Yet I don't have to give up on you; my fallback is not a judgment of exclusion, a turning away. Our impotence (that of our ordinary rules) turns us toward each other--rather than necessitating we solve this (always eminent) failure with authority, agreement, knowledge, better rules, more logic, a foundational bedrock--we resist philosophy's anxiety to be better than, a solution for, the ordinary by removing our (uncertain, frightening) part and responsibility. — Antony Nickles

Weren’t you instructing me (or “someone”)? How does your not giving up on me in your instruction (about what constitutes obeying a rule) suddenly become you and I both resisting philosophy’s anxiety? How does that help me?

Isn’t it just the case that we obey the rule because that’s the practice/convention and that’s what people typically do here? Or else we don’t follow the rule for whatever reason, yet the rule still exists because that’s how most people do this particular thing, as a rule. Or we might even try to change the rule and get everyone to follow a different practice/rule.

Isn’t it just the case that we obey the rule because that’s the practice/convention and that’s what people typically do here? — Luke

We can point to rules, we can give examples, we can threaten consequences; at a certain point sometimes they run out, you don't continue as expected--it is meant to be a situation which summons skepticism.

Or else we don’t follow the rule for whatever reason, yet the rule still exists because that’s how most people do this particular thing, as a rule. — Luke

Kripke's take on the passage is that this leaves us with only the options of following the rule, change the rule, or be excluded--that it is conformity to a rule. Where Cavell takes Witt as showing that people's judgments are attuned, they share the same interests, etc.--not as an agreement, but because our lives are similar. Because this happens mostly implicitly, he is trying to make explicit a case in which it doesn't happen. And we can do lots of things, but we do not just point to a rule. So the exhaustion of justifications for how you should obey a rule, make a wish, apologize, mean what you say, etc. can be that you refuse to follow the rules, but it can also be that we have not yet imagined all the implications, shown you how our interests are aligned, etc.--that there is not only force and defiance, which says something about knowledge and reason and pre-determined deontological morals (rules).

What do I mean when I say that the teacher judges that, for certain cases, the pupil must give the 'right' answer? I mean that the child has given the same answer that he himself would give... that he judges that the child is applying the procedure he himself is inclined to apply. — Kripke, p 90 (emphasis added).

Weren’t you instructing me (or “someone”)? How does your not giving up on me in your instruction (about what constitutes obeying a rule) suddenly become you and I both resisting philosophy’s anxiety? How does that help me? — Luke

The fear is of the inability to justify obeying a rule or justify how we obey rules. Both Cavell and Kripke leave that possibility open, but Kripke's picture pits "what we typically do" against your instincts, in judgment of your authority, in a sense, before our discussion even gets started. This is to cave into the anxiety of leaving it up to us, to the vision that there is more to us than rules and conventions, that such discussions can be reasonable, between conformity and exclusion.

The structure of the rules of math makes them determined in advance, encompassing all applications, eternal — Antony Nickles

Depends on what you refer to as "rules of math". For instance, the Law of the Excluded Middle is useful in traditional or standard math, but not allowed in constructive math. Turmoil in the jungles of the mind.

We can point to rules, we can give examples, we can threaten consequences; at a certain point sometimes they run out, you don't continue as expected--it is meant to be a situation which summons skepticism. — Antony Nickles

Is it meant to "summon skepticism", though? Maybe from Kripke's overly philosophical perspective, but I doubt it would summon skepticism from the average person. This is a very alien way of looking at obeying a rule.

Kripke's take on the passage is that this leaves us with only the options of following the rule, change the rule, or be excluded--that it is conformity to a rule. Where Cavell takes Witt as showing that... — Antony Nickles

I'm not familiar with Cavell's work, so I'll have to take your word for it. Your interpretations of Wittgenstein sometimes seem foreign to me, which may be due to your reading being coloured by Cavell. Anyway, I don't see that Cavell adds any options to the three that you attribute here to Kripke.

So the exhaustion of justifications for how you should obey a rule, make a wish, apologize, mean what you say, etc. can be that you refuse to follow the rules, but it can also be that we have not yet imagined all the implications, shown you how our interests are aligned, etc.--that there is not only force and defiance — Antony Nickles

This seems to fit into the three options cited above.

Weren’t you instructing me (or “someone”)? How does your not giving up on me in your instruction (about what constitutes obeying a rule) suddenly become you and I both resisting philosophy’s anxiety? How does that help me?
— Luke

The fear is of the inability to justify obeying a rule or justify how we obey rules. — Antony Nickles

I get that, but you (or Cavell) were instructing someone about what constitutes obeying a rule.

Both Cavell and Kripke leave that possibility open, but Kripke's picture pits "what we typically do" against your instincts, in judgment of your authority, in a sense, before our discussion even gets started. This is to cave into the anxiety of leaving it up to us, to the vision that there is more to us than rules and conventions, that such discussions can be reasonable, between conformity and exclusion. — Antony Nickles

This does not address the main point of my question, which was the main reason for my posting. You say that the teacher is unable to provide sufficient justification to the student about what constitutes obeying a rule. Then you say - crucially - that the teacher does not have to give up on the student because both teacher and student can "resist philosophy's anxiety". I guess I'm asking is: what is it that allows the student to "resist philosophy's anxiety"?

The problem might be better viewed in this way:

But teaching (indoctrinating into society) sometimes runs out of ways to convey, in this example: what constitutes obeying a rule (justifies saying how/that we obey/have obeyed). — Antony Nickles

Teaching/indoctrination is training someone how to obey a rule or how to "go on" (or behave) in a particular way(s). You cannot first teach/train someone what it means to obey a rule in order for them to then go on and obey a rule; otherwise, you would not be able to teach them what it means to obey a rule in the first place.

Depends on what you refer to as "rules of math". For instance, the Law of the Excluded Middle is useful in traditional or standard math, but not allowed in constructive math. Turmoil in the jungles of the mind. — jgill

I believe that is a rule of logic, but, yes, I'm thinking more of addition.

I believe that is a rule of logic, but, yes, I'm thinking more of addition. — Antony Nickles

Yes, of course. But even the notion of addition was expanded in 1801 when Gauss introduced the modern concept of modular arithmetic. As formalized, this was a new idea that could be considered a rule in certain circumstances I suppose. Perhaps only a "rule of thumb." Sorry to interrupt your conversation.

We can point to rules, we can give examples, we can threaten consequences; at a certain point sometimes they run out, you don't continue as expected--it is meant to be a situation which summons skepticism.
— Antony Nickles

Is it meant to "summon skepticism", though? Maybe from Kripke's overly philosophical perspective, but I doubt it would summon skepticism from the average person. This is a very alien way of looking at obeying a rule. — Luke

Summon the specter of skepticism for the philosopher (reader), yes; the fear that leads to our need to have a foundational bedrock to justify our acts. An average person might feel an inability to communicate, that words/fact/truth lack power, discouraged at the prospect of (or empowered by) not having anything else to say... but, yes, Witt's example is meant to show us something about philosophy; its powerlessness, and hope.

Kripke's take on the passage is that this leaves us with only the options of following the rule, change the rule, or be excluded--that it is conformity to a rule.
— Antony Nickles

So the exhaustion of justifications for how you should obey a rule, make a wish, apologize, mean what you say, etc. can be that you refuse to follow the rules, but it can also be that we have not yet imagined all the implications, shown you how our interests are aligned, etc.--that there is not only force and defiance
— Antony Nickles

This seems to fit into the three options cited above. — Luke

Maybe not my best work trying to show a distinction (part of the problem is Witt is discussing justification for how we follow a rule; and Kripke is reading that as we act from inclination ("inspiration" #232) and then are judged as right or wrong based on if we follow the rule, conform to the rule (before there is any justifying why/how you did or didn't follow the rule)). Cavell takes Witt as leaving open the judgment/exclusion to begin a conversation about what it means to have followed a rule (what counts, what matters, etc.). One view ends the relationship, the other begins a moral discussion.

The fear is of the inability to justify obeying a rule or justify how we obey rules.
— Antony Nickles

I get that, but you (or Cavell) were instructing someone about what constitutes obeying a rule. — Luke

What constitutes justifying that I obeyed a rule. And Kripke wants to resolve the worry that we may not be able to justify how we obey a rule or what constitutes obeying a rule, just between our impulse to act and your judgment and exclusion; Cavell takes Witt as leaving that possibility of failure open, but also continuing a conversation beyond our pre-determined judgment. An ongoing conversation about, say, what constitutes an example (#223)--rationalizing our relationship instead of it relying on, say, violence (understanding rather than just change).

