I honestly don't see the contradiction. Intrinsic means "belonging to the essential nature or constitution of a thing." The government constitutes the "thing" (fiat money) and imbues it with value by printing denominations on it. People worldwide recognize that value. You're getting hung up on the fact that nobody would trade anything valuable for a plain piece of paper, but of course a piece of paper is a different "thing" when it has a government's markings on it.
More importantly, I think it's rather lame of you to parachute out of the discussion based on a single paragraph highlighting our different interpretations of a rather murky concept like intrinsic value. You made some debatable claims earlier, and in my response, I highlighted what I saw as weaknesses in your argument. If you simply didn't feel like defending your claims, then that's fine, but it's pretty low-rent to bail out based on the notion that I'm not thinking for myself or don't understand what I'm talking about, and therefore can't be reasoned with.
And, not for nothing, but I never said or implied that libertarianism was a premise. I said it was a world view, but of course world views are often arrived at after careful study and consideration, and I don't doubt that's the case with you based on our previous interactions. If I felt otherwise, obviously I wouldn't have wasted my time engaging you on this topic.