This isn’t about hinges corresponding to facts in a propositional sense but about their truth being a lived engagement with facts as prelinguistic realities. — Sam26

Wittgenstein in Tractatus did not describe facts as lived truths

2 What is the case - a fact - is the existence of states of affairs

Do you have any reference that supports you in describing prelinguistic facts as lived truths?

Hinges are layered, arational (arational because they are not subject to the rational processes of justification, doubt, or proof that characterize traditional epistemological theory), foundational convictions shared by all humans within our forms of life that serve as indubitable certainties grounding our epistemological language, systems of doubt, and justification. They exist both prelinguistically and linguistically, with their truth shown through our actions rather than propositional validation. — Sam26

:smile: I appreciate your definition.

Prelinguistic

In the world are facts, such as i) here is one hand, ii) the apple is green, iii) the mountain is next to the tree.

These facts exist within human Forms of Life. They exist prelinguistically and are beyond doubt. They are bedrock certainties.

Question 1. Are these prelinguistic facts hinges?

The notion of truth is redundant.
If the apple is green then the apple is green.
Nothing is added - if the apple is green then it is true that the apple is green.

Linguistic meaning

Today, that "here is one hand" means here is one hand is beyond doubt.

The notion of truth is redundant
If "here is one hand" means here is one hand then "here is one hand" means here is one hand
Nothing is added - if "here is one hand" means here is one hand then it is true that "here is one hand" means here is one hand.

Linguistic correspondence

"Here is one hand" is a hinge proposition because its meaning is beyond doubt, as we know that it means here is one hand.

"Here is one hand" is true IFF here is one hand

The truth of the proposition "here is one hand" is contingent on there being here is one hand in the world.

1) What makes Moorean propositions ("Here is one hand.") a hinge, according to Wittgenstein, is their status as bedrock certainties.
2) This particular bedrock certainty is prelinguistic (not all hinges are prelinguistic, but bedrock certainties are), i.e., it's shown in our actions — Sam26

How are you defining "hinge"?

Is the hinge 1) the Moorean proposition "here is one hand", or 2) the prelinguistic bedrock certainty, here is one hand.

I build on this by showing how the truth of hinges is demonstrated in our actions. — Sam26

Today, that "here is one hand" means waving one hand is beyond doubt, and is therefore a hinge.

Neither "here is one hand" nor waving one hand is a hinge. "Here is one hand" means waving one hand is the hinge.

But suppose, as you say, that this hinge is true.

Then, this hinge is true because "here is one hand" means waving one hand.

IE, "here is one hand" means waving one hand is true because "here is one hand" means waving one hand.

But this is an example of the Law of Identity. where the notion of truth is redundant. We say A is A. We don't say A is true because A.

The world is not divided ontologically into any parts, things over there, thoughts and feeling here, and there is no epistemic distance between me and this tree at all. There never was! — Astrophel

I can understand Phenomenology as part of a personal philosophy, but it seems limited if it made up the whole of a personal philosophy.

Phenomenology rejects rationalism and empiricism in favour of a person's "lived experience", relying on an intuitive grasp of knowledge free from any philosophical intellectualising.

For example, in Bracketing, one withholds any conscious opinion of what is perceived, taking no position as to the reality of what is seen, but simply to witness it as it presents itself.

I agree that Phenomenology can be insightful in our understanding about the relation of the mind to the sensations it experiences, but it seems insufficient not to question these sensations and only witness them.

Philosophy must surely be about questioning, not simply about phenomenologically accepting.

Key Ideas in Phenomenology by Marc Applebaum, 2012

One might ask, is General Motors real? — Astrophel

There are thoughts, language and the world, and there is the question as to how these relate.

The three theories of perception, Idealism, Direct Realism and Indirect Realism are primarily interested in the relation between thought and the world, though of course language is needed to express their different epistemological positions. What we do know for certain are our thoughts and sensations.

I cannot answer for the Direct Realist who knows that they directly perceive the world as it is through their sensations, as I don't agree with them.

As an Indirect Realist, I believe that there is a world independent of my observing it that has caused my sensations. I can never know, but I believe that there is, because it a satisfactory explanation for the sensations that I experience. What is real is a mystery, a world of things-in-themselves. I believe a real world exists, but only because this is the most satisfactory explanation.

As regards thought, the phenomenological approach makes sense. In part by removing the Cartesian separation between the mind and the mind-independent and in part by removing the problem of the unknowable thing-in-itself. Phenomenology attempts to create the conditions for the objective study of what is usually regarded as subjective, our judgements, perceptions and emotions of our conscious experienced sensations. Phenomenology rejects both Rationalism and Empiricism in favour of the person's lived experiences.