You say that the teacher is unable to provide sufficient justification to the student about what constitutes obeying a rule. Then you say - crucially - that the teacher does not have to give up on the student because both teacher and student can "resist philosophy's anxiety". I guess I'm asking: what is it that allows the student to "resist philosophy's anxiety"? — Luke

To make themselves intelligible. They might claim they did obey the rule; or explain their aversion to conformity--examine their "blind" obedience (#219); as normally we do not "follow" rules (#222). Not to take the position that their actions are unable to be communicated--to feel there is something private, unknowable (not just personal). But really this is an examination of the teacher, and the limitation/impotence of our knowledge (what comes after it).

But teaching (indoctrinating into society) sometimes runs out of ways to convey, in this example: what constitutes obeying a rule (justifies saying how/that we obey/have obeyed).
— Antony Nickles

Teaching/indoctrination is training someone how to obey the rules or how to "go on" (or behave) in a particular way(s). You cannot first teach/train someone what it means to obey a rule in order for them to then go on and obey a rule; otherwise, you would not be able to teach them what it means to obey a rule in the first place. — Luke

I agree with framing it as training, but I am trying to show two "particular ways" we can be seen as going on--that maybe it isn't (as in teaching math), that we behave (obey) or not, but that we are learning the skill of how to continue, to be able to justify our actions at all--to move forward rather than not be able to "conflict" or "accord" at all (#201) @Banno.

You cannot first teach/train someone what it means to obey a rule in order for them to then go on and obey a rule; otherwise, you would not be able to teach them what it means to obey a rule in the first place. — Luke

Maybe it helps that Witt notices that we learn our whole lives in learning something new (or something like that). That we already: follow, explain ourselves, disobey, judge, defend, etc. So we are not teaching "what it means", as if providing the correct directions, delineating ahead of time what it is to "obey", all other actions being judged as incorrect. I may ask why you didn't obey, say, the golden rule, and you may claim that you did, and then go on to try to justify how what you did was still an instance of obeying the rule. If Kripke's reading is correct, the discussion of what is right happens before my personal action, upon which I am judged. If we take Witt to be reserving judgment, then we begin a dialogue of what it is to, say, treat the other as having a soul (p, 152; 3rd 2001), or convince ourselves we can not know them (p. 192).

Introducing Kripke complicates the issue, in that as one reads your posts it is unclear if you are referring to the orthodox reading of Wittgenstein, or Kripke's reading.

Seems as you might set out in some detail what you think is Wittgenstein's orthodoxy, Kripke's variant, and Cavell's reply.

Especially the latter, since there are so few tertiary references to it.

If I were to jump the gun, so to speak, and offer an opinion on what has been said so far, it would be that Cavell's proposing obedience as a replacement for following a rule looks misguided. Hnece certain phrases you have used look ill-formed:

teaching (indoctrinating into society) — Antony Nickles

But humanity aspires to mathematical rules rather than our ordinary "rules" — Antony Nickles

I agree with framing it as training, — Antony Nickles

When, for example, @Metaphysician Undercover repeatedly misunderstands certain notions in mathematics, there is a point at which one concludes that he is simply not participating in the game. One might then either turn away or attempt to follow the path of the eccentric. The question becomes one of what is to be gained in going one way or the other.

But even the notion of addition was expanded in 1801 when Gauss introduced the modern concept of modular arithmetic. — jgill

This actually helps to clarify, so thank you. It is not that math cannot change, or be expanded, but there is a structure/conditions to math (as there is a method for what we consider science, why it produces a certain kind of "fact"). We count (pun intended) something as math because it is predictable, universal, eternal, etc., which is unlike our ordinary criteria for how/when something counts as a justification for obeying a rule.

Seems you might set out in some detail what you think is Wittgenstein's orthodoxy, Kripke's variant, and Cavell's reply. — Banno

This is well-taken; the OP does jump past some groundwork. Broadly, I would say there is the traditional skeptic, who sees that our actions are groundless, and thus "aspires to mathematical rules rather than" what Witt would call a concept's grammar; what Cavell refers to as our "ordinary" criteria, framed as the opposite of the skeptic's imposed criteria of ("mathematical"-like) certainty (also referred to as "metaphysical").

Then there is the superficial (the "orthodox" perhaps) reading of Witt as solving (or dissolving) the problem the skeptic is reacting to with our forms of life, which they take as grounding meaning, actions, etc. in the same framework, or by calling skepticism nonsense, or a trick of language.

Cavell and Kripke share the desire not to dismiss or solve the problem the skeptic sees; to acknowledge that there does come a point at which our justifications come to an end. (Here I may get stuck in the same problems I appear to have in the initial reading.) Kripke pictures that we have already (ahead of time) agreed on what the rules are (or practices/criteria/justifications); then I act instinctively yet correctly (without reference to the rules--"as I am inclined to", in his reading), and then I am judged on whether I followed the (circumscribing) rule or not--in or off the island.

Cavell takes the passage not to be the moment of judgment, but the (at least possible) beginning (at the end) of a discussion of our continuing together in the same moral realm, my understanding of your action without society's pre-arranged consent (our immoral act as Nietszche might say), our furthering justification(s) into un-ventured contexts, etc. He sees this as possible because the type of "agreement" we have is not in rules, as to a contract (though we can), but in the way our lives have (so far) been aligned, the possibilities that affords for development.

This would be why Witt words it as training, as we are not teaching (telling) rules, but the practice or skill of, here, how to obey a rule (which Austin would say we could further understand in examining how to disobey, how to be seen as obeying, how it differs from being forced, ordered, etc.--Kripke has this all worked out in advance, Cavell is continuing after Austin). Cavell might add indoctrinating (accepted without justification) because we have yet to imagine all the justifications we might have, and thus where we might go (together, alone) once we feel we are at the end of them.

When, for example, Metaphysician Undercover repeatedly misunderstands certain notions in mathematics, there is a point at which one concludes that he is simply not participating in the game. One might then either turn away or attempt to follow the path of the eccentric. The question becomes one of what is to be gained in going one way or the other. — Banno

And this is perhaps an example of such a (moral) moment. There are many examples in Philosophical Investigations that verge on insane, alien, strange reactions or responses. If we "conclude that he is simply not participating in the game", we have reached the bedrock--if we follow Kripke, this is the point of judgment, conclusion. But, conclude how? Are we really aware of what matters to considering it part of/not part of, the game? Even granted we have rules for inclusion, do we have answers about their desire to be excluded from those rules? What does it mean for who I am if I measure the other by my gain or loss? These questions can continue or stop. We might then "turn away", but, if we don't, do we only follow another path, having already judged an "eccentric" from without? This is at least possibilities (grounds?) for a discussion, where the skeptic and their nemesis fight over grounds (before) to avoid having the discussion at all (in the future).

Broadly, I would say there is the traditional skeptic, who sees that our actions are groundless, and thus "aspires to mathematical rules rather than" what Witt would call a concept's grammar; what Cavell refers to as our "ordinary" criteria, framed as the opposite of the skeptic's imposed criteria of ("mathematical"-like) certainty (also referred to as "metaphysical"). — Antony Nickles

So, small steps.

You or Cavell - not sure which - are differentiating between mathematical rules and grammatical rules. How is this distinction to be made?

I gather we are talking in terms of the broad notion of "grammar" Wittgenstein used, roughly the way appropriate to a given language game... but isn't mathematics a language game? If so, there is no prima facie distinction to be made here.

When, for example, Metaphysician Undercover repeatedly misunderstands certain notions in mathematics, there is a point at which one concludes that he is simply not participating in the game. One might then either turn away or attempt to follow the path of the eccentric. The question becomes one of what is to be gained in going one way or the other. — Banno

When. after repeated attempts, the rules are apprehended as impossible to understand, due to the appearance of inconsistency and incoherency, the best course for this person is not to participate in that game.

Are we really aware of what matters to considering it part of/not part of, the game? — Antony Nickles

I've bolded the bit the is bothersome. A critical technique I've found most helpful is to remove a word and see what remains:
Are we aware of what matters to considering it part of/not part of, the game?
Well, yes, we are. There is a difference between plus and quus.

Cavell [is] differentiating between mathematical rules and grammatical rules. How is this distinction to be made?

I gather we are talking in terms of the broad notion of "grammar" Wittgenstein used, roughly the way appropriate to a given language game... but isn't mathematics a language game? — Banno

This is a good thing to have clarified. You are already aware that Austin provided a lot of examples to show that there are more types of statements than just ones that are true or false (also, this harkens to Kripke's black-or-white treatment of the Other). And that Wittgenstein spent a lot of time showing us that there is not one theory of meaning; that there are many other "games", as you say (he also calls them "concepts"), within which to mean something, then just reference. They showed that we can not think in just one way. They also both showed how each concept--like, pointing, meaning, intending, playing chess, apologizing, marrying, etc--was differentiated from others, what counted for identity, felicity, how we judge, why a distinction here is important, etc. with each concept, and even differences (sense, uses) within one concept in different contexts. Cavell calls these our criteria, Witt calls them the grammar of a thing.

