“This sentence is false” marks the essence of Quine’s paradox. If it is true that “this sentence is false” then how it can be false? In other words, how a sentence can be true and false at the same time? Now you get the inkling of Quine’s paradox.

Let’s analyze the source of confusion. One one hand “this sentence is false” is a self-referencing stipulation that claims falsehood at the time it is being made. The next moment an observer examines this stipulation and finds it to be true, i.e. the previous statement is true.

The key to resolving this paradox has two facets:

1. First of all, the self-stipulation of falsehood by the statement happens at an earlier moment in time compared to the claim the observer makes about the statement being true, which happens at a later moment in time. That is the claim of the falsehood and our evaluation of the claim happen at TWO DISTINCTLY DIFFERENT moments in time. Thus, the statement is question is not being true and false at the same moment in time, but rather it is false at one moment and true at another. This is perfectly fine as this happens all the time in our daily experience. E.g. a statement “I have money” may be true at the moment the statement is made and false the next moment (e.g. when the money is spent). Thus, time saves us from logical inconsistency because the stipulation “this sentence is false” is not true and false at the same time, but rather false at one moment in time and true at another.
2. Second of all, we must examine the nature of the stipulation itself. It is hollow in the sense that it does not contain any information about a fact but rather contains information on and about itself (meta-information if you will). “This sentence is false” is completely different from “the boiling temperature of water is -100°C”, which is a statement about a fact (e.g. the boiling temperature of water), which happens to be false. When we evaluate the second statement we can determine it to be true or false without paying attention to the time of said determination (e.g. the falsehood of water boiling at -100°C is true at the time the stipulation was made and at the time the stipulation was examined and found to be false). However, the stipulation “this sentence is false” contains no such factual information, it is therefore hollow like an empty box devoid of content to be examined. Therefore when we examine the stipulation and find it to be true we do not make a claim about falsehood or truthfulness of any facts, instead we merely acknowledge the claim (i.e. the mere existence of the sentence) without really passing any judgement about its factual content because it contains no facts to be judged as being true or false. It is as if trying to determine the truth or falsehood of missing information. Is no information true or false? It could be either, and maybe the best way to go about it is to acknowledge that no such determination can be made; the outcome of examining missing information is undefined.

Thus, the statement “this sentence is false” is ought to be neither true nor false if one is pressed to assign a ‘true’ or ‘false’ label to this statement at the time the statement is being made. Because of the hollow nature of the statement this property of the statement cannot be defined at the moment the statement is made.

However, if we are allowed to assign the ‘true’ or ‘false’ label to this statement at a later time we can do so without loosing logical consistency. The statement was false when the the statement was made but it is true now when we examine it.

Regardless, the question is moot because the statement itself is hollow since it does not pertain to a fact. Because we are not confirming or falsifying any facts we are attempting to pass a logical judgement about missing information, which in itself is a logical error. The end.