Reading Wittgenstein's On Certainty as a Whole: An Interpretive Picture

Metaphysics & Epistemology
31

This objection applies equally to what you said Wittgenstein says about doubt. Here:

It’s only the claims made, in language “I know”, and "I doubt”, which demand justification. The actual certitude which lies behind the claim “I know” doesn’t need to be justified unless the claim is made. Nor does the doubt which lies underneath skepticism need to be justified unless the claim is made. And, when we look at these two things in themselves, the underlying certitude, and the underlying doubt, we see that they are completely different.

In the case of making the claim “I doubt it”, it is not the case that the one who claims to doubt, ought to be held to the same standard as the one who claims to know. This is due to the significant difference between these two claims. The knower claims certainty, and it is warranted to ask for the principles which support that certainty. The doubter claims uncertainty, and that is produced by a lack of supporting principles. So we cannot ask the doubter to provide the principles which support the doubt, because “doubt” implies a lack of such.

Therefore, I think you’ve misinterpreted 24, Sam26. You say: “The skeptic’s doubt and Moore’s assertion fail for the same reason.”. But this is clearly not the case. One is a claim of certainty the other a claim of uncertainty; “to doubt the existence of my hands”. In the case of a claim of certainty we look for support. In the case of a claim of doubt, uncertainty, a completely different process is required.

So Wittgenstein is lead to a question here. “Hence, that we should first have to ask: what would such a doubt be like?”. That’s a completely different type of question from asking for the supporting principles of “I know”. It is to ask, why are you unsure. And Wittgenstein at this point does not offer an answer. He will continue to investigate this question.

So the skeptic then could reply with, ‘until we have a clear definition of what “hands” means, and a clear definition of what “existence” means, I cannot judge the question of whether my hands have existence, therefore I doubt it’. Notice, that the skeptic’s uncertainty is a manifestation of what is essential to natural language, ambiguity, because the same words are used in a multitude of language games.

32

The competences you’re pointing to are real, but I definitely wouldn’t call them epistemic. Epistemic practices are necessarily linguistic. To justify a belief, to evaluate a claim, to challenge an assertion, these are all moves within a language-game, and you can’t do any of them without language. There’s no such thing as a non-linguistic epistemic move. There are only nonlinguistic hinges and hinges aren’t epistemic.

What there are, and I think this is what you’re getting at, are non-linguistic competences and certainties that underlie our epistemic practices. The capacity to navigate the physical world, to recognize continuity in experience, to respond to other beings. These are real and they do underpin our language-games. But they aren’t epistemic. They operate at the level of what I’ve been calling non-linguistic hinges, the pre-epistemic foundation on which our epistemic practices are built. They become epistemically relevant only when they enter the space of language.

So, I agree with you that not everything underlying the language-game is linguistic. But I wouldn’t call those underlying competences epistemic. Keeping that distinction clear is essential to the framework I’m developing in this thread. Hinges, whether linguistic or non-linguistic, are the foundation of epistemic activity. They aren’t themselves part of it.

33

This is why I have such difficult time responding to you, viz., because you not only mischaracterize what Witt is saying, but you also misinterpret what I’m saying.

I think there are a couple of things that need untangling. You say that the actual certitude behind I know doesn’t need to be justified unless we make a claim. But this mischaracterizes what Witt is saying and doing. Witt isn’t saying that there’s a hidden certitude sitting behind our knowledge claims that only needs justification when we put them into words. There’s a level of certainty beneath our epistemic claims, and that’s what I’ve been calling hinge certainty throughout this thread. But hinge certainty isn’t the same kind of thing as knowledge (epistemic certainty), just unexpressed. It’s a different kind of certainty entirely, operating at a different level. It doesn’t become epistemic by being put into words. It’s the foundation that makes epistemic activity possible at all. Treating it as unexpressed knowledge that gets activated by language collapses the very distinction that Witt is working to establish.

