Liar's Paradox and Truth

Question

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

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*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").

Answer 1

Imagine that you never used the words "true" or "not true" or "false," but then constructed a sentence, "This sentence doesn't correspond to a fact." Would you still be able to derive a contradiction from this? For then:

1. Assume that, "This sentence doesn't correspond to a fact," doesn't correspond to a fact. Per bivalence, we might have, "Every sentence corresponds to a fact or corresponds to a non-fact," so let's assume that, "This sentence doesn't correspond to a fact," corresponds to a non-fact. What would this mean?
2. Or assume on the contrary that, "This sentence doesn't correspond to a fact," does correspond to a fact. Then, though the sentence claims to not correspond to a fact, yet it does so correspond. What would this mean? What fact does it correspond to? Suppose it corresponds to the fact that 2 + 2 = 4, for example, or some other random fact. What is it about the notion of correspondence-to-facts that does the work, here, of dividing true sentences from untrue ones? For presumably we could have sentences corresponding to multiple facts, perhaps by mentally associating a sentence with random other things.

One might think, then, that correspondence-to-facts is too opaque of a replacement concept for being-true, because we seem to be able to understand what it means to construct a sentence that refers to itself as false, but if falsity is non-correspondence to a fact or correspondence to a non-fact, this intelligibility seems perhaps to go away, or is underdetermined (because correspondence is underdetermined).

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Generally, the Stanford Encyclopedia of Philosophy article on the liar paradox is a good resource for reflection on the topic, including the question as to whether the liar sentence expresses a proposition. See also Żełaniec[07], which compares, "This sentence is false," to, "This sentence is true," and draws a conclusion resembling yours. From an abstract for another essay by that same author:

In this article the author argues that the 'Liar' Paradox sentence: "This sentence is false" is neither true nor false because it does not express any proposition or "Satz" in the sense of Bernard Bolzano. The difficulty left open is that by a similar line of reasoning also the sentence "This sentence is true" would not express any proposition, yet it is sometimes taken to be true (on the strength of a theorem by Loewe)

The mention of a certain Loewe is presumably of Benedikt Löwe, whose ResearchGate bibliography includes "Revision Forever", an exploration of, among other things, the considerations that go into another approach to the liar paradox, the revision theory of truth.

Answer 2

What is the basis for your belief that the sentence 'This sentence is false' is not analytical? The concept of a proposition being analytical is not "solely based on definitions", but rather that it is true or false solely based on the meanings of the terms and concepts involved. Therefore, while the sentence 'This sentence is false' is not empirical, it creates an analytical contradiction. That's why it's problematic.

Moreover, I understand that in contemporary logic, there is a perspective that treats only things that can be evaluated as true or false as 'propositions,' which aligns with your approach, I believe. In this case, the sentence 'This sentence is false' would not be a proposition, but merely a statement, just an utterance.