I found myself thinking about the liar's paradox of the form "This sentence is false" and how it relates to one's conception of "Truth" and "Falsity". After deliberating on the matter, it seems that if one takes a Correspondence Theory-like notion of Truth, then the statement above should not lead to a paradox. The reasoning goes as follows:
Statements, in general, are true or false either analytically or synthetically, i.e., via definition or via empirical-ish ("outside word") fact*, in which if the claim the statement makes accurately corresponds to an analytic or empirical-ish fact (depending on the type of claim that is being made), the statement is true, and if the statement contradicts an analytic or empirical-ish fact, then it is false.
The statement "This sentence is false" is not a matter of empirical-ish inquiry nor is it an empirical-ish claim**. Likewise, the statement is not a matter of analytic inquiry and makes no analytical claim, hence it seems as if the statement cannot contradict nor correspond to a definitional fact or empirical-ish fact, resulting in the statement not being truth-apt (just as emotive and imperative sentences are not truth-apt).
Does this seem like a "reasonable" solution? If anyone is aware of any source material that deals with this topic from this angle, please feel free to recommend it. -Thank you
*The term "empirical-ish" here means "outside world". Statements relating to things that exist in the outside world, statements such as "Max is thinking about ice cream" or "Abstract objects exist", along with general empirical statements ("John is 6 feet tall"), would be categorized as "outside world statements".
**While one might attempt to categorize the statement "This sentence is false" as an "outside word" statement, it seems clear enough that there is no "outside world" fact that corresponds to or contradicts this [statement] (recall that "Truth" and "Falsity" are deduced from the facts, the facts themselves are not things such as "x is true").