The idea that there’s an “underlying doubt” behind skepticism that exists independently of any claim is not only problematic but incorrect. Witt’s point in OC 24 is precisely that doubt doesn’t work that way. Doubt isn’t something that exists beneath or behind language, waiting to be expressed. Doubt, like knowledge, only has its life within a language-game. You can’t have a doubt without a context that gives the doubt its shape, its grounds, and thhe conditions that make resolution possible. There is no free-floating doubt underneath skepticism any more than there is free-floating knowledge underneath Moore’s assertions. Both require a language-game to have any sense at all. This is why the suggestion that certitude and doubt are “completely different” doesn’t hold up in the way you seem to think. Witt’s point is that as epistemic moves they share the same grammar. Both require grounds. Both operate within language-games. Both lose their sense when detached from those games. Hinge certainty is indeed something different from epistemic doubt, but that’s because it operates at a different level entirely, not because certitude and doubt are opposed in the way you’re suggesting.

35

I want to comment on what AI can contribute usefully to philosophy, but it doesn’t yet do philosophy in the human sense. It’s strong at organizing ideas, spotting patterns, and clarifying arguments, yet it struggles with long evolved philosophical analysis because it doesn’t hold stable commitments or understand why a certain idea matters. Its reasoning can drift, contradict itself, or miss the deeper stakes of a problem because it has no lived background, no form of life, and no internal sense of truth or error. What it offers is a powerful tool for exploration and clarification, not something capable of genuine philosophical thought (not yet). It helps with writing but lacks real depth in philosophy. When I’ve used it to analyze Witt it constantly falls short.

36

OK, but this has very little bearing on what I said. I said there is some form of certitude behind claims of “I know”. You are dividing this certitude into two types, “hinge certainty” and “epistemic certainty”. I agree that Wittgenstein is pointing to two principal types of certainty, but I don’t agree with your classification.

So far Wittgenstein has pointed to subjective certainty (Moore’s), which he thinks is pointless, and he has also pointed to a more objective form of certainty, which is supported by the grammar of language-games.

On the other hand, your way of classification is very confusing and not properly representative of what Wittgenstein has actually said at this early stage of the book.

This is just more evidence that you have misinterpreted OC 24. Please go back and reread. Wittgenstein says “What right have I not to doubt the existence of my hands?”. This means, what justification do I have for taking the existence of my hands as certain. By what means would I conclude that I ought not doubt the existence of my hands?

Then he suggests that a doubt about “existence” could only exist within a language-game. So he says we’d have to ask the skeptic, “what would such a doubt be like?”. And, he says that we probably wouldn’t understand the skeptic’s explanation “straight off”.

Now, I understand the skeptic’s position, being a skeptic myself, and I can provide an answer. This is, as I explained above. Due to the ambiguity of natural language (caused by a multitude of language-games), the skeptic is not ready to judge whether “my hands” have “existence”, without precise definitions of those terms.

The reason why you, and others, as Wittgenstein suggests, “don’t understand this straight off”, is because of the premise “a doubt about existence only works in a language-game”. You assume there is a language-game in which “existence” is well defined, and the skeptic’s doubt must be within that game. But when the skeptic explains that “doubt” is not confined to being within “a language-game”, but encompasses a multitude of language-games, then that premise is shown to be wrong, through the appropriate understanding of what “doubt” is.

Doubt is not an epistemic move. This is how your unWittgensteinian category of “epistemic” is misleading you in your interpretation. A grammar is specific to a language game. The skeptic’s doubt, as I explained above, is the product of ambiguity and inconsistency between a multitude of language games. “Epistemic moves” must share the same grammar, that of epistemology, and we can call this the language-game of epistemology.

However, the skeptic’s doubt is produced from the fact that there is a multitude of language-games, with ambiguity and inconsistency between them. Therefore the skeptic’s doubt is not confined to being an epistemic move. It is not a move within a language-game, but something validated by the reality of “language-games”. The important point being that certainty and “epistemic moves” are products derived from the restrictions of a single game, while doubt can only be understood from the fact that there is a multitude of games.

37

No game is just about words. What the builder can do with a block is different to what she can so with a slab. That’s not only a difference only in words, but also in how things are. In a language game we cannot seperate the syntax from the semantics; we must include the interpretation.

Take care not to fall for the myth of the given.

We might presume that there is a separation between world and word, that there are blocks and slabs and such “out there” that are referred to in the game; and so we suppose that we can have blocks and slabs “prior” to language. But we both understand that “block” and “slab” only have a meaning within the game, that they are not distinct from the game. That’s a huge inconsistency. We can’t consistently hold that there is a world seperate to our talk of it, and that the world is constituted in our talking. Better: We can’t consistently hold that there is a world seperate to what we do int he world, and that the world is constituted in our doing.