I gather we are talking in terms of the broad notion of "grammar" Wittgenstein used, roughly the way appropriate to a given language game... but isn't mathematics a language game? If so, there is no prima facie distinction to be made here. — Banno

What Witt shows is that there is a desire to impose grammar (criteria) on the concepts of which we are skeptical, the criteria/grammar which here Cavell refers to as "mathematical". The term is not meant to imply math is categorically different than a concept (not a "language game"); just that "the way appropriate to" math, its grammar/criteria--certainty, repeatability, universality, predictability, etc.--are similar to the skeptic's requirements for morality, rationality, aesthetics, etc. The "mathematical" is also analogous to the criteria Plato's metaphysical forms have, or Kant's conditions for rationality, or positivism's logic. So in contrast to that are the "ordinary" different, unpredictable, specific grammar of each concept. Now there may not be certainty, or universality, but Cavell's point is that we are left with a rational path when certainty runs out, when we are unsure if our concepts can be, if not universal, at least aligned. Though our actions can not be made predictable, they can be understood as reasonable, taken as good enough (fair, just).

This is a good thing to have clarified. — Antony Nickles

Thanks for your patience. I remain at a loss to understand the difference between - taking from the thread title - a rule's end for mathematics and an ordinary rule's end; that is, while I understand the difference between mathematics and ordinary language, there is something here that I do not understand. You or Cavell seem to want there to be a difference between the spade being turned at the end of an analysis of mathematics, and a spade being turned in ordinary language - or something along those lines. Or is that such a distinction might be made the topic here?

I would have thought hat the spade was turned, in either case, when there was nothing more to be said, and only the "exhibition of what we call obeying the rule" as in §210; the point at which every interpretation is no more than the "substitution of one expression of the rule for another".

This, by way of a sideline, is tantamount to the rejection of coding as meaning (was that @god must be atheist?); coding is just an different expression of the rule, but what we want is to follow the rule.

So, back to my puzzlement: maths is different to ordinary language, sure. but following a rule is following a rule, be it a mathematical rule or a rule of ordinary language. The thread title and the OP seem to think this not to be so, yet I don't see how or why.

We are "left with a rational path when certainty runs out" in both cases.

Summon the specter of skepticism for the philosopher (reader), yes; the fear that leads to our need to have a foundational bedrock to justify our acts. An average person might feel an inability to communicate, that words/fact/truth lack power, discouraged at the prospect of (or empowered by) not having anything else to say... — Antony Nickles

In my experience, the average person does not typically have "the fear that leads to our need to have a foundational bedrock to justify our acts." That is a "fear" (if you can call it that) which is peculiar only to some philosophers.

Witt's example is meant to show us something about philosophy; its powerlessness, and hope. — Antony Nickles

And its recurring, thematic, archetypal problems, which he is attempting to resolve.

Maybe not my best work trying to show a distinction (part of the problem is Witt is discussing justification for how we follow a rule; and Kripke is reading that as we act from inclination ("inspiration" #232) and then are judged as right or wrong based on if we follow the rule, conform to the rule (before there is any justifying why/how you did or didn't follow the rule)). Cavell takes Witt as leaving open the judgment/exclusion to begin a conversation about what it means to have followed a rule (what counts, what matters, etc.). One view ends the relationship, the other begins a moral discussion. — Antony Nickles

I'm not sure whether you would agree that Kripke's is a terrible misreading of Wittgenstein, albeit one which might help to raise some interesting issues. If so, then the question I have is whether you consider Cavell to be in disagreement with Wittgenstein, and whether Cavell is saying anything different to Wittgenstein, or if he says mostly the same thing by interpreting him better than Kripke. That is to say, I agree with Banno's assessment regarding the opacity of your distinction between them here.

I disagree that Wittgenstein is inviting a moral discussion at all, nor any further justification in general terms, although he might consider a place for philosophy or justification to intervene in relation to some specific issue. Generally speaking, the matter is fairly black and white: people do manage to follow rules and are able to be judged as following them or not. As W says: "there is a way of grasping a rule which is not an interpretation, but which, from case to case of application, is exhibited in what we call “following the rule” and “going against it” (201). See also 240-241. I view 232 as a continuation of the thread that brings into relief the impossibility of privately determining a rule (see 202).

What constitutes justifying that I obeyed a rule. — Antony Nickles

Pointing to the existing practice that constitutes the rule. "You're not allowed to move your knight like that!" (in chess) because that's not the practice or the way it's done.

“So is whatever I do compatible with the rule?” — Let me ask this: what has the expression of a rule — say a signpost — got to do with my actions? What sort of connection obtains here? — Well, this one, for example: I have been trained to react in a particular way to this sign, and now I do so react to it.
But with this you have pointed out only a causal connection; only explained how it has come about that we now go by the signpost; not what this following-the-sign really consists in. Not so; I have further indicated that a person goes by a signpost only in so far as there is an established usage, a custom. (198)

To follow a rule, to make a report, to give an order, to play a game of chess, are customs (usages, institutions). To understand a sentence means to understand a language. To understand a language means to have mastered a technique. (199) — LW

And Kripke wants to resolve the worry that we may not be able to justify how we obey a rule or what constitutes obeying a rule — Antony Nickles

It's an odd reading to think that Kripke is attempting to resolve this worry, when, by design or by folly, he exacerbates it.

Cavell takes Witt as leaving that possibility of failure open, but also continuing a conversation beyond our pre-determined judgment. An ongoing conversation about, say, what constitutes an example (#223)--rationalizing our relationship instead of it relying on, say, violence (understanding rather than just change). — Antony Nickles

I'm not sure what you mean here, but I don't see 223 as questioning what constitutes an example.

To make themselves intelligible. They might claim they did obey the rule; or explain their aversion to conformity--examine their "blind" obedience (#219); as normally we do not "follow" rules (#222). — Antony Nickles

This is not my reading of 219 or 222.

I agree with framing it as training, but I am trying to show two "particular ways" we can be seen as going on--that maybe it isn't (as in teaching math), that we behave (obey) or not, but that we are learning the skill of how to continue, to be able to justify our actions at all--to move forward rather than not be able to "conflict" or "accord" at all (#201) — Antony Nickles

The issue that Wittgenstein identifies (or forecasts) is that philosophers such as Kripke are sceptical or dissatisfied with any and all justifications of behaving in accordance with, or obeying, a rule. So it is not the person learning a rule that needs to justify their actions (as being in accord with the rule); rather, the philosopher is confused into thinking that no justification is possible or sufficient. This is who Wittgenstein is writing for. A teacher can determine whether or not the student is acting in accordance with the rule. The rule is not (privately) determined by the student. There is no middle ground in obeying the rule for how the knight moves in chess, only conflict or accord.

206. Following a rule is analogous to obeying an order. One is trained to do so, and one reacts to an order in a particular way. — LW

I may ask why you didn't obey, say, the golden rule, and you may claim that you did, and then go on to try to justify how what you did was still an instance of obeying the rule. — Antony Nickles

I don't think the principle or maxim of the Golden Rule is the same sort of rule Wittgenstein is talking about (it is not mentioned in PI). For the sake of clarity, let's use the example of a very straightforward rule instead, such as a rule of chess or a signpost.

If Kripke's reading is correct, the discussion of what is right happens before my personal action, upon which I am judged. If we take Witt to be reserving judgment, then we begin a dialogue of what it is to, say, treat the other as having a soul (p, 152; 3rd 2001), or convince ourselves we can not know them (p. 192). — Antony Nickles

I don't see Wittgenstein as talking about ethics or about "what is right" in general (in life) in PI. Or at least, not in relation to his discussion on rule following.

Are we really aware of what matters to considering it part of/not part of, the game?
— Antony Nickles

I've bolded the bit that is bothersome. — Banno

Yikes, caught me; red-handed. I'm burning all my Austin--shameful.

Are we aware of what matters to considering it part of/not part of, the game?
Well, yes, we are. — Banno

The word I was looking for (maybe) was: are we always aware? aware of every consideration? (not that we can't be, but that the questions sometimes come after the act; the questions can be without end).

There is a difference between plus and quus. — Banno

Oh, this looks like a rabbit-hole. I'm not entirely versed in this scenario, but Cavell would acknowledge with Kripke that there is no fact to you/me obeying a rule, or meaning a sentence; nothing in me or about our world. But Cavell takes Kripke to read #201 as a paradox that must be solved--that our relationship with rules must/can be fixed. Maybe too simply, Cavell argues that rules have grammar, and they are (and obeying them is) not more fundamental than the grammar for other actions, and that the "fact" is the requirement (creation) of the skeptic.

But we fear that I may become, or be seen as, the deviant--that I might mistake plus-ing for quus-ing. The skeptic sees this as eminent tragedy, and scrambles to ward it off. Cavell "wants to say" there is the fact of "me", here, ready to be responsible for my act, or not; to apologize, rescind it, defy your law (ironically, subversively), explain these differing circumstances; stand as an example, waiting...

