Q&A: Are self-referential statements necessarily logically invalid?
Are self-referential statements necessarily logically invalid?
Question
People claim that “This sentence is false” is not a paradox, because the phrase “this sentence” refers to the entire sentence and therefore it is not well-defined. Does that mean that the sentence “This sentence is true” is also not well-defined for the same reason?
Answer
I didn’t understand the claim.
Discussion on Answer
I don’t understand why you keep going.
Indeed, the claim is: “ ‘This sentence is false’ is false.”
In any case, even if it is open to interpretation, it is clear that this is the interpretation they mean.
Why stop at “This sentence is false” is false? Here too you have to ask what the phrase “this sentence” means. From here you reach the conclusion that the meaning is that this sentence is false is false false, and so on.
Because that is the meaning of the sentence I stated, but I did not state that sentence. The sentence that came out of my mouth is false.
Moreover, suppose I were to say the following words: “ ‘This sentence is false’ is false.” There is no need to continue here, because I clarified what I am referring to. Only the statement “This sentence is false” requires decoding the words “this sentence,” because there I am referring to some sentence that is not defined by the words themselves.
People say that the problem with the paradox “This sentence is false” is that it’s unclear what the phrase “this sentence” refers to. If “this sentence” = “This sentence is false” (that is, the phrase “this sentence” refers to the whole sentence), then you can keep going and write: “This sentence is false” = “This sentence is false” is false = “This sentence is false” is false is false, and so on…