Davidson has said that animals without language also lack belief. While that’s a step too far, it’s at least int he right direction. What we have is consistent behaviour that we manifest in propositions. Propositions are after all more behaviour.

(this accidentally posted before I finished it - I’ll leave it ill-finished for now. )

38

I’ll reply to what’s written so far.

I think there are a few things here that need clarification.

First, I’m not claiming that there’s a world of pre-interpreted facts sitting out there independent of all human engagement. That would be the myth of the given, and the appeal to it here is a red herring. The myth of the given is a worry about foundationalist epistemology, about treating raw experience as providing unjustified justifiers for knowledge claims. But non-linguistic hinges aren’t justifiers. They aren’t doing any epistemic work at all. I’ve been clear throughout this thread that hinges are non-epistemic. They’re the background against which epistemic activity becomes possible, not a foundation that provides evidence for anything. So, the critique simply doesn’t apply to what I’m arguing.

Second, the claim that “propositions are after all more behaviour” actually works against your argument. If propositions are behavior, and non-linguistic creatures clearly behave with certainty, then the certainty is there in the behavior whether or not it gets expressed propositionally. A dog doesn’t hesitate at the ground. An infant reaches for a toy without doubting its persistence. That certainty is displayed in what they do. You’re conceding that behavior is primary and then insisting that only the propositional expression of that behavior counts as certainty. But that’s the very question at issue, and asserting it doesn’t constitute an argument for it.

Third, your own concession that Davidson’s denial of belief to animals without language is “a step too far” is telling. If it’s a step too far to deny belief to animals without language, then on what grounds do you deny certainty to them? You’re drawing a line that allows animals to have something but insists it can’t be called certainty unless it takes propositional form. But Witt’s whole point is that certainty at its deepest level shows itself in action, in how creatures engage with the world, not in what they assert. Requiring that all certainty be propositional because we use propositions to discuss it is still the same confusion I pointed out in my earlier post. We can describe non-linguistic certainties in language. We have to if we’re going to do philosophy. But describing something in language doesn’t make the thing itself linguistic.

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39

I want to tighten up the wording so we’re not talking past each other.

When I say “non linguistic hinge,” I’m not saying “uninterpreted Given,” and I’m not picturing a world of raw facts sitting out there before anyone engages with it. I’m also not denying that language games involve interpretation, or that words and actions are inseparable. Witt’s builder example is exactly my point, viz., the game is not just talk, it’s the trained doing, the corrections, the shared way of going on. I’m with you on this.

However, I have a narrower point. “Non linguistic” for me does not mean “unsayable.” It means, “not normally functioning as a proposition inside the space where we give grounds, check, doubt, correct, and argue.” Yes, I can state a hinge, because we’re doing philosophy. But stating it isn’t how it does its work in everyday life.

So, when I write, “the world holds together from moment to moment,” you’re right, I’ve put it into words. But the certainty I’m pointing to is the standing fast that shows itself in how a creature expects continuity, reaches, navigates, gets surprised, and corrects itself. That is why I used the dog and infant examples, not to claim they have philosophical beliefs. Our sentence is a description of that standing fast, it is not what constitutes it.

This is also why the “myth of the given” worry is a red herring here. The myth of the given is a warning about treating raw experience as an epistemic foundation, as something that supplies justifiers without itself needing justification. But hinges, as I’m using the term in OC, are not justifiers. They are not evidence for anything. They are the background that makes the whole language game of evidence, doubt, and mistake possible.

On “we cannot separate syntax from semantics,” I agree, but notice what that does and doesn’t show. It shows that meaningful talk is always within a practice, with interpretation built in. It doesn’t show that everything that stands fast in the practice must itself be a proposition, or is shown by the activity of asserting propositions. If anything, the builder example pushes the other way, i.e., the grasp of “block” and “slab” is not primarily a pair of sentences, it is a trained ability to do something correctly, and to be corrected. That is precisely the kind of thing OC keeps pointing us toward, what shows itself in our going on, not what we explicitly claim.

And on Davidson, even if someone wants to deny “belief” to animals without language in a technical sense, that still doesn’t touch the phenomenon I’m describing. The issue here isn’t whether the dog has beliefs with propositional content. The issue is whether there are certainties that function as what stands fast, so that doubt and checking can even get a grip. Witt is trying to make that background clear to us.

