Muth Rationality, Meta-metaphoricity & Kripkenstein's sceptical paradox.

 “this was our paradox: no course of action could be determined by a rule, because every course of action can be made out to accord with the rule.”

How can a rule determine or control anything? This is merely an emotive manner of speaking. We may say 'I am following such and such a rule' but this is merely a metaphor- a figure of speech. There isn't something ahead of me which shows me how to proceed. Suppose we believe that the rule creates some occult being who goes ahead of us and whose actions we imitate. Then we are treating a metaphor- viz. that of following a rule- as a concrete reality. We can go a step further and say that this occult being who goes ahead of us and whose actions we imitate is, so to speak, 'controlling' us. This is a meta-metaphor. It is a falsity based on another falsity.  It is not an interpretation of anything nor a theory about anything- rather, it is merely a lazy or emotive of speaking about something everybody already understands and knows to be other than how it is being presented.

Suppose my meaning is- 'I am imitating the actions- e.g. that of walking down a particular path- of some imaginary person whose actions are in complete consonance with such and such rule.' Could you object saying- 'you are not following the rule at all. Any action of yours would be in consonance with the rule.'?

The plain answer is- 'no. I can specify what course the imaginary person takes and I can specify what course I myself take. There are bound to be contingencies and personal preferences which cause the two courses to diverge.'

You might then makes some other objection but I am likely to lose patience and reply- 'thank you for endorsing my view by turning into a cat and licking your unmentionables and then saying 'O Long Johnson' on Jew Tube'. If you resort to meta-metaphors, so can I. If you say something silly, my best recourse is 'to answer a fool according to his folly'.

The cat now having got Kripkenstein's sceptical objection's tongue only a robustly cynical response- viz. barking and biting- can re-establish its position up the arse of the celestial choir of pre-established harmony. Either that or some other bunch of meta-metaphors which are equally meaningless.


Why?

The answer is that logic has nothing to do with a meta-metaphor- i.e. a figure of speech constructed by taking some other figure of speech as representing actual reality- though the result is not physically compossible or logically coherent in any way.

What about a Wittgenstein type 'language game'? Can it tell us anything about a meta-metaphor? Nope- unless the thing is 'dead' and is just an idiomatic way of referring to some univocal truth everybody already grasps. However, in that case, there is a Muth rational 'reflective equilibrium', or a canonical Schelling focal point, which lazy meta-metaphors are gesturing at.

This is not to say that philosophy's 'distinctions without a difference' are univocal. As Collingwood pointed out, some future 'fact of the world' may cause a branching event such that there is an independent discourse where the distinction points to an actual difference.

There are co-ordination games for 'pooling equilibria'- such that no branching of discourse occurs because there is no 'income effect', i.e. no agent gets a big enough pay-off by branching discourse- and these may or may not feature a Wittgenstienian 'language game' at some point in their trajectory. For extensional 'e-language' there is no big problem.

 However, where 'income effects' are substantial, intentionality and strategic behavior will feature 'costly signals', not 'cheap talk', and thus give rise to 'separating equilibria' and dis-coordination games. E-language can be studied as a statistical ensemble because it refers to the physical. I-language can't because it is meta-metaphorical and ontological dysphoric in an incompossible manner.

This is something we all already know. In a Law Court, one attorney may say to the Judge- 'the facts of the case are such that the rule in such and such case applies. Kindly pass judgment accordingly'.
The other lawyer may say, 'No! The facts here are quite different! It is the rule in a different case which applies!'

After the judgment is given, one side may appeal to a higher Court on a point of law. But how would that appeal be phrased? Do lawyers say 'the Judge said he was following the Rule in such and such  case. He was lying. What he should have said was 'I think I am following such and such Rule'. He couldn't possibly have known whether or not he was following that Rule or any other. This impugns his Ruling which should be struck down.'?

Obviously, such arguments are not made because they impugn the very possibility of Judgment. What actually happens is that an appeal is made on the basis that the Judge chose the wrong Rule or else, in certain jurisdictions, because new facts have come to light. It is not always easy to untangle questions of law from questions of fact but there is a protocol bound extensional language in which 'buck stopping' occurs- i.e. the doubt is resolved, at least for the time being.

What does this line of Wittgenstein's mean?

“there is a way of grasping a rule which is not an interpretation, but which is exhibited in what we call ‘obeying the rule’ and ‘going against it’ in actual cases.”

'Grasping a rule' is a metaphor. We can't actually hold a Rule in our hand the way we can hold a tool or weapon. Metaphors aren't facts. They can give rise to various interpretations or none at all. The same is true of 'obeying the rule' or 'going against it'.

