“This sentence is false." Is it true or false?
not every sentence is true or false. there are, for example, bad syllogisms, usually three sentences. john is a boy. all boys are green. therefore john is.... everyone knows the answer is green. good, if silly, syllogism. within its own reality all the sentences are true, even though outside of the syllogism we know damned well that only left-handed boys are green, and only on tuesdays. but how about: john is a boy. john is green. therefore all boys are.... it's a bad or false syllogism and the only proper answer is "there is no enough information to proceed." your sentence has a similar problem. it is neither true nor false but it's a bad sentence, just as "when did you stop beating your wife?" is a bad question.
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“This sentence is false.” Is itself a sentence and is therefore a true statement .
It is a pronoun. Weren't expecting that answer were you?