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Are the foundations part of the building or not. If the house is built on sand or bedrock, then no. If the foundations are concrete poured into a ditch, then yes. Without some such criterion, there’s nothing to argue about.
I thought Witt talks about “hinge propositions” as opposed to simply hinges. In which case there are no non-linguistic hinges. But perhaps if a propositions describes a state of affairs, that state of affairs migh have the place of a hinge. I’m not dogmatic about this.
I would have thought the ability to see was epistemic, but that being alive and breathing was not.
Sometimes Witt gives the impression of giving us a first sketch or outline of a philosophical map. He almost invites us to fill in or complete it. But other times, one feels that his remarks are like 1,2,3,… - the dots of infinity.

I don’t think it’s that simple. Many games have a concept of winning. But it doesn’t follow that winning is the same in all of them. On the contrary, winning at poker and winning a race are very different. Similarly doubting and being certain are found in many language games, but it is almost certainly inappropriate to think of doubting and being certain as the same thing in every language game.

I’m sorry, I really don’t get this. Can you say a little more?

That’s is indeed one of the mistakes that the sceptic makes. But you seem to assume that this doubt is the same in all language games. That means it has no rationale and consequently nothing could count as resolving it. Why is it not irrational?

I think you are over-simplifying. Even in this very basic game, surely blocks and slabs are also physical objects and exist, to put it this way, in other language games, as physical objects, for instance. Building involves language games, but it also involves rearranging the physical world. Surely?

I wouldn’t argue with that. Except that “Propositions are behaviour” sounds very odd to me. Perhaps we should say that belief in/knowledge of propositions can be expressed in behaviour.

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I can’t see your point Ludwig. My point was that certainty and doubt do not share the same grammar, and therefore cannot be contrasted in that way. Certainty is produced within the grammar of a single language-game, the requirement of consistency being essential. On the other hand, doubt is produced by words serving different, and inconsistent purposes (meaning) between one language-game and another. Certainty is the product of a single game, doubt the product of a multitude of games.

So to take your analogy, that “winning” is different in poker and racing, we could also say that “certainty” is different in science and ethics. However, just like “winning” in one sense is specific to one game, and “winning” in the other sense is specific to the other game, “certainty” in one sense is specific to that field, and “certainty” in the other sense is specific to the other field.

Now “certainty” as a general thing maintains the character I assigned, of being produced by adhering to the grammar of the field, regardless of the field. Likewise, “winning” in general is produced by following the rules of the specific game regardless of the game.

Doubt, as I described is produced from the reality of a multitude of different language-games. The skeptic says that if “winning” is different in poker and racing, then there is really no such thing as “winning”. It is not a well defined word, and skepticism about “winning” is warranted. Likewise, if “certainty” means something different in science from what it means in ethics, then there is no such thing as “certainty” itself, and doubt is justified.

Wittgenstein’s example is “existence”. What would justify me not doubting the existence of my hands? Clearly, even within the study of philosophy, “existence” has a multitude of meanings. Some say only ideas exist, some say only material objects exist, and there is a multitude of other claims about “existence”. So a clear definition of “existence” is required as a first step toward justifying not doubting the existence of my hands.

42

Would you make a distinction between linguistic propositions treated as formal statements of the form S is P, and a proposition treated as a move in a language game? I read Wittgenstein as arguing that the former are confused ways of thinking about how language works, and the latter reveal what words are actually doing as we use them. I would also avoid treating hinges as if they functioned outside the space where we give grounds. To me hinges are not outside the space of language games and languages games are not outside the space of moves within them.

We are tempted to treat hinges and the rules of language games as conditions of possibility which sit in the background imposing overarching schemes of meaningful organization on actions. But a fundamental feature of the application of a rule or our functioning within the purview of a hinge is that every action involves an element of creative improvisation.No rules or criteria can tell us how to go on. When we make a move within a language game the move subtly redefines the sense of the game, and subtly redefines the sense of the hinge which ties together a system of language games.

That’s why I think it’s better to understand rules and hinges as dimensions of each new action, verbal, gestural or otherwise, that we make, rather than as before, outside or encompassing of them. The only way we can know how a hinge functions is to discover freshly how it is used in a present action. The use of a word or gesture tells more about what the hinge is doing than the hinge can tell us about what the word is doing.

