Before I continue any farther I should probably label what a paradox even really is. A paradox is anything that would contradict itself and still seem like it should be true even if it's not. Paradoxes are quite real because they are merely concepts of how we process information.
The concept of a paradox also exists in more languages that English. Paradoxes date all the way back to Greece with the most famous being the "all powerful" making an "unliftable rock."
Mathematical paradoxes can prove this and there are plenty good ones that Brilliant.org has https://brilliant.org/wiki/introduction-to-paradoxes/ I'll let you take a look at that to see a few examples of what I'm talking about as well as a few anecdotes. They come in mathematical form, anecdotes, statements and even as optical illusion images.
Also in your example above it would have to be that one of the statements claimed the other to be true for it to be paradoxical. "Statement A is false" "Statement B is true"
It doesn't matter when the information is given or received even to determine how useful it is. Contesting validity of information in time doesn't work. Linear thinking is how computer brains function. There is never a need to restate information given to process. Visual paradoxes can show us just that: https://1millionmonkeystyping.files.wordpress.com/2013/11/currys.jpg
Oh also I owe you a big thank you for your patience and understanding. Internet debates are scary and many people are rude during things like these. I appreciate that we have kept it civil :)
Get on wattpad and leave him some insight about this as this will be a game plan how to rebuke Answers in Genesis; interested in the pdf I did addressing one of them. Drop me a message as I am giving her a change of venue.