Defining the indefinable

Defining the indefinable…?

If you see a thing and describe it, there is always something outside that description. E.g you describe a farmhouse it has fields ~ a world outside of it, describe the world… universe and there must be something external to your description even if it were exact.

The set of the collection of all objects must always be limited by it’s descriptiveness [it’s cardinality]. Even if we were to say that the collection of things = ‘everything’, there would still be the class of non-things beyond it no matter what you add into the set.

You could arrive at a denumerable amount of things, uncountable, and you would know mathematically they are part of the set. No matter how large the set get it’s still a collection of things in a box - so to say, and there must be an infinity remaining which cannot be built up to [because there will always be an infinity remaining].

Consider Hilbert’s paradox of the Grand Hotel It is assumed that by moving the guests into the next room respectively, you can add other guests up to an infinity of other guests. This is done because there are different mathematical sets such as bijective sets and such, so by moving them around you can play with the maths e.g. where some numbers are primes and some not, hence their different properties lend themselves to leaving unoccupied rooms once you start moving the guests around. Because there are an infinity of rooms, even if all occupied then due to there being different kinds of infinite sets within that, the numbers can be toyed with.

However, this requires the utility of the incongruity in >finite< numbers!

This is fine in maths ~ for calculus e.g. for when we are dealing with how denumerable amounts of numbers act in the universe.

The problem is that a true infinite set of the aleph omega would either be full or empty, and there would be no empty rooms no matter how much you moved people around. This is because we cannot add the properties of the finite to the infinite. There would be no prime numbers the metaphors of rooms in a hotel is defunct, there would be no such limits upon the unlimited.

This [Hilbert’s paradox and such] is all pinned upon the Hindu notion ‘if you take an infinity from an infinity, there would be an infinity remaining’. So the ole mathematical brain ticks along thinking that you can just keep adding infinities as if they are like rooms ie. Have finite qualities. Then because you cannot build up to an infinity you have to jump straight to there being and infinity of infinities - hence the infinite rooms in the hotel.

However, an infinity taken from another infinity ~ if that’s even possible… Would not have a line nor any manner of division betwixt the two or more infinities. So the infinity drawn from an infinity would occupy the same infinite space and would not be divided in any manner. We could actually just say that there are not two infinities, except e.g. You could theoretically have say an infinity of red light and an infinity of blue light, but there would be nothing separating them as that would be a finite quality attributed to the infinite. In fact you would have a purple light infinity comprising both the red and blue infinities, and so in the same way as you supposedly may take an infinity from an infinity, we would add an infinity to the original infinity leaving only an infinity.

If we performed the entire procedure upon all infinities you would always arrive at a the one infinity. All opposite infinities would negate and our infinity would be empty! In fact you simply cannot have different infinities because they would always blend with others, not to mention that you have to give them non-infinite properties such to distinguish one from the other in the first place.

You see how on our journey we are always adding finite properties to our sets, even when dealing with infinities. Yet ultimately we can add as much as we like to the set of all things and it can never comprise the whole, there will always be something more, something outside the set.

The entire set of all definitions cannot equal the whole! You define and you reduce, it’s that simple.

This is why our reality can only be ultimately indefinable.


Who said the universe, or reality is actually infinite?

It isn’t, but reality includes the infinite and the universe is part of that.

Not to mention that nazi’s and Nietzschean’s alike tend to believe in infinite recurrence ~ i had thought you did?

To add to the op, an infinite set would have no beginning nor end, so there is nothing to extrapolate a series from.

Equally, each segment or room would have the same problem with it’s cardinality.

The problem is, how to add duality to the infinite and the greater reality. However we know there is some manner of duality simple because we are here in this place. Yet you cannot add duality to the infinite, is arises at the later stages of manifestation but from what?


Well, I think once you describe something, you make it into a particular, which means it will contrast with other particulars which warrant different descriptions. So it suggests things outside the object.

This is more psychological though than real.