43

“Losing” is simply “not winning”. Winning is well defined in each game that it occurs in. Therefore Losing is also well defined in each game it occurs in. So scepticism about losing is not warranted.
There are many other terms that a like these two - they (and the related opposite) are well defined in each context that they occur in. The attempt to use them outside any context is empty.

You give the game away by suddenly introducing this new concept of “certainty itself”. What does that mean, exactly? By doing so in this way, without any explanation of what you mean, you leave your reader to supply a meaning - or not.

In fact, “winning” and “losing” may have different meanings in each game, but there is a common thread. Roughly winning is what players are expected to try for; if they win, they succeed. If they do not even try, they are not even playing the game. So there is a role in those games that have the concept and this role can be identified across games. It is the detail of what counts as winning that changes. Something similar can be said of “certainty” (objective sense) and “doubt”.

Your sense of doubt has the apparent strength of being proof against any answer. But the weakness of not saying anything concrete.

44

By this definition, there is a multitude of losers, second place, third place, they’re all losers. But this is not an accurate definition of losing, so your analogy fails.

That is the point, and why doubt is justified. Wittgenstein’s example is “existence”. Even within the discipline of philosophy “existence” has different meanings, depending on if you follow idealism, materialism, etc.. Therefore until we settle on a definition of “existence”, we’d be fools not to doubt the “existence” of our hands. So doubt is fundamental to philosophers.

Again, your analogy doesn’t work. On the one hand you are repeating what I said about “certainty”, it can be identified across games, as something sought produced, and defined within the context of a specific game, just like winning.

But you are not paying attention to what I said about doubt. It is not proper to any specific game, as winning is, but it is a feature of the fact that a multitude of different games use the same words in different way. Try this to help you understand. Suppose a word is a rule. Now imagine that a number of games use the very same rules, but expect you to interpret the very same rules in different ways depending on the game. That is cause for doubt.

So winning and certainty are similar in your analogy, but doubt is dissimilar. And doubt doesn’t even compare with losing because the skeptic is not trying to win, or even to play the game, but to question the required interpretation of the rules. Maybe the doubter could be portrayed as playing a meta-game.

I think that’s right, it seems to be exactly what doubt is. As a suspension of judgement, it may be applied against anything that one is supposed to judge, but at the same time it provides absolutely nothing concrete. That’s why it can’t be placed in the same category as certainty. Doubt doesn’t provide a weak foundation in contrast to certainty’s strong foundation, it doesn’t provide a foundation at all, the intent is to deconstruct.

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No, it doesn’t. A given form of words with two or more different interpretations is not the same rule.

That presupposes that all those systems are equally legitimate. Someone might take that position and I would have some sympathy with it. Given that they all have different definition of “exist”, there’s a case for saying that on this view, they are simply talking past each other. But most philosophers think that they are not all equally legitimate.

Yes, it is possible to argue that the person who comes second or third in a race has not lost. But in many games there are only two players (or sides), so the definition works there. In other cases, we might explain that the binary win/lose is not appropriate and develop a more complex structure. That doesn’t change anything.

If idealism and materialism have different definitions of existence, they are simply talking past each other. Your doubt is not necessary, since what can be doubted is differently defined in different games.
Besides, part of the point of all this is the idea that philosophy gets itself into endless pointless debate by trying to think and talk in that way.You can’t assume that philsophical doubt is meaninful. You are begging the question.
Yes philosophy does change if you abandon Cartesian doubt. It changes for the better, since meaningless debates are identified and abandoned.

It is certainly possible to consider changing the rules of a game, or creating a new game by altering some of the rules of an existing game. But truth and falsity don’t play any part in that debate. The relevant criteria are not those of the game. Call that a meta-game if you like.

It depends what you mean by “deconstruct”. Once you have defined that, you will have developed a new game, and people will decide whether it is playable or interesting.
I’m wondering whether we would do better to think of the opposite of certainty as uncertainty and leave you with doubt as this vacuous kind of suspension of judgement.

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I think that this little digression has only demonstrated that you and I do not agree on what “doubt” means in this context. I think that’s what Wittgenstein expected when he said at 24: “Hence, that we should first have to ask: what would such a doubt be like?, and don’t understand this straight off”.

We should probably not pretend to understand this straight off.

