But how do you realise it was 'wrong'. Different, yes, but 'wrong'? — Pseudonym

When you fail to achieve the desired effect for example, you know there was a mistake. If there was a mistake, then something was done wrongly.

Great, let's have a look at one of those examples for a public rule then, that might get us somewhere. If you provide an example of a public rule where the 'correct' interpretation or use of it can be derived by some means other than
consensus, we could resolve the problem. — Pseudonym

I am not claiming that "the correct" interpretation can be derived at all. As I said, the right interpretation is an ideal. I don't believe that the ideal is ever achieved. As you argued concerning Wittgenstein's PI. varying interpretations may all be "correct". There is no such thing as "the correct" interpretation, in the sense of the best, the ideal interpretation.

The rest of your argument is based entirely on an error of mine. I meant to say the correct interpretation of the rule is 'judged' publicly, not is 'held' publicly. — Pseudonym

This does not avoid the problem I described. Individual human beings make judgements. To say that something is "judged publicly", is to say that there is a vote or some such thing. Just because the majority constitutes consensus, does not mean that the interpretation chosen by the majority is the correct interpretation. And, that interpretation which is accepted by consensus still needs to be itself interpreted by each individual member of that voting public, causing the infinite regress problem.

I can only blame trying to write too fast, I'm sorry to have made you painstakingly explain the infinite regress argument for no reason. — Pseudonym

So, you thought at the time that you were following a rule. But you now realize that you were trying to write to fast, and you really weren't following your rule. See what I mean?

For, if one were to follow a rule, then the criteria for following it is dictated by something beyond the rule itself. — Posty McPostface

Yes, that's exactly my point. That's what allows that an individual can think that oneself is following a rule, a private rule, then later realize that the rule was actually not being followed. Whether or not the rule has been followed, as judged after the action, requires a completely different form of judgement from the judgement of whether or not the rule is being followed, as judged prior to the action. The former is a judgement in relation to the past, how the rule was applied, the latter is a judgement in relation to a future act, applying the rule toward possible acts. One is posterior to the act, the other prior to the act. and these are distinct forms of judgement. One judges actual activity in relation to the rule, the other judges possible activities in relation to the rules. Each has criteria beyond the rule itself, but very different types of criteria.

We're going round in circles and I don't think my replies are helping at all. Let's see if I can clear up a couple of points where I think we might be talking across one another and maybe some idea of what we really disagree on might emerge.

1. Wittgenstein does not conclude anything at all about the solution to the rule-following paradox, a paradox has two sides which together seem incompatible. He does not say which side is right, if anything he's claiming that the paradox emerges because we are confused about the definitions of the terms we use (but that is only a general and speculative conclusion). I'm trying to argue that the paradox is real, I think you might be trying to argue that one side of the paradox exists. If that's the case, then we completely agree, the point is not that one side of the paradox doesn't exist, it's that both sides seem to exist which is a logical impossibility - hence the paradox.

Wittgenstein explains some of this slightly better, I think, in MS109-110.;

"Suppose that a general rule is given. One can, nonetheless, apply the rule only if he understands its application. Suppose, for instance, that someone should translate a sentence from one language into another. He is given the set of sentences to be translated and a dictionary, which is the set of rules of translation:
One could say then: But it is not enough to give him both things; you have also to tell him how to use them as well. But in this way a new plan would be created, which would need an explanation as much as the first one." (MS 109, p. 82).

and

"…I don’t need another model that shows me how /the depiction goes and, therefore/ how the first model has to be used, for otherwise I would need a model to show me the use/application of the second and so on ad infinitum. That is, another model is of no use for me, I have to act at some point without a model." (MS 109, p. 86)

This might be an expression of the paradox that you find more acceptable - It would appear I need a further rule to tell me how to interpret the rule (the dictionary and the foreign language alone does not tell me how to translate), and yet I nonetheless do appear to follow rules without a rule telling me how to do so. Hence a paradox. It is not sufficient to resolve this paradox by showing that we do follow rules without the apparent need for a model to tell us how, that's just one side of the paradox. In order for it not to be a paradox, it is necessary to show the the logic of the first statement is flawed. You're only providing demonstrations of how the second statement appears to be true, but of course the second statement appears to be true, that's why it's a paradox, because the first statement appears to be true also and yet the two contradict one another.