I’m not sure what you’re saying here. An infinite set is either full or empty? I can see how it might be empty in a sense: no matter how numerous the set of objects, when compared to infinity, it is always infinitesimal. Even a billion objects approaches 0% of infinity the more you approach infinity, and “at” infinity, a billion objects becomes 0% of the whole.

This might even work if you had an infinite quantity of things in the set, like the infinite number of points in a line. You can always add more lines parallel to the first, thereby adding infinity to infinity, and compared to an infinite number of lines, the first line will seem to consistute 0% of the whole set of lines.

But in what sense is an infinite set “full”? Are you saying that no matter how much you add to an infinite set, it’s still infinite? And therefore it’s as if you can’t ever add any more?

Yes, infinities don’t add (or subtract), but I don’t think the objects in infinite sets necessarily end up blurring together. You can still tell the difference between all the odd numbers and all the even numbers even though they are both infinite sets and part of the same infinite set of integers.

I’m not sure I follow why infinite sets cannot be described with finite properties. The infinite set of all even numbers has the property of being divisible by two, but is that an “infinite” property?

I agree that once you fully describe something, you’ve effectively shown it to be finite, and if reality is essentially infinite in whatever sense, such descriptions can never suffice to fit all of existence. But I’m not sure the set of all definitions (or descriptions) counts as a description itself. However, it does seems silly to think we could enumerate all definitions in the first place. But besides that, I think the whole is always greater than the sum of the parts, so even the set of all definitions will not amount to the whole, but this has more to do with the way the brain identifies objects and the essence of things.

Its just a nickname…Its not infinite, just really long and tedious.


Descriptions are yes, but i am attempting to speak of the things they represent as they too have cardinality/limits.
Hmm, you could be right in that the real world is more fluid than our linguistic representations. I sometimes wonder if quantum mechanics are resultant of such a fluidity rather than the limits in our minds.

The aleph omega of the rooms of the hotel are either full or empty. You cant have them partly filled as that would necessarily be a limit ~ finiteness.

A quantity, line or a point has cardinality though. …oh and almost 0%.

Yes, infinities don’t add (or subtract), but I don’t think the objects in infinite sets necessarily end up blurring together. You can still tell the difference between all the odd numbers and all the even numbers even though they are both infinite sets and part of the same infinite set of integers.

This is because we are thinking of finite numbers, odds and evens, primes [bijectives/injectives]. I see your point though, an infinite universe could have e.g. The set of red or the set of blue planets.
What i meant though is that infinity fills the entire ‘philosophical space’, so an additional infinity must be within the same ocean - so to say.

Exactly! The duality ‘odd’ and ‘even’ are distinctions in context to finite numbers. The ‘rooms’ if the paradox makes any sense et al, should represent ‘oceans’. We then have to make distinctions betwixt rooms or oceans, and we cannot because that would be adding a duality/limit to the unlimited. hence there is a necessity to merge all rooms/oceans.

On the other hand, we have to somehow get from infinity to universe and that’s where i am stumped. My intuition tells me it’s at the other end of finite ~ denumerable amounts, and how they interact fluidly with the ocean.

Lets say that all the occupants of all the rooms in Hilbert’s hotel, each made a description, all of those descriptions would tell them they are in a hotel, only what each of their rooms are like.
Yea lets just say the whole is greater than the sum of it’s parts.


Yes, I believe this is the way it is.

What about having every odd room occupied and every even room vacant?

Well, it depends on what space the first infinity is taking up. The points on a line take up the whole line, but you add another infinity of points and they might take up a different space: the space of a second line parallel to the first. I guess this depends on what you mean by a “philosophical space”. The idea that infinity + infinity = infinity just means that if you have something without any ends or limits, and you add something else that also has no ends or limits, this feature will not change in the sum–it will still have no ends or limits. Is this what you mean?

I still don’t get it. Why can’t we make distinctions between the rooms? There’s no reason an infinite set of things can’t be made of finite things.