Something different happens when you construct a meta-metaphor- like 'grasping x such that it is obeyed but not interpreted'. Here, something figurative- viz. 'grasping'- is treated as though it is real and concrete. Furthermore, it obtains in at least two different states- viz. that of being interpreted and obeyed and not being interpreted but nevertheless obeyed. But 'grasping' does not exist. It is an allusion to something else most of us don't have a name for. In specific, protocol bound e-languages, a term like 'grasping' could be 'buck stopped' such that we can say 'x grasped y and interpreted y and obeyed y'- and this would materially affect a judgment such that some loss or gain is sustained because 'interpretation' supervened on obedience.

Let us suppose you are a security guard employed by McDonalds. You see me approach the doorway. You block my entrance in obedience to the rule 'do not permit the ingress of prostitutes seeking to ply a nefarious trade'. I lodge a complaint of racial discrimination and seek exemplary damages. If, on the witness stand, you say- 'I interpreted the rule to mean 'keep out elderly Tambram cross-dressing prostitutes like Sanjay Subhramaniyam & Ramacandra Guha', then- clearly- an offense has occurred and I get my damages.

 On the other hand, if you had no interpretation at all in your head of the aforementioned rule and barred my entrance only because you were sure I actually was Sanjay Subhramaniyam or Ramachandra Guha, or some insalubrious conjunction of both, seeking to ply a nefarious trade on McD premises, then the outcome would be different.

The following quotations are from Wikipedia. My comments are in bold-

Suppose that you have never added numbers greater than 50 before. As a matter of fact, we have all at some time or another 'never added numbers greater than 50'.  Further, suppose that you are asked to perform the computation '68 + 57'. Our natural inclination is that you will apply the addition function as you have before, and calculate that the correct answer is '125'. Nonsense! I certainly would not have got the answer right the first time. Very few children would. I still make mistakes adding up quite small numbers. Take a bunch of mathematical economists trying to split a restaurant bill. Each is likely to make at least one mistake in adding up the cost of his own menu choices. But, these mistakes are seldom consistent. 

But now imagine that a bizarre skeptic comes along and argues:

1. That there is no fact about your past usage of the addition function that determines '125' as the right answer.

Quite true. However, there is some protocol I am obliged to accept which confirms or denies that a particular addition is correct.

1. That nothing justifies you in giving this answer rather than another.

It is the correct observance of a protocol which 'justifies' me in a court of law or before the bar of a professional association. Thus, if I am casting up accounts using the machine sanctioned for the purpose and, because of some mechanical glitch, the wrong answer is arrived at, I am still 'justified'.

After all, the skeptic reasons, by hypothesis you have never added numbers greater than 50 before. This is irrelevant. I may have incorrectly added such numbers in the past and been sacked as a result. If I carry on doing so in a professional context, I am likely to face serious censure.  It is perfectly consistent with your previous use of 'plus' that you actually meant it to mean the 'quus' function, defined as:

What you meant something to mean is known to you. In a court of law, your testimony can establish this as a fact. Of course, if you give an inconsistent or self-serving narrative regarding how you knew you meant something to mean something, you may be disbelieved and censured.

The skeptic argues that there is no fact about you that determines that you ought to answer '125' rather than '5'. Your own knowledge of your reasoning is such a fact. Your past usage of the addition function is susceptible to an infinite number of different quus-like interpretations. Not by myself- the only person in a position to judge. Other people may interpret my actions in a bizarre manner. However this only reveals a fact about their mental ill health or inveterate stupidity or pretence of doing philosophy. It appears that every new application of 'plus', rather than being governed by a strict, unambiguous rule, is actually a leap in the dark. This 'appearance' only arises if a person is 'interpreting' other people's actions in the manner of a lunatic or a psilosopher.
The obvious objection to this procedure is that the addition function is not defined by a number of examples, but by a general rule or algorithm. But then the algorithm itself will contain terms that are susceptible to different and incompatible interpretations, and the skeptical problem simply resurfaces at a higher level. Algorithms either have a protocol bound interpretation or they are not algorithms at all. In short, rules for interpreting rules provide no help, because they themselves can be interpreted in different ways. Protocols are a specific type of rule of an inter-subjective, 'social', character. They have some social process of binding adjudication. Or, as Wittgenstein himself puts it, "any interpretation still hangs in the air along with what it interprets, and cannot give it any support. Interpretations by themselves do not determine meaning" (PI 198a). Where this occurs, the interpretation probably has no social utility and cashes out as nonsense.
Similar skeptical reasoning can be applied to any word of any human language. The power of Kripke's example is that in mathematics the rules for the use of expressions appear to be defined clearly for an infinite number of cases. Only an infinite number of cases all belonging to the same class. But this is true of any rule- e.g. drive on the left is defined for an infinite number of cases. It applies me at every of an infinite number of instants of time.  

