Skolem's paradox

I was cruising the net looking for information about skolemization when I stumbled on a paradox that I'd never seen before. Skolem's paradox is one of the most astounding paradoxes that I've ever seen. Here are a few links I dug up on the subject: The Löwenheim-Skolem Theorem MOORE ON SKOLEM'S PARADOX Reflections on Skolem's Paradox I'm don't totally understand all the implications of the paradox, but I do understand some of them and I find it both fascinating, and in some ways disheartening.