The infinite condition is itself a paradox, as it must necessarily include its own finite limitations, lest it create finite limitation through exclusion.
Just an (ahem!) internal memorandum, sort of. It’s an abstract notion sometimes manifesting in applied logical argumentation, but only in finite and situational considerations. The formulation that struck was that, The infinite must necessarily include its own limitations. Which is, of course, a problematic notion.
Nor can I claim any sense of originality; the statistical likelihood that I am the first person to tread into this realm is precisely measurable: exactly zero. And while it is unclear what role exactly we might ascribe, it is also true that Radiolab visited Gödel during last night’s broadcast.
At any rate, this clumsy paradox exists somewhere in the record, and in much more refined expression. In turn, refined expression is crucial because application of such a crude tool invites catastrophic potentials. The point is remembering to chase it down, lest the idea strike again sometime in the future, and meet similar apathy.
B.D.'s Last Refuge 