Matheologians are accustomed to ignore the difference between potential and actual infinity. Usually they even deny that there is any difference. In this paragraph I will make another attempt to show this difference.
Potential infinity is a never ending, never completed sequence or chain of steps like the following, constructed of initial segments of the ordered set of positive even numbers.
This sequence is not more than all its terms. It cannot surpass all its terms. It is incapable of reaching a cardinality larger than every positive even number, the failure getting clearer and clearer with every term at every step.
The existence of alephs, however, requires actual infinity, completed infinity, finished infinity. But then we have to swallow results like the following:
Consider an urn and infinitely many actions performed within one hour (first one needs 1/2 hour, second one 1/4 hour, third one 1/8 hour and so on).
Fill in 1, 2, remove 1 Fill in 3, 4, remove 2 Fill in 5, 6 remove 3 continue.
After 1 hour the urn is empty, because for every number the time of removal can be determined. So for the set X of numbers residing in the urn we obtain Lim |X| =/= |Lim X| This prevents any application of set theory to reality although it was Cantor's outspoken aim to apply set theory to reality (cp., e.g., his letter to Mittag-Leffler of Sept., 22, 1884).
Or assume the existence of all rational numbers of [0, 1], enumerated, for instance, according to Cantor's method, starting with 0. If they all exist, then all permutations should exist, because each number is in finite distance from the first number 0, enumerated by 1. But then also the permutation with all rational numbers enumerated and sorted according to magnitude should be obtainable within aleph_0 steps and, therefore, should exist, shouldn't it?
Therefore, in the latter cases, only potential infinity can prevail. This is the true reason, why matheologians deny to recognize the difference between potential and actual infinity. While most of the followers certainly honestly claim that they never thought about that problem, I cannot believe that the leading matheologians always have observed the same ignorance.