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Your opening definition of “non-linguistic” as “not normally functioning as a proposition inside the space where we give grounds, check, doubt, correct, and argue” is very close to what I mean by non-epistemic. So, there may be common ground here. But then you say you’d avoid treating hinges as if they functioned outside the space where we give grounds, and that’s where I think you part ways with the text. Witt’s point is precisely that some things do stand outside that space. That’s what makes them hinges.

OC 166 says, “The difficulty is to realize the groundlessness of our believing.”

OC 204 also “Giving grounds, however, justifying the evidence, comes to an end; but the end is not certain propositions’ striking us immediately as true, i.e. it is not a kind of seeing on our part; it is our acting, which lies at the bottom of the language-game.”

OC 205, “If the true is what is grounded, then the ground is not true, nor yet false.” OC 253, “At the foundation of well-founded belief lies belief that is not founded.”

OC 341-343, “The questions that we raise and our doubts depend on the fact that some propositions are exempt from doubt, are as it were like hinges on which those turn… If I want the door to turn, the hinges must stay put.”

OC 559, “You must bear in mind that the language-game is so to say something unpredictable. I mean: it is not based on grounds. It is not reasonable (or unreasonable). It is there — like our life.” The cumulative force of these passages is hard to resist. Witt is saying repeatedly that there is a level at which giving grounds comes to an end, where what we find is not more justified belief but our acting, our form of life. Hinges aren’t moves within the game. They’re what makes the game possible.

Your point about creative improvisation is interesting and I think it applies to moves within language-games. Every application of a rule involves judgment that can’t be fully captured by further rules, and OC 26-29 make exactly this point. But hinges are precisely what doesn’t get improvised, at least at the bedrock level. They’re the stable background that makes improvisation possible. If the ground shifted with every step, walking wouldn’t be creative. It would be impossible. You say hinges are dimensions of each new action and that their sense is subtly redefined by each move. But Witt says hinges stand fast. That’s their defining characteristic. OC 94 says our world-picture is “the inherited background against which I distinguish between true and false.” The riverbed can shift over time, yes, but at any given moment the bed holds and the water flows because it holds.

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But he also says there is no categorical distinction between bedrock and flowing river, it’s a matter of degree.

It might be imagined that some propositions, of the form of empirical propositions, were
hardened and functioned as channels for such empirical propositions as were not hardened but fluid;
and that this relation altered with time, in that fluid propositions hardened, and hard ones became
fluid.

The mythology may change back into a state of flux, the river-bed of thoughts may shift. But I
distinguish between the movement of the waters on the river-bed and the shift of the bed itself;
though there is not a sharp division of the one from the other.

And the bank of that river consists partly of hard rock, subject to no alteration or only to an
imperceptible one, partly of sand, which now in one place now in another gets washed away, or deposited.”

If the alteration of the hinge is imperceptible, isnt it still
an alteration? I think this matters because it seems to me the only way hinges form and change is through our actual moment to moment, day to day use of words and gesture. If the hinge is the larger system of practices that participates in, informs and organizes our interactions, if each interaction provides an element of creative improvisation, and if we eventually find ourselves moving through a course of interactions which have the ability to significantly alter that hinge bedrock, mustn’t this potential responsiveness of hinges to certain life-altering varieties of experience be made possible by the tacit responsiveness of hinges to familiar rule-governed interactions?

I’m reminded of Piaget’s overarching epistemological schemes, which maintain their overall stability even as they accommodate themselves to the novel particularities of events. If hinges define the meaning of the theme, then variations within the theme don’t just occur within it but extend, enrich and redefine the meaning of the system as a whole.

If we were to insist that a hinge, as a reciprocally unified system of practices, could remain utterly unchanged by the routine events which
add a creative element to that system (i.e. moves within chess), then where do we locate the point of unresponsiveness in this unified reciprocal system of actions such that the superordinate dimension is cut off from changes in subordinate events? Could this direction of influence ever be just one way, from superordinate to subordinate?

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Josh, this is a more nuanced than before and I think the riverbed metaphor already explains it. Witt says that hinges can shift over time. The riverbed generally isn’t permanent. But the shift is gradual and happens across the life of a practice, not in each individual interaction. When you ask whether imperceptible alteration is still alteration, the answer is yes, but that doesn’t make hinges responsive to individual moves in the way you seem to be suggesting. The erosion of a riverbed by water is real, but at any given moment the bed is what makes the flow of water possible. You can’t explain the flow by saying the bed is constantly being redefined by each drop. The asymmetry between bed and water is what makes the metaphor work, even though over time the bed shifts.

