(5) There are cardinally more things of kind (3) than there are things of kind (3)
That follows from (4), given (3), but is contradictory, and hence false.
My resolution begins by observing that apparently timeless possibilities could possibly become more numerous over time. It begins that way because if possible selections are becoming more numerous, then that could easily change the meaning of (3) enough to avoid (5). There is no other way of avoiding the contradiction that I can think of (and note that the main resolutions were constructivism, with its potential infinities, and going axiomatic, which means not addressing numbers of things directly); which is, after all, why this is a paradox.
Consequently this is essentially a proof by reductio ad absurdum that possible selections do become more numerous over time. And how could possible selections become more numerous, if not by a transcendent creator making definitive selections, constructing arithmetic as part of the creation of all things? There is no other way that I can think of; whereas this way is a serious possibility, because
A) mathematicians have taken constructivism surprisingly seriously, and constructivism would only be more Platonistic, and Millian, were the definitive constructions made by a transcendent creator, and
B) theologians have taken the idea of God being beyond our conception of number very seriously, e.g. the Trinity.
In 2003 I was published in the British Journal for the Philosophy of Science, but I've DONE little since then, although I am currently writing a book. Blogging since 2007, originally as enigMan (a "Meaning"-full name), my main involvement was via the Philosophers' Carnival because I started a PhD in Philosophy in 2007. The preliminary work for my book having got boring, in 2014 I started taking photos of my village and processing them with Windows' Photo Gallery (for example, sunlit willow twigs reflected in a shadow on the village duck pond, posted to the right of this text box). I was sharing them on google+ and now share them on MeWe, sharing the videos on YouTube.