Introduction[]
Absolute Incomprehensibility (Absolute Incomp for short) is not a degree of Absoluteness in the usual sense. It is not merely a Foundation, but a "Foundation of Foundations". It is an Absolute Beyond all Absolutes.
It's symbol is ת (Tav), the Last Letter of the Hebrew Alphabet. It can be thought to complete what א (alef) began. It is in some sense a completion of the notion of Foundations themselves. It does not receive nor can it receive an ordinal indexed subscript, because if it did it would just be claiming to be the Supremum of a Foundation, which it is not.
Definition[]
For any hyper-transfinitely indexed set of Foundations from below, we can form another Foundation, which can be used to form another hyper-transfinitely indexed set of Foundations. The Total Potentiality, inexpressible as any Foundation is defined as the size of Absolute Incomp (ת).
Ramifications[]
This leads to a 2nd level Paradox. It is now not even enough to claim that Absolute Incomprehensibility does not exist, because that would imply there was a Foundation it "did not exist" relative to, but we do not even have that luxury anymore. Any technique used to Transcend a Foundation can not be used to transcend Absolute Incomprehensibility. Worse, Absolute Incomprehensibility can not be a Foundation ... even though it fits the definition of one. It is doubly inescapable. Any set of properties one could claim to have violated in order to escape it, would just be the beginning of yet another foundation within Absolute Incomprehensibility. This now breaks logic in a very fundamental way.