Infinity is a side-effect inference which seeps over analytical a priori rationalizations when occuring through a conscious negation of some being.
A priori because it isn’t empirical, it is rational, something deduced and self-evident via Cartesian doubt. Quantification of the world begins with the ontological life of the concept “Self.” That is the first and only “one” entity. All mathematics are negations of gratuitous being and number concepts are rational depictions of phenomenological experience in profiling the world: “That” is a “one.” “Those” are a “two.” Completely rational constructs that are not verified in experience but by experience. Mathematics is a mode of arranging sensibility into pattern, repetition and frequency, what would otherwise be non-existent without the presence of negation, the “breach” of pure being, so to speak. The cogito.
“Counting” takes place when the Self reflects on objective beings…empirical as substance, having mass and form occupying space, though not countable as distinct entities…the apple is the same stuff as the chair, only extended differently via empirical sensibilities. We look at an apple and call it “one” object…we look at the chair and call it another object. We look at them both and call them “two” objects. In reality the items are not different, not in the least, as every characteristic assigned to each item during the profile of its identity is yet another subject of objectivity, that is, to prove its existence, some quality or another must be reflected on, opening an endless deduction of sub-characteristic-characteristics, etc., etc. So we don’t arrive at the postulate “one object” through the empirical experience of some being, as everything is composed of “even more” qualities, but by the rational application of Self first, and then the object as “other-than-me.” Mathematics is essentially adjective, that is to say, giving an object the value of “one” is no different than giving an object the value of “good.” Describing something will always involve transcendent evaluations, begging the question unless the cogito is admitted, as “counting” is nothing more than this:
“I see a chair”= “(A)Me and a chair.”
“I see a chair and an apple”= “(B)Me and a chair-and-apple”
“I see a chair, an apple, and a Monooq”= “(C)Me and a chair-and-apple-and-Monooq.”
Notice that the value of the items I “see” are morphological. A, B, and C are single experiences. There are only two ontological distinctions here; me-ness and that-ness.
The concept of infinity comes about when one begins to break A, B, and C into individual values, setting off the “infinite” deduction of qualities and sub-qualities. Being is infinite in so far as there can be no nothingness without a negation…being is fullness but it is not something that can have the attribute of “many.” These descriptions are purely structures of consciousness.
We might treat the river paradox this way.
Just as I say to myself now that that river isn’t the same, as I can conceptualize “change” rationally, but not experience it via Imp’s “now-ness,” (which I agree completely with), I also say to myself that phenomenologically the river doesn’t change if by change I mean “things are no longer composed of more things,” which is originally the case to begin with, and I know that. By calling out “river” I am profiling a state of being which is contradictive by its very definition: A thing consists of changing things, which changes that thing, but doesn’t change things because they always change anyway.
I gotta tell ya’, I’m stumped on that one.