I believe that is a rule of logic, but, yes, I'm thinking more of addition. — Antony Nickles

They are similar, in admitting of the same crucial change in perspective as urged by Goodman (the "see also" on the Kripkenstein page is no accident) in a rather different context, that of characterising musical and other notations:

What distinguishes a genuine notation is not how easily correct judgements can be made, but what their consequences are. [...] Marks [= tokens] correctly judged to be joint members of a character [= type] will always be true copies of one another. — Languages of Art, p134

'True' here means - in effect, in consequence - safely taken as license to make more copies, because the copying relation is maintained in such a way as not to impair the mutual exclusivity of types. No chain of copies will reach from one type (or 'equivalence class') into another. That would indeed be fatal to the system, as all the types would eventually merge, e.g. every tune would be identified as a true copy of every other. A similar (though different) demise is envisaged as the 'principle of explosion'. (Allegedly a false alarm, which is interesting of course.)

The point is that the extension or range of application of any word is a fiction, continually up for negotiation. What distinguishes the 'mathematical' from the 'ordinary' is the reasonable expectation that, however one's own utterances are interpreted (e.g. as plus or as quus), the consequent discourse will be well behaved in maintaining the distinction between distinct extensions, whatever they 'truly' are. This may or may not depend on those extensions being, like tunes, mutually exclusive.

I remain at a loss to understand the difference between - taking from the thread title - a rule's end for mathematics and an ordinary rule's end; that is, while I understand the difference between mathematics and ordinary language, there is something here that I do not understand. — Banno

Yeah that was maybe being more poetic than informative. I guess I should have said this is the imposition of the standards for math in place of (sublimizing) those of the rest of language. The desire for our actions to meet the criteria we have for math (or rules) when each action has its own grammar (including that of obeying rules). That math is circumscribed by rules, but that grammar is not.

You or Cavell seem to want there to be a difference between the spade being turned at the end of an analysis of mathematics, and a spade being turned in ordinary language or something along those lines. Or is that such a distinction might be made the topic here? — Banno

Perhaps; it is two reactions to the ("mathematical") desire in the face of a skepticism--for some rule or other foundation--that divides the readings to the Witt passage; that for Kripke the criteria is decided (learned or not) before I make my final/initial claim (without further justification) that is then correct, or not. For Cavell, Witt leaves our response open, that we do not point to rules (or not always)--creating a space between skepticism and foundationalism.

I would have thought that the spade was turned, in either case, when there was nothing more to be said, and only the "exhibition of what we call obeying the rule" as in §210; the point at which every interpretation is no more than the "substitution of one expression of the rule for another". — Banno

Just that Kripke takes it that an action would be held to judgment of whether the rule was followed, and Cavell reads it that, yes, I can not tell you anything more, that we cannot just explain something (a rule, even its grammar) and you will/must continue. But we can wait; for a response, an inquiry. That we continue to be (exhibit) an example. That to continue a concept into a new context will require more than rules (Cavell refers to this as "the human voice", echoing Niestzche); that in contrast, what it is to be mathematical does not require me (it could be anyone adding).

Witt's example is meant to show us something about philosophy; its powerlessness, and hope. — Antony Nickles

And its recurring, thematic, archetypal problems, which he is attempting to resolve. — Luke

Both Kripke and Cavell take Witt as pointedly not trying to resolve skepticism (the "orthodox" view I described earlier), but take it seriously, investigate it, see what it shows about us.

The issue that Wittgenstein identifies (or forecasts) is that philosophers such as Kripke are sceptical or dissatisfied with any and all justifications of behaving in accordance with, or obeying, a rule. — Luke

In the passage starting this OP, Witt acknowledges the possibility of the exhaustion of justifications.

There is no middle ground in obeying the rule for how the knight moves in chess, only conflict or accord. — Luke

And this would be Kripke's stance. But Cavell is attempting to draw out that there is grammar (not just judgment) in obeying a rule; that there are cases that exhibit what these criteria are (#201); that we can go over these examples and see if the context matches ours, whether it is an example, etc. And that grammar, even that of obeying a rule, is different than rules--even leaves us in a different place in the end.

For the sake of clarity, let's use the example of a very straightforward rule instead, such as a rule of chess or a signpost. — Luke

It gets even more straightforward, let's use the example of math. The idea is that things are not straightforward like rules (#426), that our criteria (our lives) are open-ended, unpredictable, etc.

I disagree that Wittgenstein is inviting a moral discussion at all, nor any further justification in general terms, although he might consider a place for philosophy or justification to intervene in relation to some specific issue. Generally speaking, the matter is fairly black and white: people do manage to follow rules and are able to be judged as following them or not. As W says: "there is a way of grasping a rule which is not an interpretation, but which, from case to case of application, is exhibited in what we call “following the rule” and “going against it” (201). See also 240-241. I view 232 as a continuation of the thread that brings into relief the impossibility of privately determining a rule (see 202). — Luke

The further point of the passage of the turned spade is that, though I can wield rules the way you point to (as Kripke grabs onto them as finalizing), we do not have to, there is nothing necessary in treating the other on black and white terms--unless you don't want to address the Other (open the moral realm), that you just want, as it were, to apply the rule. On p. 192, Witt calls this a "conviction". I would say #240 clarifies our need to be able to know how to fight well (keep open the possibility for reasonable moral debate), and that #241 does not solve those issues, by pointing to our way of life in the way Kripe takes it as a contractual (enforceable) agreement.

Pointing to the existing practice that constitutes the rule. "You're not allowed to move your knight like that!" (in chess) because that's not the practice or the way it's done. — Luke

This is to justify the judgment of not obeying a rule by pointing to our practice. We (teacher-student) are at the moment where I claim there is an attempt to convey what it is to obey a rule, how it is that we obey a rule. That this has an ordinary (non-"mathematical") grammar that is not just pointing to a rule (Kripke as it were, generalizes this practice/picture).

It's an odd reading to think that Kripke is attempting to resolve this worry, when, by design or by folly, he exacerbates it. — Luke

Cavell is trying to examine how and why Kripke ends up there.

Cavell takes Witt as leaving that possibility of failure open, but also continuing a conversation beyond our pre-determined judgment. An ongoing conversation about, say, what constitutes an example (#223)--rationalizing our relationship instead of it relying on, say, violence (understanding rather than just change). — Antony Nickles

I'm not sure what you mean here [the discussion of what constitutes an example], but I don't see 223 as questioning what constitutes an example. — Luke

One might say to the person one was training: "Look, I always do the same thing: I . . . . . — Witt, PI #223

And the other might claim his is an example, but responsive to a new context. "This is justice, but here we must do harm in this case."

To make themselves intelligible. They might claim they did obey the rule; or explain their aversion to conformity--examine their "blind" obedience (#219); as normally we do not "follow" rules (#222). — Antony Nickles

This is not my reading of 219 or 222. — Luke

When I obey a rule, I do not choose.
I obey the rule blindly. — Wiit, PI # 219

This is in contrast to the "mythological" description (#221) of "all the steps already being taken". But it is not that we cannot choose to obey a rule (its all about rules), only that when (grammatically) I (choose to) obey a rule (am to be said (judged) to have obeyed), I do not (thereafter) make (further) choices. I do not then "follow" the rule, as in watch it go on ahead of me (#232). Kripke takes it that our justifications end (I act blindly) when I obey the rule, and then as if this is how we are said to act at all, with no space for discussing (justifying) that choice afterwards, for rescission if your suggestion to obey the rule was irresponsible, that I would no longer (morally) say I obeyed the rule, but that I obeyed your intimation (#222).

I don't see Wittgenstein as talking about ethics or about "what is right" in general (in life) in PI. Or at least, not in relation to his discussion on rule following. — Luke

It is peppered throughout, in his insistence not to treat our practices mathematically, singularly, but also (albeit cryptically), in Part II, with his discussion of attitudes, seeing aspects.

@Luke @Banno I hope adding some direct language of Cavell's, may provide more grist than my attempts to paraphrase.

The rule for addition extends to all its possible applications. (As does the rule for quaddition...otherwise it would not be known to us as a mathematical function.) But our ordinary concepts are not thus mathematical in their application: we do not intuitively, within the ordinary, know in advance... a right first instance... know whether to say an instance counts... no concept is "bound" by ordinary criteria....

When the child starts to walk, they walk, [ though ] tentatively, as I do; we agree in walking; but we have not achieved this agreement, come to agree... If chairs ceased to exist... then something would happen to our concept of a table. I do not insist that one agree that the concept would change, but the role of the concept of a table [ would be different ] because the role of tables in our lives would be different.