2. The Rule-following paradox is only tangentially linked to the private language argument. The additional difficulty of following a rule private applies to a specific set of rules that are about the correct interpretation of signs. The private language argument is about the correct interpretation of signs, not about the correct application of a prediction. You seem to be likening having a private rule to something like " I wish to stop smoking to make me healthier, I must not have any cigarettes" Such that if a new cigarette-like thing enters the market and you must judge whether smoking it breaks your rule, you can do so by perhaps smoking it, noticing your health is worsening again and thinking "Oh, this must be one of the things I must not have because it is having the effect my rule is trying to avoid"

But this is not the kind of rule Wittgenstein is talking about in the private language argument (though it is a rule that would suffer from the rule-following paradox). So disputing the private language argument and disputing that the rule-following paradox is really a paradox are two different things and you seem to be conflating the two.

We're going round in circles and I don't think my replies are helping at all. Let's see if I can clear up a couple of points where I think we might be talking across one another and maybe some idea of what we really disagree on might emerge. — Pseudonym

To clarify my position, I believe that there is no such paradox. The apparent paradox is the result of Wittgenstein describing "rule" in an unacceptable way. A rule is something which exists within human minds, not in the public domain. What exists in the public domain is physical material, in various shapes and forms, which we all sense, therefore it is public. This includes written, or spoken, physical representations of rules. Wittgenstein fails to properly distinguish between these two, the rule and the physical representation of the rule, when describing what a rule is, so he uses "rule" to refer to both. Since the two are not the same, yet he uses the same word to refer to both, as if they were, an apparent paradox arises. The appearance of a paradox is the result of Wittgenstein using the same word to refer to two distinct things, the rule, and the representation of the rule. That's equivocation.

"Suppose that a general rule is given. One can, nonetheless, apply the rule only if he understands its application. Suppose, for instance, that someone should translate a sentence from one language into another. He is given the set of sentences to be translated and a dictionary, which is the set of rules of translation:
One could say then: But it is not enough to give him both things; you have also to tell him how to use them as well. But in this way a new plan would be created, which would need an explanation as much as the first one." (MS 109, p. 82). — Pseudonym

See, his misuse of "rule" is very evident here. "Understanding" the application of a rule is something which occurs within human minds. But then he says that the dictionary "is the set of rules", and this is false. Neither is the dictionary a set of rules, nor is it even a representation of a set of rules. It is a representation of how words are commonly used.

If we proceed and consider a game, and refer to the spoken words, or written words, which represent "the rules of the game", it is evident that these are just physical representations of rules, because it is necessary to interpret these words, to understand "the rules". Common parlance allows us to say that these are "the rules", the written words, but we must differentiate between this common usage, and when we say that someone "understands the rules", because what is understood as "the rules" is the limitations as to how to play the game, not just the words on the paper. What is added by the interpreting mind, is the "ought", and this is not part of the words, it is part of the interpreting mind.

This is the is/ought divide. The words on the paper say something. The player interprets this as how one "ought" to behave. But there is nothing within the words themselves which dictate that the player "ought" to behave in any particular way, the player interprets the words as saying what one ought to do. Since the "ought" is the essential aspect of the rule, making the rule what it is, a guideline for future behaviour, and the "ought" is only assigned to the words by the minds of the writer and interpreter, then what is on the paper does not exist as "rules", in a more strict sense of "rule", when we talk about a person "understanding the rules".

2. The Rule-following paradox is only tangentially linked to the private language argument. The additional difficulty of following a rule private applies to a specific set of rules that are about the correct interpretation of signs. The private language argument is about the correct interpretation of signs, not about the correct application of a prediction. You seem to be likening having a private rule to something like " I wish to stop smoking to make me healthier, I must not have any cigarettes" Such that if a new cigarette-like thing enters the market and you must judge whether smoking it breaks your rule, you can do so by perhaps smoking it, noticing your health is worsening again and thinking "Oh, this must be one of the things I must not have because it is having the effect my rule is trying to avoid"

But this is not the kind of rule Wittgenstein is talking about in the private language argument (though it is a rule that would suffer from the rule-following paradox). So disputing the private language argument and disputing that the rule-following paradox is really a paradox are two different things and you seem to be conflating the two. — Pseudonym

The private language argument only follows from this equivocation of "rule". The equivocation of "rule", described above, which Wittgenstein employs, allows him to proceed into the private language argument. If we deny the equivocation, and keep a clear separation between a rule, and a representation of a rule, there is no premise to even start the private language argument. That premise, at 202, concerning the nature of rules, which allows for the private language argument, is rejected. Nor is there the appearance of a paradox. And the appearance of the paradox is what inclines Wittgenstein to propose that premise.