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.

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