Actual Infinities Empirically Exist?

It is obvious that actual infinities are rationally (metaphysically) impossible, in the sense of their capability of being empirically conceptualized. One can't conceive such an  infinity in empirical terms. The only way  one can try to conceptualize such is by attempting a measurement function that is potential in nature. Zeno demonstrated this long ago in order to discredit the credibility of phenomenal experiences, which accordingly are logically untenable. (See Achilles and the Tortoise and The Stadium). Zeno used the paradoxes to support his monist metaphysics. However, the arguments could, I think, be equally used to dump the reliability of rational metaphysics and cheer pluralistic realism.

W L Craig interprets Zeno's infinite divisions as potential and not actual.  What he means is that one can go on, empirically,  dividing a distance endlessly and never reach a metaphysical point of indivisibility, though in reality (experience), traversing distances is a daily affair - we do cross roads. He sticks to the empirical angle of interpreting the paradox. What I think Craig has done is to reiterate that actual infinities are not metaphysically possible, though the empirical concept of crossing roads, for instance, shows that an actual infinite distance was traversed in actual time (empirical sense, also infinitely divisible). In other words, when the rational function is applied to an empirical fact, a paradox ensues. Subjective and objective epistemology vs ontology issues are tense here. It can also mean that the distance between two points is an objectively actual infinity of points, and the act of traversing is potential meaning that the athlete cannot metaphysically traverse the distance, though he physically does it. The problem is there because a distance between points is an empirical concept while division is a rational category. The problem still remains.

However, it seems to me that strictly speaking, potentiality is an empirical category and not a rational one. Rationally speaking, the objective infinity of divisions is actual, though empirically absurd.


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