Well, in formal logic it doesn't exist as a paradox. Basically, Fermi was talking casually and people have tried to formalize the point he made (namely, "Where is everybody?") into a logical argument for the existence of ET or for a government coverup, which isn't the same thing.
My basic view is this. It's likely that intelligent life exists, has existed or will exist somewhere and at some time in our galaxy, but it's unlikely that they'd go to any lengths to visit a species that still wars with itself and can't get off their home planet.
That's assuming they know about us, have any interest in meeting other species, can travel to us, and would within the relatively short period (~5000 years) that humans have had civilization.
For all we know, they could have found out about us the first moment we made fire, and still not have visited because they live on the other side of the galaxy. Maybe two space faring species in a galaxy is a lot. Maybe two thousand is a lot. That still leaves... what, 2 billion unpopulated stars in the galaxy? Long odds of crossing paths indeed.
Edit: I can't stop thinking about this question now. I read a really great short story on the subject. Aaand now that I've pulled the collection it's in, I'm not at all surprised by the title, which I couldn't remember. It's called The Fermi Paradox is Our Business Model by Charlie Jane Anders (read it here). The author makes the point that intelligent life destroys itself rather more commonly than our experience has led us to believe.
Your answer is even better than I could have hoped. Thanks for the link to the story. I will read it tonight after I'm done slogging through my quantitative methods class stuff.