This is only a paradox under naive definitions of infinity. Once one starts talking about cardinality, the “paradoxical” nature of the thought experiment fades away.
In other words, this is not really responsive to James_Miller’s comment.
If an infinite number of aliens have the potential to make contact with us (which I realize isn’t necessarily implied by your comment) then some powerful subset must be shielding us from contact.
Not necessarily—See Hilbert’s Paradox.
https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel
This is only a paradox under naive definitions of infinity. Once one starts talking about cardinality, the “paradoxical” nature of the thought experiment fades away.
In other words, this is not really responsive to James_Miller’s comment.
If an infinite number of aliens have the potential to make contact with us (which I realize isn’t necessarily implied by your comment) then some powerful subset must be shielding us from contact.
Infinity is really confusing.