 Kripke doesn't question the validity in mathematics of the '+' function, but rather the meta-linguistic usage of 'plus': what fact can we point to that shows that 'plus' refers to the mathematical function '+'. There is no 'meta-linguistic' usage of 'plus'. There is are 'meta-metaphoric' usages of 'plus'- I am non-plussed that I still take a plus size despite going on a juice cleanse. But this is not 'meta-linguistic' at all.

 Kripke, following David Hume, distinguishes between two types of solution to skeptical paradoxes. Straight solutions dissolve paradoxes by rejecting one (or more) of the premises that lead to them. Skeptical solutions accept the truth of the paradox, but argue that it does not undermine our ordinary beliefs and practices in the way it seems to. Because Kripke thinks that Wittgenstein endorses the skeptical paradox, he is committed to the view that Wittgenstein offers a skeptical, and not a straight, solution.^[2]The rule-following paradox threatens our ordinary beliefs and practices concerning meaning because it implies that there is no such thing as meaning something by an expression or sentence. John McDowell explains this as follows. We are inclined to think of meaning in contractual terms: that is, that meanings commit or oblige us to use words in a certain way. When you grasp the meaning of the word "dog", for example, you know that you ought to use that word to refer to dogs, and not cats. Now, if there cannot be rules governing the uses of words, as the rule-following paradox apparently shows, this intuitive notion of meaning is utterly undermined.

Why? If there is some social utility in 'governing the use of a particular word'- e.g. 'plus' for any discipline or profession where it is important that addition is a protocol bound operation- then there will be some more or less formal or social method of adjudication which certifies or 'buck stops' acceptations of crucial words.

Intuitive notions of meaning don't have to be stupid notions of meaning. 

Kripke holds that other commentators on Philosophical Investigations have believed that the private language argument is presented in sections occurring after §243.^[3] Kripke reacts against this view, noting that the conclusion to the argument is explicitly stated by §202, which reads “Hence it is not possible to obey a rule ‘privately’: otherwise thinking one was obeying a rule would be the same as obeying it.”

Actually, 'thinking one was following a rule' would be evidence one was following the rule if one were capable of following it. This would not be wholly 'private' provided one belonged to a species which evolved under conditions of scarcity and Knightian uncertainty. Hunger and Thirst and acute Pain focuses the mind. It informs you that you have been following the wrong rules or not following the right rules. 

Further, in this introductory section, Kripke identifies Wittgenstein’s interests in the philosophy of mind as being related to his interests in the foundations of mathematics, in that both subjects require considerations concerning rules and rule-following.^[4]

This is one view- a wrong one- of 'the foundations of mathematics'.  The truth is maths has social utility. We are perfectly happy to use a heuristic or a lemma whose axiomatic'foundations' we don't understand if this means we can make better predictions or get better technology. It may be that, in the future the 'Reverse Mathematics' project will have salience and arguments like the one given above will seem absurd and unscientific.

Kripke's skeptical solution is this: A language-user's following a rule correctly is not justified by any fact that obtains about the relationship between his candidate application of a rule in a particular case, and the putative rule itself (as for Hume the causal link between two events a and b is not determined by any particular fact obtaining between them taken in isolation), but rather the assertion that the rule that is being followed is justified by the fact that the behaviors surrounding the candidate instance of rule-following (by the candidate rule-follower) meet the expectations of other language users.

What is important here is whether 'other language users' are bound to observe certain protocols adjudicated in a 'buck stopping' manner. However, this protocol bound adjudication would be defeasible by virtue of some new fact coming to light or some infirmity being revealed in the ratios used.

That the solution is not based on a fact about a particular instance of putative rule-following—as it would be if it were based on some mental state of meaning, interpretation, or intention—shows that this solution is skeptical in the sense Kripke specifies.

The 'expectations of other language users' cashes out as 'my expectation of the expectation of other language users'. But why should my expectations of other people's expectations be less susceptible to a sceptical challenge than 'my expectations of my own expectations as a language user'? As a matter of fact, in Economics, the notion of Muth Rationality solves the problem caused by 'expectations of others expectations'. The Rational Expectations solution is simply to expect the prediction of the correct Economic theory. 

The reason we use meta-metaphors is because we have an interest in 'hedging' on ontologically dysphoric worlds and incompossible 'dis-coordination' games. This shared inter-subjective world is one of humiliation and ultimate futility. Talking worthless shite is our only taste of personal immortality.