Note:
-I have been often using mathematical concepts as analogies, as they seem to be the most appropriate in this discussion. I have been defining mathematical concepts that I use, and will continue to do so, because I have no knowledge of your level of knowledge in mathematics, and also because I can't know the level of knowledge of readers/lurkers of this thread.
I´m pretty sure that there is an essential difference - however, you are entirely free not to consider it relevant for any of your purposes.
If I have an incredibly high number, I can be sure that by counting up I will at some point get there.
Whereas an infinitely high number is exactly characterized by the idea that I can never get there.
I do think that this already constitutes a significant and essential difference. It´s not an extension of a concept that derives its meaning from the frame of reference of our existence, but it´s very negation.
We seem to have had a misunderstanding.
Earlier, I used the example of an asymptote (a finite approximation/abstraction of an infinite concept) as an analogy to eternity.
You said:
So let me try again:
There is an essential difference between extremely high numbers/increasingly small distances/extremely long time spans etc. and "eternity"/"nothingness"/"infintity".
While I see how - on a certain level of abstraction - we may extrapolate the latter from the first, this doesn´t do away with that essential difference.
You seem to have believed to have separated finite concepts from infinite concepts, stating that there is an essential difference between the two. I agree that there is an essential difference between finite and infinite. But that's not how you defined your groups. Because of the groups you formed, I assumed you were including some infinite concepts in with your first group and therefore declaring an essential difference between different types of infinite concepts The part I put in bold above is the discrepancy.
An increasingly small distance, which seems to be a reference to my asymptote analogy, is indeed an infinite concept, because the curve is becoming infinitely close to the line, without ever touching it, as they both extend for an infinite length. That's what an asymptote is.
Because you separated the groups in such a manner, I assumed you were trying to form an essential difference between different types of infinite concepts. That's why I argued there was no essential difference. But, in the process, I had defined a subtle difference between two primary types of infinite concepts. I don't regard this as an essential difference, however, because humans can understand certain examples of all three types. In summary, I will list three primary concepts as I see them and provide examples of each.
The
first concept is a finite one. It's is easily understood. Examples include:
A) A really big number. 1 billion. Given enough time, we can count that high, or even acquire that much money.
B) A really big amount of space. 20 lightyears. We can't grasp the largeness, but it's directly measurable.
The
second type of concept is an infinite concept that has a readily understood pattern. Examples include:
A) The fact that a line extends for an infinite distance.
-Although a human cannot grasp an infinite distance, by explaining the line with a finite equation, the human can understand all useful aspects of that infinite line, including the fact that it extends infinitely.
B) An asymptote.
-Although a human cannot grasp an infinitely small distance, or an infinitely large distance, their understanding of an asymptote allows them to understand both in certain contexts. An asymptote is a curve that approaches a line, but never reaches it (approaching an infinitesimally small distance between them), as they both extend infinitely. If you have the finite equation of the line and a finite equation of the curve, all useful aspects of the situation are understood.
C) There are an infinite number of numbers between any two numbers.
-Although a human cannot readily understand that there could be an infinite number of numbers, let alone the fact that there are an infinite number of numbers between any two numbers, a human can still grasp this concept by understanding the underlying mechanism of fractions, and therefore be able to understand how this can be true.
D) The original post of this thread: Eternity in hell.
-Although a human cannot grasp an infinite amount of time, they can approximate the concept by making rational statements about such a situation. "It never ends", "It lasts for as long as you can imagine, and then longer." And so forth. Think of an eternity in hell as an infinitely long line. It can be understood by an expression of finite rules or facts that govern the infinite.
The
third concept is an infinite concept, or seemingly illogical finite concept, that has no pattern to better understand it. Examples include:
A) The Big Bang.
The prevailing theory about the expansion of the universe is the Big Bang theory. In the theory, the very fabric of space and time itself expanded from a singularity. It's difficult or impossible for a human being to imagine what spaceless and timeless state could possibly mean, as we have no means of experiencing such states. Furthermore, there is no readily understandable pattern to grasp the concept- we only have evidence and such. And yet, our best scientists can still study such a strange thing.
B) An imaginary number.