In reaching the gesture expressed as, "This is simply what I do"... I say I cannot then say I am right [ as Kripke's society does ]; and in going on to say that the repudiation of deviance is a stance, a voice taken in disapproval, betokening social repression; and in remarking further that the violence in claiming to be right where there is no right repudiates the ordinary (the ordinary criteria for the application of everyday [ nonmathematical ] concepts, e.g... of "this"--since it counts on criteria that are already rejected--of "I"--since it seeks to represent a community that does not exist — Stanley Cavell, Conditions Handsome and Unhandsome, p. 89, 94, 95

.

Very interesting!

So, we're, in our "ordinary" lives, stuck with rules that are neither justified to our satisfaction nor universal in scope. We then look at math and are bowled over as it were by the rules therein that are well-justified and universal to boot. Thus, we come to the realization that we're stuck with flawed rules (ordinary) while also being completely in the know about flawless rules (math) - disappointment is a given (we're missing out on something "better"), fear is unavoidable (our lives are structured around rules that have no underlying truth i.e. we're lost).

What if, in keeping with Wittgenstein's ludological analogy, rules are more about making the "game" more fun, more interesting and less about justification? In other words, rules don't need to be justified in that they have to make sense, instead they have to ensure the "game" is enjoyable, exciting, and pleasurable but also "painful" enough to, ironically, make the "playing" the "game" a serious affair.

Off-topic?!

So, we're, in our "ordinary" lives, stuck with rules that are neither justified to our satisfaction nor universal in scope. — TheMadFool

Maybe consider that those ordinary concepts are not composed of rules at all. It's possible that when we see non-ordinary concepts like mathematics as composed of rules, through a faulty extrapolation we wrongly conclude that ordinary concepts are also composed of rules.

What if, in keeping with Wittgenstein's ludological analogy, rules are more about making the "game" more fun, more interesting and less about justification? In other words, rules don't need to be justified in that they have to make sense, instead they have to ensure the "game" is enjoyable, exciting, and pleasurable but also "painful" enough to, ironically, make the "playing" the "game" a serious affair. — TheMadFool

Living is like that, enjoyable, exciting, pleasurable, and painful. Living is not a game though, nor is it composed of rules. And I don't think rules are necessarily about making life more fun, they are about obtaining ends, goals. Although this is one way of making life more fun..

Both Kripke and Cavell take Witt as pointedly not trying to resolve skepticism (the "orthodox" view I described earlier), but take it seriously, investigate it, see what it shows about us. — Antony Nickles

I've just finished reading the second chapter of Cavell's Conditions Handsome and Unhandsome; the chapter on Wittgenstein and Kripke. While interesting in places, I find Cavell misreads Wittgenstein and/or is too generous to Kripke, giving his reading more respect than it deserves.

I note that Cavell says PI is not meant to refute scepticism; but that's not the same as saying that Wittgenstein attempts to resolve scepticism.

What I found most interesting in Cavell's paper is the view - which he says he had found elsewhere only in Kripke's reading - of "the possibility of skepticism as internal to Wittgenstein's philosophizing." As he later expands:

...the irreconcilability in Wittgenstein between our dissatisfaction with the ordinary and our satisfaction in it, between speaking outside and inside language games, which is to say, the irreconcilability of the two voices (at least two) in the Investigations, the writer with his other, the interlocutor, the fact that poses a great task, the continuous task, of Wittgenstein's prose, oscillating between vanity and humility. Skepticism appears in Philosophical Investigations as one of the voices locked in this argument, not as a solution or conclusion. — Cavell

It could be tempting to view PI in this way, seeing all the voices in it as Wittgenstein's own, including an expression of Wittgenstein's own geniune scepticism and philosophical doubts via the voice of an interlocutor. But the interlocutor could alternatively be viewed as a mere literary device which allows Wittgenstein to express these typical philosopical concerns only so he can provide his response (or philosophical viewpoint) to them.

The issue that Wittgenstein identifies (or forecasts) is that philosophers such as Kripke are sceptical or dissatisfied with any and all justifications of behaving in accordance with, or obeying, a rule.
— Luke

In the passage starting this OP, Witt acknowledges the possibility of the exhaustion of justifications. — Antony Nickles

Do you view this as Wittgenstein conceding to the sceptic? The quotes from 198-199 in my previous post include his reply to the sceptic (that following a rule is a custom, a practice, a usage, an institution).

But Cavell is attempting to draw out that there is grammar (not just judgment) in obeying a rule; that there are cases that exhibit what these criteria are (#201); that we can go over these examples and see if the context matches ours, whether it is an example, etc. And that grammar, even that of obeying a rule, is different than rules--even leaves us in a different place in the end. — Antony Nickles

Cavell references Wittgenstein's PI 199 regarding the grammar of obeying a rule. I don't know what you mean by the rest, starting from: "see if the context matches ours, whether it is an example, etc."

It gets even more straightforward, let's use the example of math. The idea is that things are not straightforward like rules (#426), that our criteria (our lives) are open-ended, unpredictable, etc. — Antony Nickles

What has this got to do with rule following?

The further point of the passage of the turned spade is that, though I can wield rules the way you point to (as Kripke grabs onto them as finalizing), we do not have to, there is nothing necessary in treating the other on black and white terms--unless you don't want to address the Other (open the moral realm), that you just want, as it were, to apply the rule. — Antony Nickles

I don't see Wittgenstein or Cavell as talking about "the moral realm" with regard to rules, so I don't see that as being "the further point of the passage of the turned spade". But I invite you to make a case for it.

On p. 192, Witt calls this a "conviction". — Antony Nickles

In which edition? The word "conviction" does not appear on p. 192 of my copy.

240. Disputes do not break out (among mathematicians, say) over the question of whether or not a rule has been followed. People don’t come to blows over it, for example. This belongs to the scaffolding from which our language operates (for example, yields descriptions).
— LW

I would say #240 clarifies our need to be able to know how to fight well (keep open the possibility for reasonable moral debate), — Antony Nickles

You might need to expand on why you think that. I don't see that at all. 240 is simply describing the wide (world-wide) consensus that exists among language users and among mathematicians.

241. “So you are saying that human agreement decides what is true and what is false?” — What is true or false is what human beings say; and it is in their language that human beings agree. This is agreement not in opinions, but rather in form of life.
— LW

...and that #241 does not solve those issues, by pointing to our way of life in the way Kripe takes it as a contractual (enforceable) agreement. — Antony Nickles

I think your assumption that Wittgenstein intends 240 or 241 to be about a "moral debate", or about a solution to it, still requires justification. I don't recall Kripke talking about a moral debate either (although it's been a while and I may not have read it too closely). I take 241 only to be clarifying the type of agreement/consensus Wittgenstein is referring to at 240.

Pointing to the existing practice that constitutes the rule. "You're not allowed to move your knight like that!" (in chess) because that's not the practice or the way it's done.
— Luke

This is to justify the judgment of not obeying a rule by pointing to our practice. We (teacher-student) are at the moment where I claim there is an attempt to convey what it is to obey a rule, how it is that we obey a rule. That this has an ordinary (non-"mathematical") grammar that is not just pointing to a rule (Kripke as it were, generalizes this practice/picture). — Antony Nickles

Sorry, I don't understand. How can you convey what it is to obey a rule without pointing to our practice? Are you referring to the student's (and/or teacher's) thought processes or something? And what do you mean by "grammar" here?

And the other might claim his is an example, but responsive to a new context. "This is justice, but here we must do harm in this case." — Antony Nickles

That would require that the student/trainee already understands what "justice" means; that they are not being taught the rule for how to use the word.

When I obey a rule, I do not choose.
I obey the rule blindly. — Wiit, PI # 219

Right, like when you move the knight in chess; if you know the rule, then you don't think about how the piece can move. But let's go back to what you said and to my original concern:

You say that the teacher is unable to provide sufficient justification to the student about what constitutes obeying a rule. Then you say - crucially - that the teacher does not have to give up on the student because both teacher and student can "resist philosophy's anxiety". I guess I'm asking: what is it that allows the student to "resist philosophy's anxiety"?
— Luke

To make themselves intelligible. They might claim they did obey the rule; or explain their aversion to conformity--examine their "blind" obedience (#219); as normally we do not "follow" rules (#222). Not to take the position that their actions are unable to be communicated--to feel there is something private, unknowable (not just personal). But really this is an examination of the teacher, and the limitation/impotence of our knowledge (what comes after it). — Antony Nickles

The student and teacher can "resist philosophy's anxiety" in order to "make themselves intelligible"? I presume you are talking about the student when you say "They might claim they did obey the rule; or explain their aversion to conformity" -- if the student does not know the rule (otherwise why are they being taught the rule?), then they are in no position to claim that they did obey the rule. To "explain their aversion to conformity" implies that they did not obey the rule. Unless they already know the rule, then the student would not have a "blind obedience" to it. And 222 neither states nor implies that "normally we do not follow rules".

