Infinity

If past time is to retain its distinct intelligibility, it can only be viewed as “having occurred,” “achieved,” and “actualized.”

Now let us turn to the other side of the expression, namely, “infinite.” Throughout this Unit, I will view “infinity” within the context of a continuous succession because I will show that real time in changeable universes must be a “continuous succession of non-contemporaneous distension.” Now, infinities within a continuous succession imply “unoccurrable,” “unachievable,” and “unactualizable,” for a continuous succession occurs one step at a time (that is, one step after another), and can therefore only be increased a finite amount. No matter how fast and how long the succession occurs, the “one step at a time” or “one step after another” character of the succession necessitates that only a finite amount is occurrable, achievable, or actualizable. Now, if “infinity” is applied to a continuous succession, and it is to be kept analytically distinct from (indeed, contrary to) “finitude,” then“infinity” must always be more than can ever occur, be achieved, or be actualized through a continuous succession (“one step at a time” succession). Therefore, infinity would have to be unoccurrable, unachievable, and unactualizable when applied to a continuous succession. Any other definition would make “infinity” analytically indistinguishable from “finitude” in its application to a continuous succession. Therefore, in order to maintain the analytical distinction between “finitude” and “infinity” in a continuous succession, “infinity” must be considered unoccurrable (as distinct from finitude which is occurrable), unachievable (as distinct from finitude which is achievable), and unactualizable (as distinct from finitude which is actualizable).