In mathematics, there exist what are called "imaginary numbers". An imaginary number is some multiple of the imaginary unit, usually identified with the letter "i" when it's used, that is equal to the square root of negative one. Anybody familiar with mathematics knows that a square of a number is always positive, because a number multiplied by itself (whether positive or negative) is always equal to a positive number. So, to ask what the square root of a negative number is, is a nonsensical question. But, it was asked anyway by some inquiring minds, and since the answer is illogical, it is simply referred to as "i". This "i" can be used in mathematical equations just like any other. When I was learning about this in middle school, I felt it was useless. I even asked the teacher why we were bothering to learn about numbers that don't exist, as it seemed so ridiculous. When I began studying mathematics and engineering in my university, however, I realized how important imaginary numbers are. They are used in all sorts of mathematics, and even more strangely, are used in all sorts of engineering. The engineering behind AC power, stable control systems, signal processors, and many circuits all rely on the concept of imaginary numbers to be designed. Without the use of such a strange mathematical function, that doesn't even make sense within the realm of human experience, these things would likely not exist, and yet, they do. It's an unreasonable concept, yet one that is useful and produces results.
C) God, eternity, etc. Just like the above examples, where something seems illogical and removed from some portions of human experience and logic, it may still be conceived of and explored within the human mind. One can imagine things outside of their own experience. Now, of course it's useful if they can provide evidence and utility, but even if they can't, it still can be a coherent thought shared among individuals.
I guess a human can grasp the abstraction, but I suspect that that´s it.
But often enough, the approximation or abstraction contains nearly all of the information that the original, un-graspable concept had. Think of it like a JPEG image. It's a compression of a raw image file (for taking up less space and for quicker transmission), yet still contains most of the information of the original. As far as humans can use these images, there is little difference, as the JPEG image is as complete to them as the original is.
Or think of it like a curve on a Cartesian plane. If I graph the equation y = x^2 +3x + 2, then any information I want out of that infinitely long curve is available to me. Even though I can't grasp the concept of an infinitely long curve, I can readily grasp the finite mathematical equation of it, which contains all useful information about it.
Again: I think "nothingness" is not a concept since it requires us to negate the reality that renders our words meaningful and concepts.
See my above big bang example. "Nothingness" in some senses of the word, is a meaningful concept.
In the case of "eternal suffering" I am wondering the following: Even if "eternity" were meaningful and a concept (as opposed to being merely a negation of that which can be meaningful and a concept, as is my position), why would anyone try to make the monstrosity more imaginable by introducing a concept that requires us to make all those abstractions?
For the same reason any mathematician has thought up an infinite concept with his or her finite mind: because humans are curious and they can do so. The belief and acceptance in eternal suffering is a showcase of the darkest aspects of the human mind.
I must confess that I don´t understand the concept at all. Or, more precise, I do understand the abstract concept, but I don´t understand how it can possibly point to something outside itself.
This would be pretty close to the way I tend to see it.
However, I have problems with the term "not truly grasping a concept". It suggest that there is something about it that we cannot grasp (and this part is not a concept).
Assuming that there are concepts we cannot (fully/truly) grasp means entering the metaphysical realm. I would be a concept out there (held by something beyond us) that we do our best to grasp. As opposed to human concepts that are our own making and necessarily grasped by those who hold them).
This can be seen in several of my examples. A human cannot "truly grasp" an infinitely long line, because we cannot experience it, but we can explain it and extrapolate all useful information from it. We can't grasp an eternity of time, but we can still make several finite statements in order to extrapolate all useful information from it.
Yes, I see how this could be understood as an attempt to stack the deck.
This was not my intention, though. Rather, my idea was: Let´s forget about "eternity"/"infinity"/"nothingness" for a moment and take a look at "unimaginable", "the ungraspable", "the unfathomable", "the unthinkeable" instead. These are words, we do use them - but do they point to concepts, or are they not rather mere negations of that which can be imagined, fathomed, thought, grasped - without any positive content or definition? Or, if we assume them to be concepts beyond our grasp, doesn´t that necessarily mean we have introduced a metaphysical realm?
Agreed. On top of that, we can even string together grammatically correct sentences consisting of words from the dictionary that make no sense whatsover, nonetheless.
Things are unimaginable, ungraspable, and unthinkable only in the sense that we cannot experience them, like several of my above examples. We can, however, rationalize or explain many of them.
My conclusion is that, in referencing your original post, humans are fully capable of imagining a concept like hell, even if it's out of the realm of things they can experience. By using effective language, finite approximations that contain all useful information from the concept, and a set of understood finite statements about the concept, humans can, in a variety of different fields, imagine or explain the infinite.
-Lyn
