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i did already. i defined it as a negative concept, one produced through inversion of notions like finitude. it has no particular referent. to generate notions like infinity, all you need is the capacity to negation, which is a formal matter.
within christianity, negative theology came closest to addressing it's meaning: we have no access to the infinite because our understanding is finite. so if god is infinite, human beings can know nothing about this god, not even whether she exists or not, and the name "god" is nothing but a name.
that repeats the act of creating a notion through negation of an existing one. but at least it's consistent.
from that viewpoint, mathematical notions of the infinite are just one of any number of ways to locally define the category, one which produces some interesting effects and is useful within certain games.
what i think makes the category of the infinite interesting is how it gets used and what those usages do, not what putative referent there is in the world/universe. it's interesting as a generator for speculative thinking in some contexts. but these usages are conditioned by rules, so the meta-question (to my way of thinking anyway) has to do with rules usage and phenomena in the world, how relations are established, how they condition processes of meaning generation, and how the results of these processes frame experience of the world.
so i wouldn't go in the same direction as you in pursuing the question of what the infinite is, really.
not that yours isn't interesting...it's just not how i'd approach it.
but this all follows from the premise that the infinite is the product of an act of negation, so is the result if you like of a formal operation. in other words, it is a noun that is not a name.
that's what i think the category is.
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a gramophone its corrugated trumpet silver handle
spinning dog. such faithfulness it hear
it make you sick.
-kamau brathwaite
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