Your second reference is somewhat odd, since he has a valid Aristotalian line of thinking until he drops the bomb about being "theistic" in the last sentence. Huh? I have no idea how this article, which Ayn Rand could have written, functions in any way as a Christian "apologetic," unless he falls into the common conservative trap that absolutes and morality require a supernatural underpinning, which your third reference seems to indicate.

Absolutes and morality can be defined quite nicely without reference to religion, although unfortunately it is not commonly done. You get started on the right road when you realize the first absolute either-or is "alive" or "dead."

For the record, anyone who tries to convince you that there is no way to tell what is "true" or "false," is trying to pull something on you. I have found no exceptions to this so far. In more general terms, this is often true of anyone who attempts to get you to disconnect rationality from reality.