But doesn't this support my argument?
No. Your argument is that this is beyond human logic and understanding.
You (again, this is what drkitten did!) attempt to resolve the issue by stepping out one level.
If by "the issue", you mean demonstrating my understanding, then... guilty as charged! But: ...
Instead of trying to assign a truth value to the statement, you try to assign a truth value to a claim about the statement.
...it appears that you think I was trying to "solve the issue". I wasn't. I'm trying, instead, to show you what "the issue" actually is. That's the motive for stepping out.
But it doesn't solve the problem of it being different from all other well formed sentences,
Actually, that
is in fact the very problem that it solves. The entire reason for stepping out one level is to show understanding, and the whole point is to show
precisely how those statements are different from other well formed sentences.
And the analysis does, in fact, illustrate an understanding not only
that the statements differ, but
how, and
why. What's left to understand?
because if you do the same for other well formed sentences -- as you show! -- you can always find at least one way to make a true claim about them.
But it's not surprising. That the claims are self referential isn't the essential point here. The same sort of issue occurs if you give me a choice, and a prediction, and let me choose. I can pick independently from your prediction, or dependently. If I pick dependently, I can spite your prediction, in which case it's impossible for you to be correct, or I can humor it, in which case it'd be impossible not to be correct. These are simply "self spiters", or "self humorers", and they get to be simply because the thing they are about is bound to the evaluation of their validity.
The essential point is that self referential statements have such "outputs" hooked to "inputs" at all, and yeah, there are more complicated ones that make me scratch my head. But the simple one? What is it you suppose I don't understand about it?
I say people never come to a conclusion about it, you say you give up and give a postmortem -- same thing.
But you initially said that it was beyond human logic and understanding. That's what I'm objecting to. Were you to merely say "we don't come to a conclusion about it", you'd be correct. But it's no more meaningful than my not coming to a solution to an impossible sudoku puzzle (even after demonstrating it impossible). Once you claim that I don't
understand it, you overstep your bounds--if I know exactly why that sudoku puzzle is impossible, I
do understand it. That I can't find a solution is simply because it's impossible.
And less face it... sudoku's a great analogy, because it's not really even an
analogy so much as it is an
example.
The point is, we can't figure it out like we can figure out other sentences.
But isn't that because it's
not like other sentences? Is your problem merely a manufactured one?
I get it that they are not like other claims. What you don't seem to grasp is that I
get it that they are not like other claims. Even self referential claims for which there
are assigned truth values fall into this class. The class can be called... quite legitimately... simply, self referential (i.e., in a logical sense, we can formally describe a statement as self referential when the statement is about, even in part, its own truth value).