself. — unenlightened

So you would say that there is a hole in pacman's world, because the hole is a relation -- one which changes description depending on the donut. Do I understand you correctly?

I don't know where predicates and variables sit though they seem like linguistic affairs...

They are! But the approach I'm using puts emphasis on linguistic affairs :D

If we can truthfully predicate of some subject, then we are justified in inferring that there is such a subject. So the form of the statement is very important. Now, clearly we understand that there are things like gerunds and such, so we have to have a way of understanding subjects that aren't actually existent things. For that we analyze ordinary expressions into a clear statement.

Hence why I was asking about the relation you'd posit specifically -- but I think you're using a different idiom.

Also, I think it's important to note here that there are some statements which do not predicate of a subject -- statements that deal with relationship between entities are often like this. So the hole is in Kimberley. I know I started out like that, but I was being sloppy. I should have dealt with a property of the hole, i.e., its surface area, rather than its relationship -- though its curiosity is just that it is, as @fishfry pointed out from the SEP, a parasitic entity that does not exist unless there is something like "Kimberley" to be a hole within.

So it is quantification which indicates existence. We quantify over a predicate, and if said quantification produces a true statement, then we can say the subject of said sentence exists.

Also, this is why I tried to translate sentences into philosophically clear ones. That's all I mean by analysis here.

Incidentally, the topology of Pacman's world is rather odd, the corners all join together as if they were all bent round as in a sphere, but the way they join up is backwards, as if one were on the inside of the sphere. Hence the hole/no hole that doesn't know whether it runs one way or the other.

I think that might just be an artifact of it being a donut designed for 2-dimenional space. Like, if you imagine pulling pac-man's world into our space where the edges of the screen are are where they reconnect -- and that corner is just the place where we opened up the donut in two direction -- but we could have chosen to cut in the middle of the screen, so the speak -- it just would be very confusing for the player to play then :D

hat which is is that which stands out as a whole, and thereby stands out as an entirety which is other than its context, else other relating to that which is in relation to it, such as its parts. A hole stands out as an entirety which is other than its ground, and thereby is. There are parts to a hole (e.g. its left or right boundary or quadrant) but it nevertheless is cognized as an entirety and thereby stands out. Fairly confident there will be drawbacks to this approach - which, acknowledged, assimilates being with existence - but its an idea. — javra

Sounds good to me. Reading the SEP article the cognitive aspect of holes is part of why people think they exist -- as you say, they stand out as a whole.

Materiality' is full of holes (wholly holey). Atomic structures are 99.99% empty. Some ancients say 'atoms swerving in void'. Yes, :ok: is an aspect of reality. — 180 Proof

I think that we're assuming a lot in making an assertion about atomic structure. Also, even granting their reality, I'm a little uncertain about calling the particle in a box a hole -- quantum stuff is weird, and doesn't really match up with things like chairs and holes and stars.

If a hole is an aspect of reality, then what is that aspect? What are the other aspects? Wouldn't everything that is real share in this aspect?

I take the position that holes do not exist. There is no difference between the Grand Canyon and the Great Plains other than location, although I am not committed to location existing because, while we all talk about it, no one can tell me where it is. — Hanover

:D

It's right there, of course.

and that corner is just the place where we opened up the donut in two direction -- but we could have chosen to cut in the middle of the screen, so the speak -- it just would be very confusing for the player to play then :D — Moliere

I don't think it works like that. Consider that you can make a doughnut from the plane in two ways; make a horizontal cylinder and bend it round, or make a vertical cylinder and bend it round.

So I make a horizontal cylinder, but standing at the back of flat Pac-world, and the 'corners are now left and right middle facing me. Now I bend the cylinder around, and the corners are on the inside of the hole facing away from me. Or I can do the same thing with the vertical cylinder. So is the hole N-S or E-W? Or to put it another way, one pair of edges forms the inner ring around the hole, and the other pair goes through the hole. But which is which?

If we can truthfully predicate of some subject, then we are justified in inferring that there is such a subject. — Moliere

Hmm. Unicorns have a single horn. Harry Potter has a scar. ??? This seems a dangerous way round to put things, even if there is some way it makes sense. The danger is that one might think one can talk things into existence, and that is the essence of magic. I'd be much happier if you turned it around - 'if there is such a subject, then we are justified in inferring we can truthfully predicate.' Make the truth depend on the world rather than the world depend on truth.

Hmm. Unicorns have a single horn. Harry Potter has a scar. ??? This seems a dangerous way round to put things, even if there is some way it makes sense. The danger is that one might think one can talk things into existence, and that is the essence of magic. I'd be much happier if you turned it around - 'if there is such a subject, then we are justified in inferring we can truthfully predicate.' Make the truth depend on the world rather than the world depend on truth. — unenlightened

I'm comfortable with that. Still thinking on your first paragraph.

What?