The hole paradox I came up with
The Paradox:
(Edited for clarity): The hole paradox arises from a misconception about the nature of empty space. While a hole might initially seem to be just empty space, it is not a true void but rather a space defined by its lack of something, such as the absence of material or substance. This leads to a paradox: How can we define a hole as a type of nothing when empty space itself is considered a positive value?
In traditional ontology, objects are typically defined by their properties and characteristics. However, a hole lacks these defining properties and exists as a space where something could be, but isn't. This raises the question: How can something that appears to be nothing have properties?
This paradox challenges our understanding of identity and existence by highlighting the complexities of defining and understanding concepts that are defined by their negation or absence.
Solution:
A "hole" is a word which is used for two different things, but people often think you can use the word hole to mean both of those two different things at the same time (which is the absence of dirt and the ground around the hole affecting the value of the hole).
In math, a hole would not be the dirt around the hole when trying to figure out how much dirt you have in a certain space, it would be 0 (because you cannot understand it as being dirt). But if you're trying to figure out how much space you have available, it would be a positive value (something you understand as being available space), and the dirt would be 0 (something you don't understand as being available space). However, in the case of the hole being a positive value in math, the dirt around the hole would be right next to the borders of the hole, giving the dimensions needed to understand the amount of space in the hole via math formulas. But even in that situation, the dirt is not something you understand as a positive value, it's the exact point that you can't understand which causes you to "see" the dimensions of the hole via the max limit of the space available (the edges of the space).
But if you mix those two types of holes up, you see it as both a positive and non-value, or in other words, a type of nothing you understand, which is illogical because nothing is the absence of understanding.
(Edited for clarity): The hole paradox arises from a misconception about the nature of empty space. While a hole might initially seem to be just empty space, it is not a true void but rather a space defined by its lack of something, such as the absence of material or substance. This leads to a paradox: How can we define a hole as a type of nothing when empty space itself is considered a positive value?
In traditional ontology, objects are typically defined by their properties and characteristics. However, a hole lacks these defining properties and exists as a space where something could be, but isn't. This raises the question: How can something that appears to be nothing have properties?
This paradox challenges our understanding of identity and existence by highlighting the complexities of defining and understanding concepts that are defined by their negation or absence.
Solution:
A "hole" is a word which is used for two different things, but people often think you can use the word hole to mean both of those two different things at the same time (which is the absence of dirt and the ground around the hole affecting the value of the hole).
In math, a hole would not be the dirt around the hole when trying to figure out how much dirt you have in a certain space, it would be 0 (because you cannot understand it as being dirt). But if you're trying to figure out how much space you have available, it would be a positive value (something you understand as being available space), and the dirt would be 0 (something you don't understand as being available space). However, in the case of the hole being a positive value in math, the dirt around the hole would be right next to the borders of the hole, giving the dimensions needed to understand the amount of space in the hole via math formulas. But even in that situation, the dirt is not something you understand as a positive value, it's the exact point that you can't understand which causes you to "see" the dimensions of the hole via the max limit of the space available (the edges of the space).
But if you mix those two types of holes up, you see it as both a positive and non-value, or in other words, a type of nothing you understand, which is illogical because nothing is the absence of understanding.
Comments (41)
No, not said. 'Nothing' has no existence and 'it' cannot even be meant.
Yes, indeed, I understood Everything when science confirmed my First Philosophy, but this thread is about holes (which cannot be, because 'nothing' cannot have existence), unless you want to broaden it to the understanding of the Eternal/Permanent Basis of All and it's temporaries, and on up to life now and into the future.
The hole is not 'nothing'; there is no paradox; it has quantum field. 'Nothing' cannot have properties, much less be. Your other "sure's" don't apply. In this thread's terminology, "nothing" is also standing in for not understanding, yet I understand All.
From a 2022 thread Does nothingness exist? ...
https://thephilosophyforum.com/discussion/comment/707639
examples: a
donut or
hole in a bucket / boat or
negative space or
randomness (i.e. total symmetries) or
blindspot or ...
IMO, no "paradox". Check (correct) your assumptions / premises.
It takes three men two hours to dig a hole. How long does it take them to dig half a hole?
To exist is to stand out, to be distinguishable from - let's say as vaguely as possible - "the background". Thus a hole in the road, for example, stands out as a feature from the background levelness of the rest of the road. This is the opposite standing out, geometrically, to the way a mountain stands out from the plain or an island from the sea.
There is no need to resort to quantum mechanics to understand basic English. Anyone who thinks that holes don't exist should be dropped down a mineshaft until they realise and admit their mistake.
Quoting unenlightened
You're talking about a specific hole in this instance when there are two different types of holes:
Non-value hole= not being matter/dirt/etc. and not understanding how it could be any of those things.
Positive value hole = being available space and understanding why
To make it simpler, let's call a non-value hole a NV hole, and a positive value hole a PV hole.