I do not then "follow" the rule, as in watch it go on ahead of me (#232). Kripke takes it that our justifications end (I act blindly) when I obey the rule, and then as if this is how we are said to act at all, with no space for discussing (justifying) that choice afterwards, for rescission if your suggestion to obey the rule was irresponsible, that I would no longer (morally) say I obeyed the rule, but that I obeyed your intimation (#222). — Antony Nickles

Wittgenstein is only talking about the teaching and learning of existing rules. I don't see him as talking about morality, justifying choices or changing rules.

It is peppered throughout, in his insistence not to treat our practices mathematically, singularly, but also (albeit cryptically), in Part II, with his discussion of attitudes, seeing aspects. — Antony Nickles

Where does he insist "not to treat our practices mathematically"? Perhaps you could provide an example or two?

@Banno

I've just finished reading the second chapter of Cavell's Conditions Handsome and Unhandsome; the chapter on Wittgenstein and Kripke. — Luke

Great, I appreciate the effort. I hope it was worth the time. I find the Introduction and defense of Nietszche/Emerson moral perfectionism in the first essay worthwhile. This is Cavell's later work, which assumes a lot of arguments built from his first book and The Claim of Reason, which are more detailed analytical arguments, especially closer readings of Wittgenstein.

I note that Cavell says PI is not meant to refute skepticism; but that's not the same as saying that Wittgenstein attempts to resolve skepticism. — Luke

Well taken, I agree with this clarification. Cavell reads Witt as breaking philosophy's penchant to take its problems as generalized and singular (e.g., a universal theory of meaning), and abstract (without any responsibility on our part). In looking at the criteria for each concept individually--what is meaningful to us in their various ways--and considering the context of the issue, but there is no generalized solution.

So it becomes a philosophical moment: how do we continue, put our concepts and the world back together in this crisis. This cannot be accomplished ahead of time, but, in remembering our ordinary criteria, we have the rational, rough ground to possibly, as you say, resolve this (skeptical) instance, but only in this case/context, our differences there, to continue our relationship, even if we only end in rational disagreement, with the possibility of giving up.

the interlocutor could alternatively be viewed as a mere literary device which allows Wittgenstein to express these typical philosophical concerns — Luke

Witt's previous attempt to overcome skepticism (in the Tractatus) is his inner skeptic, embodied in the interlocutor in PI--Cavell takes this that we all have two "voices" within us, so that the “style” of PI must be taken seriously (as “confessions” or "compulsions", he says in The Availability of the Later Wittgenstein--a good intro his approach to PI); and that Witt is trying to find a space between those two voices (our human voice and our desire to negate that voice--our "corrective" voice).

Do you view [the exhaustion of justifications] as Wittgenstein conceding to the sceptic? The quotes from 198-199 in my previous post include his reply to the sceptic (that following a rule is a custom, a practice, a usage, an institution). — Luke

Yes, our justifications of how we practice a custom may run out; we may concede to our exhaustion. And knowledge (what I can tell you) has a limit, and then I am left with you. How/why I am following a custom/practice/usage/rule the way I am may be, at a certain point, impossible to reconcile with you, so yes, Wittgenstein keeps alive the possibility of groundlessness that the skeptic fears.

we can go over these examples and see if the context matches ours, whether it is an example, etc. And that grammar, even that of obeying a rule, is different than rules--even leaves us in a different place in the end.
— Antony Nickles

Cavell references Wittgenstein's PI 199 regarding the grammar of obeying a rule. I don't know what you mean by the rest, starting from: "see if the context matches ours, whether it is an example, etc." — Luke

The grammar of obeying a rule is drawn out through examples (the OLP philosopher, like Witt, makes a "claim" to the grammar in answering: what do we imply when we say X? e.g., "I obeyed the rule". So this is what Witt does in #199--asking us to imagine someone following a rule only once. Now the claim--about what it is about the way rules work that the activity has to recur, have some regularity, etc.--is on you to see for yourself (thus so many unanswered questions in the PI). If we disagree about the implications, we can do so rationally, productively, by, for example, seeing if my understanding of the relevant context is the same as yours, how this example is representative of my claim about the grammar for obeying rules.

Witt's realization is that our grammar/criteria for obeying a rule are not rules, so that the grammar of the custom and technique, our mastery--not knowledge--of the grammar, structurally puts us in a place where our discussion of the justification of the grammar of obeying a rule starts at the end of where Kripke's action is taken and judgment is made of whether you did or did not "obey a rule" (rules playing too large a part, as if in every action). If that is not clear, I would need more than "[ you ] don't know what [ I ] mean"--say, questions, what you take me to say, logical errors, an differing example, etc.

The idea is that things are not straightforward like rules (#426), that our criteria (our lives) are open-ended, unpredictable, etc.
— Antony Nickles

What has this got to do with rule following? — Luke

Cavell's take is that this is about more than following rules. Witt's example of an action is obeying a rule (looking at its grammar--the custom of it); but the investigation is of how action, meaning, etc. works (in each case): that even in obeying a rule the grammar is not bound by rules. We only want our forms of expression/action to be as "designed for a god"--in the sense of a mathematical rule. (#426)

I don't see Wittgenstein or Cavell as talking about "the moral realm" with regard to rules, so I don't see that as being "the further point of the passage of the turned spade". But I invite you to make a case for it. — Luke

Cavell refers to "the moral realm" as the places in PI where Witt examines how we do not know how to continue with our customs, after the limit of our knowledge of the Other, that our separateness is unbroachable by our desire for mathematical rules, at the end of our justifications for our actions (that they are right). When we are left in further ethical response to the Other: the "conviction" on p. 192, seeing an aspect of the other, what is different than an opinion of the other's soul (our reacting to them as if they have a soul) p. 152; and of course when our spade is turned. Cavell's argument is that Wittgenstein's investigation of the limitations of epistemology (its inability to substitute for us at a point) leads to the realization of our ethical relation to each other (beyond rules or grammar).

On p. 192, Witt calls this a "conviction".
— Antony Nickles

In which edition? The word "conviction" does not appear on p. 192 of my copy. — Luke

I was in the 2001 50th Anniversary 3rd edition, which is German on the left and English on the right (actually on 190-192). In the 1953 3rd Ed., it is on 191. This is the page I read in my discussion of the Lion Quote. The "conviction" there is expressed in the desire for the (referential) picture (requiring "mathematical" certainty) to "know" the Other (that their pain is the "same" as mine); that the certainty has shut our eyes (p. 192) to our responsibility to acknowledge the other (or the consequences of dismissing them)--their claim on us (there, the claim of their pain; in our discussion, the possibility of the end of our moral relationship).

240. Disputes do not break out (among mathematicians, say) over the question of whether or not a rule has been followed. People don’t come to blows over it, for example."
— LW

I would say #240 clarifies our need to be able to know how to fight well (keep open the possibility for reasonable moral debate),
— Antony Nickles

You might need to expand on why you think that. I don't see that at all. 240 is simply describing the wide (world-wide) consensus that exists among language users and among mathematicians. — Luke

Sorry, yes, cryptic. I was reacting to the (I would say conscious by Witt) contrast to what is set out by Plato between the mathematical, which Witt is describing here, and everything else.

If we disagree, you and I, about quantity, over which of two groups is greater, would our disagreement over this make us enemies and angry with each other, or wouldn't we quickly resolve the issue by resorting to counting?
Euth: Certainly.
* * *
So: Then what topic, exactly, would divide us and what decision would we be unable to reach such that we would be enemies and angry with one another? Perhaps you don't have an answer at hand, so see while I'm talking whether it's the just and the unjust, and the noble and shameful, and the good and the bad. Isn't it these things that divide us and about which we're not able to come to a satisfactory decision and so become enemies of one another, whenever that happens, whether it's me and you, or any other men? — Plato - Euthyphro Sec. 7

Cavell's point being that, rather than Kripke's (pre-)judgment and exclusion, Witt is asking us to remember our lives and their ordinary criteria, and, at their end, the beginning of our moral relation to each other, its possibilities (if only for rational disagreement).

I think your assumption that Wittgenstein intends 240 or 241 to be about a "moral debate", or about a solution to it, still requires justification... I take 241 only to be clarifying the type of agreement/consensus Wittgenstein is referring to at 240. — Luke

If we are discussing how to obey a rule (as with: how to apologize, how to judge justice)--if we are discussing the grammar of an act (not "a rule")--and we come to a place where I cannot offer a motivation for you/justification to you, then we can not agree on what is the "right" or "correct" or "felicitous" example of such an act (and/or its justification). The discussion of what is right is a moral discussion. So this is a conversation about politics/justice; the relationship between society and the individual. The breakdown of the discussion of the justification of how to obey a rule--is a moral moment.

