I’m reading Appiah’s Thinking it Through and I am having a little bit of trouble understanding grasping his statement of the crux of the private language argument(s). In particular, I don't understand the "punchline" or why Wittgenstein says such private languages cannot exist. Appiah seems to be giving two different reasons that such language can't exist, and I can't tell if they're related or just unrelated and separate arguments which prove the same point (here Appiah uses "twinge" in place of Wittgenstein's classic "S"):
(1) First, Appiah seems to suggest is that the point is that it's incoherent to even talk about private states:
Using the word “twinge” to refer to a private state involves conforming to the rule that you should say to yourself “twinge” only when you experience that private state. But the idea of trying to conform to a rule essentially involves the possibility that you might fail to apply it correctly, and in this case there is no such possibility. “Whatever is going to seem right to me is right. And that only means that here we can’t talk about ‘right.’” If we have mental states that are private, the argument shows that we can’t talk about them, even to ourselves! Since it doesn’t make sense to talk about such private states, Wittgenstein drew the conclusion that there could not be any: after all, if the sentence “There are private states” makes no sense, it certainly can’t be true!
(2) Next, Appiah seems to suggest that the crux of the argument is that we are led into infinite regress if we imagine that we can assign names to private marks:
In order to bring out the force of Wittgenstein’s argument, you might argue as follows. Hobbes’s idea is that the name can help you remember that you have had the experience before. If it is possible that you have forgotten the experience of the twinge, however, then it is surely possible that you have forgotten the experience of naming the twinge. Do you need another “mark” that names the experience of naming the twinge? If every memory needs a name to help us remember it, then we seem to be caught in an infinite regress.
(1) seems to have nothing at all to do with infinite regress, while (2) seems to have little to do with the incoherence of having a private mark with no criterion of correctness (and rather depends simply on the impossibility of being certain in remembering a private "thing", such that we are led into an infinite regress of needing marks for everything). Can someone put me straight here?