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Full Idea
If we supplant the sentence 'this sentence is false' with one saying what it refers to, we get '"this sentence is false" is false'. But then the whole outside sentence attributes falsity no longer to itself but to something else, so there is no paradox.
Gist of Idea
If we write it as '"this sentence is false" is false', there is no paradox
Source
Willard Quine (The Ways of Paradox [1961], p.07)
Book Ref
Quine,Willard: 'Ways of Paradox and other essays' [Harvard 1976], p.7
A Reaction
Quine is pointing us towards type theory and meta-languages to solve the problem. We now have the Revenge Liar, and the problem has not been fully settled.