That we do not come to "agreement in opinions but in form of life" is a grammatical description of the difference between Kripke's understanding of social agreement (in knowledge, explicitly, beforehand, with certainty, as a written contract--a rule) and our "agreement" in our living (Witt next says" in "judgments" #242). This is not to substitute "forms of life" for our opinions/knowledge--that our lives have all the mathematical criteria Kripke assumes---but that Cavell takes Witt to be saying that, yes, our separate judgments come to the same result (most times), but not because the criteria/justifications are certain (rule-like; followed), but because we have similar lives (as it were, coincidently). So when I act, and there is a question of why my judgment differed, this is where justification begins, or continues, not that we have decided ahead of time, and that all that is left is to act, then be judged (as Kripke pictures it).

Pointing to the existing practice that constitutes the rule. "You're not allowed to move your knight like that!" (in chess) because that's not the practice or the way it's done.
— Luke

This is to justify the judgment of not obeying a rule by pointing to our practice. We (teacher-student) are actually at the moment where there is an attempt to convey what it is to obey a rule, how it is that we obey a rule. That this has an ordinary (non-"mathematical") grammar that is not just pointing to a rule (Kripke as it were, generalizes this practice/picture).
— Antony Nickles

Sorry, I don't understand. How can you convey what it is to obey a rule without pointing to our practice? Are you referring to the student's (and/or teacher's) thought processes or something? And what do you mean by "grammar" here? — Luke

So this would be easier if we were talking (I tried to highlight above the emphasis to show the difference). I am not saying we are not conveying something about our practices, but that, to start with, you are talking about a different practice (or only one part of it). You are describing a way of judging the student--"You're not allowed"--not our practice of justifying our claim about how we obey rules (not what we do when you haven't); our justification of what we think it looks like to obey a rule, disobey a rule, how we justify (what counts as justifying) our claim to have obeyed a rule, etc. (the grammar of "justifying obeying a rule"). So you are providing an example of how judgment of obeying a rule works, but, your teacher is merely "pointing" and, in sense, saying, "No". Your example is Kripke's casting-out of the other based on the (fixed, predetermined) practice--the "way it's done". So we have not yet even started to discuss what constitutes the grammar of "movement" of a knight.

(Confusingly in this case, the grammar for movement of a knight in chess is based on rules--it falls into the category of mathematical criteria: that all the applications are circumscribed, predetermined, etc. Witt is showing this to take up the exceptions, in investigating what grammar would look like for everything else, not based on rules).

And the other might claim his is an example, but responsive to a new context. "This is justice, but here we must do harm in this case."
— Antony Nickles

That would require that the student/trainee already understands what "justice" means; that they are not being taught the rule for how to use the word. — Luke

Again, your formation takes rules as "encompassing" concepts other than math and chess, like justice (like everything not mathematical). And, although the teacher has authority over the student, that does not mean the teacher knows all there is about justice (which, my point here, is impossible--seeing the whole of each infinite series #426), that the teacher could concede that: not only has the student applied (justified) the concept of justice appropriately (within its grammar--not the "meaning", but what is meaningful to us about it), but that the student has taught the teacher something, in this instance by extending the concept into a new context (my example doesn't really fit), something about justice in a new world (say, what is just in reconciling our past incorporation of our reaction to race into our continuing institutions).

Not to open a new can of worms, but saying that justice "means" something (rather than has grammar/criteria) is going to get in the way, as the question begs Kripke's society to "know" what the thing is that is justice (and to the slippery slope: with certainty, universality, ahead of time, definitively, entirely). Also, the formation of being taught how to use a word, is different than being taught what counts as (the criteria that makes this) a particular use of the word (one of its possible senses--say the four (or more) uses/senses of "I know"), and that the concept maintains unforeseen possibilities/justifications, which is analogous to the ever-possible continuation of, answering for, our moral relationship to each other.

The student and teacher can "resist philosophy's anxiety" in order to "make themselves intelligible"? — Luke

The fear of skepticism (groundlessness) is what causes Kripke's society to work out everything head of time, almost as if they(we) don't want to have a conversation later (one that may fall apart), to be then responsible to make themselves intelligible (explicit, understood).

if the student does not know the rule.. [they are] in no position to claim that they did obey the rule... Unless they already know the rule, then the student would not have a "blind obedience" to it. — Luke

I may have mucked this up. What the student is being taught is what counts as--the grammar, or criteria of--"obeying a rule" (later, the grammar of justifying that one obeyed a rule), not learning "the rule"; but the criteria for having been said, or being able to say, that: "I obeyed the rule"--one of which would be it can be used as an excuse: "Hey, I obeyed the rule; it's not my fault it didn't turn out how you expected!" (Our desire for deontological morality--"I'm a good person! I obeyed the rule!".) But also, obeying a rule is different in different contexts--the rules of chess, like those of math, are not like a rule of thumb, the rule of law.

Again, the student is (as, analogously, we are, to society) in exactly the position of making a claim of having "obeyed the rule" without either their or our "knowing" they have (for certain), after the act, before the justifying (even without opening the moral discussion.) It is in a sense a provisional claim ("beyond" knowing, Nietszche will say), but we are not (the human condition is not) in a position to make any other type of claim--without the tyranny of mathematical criteria: its foregone judgment.

And 222 neither states nor implies that "normally we do not follow rules". — Luke

Cryptic, sorry; I meant in the sense that normally we obey rules, we do not "follow" them, as we do not "doubt" someone else's pain (#303). "Following" is grammatically not a part of obeying rules (with exceptions). I meant to point to the entire section from #218-#232 (after the passage #217 under discussion), which, following the grammatical claim that "When I obey a rule, I do not choose," (#219) in the sense that: part of the criteria for "obeying" a rule is that I do not obey "my inspiration" (#232), as it were, at each moment, like my "eye travel [ ing ] along a line" Id--as if always tracking it/myself--that, if I do that, then I am, categorically, not "obeying" the rule. At #222, Witt sees this fantasy of ours is only a picture of the line intimating to us (absolving us of being "irresponsible"--or the one who taught us being so); that the line does not nod, or whisper, or tell us (#223); that we do not follow along it as a path "on tenterhooks", anxious each second about society's moral judgment (our intention, what we "mean"). And that such a grammatical study can show us the flip side of a concept's logic: say, as grammatically we ignore someone's pain, not doubt it, and when we do not "obey" a rule, we might not necessarily simply "disobey" it.

Wittgenstein is only talking about the teaching and learning of existing rules. I don't see him as talking about morality, justifying choices or changing rules. — Luke

Well again I take #217 as about teaching someone how to be able to obey rules, presenting my justifications (say, even: myself as justification by example) for how it is that obeying rules is justified (in justifying how I have obeyed one). So, again, not teaching the rule itself, but the justification for the grammar of how a/the rule is obeyed--which are not rules (neither the justification nor the grammar (except when they are: in math, chess, or when my justification is simply to enforce a rule (we have set), say, with the threat of judgment).

Where does he insist "not to treat our practices mathematically"? Perhaps you could provide an example or two? — Luke

The "tendency to sublime the logic of our language" calling anything else "an inexact, approximate sense." #38; "Here [ in thinking something is queer about propositions ] we have in germ the subliming of our whole account of logic. The tendency to assume a pure intermediary... to try to purify, to sublime, the signs themselves."; being "seduced into using a super-expression" #192; that giving someone a number (in association with a mathematical series) is like telling what a (symbolic) machine will do because all the movements are already there, pre-determined (though even a machine can actually move in other ways) #193; turning around the "preconceived idea of crystalline purity" to still have rigor in our ordinary language without "formal unity" #108; and basically in drawing out our ordinary criteria for any other action except math (or chess).

Confusingly in this case, the grammar for movement of a knight in chess is based on rules--it falls into the category of mathematical criteria: that all the applications are circumscribed, predetermined, etc. — Antony Nickles

Do you believe that all moves (or all movements of a knight) in chess are circumscribed and predetermined? Per Banno's earlier comment, I don't see why you view the rules of chess or the rules of mathematics differently to rules of grammar or road rules.

And, although the teacher has authority over the student, that does not mean the teacher knows all there is about justice — Antony Nickles

Of course; that is the point of Wittgenstein's remarks at 208-211, for example.

And, although the teacher has authority over the student, that does not mean the teacher knows all there is about justice (which, my point here, is impossible--seeing the whole of each infinite series #426). — Antony Nickles

Why is it impossible for the teacher to know "all there is about justice"? Surely they can know enough to teach a student what the word "justice" means (i.e. how to use the word "justice"). After all, didn't someone teach you what "justice" means? And couldn't you teach the meaning of the word to someone else? I don't believe that #426 is typically regarded to be in the rule-following section of PI, but we could look at 218-221 instead.

the teacher could concede that: not only has the student applied (justified) the concept of justice appropriately (within its grammar--not the "meaning", but what is meaningful to us about it), but that the student has taught the teacher something, in this instance by extending the concept into a new context (my example doesn't really fit), something about justice in a new world (say, what is just in reconciling our past incorporation of our reaction to race into our continuing institutions). — Antony Nickles

That's all very possible; it's just not what I see as being the point of Wittgenstein's remarks on rule-following, or anything he's actually talking about.

we obey rules, we do not "follow" them — Antony Nickles

I don't understand the distinction. I consider "obey" and "follow" to be synonymous here.

