1. A paradox at its most basic is a loop.
2. The solution to a paradox never lies in the loop itself, but external to it.
Application: Cut the loop as Alexander cut the Gordian Knot
If the paradox of infinities, the infinite part is considered external to itself. In other words, the basic form of an infinite paradox is it's finite basic form. To break it, it must be turned infinite.
3. If a so-called paradox can be observed (physically), it is not a true paradox - it simply means the observational model is incomplete. A correct observational model will have no paradox.