I think so. What is a car to us? Is it merely a collection of tires, engine, cab, etc., or do these components become something more than a collection of parts when they come together? Certainly, someone from a primitive culture who was totally unfamiliar with cars would not recognize one if he saw it. To him, it would be just a collection of parts. But because we can identify cars, it is something more than just a collection of parts for us. Once those parts come together, a new entity emerges that wasn’t there before. I think the same is true for infinity or the universe. We identify it as having its own essence which is something over and above the essences of the parts even when considered collectively.


Bijective’s, yes for sure, but that wouldn’t be the aleph omega of infinities ~ all the odd and even and prime rooms would be filled. Not to mention that the very notion of Bijective’s and Injective’s are flawed logic, don’t get me wrong, they work fine in maths, but that’s because the maths is dealing in very very large numbers and not actual infinities.
An integer of the infinite would be an infinity without edges, you don’t get one followed by two, 3,4,5… infinities etc [if i may], the second infinity would exist within the first ~ because it cannot exist outside of an infinity.
I don’t know at all how you would get a division in the first place, but somehow we have to go from infinity to universe, and that does have duality.

Yes. Though a line isn’t an infinity imho, because it has edges. I think that if ‘god’ drew an infinite line it would necessarily take up all the infinite space, otherwise he would have to stop drawing at some point. The ‘philosophical space’ is indescribable…

If you put e.g. a person [or anything] in an infinity it would expand to infinity i.e. Be an ocean within an ocean. At most we can have a plurality of infinities, but i don’t see how we can mix the two contrasting things? btw I think the original Hindu notion was to describe a spiritual infinity e.g. where each of us has a corresponding eternity.

I agree. Maybe the primitive chappie would see only the car and not the parts, even though he wouldn’t know what that is? But yea i think reality is greater than infinity because it include the non-infinite universe hence is greater than infinity [even though the universe is less].

There is another problem though, because if we cast the universe against the infinite, it would be comparatively infinitesimal, but it isn’t that. That we know the universe exists can only mean that there is no infinity to cast it against! The infinite and finite are mans descriptions and don’t describe reality, they are simply mathematical functions which reality uses along with everything else.


What do you mean by the aleph (alpha?) and omega of infinities?

You’re right about this. If there is a second infinity, it makes no sense to say that it comes after the end of the first infinity. Infinity means “no end”. But I don’t know if that means a second infinity would have to be “contained” in the first. If you think about all the points on an infinit line, and then imagine a second line parallel to the first, the points in the second line aren’t “contained” in the first. What we can say, however, is that even though the points on the second line are “outside” the infinity of points in the first line, none of them come “after” the last point in the first line. There is no “last point”, so nothing can come after it.

Yes, I got the impression that what infinity really means to you is no limits. Though there are an infinity of points on a line, there are also limits. There are no limits forward or backward, but there are limits above and below, to the left and to the right. ← So that line is not really infinit to you? Surely, you’d agree that there are an infinit number of points on it, no?

Do you mean like how a finite number like 1, existing among an infinity of numbers, is itself an infinity when you consider the infinity of real numbers it is made of? As in 0.1, 0.11, 0.111,…

The idea of infinity is the result of man not being forced to always imagine an end to everything. Man can imagine things never ending.

I’m not sure what you mean by the universe becoming infinitesimal when cast against infinity. I mean, I understand that anything finite would be infinitesimal compared to infinity, but why expect the universe to appear that way to us? We are definitely finite. In order to see the universe as the infinitesimal that it is compared to infinity, we ourselves have to be infinite, or somehow arrive at that infinite vantage point.

Of course, I have to disagree.

All things =
A) Large things
B) Medium things
C) Small things
D) Size-less things.

Or more simply,
All things =
A) things that have affect
B) things that do not have affect
C) anything in-between A and B

All inclusive sets are not that hard to derive:
A) Everything the slightest to my right
B) Everything the slightest to me left
C) Everything else

A) Everything that physically exists
B) Everything that doesn’t physically exist
C) Everything not apart of A or B

They all add up to the Whole.