I meant to point to the entire section from #218-#232 (after the passage #217 under discussion), which, following the grammatical claim that "When I obey a rule, I do not choose," (#219) in the sense that: part of the criteria for "obeying" a rule is that I do not obey "my inspiration" (#232), as it were, at each moment, like my "eye travel [ ing ] along a line" Id--as if always tracking it/myself--that, if I do that, then I am, categorically, not "obeying" the rule. — Antony Nickles

This appears to be the source of our disagreement, and where I believe you are misreading Wittgenstein. You seem to think that Wittgenstein genuinely holds that "All the steps are really already taken" (219). I read him, instead, as saying that we should not become captivated by, or fear, this misleading picture. As he says at 221, this is "really a mythological description of the use of a rule."

Furthermore, his comments on "inspiration" are intended to show that one's inspiration is irrelevant to following the rule; and that it is not one's private feeling, but one's public behaviour, that determines whether a rule has been followed (it is not accidental that these remarks lead into the private language "argument" where the rules of language cannot be determined privately, either). So I wouldn't say that "part of the criteria for "obeying" a rule is that I do not obey "my inspiration"; I would say instead that obeying my inspiration is not part of the criteria for obeying a rule or for determining whether I have obeyed a rule.

At #222, Witt sees this fantasy of ours is only a picture of the line intimating to us (absolving us of being "irresponsible"--or the one who taught us being so); — Antony Nickles

I don't understand this. I take the "intimation" in 222 to mean that the line gives one a private impression or intuition about "the way I am to go". That the line gives us this kind of intuition, W says, is "of course, only a picture", and this intuition could be judged "irresponsibly" in which case he would not be following it like a rule. This is, again, arguing against the mistaken picture that a rule can be determined privately.

that the line does not nod, or whisper, or tell us (#223); that we do not follow along it as a path "on tenterhooks", anxious each second about society's moral judgment (our intention, what we "mean"). — Antony Nickles

I don't know why you bring "society's moral judgment" into it. This is simply another description to reinforce the point that rules are not privately determined.

Well again I take #217 as about teaching someone how to be able to obey rules, presenting my justifications (say, even: myself as justification by example) for how it is that obeying rules is justified (in justifying how I have obeyed one). — Antony Nickles

I see it more in accordance with his remark at #1: "Explanations come to an end somewhere."

“But then how does an explanation help me to understand, if, after all, it is not the final one? In that case the explanation is never completed; so I still don’t understand what he means, and never shall!” — As though an explanation, as it were, hung in the air unless supported by another one. Whereas an explanation may indeed rest on another one that has been given, but none stands in need of another — unless we require it to avoid a misunderstanding. One might say: an explanation serves to remove or to prevent a misunderstanding —– one, that is, that would arise if not for the explanation, but not every misunderstanding that I can imagine.
It may easily look as if every doubt merely revealed a gap in the foundations; so that secure understanding is possible only if we first doubt everything that can be doubted, and then remove all these doubts.
The signpost is in order — if, under normal circumstances, it fulfils its purpose. — LW (PI §87)

I don't see why you view the rules of chess or the rules of mathematics differently to rules of grammar or road rules. — Luke

The point of all the examples of the different types of practices/concepts is to show that there is a different grammar for each one. There are not "rules of grammar" (that sounds like a sillogism) because each grammar is different, the criteria for their employment are different. Every practice is not bound by "rules" (not all grammar is rule-like) though there is a grammar to rules, and a different kind of grammar for different kinds of rules.

Do you believe that all moves (or all movements of a knight) in chess are circumscribed and predetermined? — Luke

Well, I think so... aren't they? I'm mean, strategically unexpected, but the criteria for the rules are complete, exact; this is the category of "mathematical" criteria. There is no creativity in the application of the rules of chess, that's part of the grammar of its rules, as there are extenuating circumstances (not all the possibilities foreseeable ahead of time) in the application of criminal law. (Though predetermined is the wrong word, especially in a philosophy discussion.)

Why is it impossible for the teacher to know "all there is about justice"? Surely they can know enough to teach a student what the word "justice" means (i.e. how to use the word "justice"). After all, didn't someone teach you what "justice" means? And couldn't you teach the meaning of the word to someone else? I don't believe that #426 is typically regarded to be in the rule-following section of PI, but we could look at 218-221 instead. — Luke

I don't see why you view the rules of chess or the rules of mathematics differently to rules of grammar or road rules.
— Luke

The point of all the examples of the different types of practices/concepts is to show that there is a different grammar for each one. — Antony Nickles

Do you mean to imply that grammar pertains to more than just language use; that grammar involves something outside language use? Or what "different types of practices/concepts" are you referring to?

There are not "rules of grammar" — Antony Nickles

Then how do you account for PI §497 or PI §558?

Wittgenstein's remarks, as well as the following quotes from SEP and Baker and Hacker, indicate that there are rules of grammar:

Grammar, usually taken to consist of the rules of correct syntactic and semantic usage, becomes, in Wittgenstein’s hands, the wider—and more elusive—network of rules which determine what linguistic move is allowed as making sense, and what isn’t. This notion replaces the stricter and purer logic, which played such an essential role in the Tractatus in providing a scaffolding for language and the world. Indeed, “Essence is expressed in grammar … Grammar tells what kind of object anything is. (Theology as grammar)” (PI 371, 373). The “rules” of grammar are not mere technical instructions from on-high for correct usage; rather, they express the norms for meaningful language. Contrary to empirical statements, rules of grammar describe how we use words in order to both justify and criticize our particular utterances. But as opposed to grammar-book rules, they are not idealized as an external system to be conformed to. Moreover, they are not appealed to explicitly in any formulation, but are used in cases of philosophical perplexity to clarify where language misleads us into false illusions. — SEP

The use of a word, Wittgenstein averred, is determined by the rules for the use of that word (AWL 30). For using words in speech is a rule-governed activity. The rules for the use of a word are constitutive of what Wittgenstein called ‘its grammar’. He used the expression ‘grammar’ in an idiosyncratic way to refer to all the rules that determine the use of a word, i.e. both rules of grammar acknowledged by linguists and also what linguists call ‘the lexicon’ and exclude from grammar — i.e. the explanations of meaning (LWL 46f.). To grammar belongs everything that determines sense, everything that has to be settled antecedently to questions about truth. The grammar of an expression, in Wittgenstein’s generous use of ‘grammar’, also specifies the licit combinatorial possibilities of the expression, ‘i.e. which combinations make sense and which don’t, which are allowed and which are not allowed’ (ibid.; emphasis added). ‘What interests us in the sign’, he wrote, ‘the meaning which matters for us, is what is embodied in the grammar of the sign. . . . Grammar is the account books of language’ (PG 87). Wittgenstein contended that the questions ‘How is the word used?’ and ‘What is the grammar of the word?’ are one and the same question (ibid.). The use of a word is what is defined by the rules for its use, just as the use of the king in chess is defined by the rules (AWL 48). — Baker and Hacker, Wittgenstein: Understanding and Meaning, Volume 1 of An Analytical Commentary on the Philosophical Investigations: Part I: Essays, Volume 1, pp. 145-146

There are not "rules of grammar" (that sounds like a sillogism) because each grammar is different, the criteria for their employment are different. — Antony Nickles

How do rules differ from "the criteria for their [each grammar's] employment"?

Every practice is not bound by "rules" — Antony Nickles

I never said or implied that every practice was bound by rules. (And why the scare quotes?)

(not all grammar is rule-like) — Antony Nickles

Then I'm not sure what you mean by "grammar". I suspect you might be conflating grammar with form of life (which is wider than language).

though there is a grammar to rules, and a different kind of grammar for different kinds of rules. — Antony Nickles

For example?

Do you believe that all moves (or all movements of a knight) in chess are circumscribed and predetermined?
— Luke

Well, I think so... aren't they? I'm mean, strategically unexpected, but the criteria for the rules are complete, exact; this is the category of "mathematical" criteria. — Antony Nickles

They are certainly not complete. There have been numerous changes and additions to the rules (of mathematics and chess and grammar and the road). I'm sure there will be many more to follow. Although you could consider them as complete (or "circumscribed") at any particular time.

(Though predetermined is the wrong word, especially in a philosophy discussion.) — Antony Nickles

So not "predetermined" either...

Why is it impossible for the teacher to know "all there is about justice"? Surely they can know enough to teach a student what the word "justice" means (i.e. how to use the word "justice"). After all, didn't someone teach you what "justice" means? And couldn't you teach the meaning of the word to someone else? I don't believe that #426 is typically regarded to be in the rule-following section of PI, but we could look at 218-221 instead. — Luke

Was this quote without comment meant to signify something?