As for the hyper-reals, infinity doesn’t express itself as a totality… I tried to explain this to you with a tree analogy. There is no infinity tree that contains that set of all trees in it… though there are an infinite number of trees that are bigger than another tree (and smaller). I understand this is you’re proof… that infinity has no biggest or largest but exists. You cannot prove infinity necessarily exists using your mathematical techniques. You have to use more basic logical argumentation to do this.
We know there is basically a grid…
we have
true
false
N/A
true/true
true/false
false/true
and
false/false
It’s true that it’s true. = true
It’s true that it’s false. = false
It’s false that it’s true. = false
It’s false that it’s false. = true / paradox / false
A perfect example is “This statement is false”
The only truth value for the statement is it’s existential value, which isn’t explicit in the statement… We know the statement exists, therefor we know the statement is true on one level as existing, and false on another level, as claiming it doesn’t exist. So we can divide the paradox into different claims and resolve the paradox… it’s true in this sense, and false in this other sense.
What people generally do, is they say, if the statement is true, then it must be false, and if it’s false it must be true. The reason false and false have this effect is because “false” is OTHER THAN… so what happens with false being false is that it’s itself and OTHER THAN itself… this is why false/false on the grid creates paradoxes. The word false itself is a paradox in it’s own context… it’s OTHER THAN, but it’s OWN IDENTITY at the same time… the IDENTITY of OTHER THAN / a paradox…
False can’t exist as a word, and yet there it is for all of us to see…
Now we generally use context… other than this (instead of other than), and false doesn’t run into the paradox, but when it feeds back on itself or doesn’t have this context, it falls into the paradox.
But all you have to do to get out of the paradox is just look at it as a contradiction
It is what it is and isn’t what it is… it’s true/false ---- true that it’s false and false that it’s true, which both yield false. which only leaves you with the true/true grid, which leaves you with existence exists… it’s true that existence is existence, and all other possible solutions are false.