A quick note for those who might be interested.
I wrote this recently – “The notion of the infinite is contingent on notions of finitude. If notions of finitude are empty, so are notions of the infinite.”
That was within a Buddhist context concerning emptiness.
Classically speaking, the notion of the finite and the notion of the infinite are complicit conceptions.
Finite means, defining; definite; finished. Infinite means, not finite.
So of course both words have each a range of meanings which are not necessarily strictly synonymous, but those meanings are connected and have a logic.
Obviously, finite and infinite are inverses of each other, but it’s probably important to keep track of whatever specific inversions are in play with respect to specific notions of the finite, and their corollary, specific inversions of the infinite.
How this is useful, is where notions of the infinite do indeed rest on specific characterisations. They are infinite with respect to some specific quality, substance, tendency, extent, et cetera. Those specificities are finite structures, that is to say, defined or ‘finished’ structures, structures of the finite which are then opened up to various modes of infinity procedures or infinitisations, whether it be endless recursion of, or just endless extent of, whatever specific, finite structuring, is being addressed.
The important thing to remember is the specific complicity between the two concepts.