What is the crux of Wittgenstein’s PLA?

Question

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?

Answer 1

We have to remember that Wittgenstein thought language was a matter of use-value: one person needs to coordinate with another person to achieve a particular goal, so they develop words that help with that coordination. In other words (Wittgenstein's language game #2) a man building a brick wall needs to establish the word 'brick' so that an assistant will hand him the correct object. There's no 'use' in the wall-builder saying 'brick' and being handed (say) a carrot, or a horse, or a poem. And so in Wittgenstein's worldview there is no sense in a private language because it has no use-value. It;'s private, so it cannot be used to coordinate between people.

In other words, while I can certainly create the word 'glorschlup' to refer to something specific to my experience, that word is useless unless I enter it into common language in a way that others understand what 'glorschlup' means. I don't need the word for myself (since I can experience the state of 'glorschlup' pro-verbally); I only need it to communicate with others about the experience.

Appiah's point 1 is a recognition is a recognition that we don't need a word to express a private experience for ourselves, since we have the experience directly. Appiah's point 2 is merely an extension of that principle that says we don't need a word to remember a private experience, because we can remember it directly (or if we cannot remember it directly, we have lost the sense of the experience). In either case, we only need the word to communicate the experience to others. 'Private' language is at best redundant.

Answer 2

Private languages are completely possible. Appiah is wrong in everything he says.

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

Incorrect. There is certainly a possibility that you could experience a private state and say "twinge," but then realize that it wasn't quite the same private state that you meant to associate with the word "twinge," so by your own hindsight you were wrong. It is just like looking at a sloppily drawn number and thinking "that's a 6," and then looking more closely and realizing it's more likely an 8. (The analogy is especially close if the 6/8 is your own handwriting!)

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.

It is invalid to take the premise, "a name can help you remember an experience," and produce from it the conclusion, "every memory needs a name to help us remember it." The premise only says the name is helpful, not that it is always necessary. Some memories can have a name to help us remember them, and others can be remembered without names.

Imagine you are stranded alone on an island. You are alone but you will still use language to help think about your situation. There may be edible plants on the island that you don't know the names of, and you will make up names for them, used only by you. This is your own private language, and it is useful to you. You can be wrong about applying names; you can apply a name to a plant that you think is edible, but in fact the plant just looks similar to an edible one but is poisonous, and you will regret your mistake.