But it’s also important to recognize that not all hinges are equally susceptible to change. The distinction I’ve been drawing between non-linguistic and linguistic hinges maps directly onto this question. The deepest non-linguistic hinges, the continuity of experience, the persistence of objects, the existence of other beings, aren’t susceptible to change through practice at all. No amount of interaction is going to erode the certainty that the world holds together from moment to moment. These are conditions of any possible engagement with the world. Non-linguistic hinges at the level of bodily engagement, like the certainty that the ground will hold, are also extremely stable. Linguistic hinges are where your point has the most traction. “No one has been to the moon” functioned as a hinge in Witt’s time and no longer does. “The earth is flat” functioned as a hinge for centuries and then stopped. These hinges take propositional form within our language-games and are the most responsive to changes in practice, science, and experience. So your picture of hinges being gradually reshaped captures part of the story, but it applies to some hinges and not others, and it doesn’t apply at all to bedrock (I distinguish between bedrock hinges and general foundational hinges) ones.

Your Piaget comparison is actually helpful, though not in the way you intend. Piaget’s schemas accommodate new experience through assimilation and accommodation, but the schemas themselves maintain structural stability precisely so that accommodation can occur. If the schema dissolved with every new input, there would be nothing to accommodate to. The stability is what makes the responsiveness possible. That’s exactly the relationship between hinges and ordinary moves within language games. The hinge holds so that the moves can happen. If hinges were as fluid as you’re suggesting, they couldn’t play the organizing role that Piaget’s schemas play in his framework.

Your final question about where to locate the point of unresponsiveness assumes that if influence ever flows from subordinate to superordinate, it must flow constantly and in each interaction. But that doesn’t follow. A single chess game doesn’t redefine the rules of chess, even though over centuries the rules have changed. The fact that change eventually happens doesn’t mean each move is contributing to a redefinition of the rules. Most moves simply occur within a stable framework, and that stability is what makes them intelligible as moves. The direction of influence isn’t just one way, but the timescales are radically different. Hinges shape each interaction in the moment. Interactions reshape hinges only over the long life of a practice, and only the linguistic ones at that. Collapsing those timescales and those levels into one loses the asymmetry that makes Witt’s account work.

The points you’re making are important to the conversation.

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Here I’d like to add, that there are two very distinct types of mistakes in the employment of a rule. One is when the rule is incorrectly followed, and the other is when the rule is incorrectly applied. The first type of mistake is exemplified by invalid logic. If the rule is not properly followed there is logical fallacy. The second type is exemplified by the unsound conclusion produced from a false premise. In this case, the rule of logic is properly followed, but the rule is incorrectly applied because of a false premise.

To relate this to mathematical calculations, here’s an example. If someone concludes that 2+2=5, this is an instance of not correctly following the rule. On the other hand, if someone takes a group of two things, and puts them together with a group of three things, and claims that this is represented as 2+2=4, therefore there is now four things, that would be a case of misapplication. The group of three things has been falsely represented as 2 in the application of the rule, and this produces an unsound conclusion.

The issue with the second type of mistake, “mistake in applying”, is that this type of mistake cannot be completely understood as a failure in following a rule. We may assume rules of application, but those rules would need rules of application, so this would produce infinite regress.

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You subscribe to a more realist reading of Wittgenstein than I do.You see stable aspects of the world as grounding what you call the deepest non-linguistic hinges. According to my interpretation, there are no aspects of the world which can be extracted from the changing uses we make of them in our practices. There is no determinate scheme or context that can fix the content of utterances, and hence no way to get outside of language. How a theory or practice interprets the world is itself inescapably open to further interpretation, with no authority beyond what gets said by whom, when.

Piaget’s reciprocal approach to the relation between schemes and content is in line with my claim that assimilation and accommodation are not just minor adjustments to subordinate structures; they recursively reshape higher-level schemas as well. Piaget has written that each interaction with the environment, no matter how small, is incorporated into the organism’s total cognitive structure. Superordinate schemes are relatively stable because they are deeply integrated across multiple experiences, but their stability is always provisional. Every new experience subtly modifies them, otherwise, development would be impossible. The ‘hinge’ is never separate from action; it exists only in the ongoing structuring of experience.