NV holes and PV holes are both holes, but that's just like saying that squares and circles are both shapes, they're not the same thing, but they have similarities. In both types of holes, there is a non-understanding which exists, in NV holes it's the hole itself, and in PV holes it's the matter around the hole which can't be understood at the exact same time you're understanding the space in the hole.
In other words, if say you had 2 holes, one being a NV hole and another being a PV hole that were both circular shaped, the edges of the holes would be the same shape. But the NV hole would be just slightly larger in size than the PV hole because the measurements you would make in the NV hole would be within the dirt itself (or whatever matter the material is), but the PV hole would be measured within the empty space.
Now since I've defined what I'm talking about this much do you finally get it?
An analogy would be struggling to find an empty space in a crowded parking lot. Driving around, looking for a spot and finally finding one that's empty. That would be something because it's a PV hole.
No, the more you define things the less understandable you become.
Take a coffee cup. there is a hole that I can fill with coffee, and then there is a hole on the side I can put my fingers through to pick it up which is formed by the handle. These are topologically distinct, because the handle-hole one can pass something through, whereas where the coffee goes in, it has to come out the same way. But both holes are distinguished by and from their surroundings, or to put it another way 'a hole has to be a hole in something', and this seems to make the distinction between PV and NV impossible to sustain, beyond the way you arbitrarily decide to regard a particular hole.
That means nothing (pun intended).
Quoting Echogem222
A hole in a mug is not nothing, it is the shape that the material makes.
A paradox is a situation that results in something impossible or contradictory. This ain't one.
Quoting unenlightened
This post by Count seems related https://thephilosophyforum.com/discussion/comment/895615
Ah, I see, you wish to keep things vague, but what you're doing is just a straw person argument. If you don't want to bother to understand how what I'm saying is true, fine, but why comment?
Quoting Lionino
:up: :up:
Weak dodge. Your so-called "solution" doesn't matter ? isn't worth considering if there is not an actual problem (or its merely a pseudo-problem) in the first place.
https://plato.stanford.edu/entries/holes/
Just posting the link since SEP has a lot to say about holes. Guilty as charged on he rest of it. Guess I'll go crawl back into my, uh, hole.
While I am not a logician in any sense, and ought not comment on the paradox, qua "paradox." I think both your paradox, and the responses, illustrate the same thing. That we arrive at all of our (temporary) "conclusions" through the fundamentally empty and fleeting movement of words, we are bound to run into walls of confusion (at best), "absurdity" seeming impossibility, at worst.
To me, that is not very troubling or surprising. What is more troubling and surprising, is that we "think" those walls are not there when things appear to run smoothly in spite of them (because the intended function of the word seems to have been satisfied), and on that basis, declare (that their use--these fleeting and empty representations with walls), not just point to "truth(s)" but are certainly True.
The value in understanding this "paradox" is to better understand what the word "nothing" means since many people think that nothing means something which can be understood, something that other things cannot logically come from, when in reality, it's just complete non-understanding.
Take for example this phrase, "Nothing is greater than infinity" if you think you understand nothing as I just explained, you would think that infinity is all that there is at the most, when in reality, if something above infinity exists, we wouldn't be able to understand what that is. But because it's a possibility something greater than infinity exists actually is enough to prove something greater than infinity does exist, it's just not something we can understand, because if infinity were all that there is at the most, we would not say that nothing is greater than infinity, we would instead say something like, "infinity is the most there is" without saying anything else. So the fact something greater than infinity could exist is enough to understand that something greater than infinity does exist.
There is nothing greater or less than nothing, because if not, then that would mean that nothing isn't nothing. That is the most we can possibly understand.
Quoting Echogem222
Quoting Echogem222
:up:
How many "philosophical" hypotheses (including, admittedly, any that I may entertain) rest on just such a thing as you have illustrated; that is, on a necessary (yet, not necessarily) presumption about meaning?
A hole is defined by its boundary and volume. A hole does not exist on its own, and must be surrounded or constrained by something to fulfill its definition of a hole. A hole is not a non-value, but a negative value.
Consider a flat ground of dirt, and you decide to take a shovel and dig a hole in the dirt. What you have done is taken the equilibrium of the flat ground and disrupted it by displacing a certain amount of dirt from a certain location onto another location. The dirt you excavated has a positive value, and the hole you left behind has an opposite and equal negative value. If you take the excavated dirt and place it back in the hole, you now have restored the equilibrium of the ground back to zero.
ground = 0
hole = -1
excavated dirt = +1
I went through the article and it is a whole lot of nothing, just juggling with language to solve a problem that doesn't exist. No wonder all the references are from the last 100 years.
ground = 0 (why zero, makes no sense)
hole = -1 (if the hole is -1, then it would take +2 to become 1, not just +1)
excavated dirt = +1 (not enough to fill the hole then, which doesn't make sense since removing this value caused the hole to be)
If you take away dirt and create a hole, that dirt taken away has the positive value of being dirt (so +1), but the hole left behind is not dirt, so it's equal to 0. The ground around the hole (if dirt) is also a positive value, that had more value when the hole had not yet been created, by how much, I don't know.
