Here's my solution.
A statement is a grouping of symbols(which is what words are) and can, itself, be treated as a symbol. Symbols are used to refer to something other than themselves, but when you have the statement refer to itself, you get a paradox. When it refers to itself it becomes infinitely interpretable causing "This statement is false." to cycle between True and False for as long as you try to interpret it.
Just a minor point:
"when you have the statement refer to itself, you get a paradox" is not necessarily true. For example, the statement "this statement has five words" is self-referential and true. No paradox. Even a self-referential statement that includes its own truth value can be non-paradoxical: "This statement is true and has two words" is merely false.
By the way, this leads me to consider Prior's resolution as somewhat problematic:
"This statement is true and has eight words" "This statement has eight words"
The first statement is true and the second false, hence they cannot be equivalent. Nevertheless, adding "This statement is true and " to any statement should not change the statement's truth value if we accept that every statement implicitly states its own truth.
Here's my solution. A statement is a grouping of symbols(which is what words are) and can, itself, be treated as a symbol. Symbols are used to refer to something other than themselves, but when you have the statement refer to itself, you get a paradox. When it refers to itself it becomes infinitely interpretable causing "This statement is false." to cycle between True and False for as long as you try to interpret it.