I suppose I am assuming that the universe operates under some set of formal rules (though they might not be deterministic) independently of our ability to describe the universe using formal rules. I would also say that our inability to comprehend a given contradiction is related to the fact that we are inside the system. If God were outside the system he would not necessarily have this problem.
I disagree with your second point, though. Sure, 1 and 2 are labels for concepts that exist within a formal system we’ve developed, and sure, we can create an isomorphism to different labels. But I would consider this to be the same formal system. The example I gave (working in the integers mod 2) involves switching to a formal structure that is decidedly not isomorphic to the integers under addition.
Also, sorry if I was unclear—I did not mean to imply that mathematical formalisms as we’ve developed them are related to the fundamental laws of the universe. I only meant to say that if the universe is a formal system of some sort, and God operates outside that formal system, then it is conceivable that God could switch to a different formal system where things that we consider impossible are not, just like we can switch to a different formal system where 0 and 2. Maybe God could do something analogous and put me in the universe (mod 10 feet) so that if I walk ten feet straight across the room I’ll end up where I started; this seems like a contradiction in our universe but is definitely imaginable.
[Quick edit for clarity: maybe it doesn’t seem like a contradiction that I could walk ten feet away and end up back where I started, but it does seem like a contradiction that I could walk ten feet and both be ten feet away, and also be exactly where I started. This is what I imagine happening in the universe (mod 10 feet).]
Perhaps I have a different system of morality than other people who have commented on this topic, but I personally judge actions as “moral” or “immoral” based on the intentions of the do-er rather than the consequences. (Assuming morality is relative and not an absolute component of the universe, this seems like a valid moral system.)
If the atheists who run this website are doing so to make money by exploiting the perceived stupidity of their customers, this seems immoral to me. On the other hand, if they are running the service because they honestly want to increase the peace of mind of rapture-believing-in pet owners, then that seems like it would be a moral action. However, knowing people, I really suspect that it’s the former.
If the rapture really does happen and this really saves pets (assuming that it is a good thing to save pets), then I would still consider this service immoral. I would rather live in a world where people were compassionate enough that they did not to want to trick each other for money (even if they thought each other’s beliefs were moronic). Barring that, I’d like to live in a world where people consider tricking each other for money immoral and wouldn’t do it because of some internal moral crisis or external punishment. I hold this opinion even if some of the tricks for money backfire and end up benefiting the trickees more than the trickers.