So to fill the hole, you would just need +1.
Let's say that the ground had the value of 75 mounds of dirt before any dirt was removed from it, but when the hole was made due to dirt being removed, the ground lost a value of 1, hence becoming 74.
Quoting Echogem222
Quoting Echogem222
This--my remark to follow this preamble--is not conventionally philosophical, and as for logic, it is necessarily not that. But in my estimation it is philosophy, only it is philosopy not "thought," but "done"---(if properly executed) by the Body. I am sensitive to the fact that it may annoy (already), but who knows, it may not. So, as a well intended arrow shot in the dark,
Your topic--your struggle to resolve the paradox--has an affinity with Koans (in Rinzai Zen). Explaining would be counter productive. I'll just illustrate with a classic by Hakuin,
"What is the sound of one hand clapping?"
To which the answer is an abrupt, shallow inhale, followed by a joyful long exhale expressing, simultaneously with a blooming grin, and the breath, all barely audibly, "riiiiiight."
Necessary addendum: anyway that's how my body felt after reading those statements I quoted above.
Back to more conventional philosophy. Parmenides settled on all is one because of his construction that nothing can proceed from nothing meant there can't be a beginning (and therefore end) Thus all has always been, and always been as one. The multiplicity of things are illusions projected by One.
So, is the resolution to your, and all paradoxes, simply that paradoxes are not to be approached as things to resolve with logic. Paradoxes arise out of projections of Truth but are not true (to use a classical way) in themselves? They take us to the outer ranges of logic and leave us on a single precipice surrounded by what we think must be an empty abyss.
Your fittingly melancholy flavored conclusion "that's all we can understand," applies to the "domain" of the projections; before we arrive at the precipice, where we must abandon understanding. It turns out, its not meloncholy, but cause for celebration, the paradox and its irresolvibility! Truth is "beyond" the domain of understanding; the realm of multiplicity. It certainly cannot be harvested out of logic, nor anything involving the use of Language, arguably a projection twice removed.
The ground is considered zero at every and any point you select on the ground line or level, and the rest of the terrain is measured relative to your selected point. To select a value for that point other than zero is arbitrary, but not necessarily wrong mathematically speaking.
The ground is zero because it is the reference point. Think "sea level", or think "neutral"; not a hole and not a mound. The hole is -1 because the hole was made by removing +1 of dirt. Filling in the hole with +1 of dirt brings it back to its original value, but filling it in with +2 creates a mound of +1. You would need to dig another hole from somewhere else to add the extra +1 to the original hole, or it would break conservation.
It appears that you contradicted yourself here:
Quoting Echogem222
Quoting Echogem222
Quoting Echogem222
What would you do if you didn't know that the ground had a value of 75 mounds, but you can still dig up +1 of dirt and make a hole? What does the math look like then?
If 0 is nothing then is -7 more nothing than 0? Is -7 something or nothing?
The ground is A
The hole is 0
the dirt removed is +1
A-1=A-1 but then if you add 1 back to A, it would then just be A, not zero.
Ok, but what do you consider the value of the initial unknown variable 'A' to be? Is it 0 or is it some other initial value?
What is in the hole? If we're talking about the physical universe (reality, existence, everything that is the case, etc) then the word "nothing" (or nothingness) does not apply because even in empty space there are energy fields and subatomic particles coming in and out of existence.
In math, numbers can have words attached to them. Like this:
1 orange + 1 orange= 1 oranges, not 1 orange + 1 apple= 2 fruit. This is because if you were wanting to find out how many fruit you have, you would do it like this: 1 fruit + 1 fruit= 2 fruit. Because you could also do it like this 1A+1A=2A.
So when you're trying to find out how much empty space you have, in that moment, you are not looking for how much dirt you have in a given space, and during that time, the dirt is a non-value, in other words, 0 space. This is because you do not understand how the dirt would be space, it is nothing to you in that sense.
In a math problem when you want to try and find how much dirt you have as well as how much space, you could do that, but the dirt and the space would not ever merge in values because you can't add dirt and space together and get just dirt or just space, they will always remain separate. So when you see the value of the hole as being the dirt and the space, you are seeing the equivalent of 2 different things in one location, not 1 thing.
A computer is not just 1 thing either, it's a collection of things that have 1 purpose, to function as a computer, but that's a function, a computer is not truly a single object, it's a function that occurs when many small parts exist together in a certain way.
If you want to summarize what a computer or a hole is that's fine, but you need to remember that they are not truly 1 thing.