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.
It would also seem worth noting, and again for the sake of simply remembering, that this condition is also a problem challenging philosophies derived from monotheistic presuppositions; from Augustine to Anselm, before and beyond, the concept of infinity really should not be used for such purposes†.
† An obnoxious footnote: There is in the world a “Bible paraphrase”, called The Clear Word, and in at least one edition Genesis 3.22-23—“Then the LORD God said, “Behold, the man has become like one of us, knowing good and evil; and now, lest he put forth his hand and take also of the tree of life, and eat, and live for ever”; therefore the LORD God sent him forth from the garden of Eden, to till the ground from which he was taken”—becomes a conversation between the Father and the Son about how the Fall of Man was according to Plan. The irony, of course, is that many atheists would make the point that this is the only logical resolution of God’s omnipotence, regardless of its strange application to the verses in question; indeed, this insistent logical resolution is what compelled Anselm to redefine omnipotence.
A Note on the Title: No, really, I just couldn’t think of anything better. The obvious tip o’the hat goes to Screaming Trees.
Image Note: Composite image. Uncredited photograph of Kurt Gödel ca. 1950, via Institute for Advanced Study, Princeton, New Jersey, left; detail of stained glass window from St. Anselm Catholic Parish, Toronto, Ontario, right.