| | Ted, you wrote, I believe you do hold that:
(a) This sentence is false.
does have cognitive content,
(2) Do you not agree with me that the word "This" is equivocal unless one smuggles in an assumption as to which proposition "This" is referring to? Oh, absolutely! Could one not validly respond to (a) with the retort: "Which sentence are you saying is false?" Yes. But suppose the person says, "This sentence itself" or "The sentence I am now uttering," so that it is clear he is referring to the same sentence. Once he does that, he has resolved the ambiguity. But then we have a different problem, namely, that the sentence is paradoxical -- because if it's true, then it's false, and if it's false, then it's true -- in which case, we need to resolve the paradox. Pointing out that the sentence is equivocal, if the referent of the pronoun "this" is left unspecified, doesn't address that paradox. The paradox arises not because the sentence is equivocal, but because it is self-referential. If he said, "The sentence I am now uttering is false," the subject of the sentence would no longer be equivocal, because the sentence would then be clearly self-referential. But it would still be paradoxical, so how do you resolve the paradox? By pointing out that the only way the sentence can be meaningful is by referring to a sentence other than itself. Therefore, insofar as it refers only to itself, it is meaningless and therefore neither true nor false. I do not deny that the sentence is arbitrary, again, I believe that it has no cognitive ~import~ and only gets cognitive import if one smuggles in the (necessarily arbitrary) assumption that "This" refers to (a). I don't disagree with Peikoff's criticism of the arbitrary. I just think that one must address the equivocation here. Also, I believe that there is a difference between statements lacking "cognitive content" (since we do understand their meanings, how they could be falsified) and statements having ~import~ i.e., having necessary implications. I agree, but if a statement lacks cognitive content, then how could we understand its meaning? If it lacks cognitive content, then there is no meaning there to be understood. The meaning of a statement is what it refers to -- its referent. The sentence, "The sentence I am now uttering is false" is a statement that refers only to itself. In referring only to itself, it is referring to...its reference to...its reference to...its reference to...blank out. No matter how far you extend this process, there is no meaningful referent to which the sentence ultimately refers.
When you say, "The statement I am now uttering...," the statement you are referring to has yet to be completed, so it doesn't yet exist to be referred to, which means that the reference itself is meaningless. That is why no statement can refer only to itself -- because the reference to the statement must occur before the statement exists to be referred to. This does not, however, mean that there cannot be self-referential statements; only that no statement can refer only to itself, which was Binswanger's point. If we take the statement, "All sentences contain a subject and a verb," that statement is self-referential; however, it is still meaningful, because, in referring to all statements of a certain kind, it refers not only to those in the past and present but also to those in the future (which is an explanation that I owe to my friend Roger Bissell). So, unlike the statement, "This sentence contains a subject and a verb, the statement, "All sentences contain a subject and a verb," doesn't have to be completed in order to refer to itself, because its referent includes future sentences that have yet to be (completely) expressed.
- Bill (Edited by William Dwyer on 9/07, 12:57am)
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