Dale, I said the same thing in the other thread which you were participating in, but I'll say it again here.
Relativists want to say "there is no paradox."
In my view, they are correct, but not for the reasons they say. For that matter, different people will have different ideas of what the alleged "paradox" even is.
There is no paradox, simply a contradiction, brought on by relativists themselves.
It is contradictory to simultaneously claim both that:
(a) all frames are equally valid, that no one can be preferred over another, and that "therefore" (I put that it scare quotes because it doesn't even follow) that there is "no way to know who is moving, relative to another"
(b) We (relativists) subscribe to and propound a theory that gives you a way to tell who's moving.
With respect to this part, you can note that it is almost universally acknowledged in the twin example that it is the earth bound twin who is older and the travelling twin who is younger. It doesn't matter what they might otherwise say about how the travelling twin would "see" the earth twin's clock. As a matter of theory (and fact, given experiments) they concede that he is the one moving. If he thinks otherwise, he is simply wrong, they say (in effect). So the two frames are not"equally valid."
No one ends up claiming that "each clock is slower than the other" or that "each is correct." Yet, that's what they want to also maintain, in most contexts.
Hence it is a contradiction. But not a "paradox."