Are Russell and Whitehead's solutions to Logical Paradoxes valid?

The proposition "This statement is false" is a classic logical paradox. Russell and Whitehead argued in the Principia Mathematica that this paradox could be resolved by the principle that no proposition can describe itself, or that no function can be an argument of itself. But, doesn't this principle violate the notion of recursion, one of the fundamentals of modern mathematics, and computing science? And, after all, the proposition "This proposition, is a proposition" is certainly describing itself, and is perfectly clear, and perfectly accurate, if somewhat tautological. Wouldn't it be more accurate to say the problem with the proposition "This statement is false" is simply that it is totally ambiguous, or really, no proposition, at all?