As regards language, linguistic idealism makes sense. Language is not contingent on the world, but rather language underpins the world that we know. It is not the case that there are objects in the world that are nameable within language, but rather the objects in our world exist because they are named in the language that we use to describe them. An object being named can only exist within its context as a logical semantic part of the sentence it is within. As you say, language does stand for the world, but also "stands in" for the world. When Derrida wrote "there is nothing outside the text" some have interpreted this as linguistic idealism, which denies the existence of a real-world outside language. Wittgenstein as well said that he had come to believe that thoughts and language were two aspects of the same thing, in that we can only think using language.

We don't know for certain how thoughts, language and the world relate, but for me, a combination of Indirect Realism, Phenomenology and Linguistic Idealism seems to be a sensible combination.

There is this impossible epistemic and thus ontological distance between knowledge and the world, until, that is, this distance is closed. — Astrophel

There seems to be three main theories of perception: Idealism, Direct Realism and Indirect Realism.

For the Direct Realist, i) the external world exists independently of the mind (hence, realism) ii) and we perceive the external world directly (hence, direct). For the Indirect Realist, i) the external world exists independently of the mind (hence, realism) but ii) we perceive the external world indirectly, via sense data (hence, indirect).

In a sense we all start off as Direct Realists. As you say, in the world of infancy, the world is not something that has to be discursively determined. For the child, there is no psychological distance between their immediate sensations and the object of their sensations
.
But later, language introduces us to spatial and temporal concepts, such as near and far, above and below, before and after. These concepts make us to look more closely at the world, and philosophically question more deeply their meaning.

Some then become Indirect Realists, conscious of a distance between our sensations and the object of these sensations. Some remain Direct Realists.

There is the question about the role of language in distancing the language user to their world.. As the Direct Realist directly perceives the world as it is, there is no distance between themselves and the world. As the Indirect Realist only indirectly perceives the world as it is, there is a distance between themselves and the world. As both the Direct and Indirect Realist use the same language, it does not seem that it is language that is opening up a distance between the observer and the world.

I would rather agree with the world of Heideggerian or MP's, of which the structure or existence is disclosed or revealed by language. — Corvus

As Wittgenstein wrote, Moore knows that the earth existed long before his birth, and we all know the same as he (OC 84).

I only know about the earth because of language.

A person without language (suppose they had been born on a desert island and raised by Mona monkeys) could not know about the earth.

The problem is, how can I know about something that is independent of language when I can only know about it within language?

For example, in what sense does "earth" in language capture the reality of the earth, being 12,714 km in diameter and having a mass of 5.9722 × 10^24 kg.

You're going a bit too far. My point is that when referring to truth, Wittgenstein is not only thinking in terms of traditional propositions. He applies truth to hinges, too. This is in reference to my discussion with Banno. The truth is built into the actions. The actions show their truth. — Sam26

A historical individual or institution decided that when someone waves one hand the action is to be named "here is one hand", rather than "here are five fishes", for example. Similar to JL Austin's performative utterance.

With the passage of time, that "here is one hand" indicates the action of waving one hand is now beyond doubt, and is therefore a hinge.

Years later, Moore waves one hand and says "here is one hand"

The proposition "here is one hand" is true if and only if Moore waves one hand.

The action of waving one hand shows the truth of the proposition "here is one hand"

But the proposition "here is one hand" is not the hinge that is exempt from doubt.

Therefore, the action of waving one hand doesn't show the truth of the hinge.

The hinge that is exempt from doubt is that the proposition "here is one hand" indicates the action of waving one hand.

The hinge is neither true nor false. The hinge enables truth and falsity in the language game.

The world is totally separate from us, existing on its own never saying anything at all. — Corvus

You believe that the world is totally separate to us.

However, this was not the case for Wittgenstein.

According to GEM Anscombe in her paper "The Question of Linguistic Idealism", she considers Wittgenstein to be a partial linguistic idealist.

Partial, in that for Wittgenstein some things don't depend on linguistic practice, such as numbers, horses, wolves, days, etc, whilst some things do depend on linguistic practice, such as rules, rights, promises, etc.

Linguistic idealism is the position that our language does not describe an empirical reality that we are aware of through our sense perceptions, but rather our language determines what kind of contact we have we the reality of the world. Linguistic Idealism undermines the traditional Realist/Idealist debate.

For Wittgenstein, the world is not totally separate to the language that we use to describe it.

My point is that OC 206 says, "If someone asked us 'but is that true [referring to a hinge]?' we might say 'yes' to him..." — Sam26

OC 206. If someone asked us "but is that true?" we might say "yes" to him; and if he demanded grounds we might say "I can't give you any grounds, but if you learn more you too will think the same"

In other words, if someone asked me "is it true that hinges are beyond doubt", I might say "yes".

If someone asked me "is it true that one feels pain when stung by a wasp", I might say "yes"

The truth is that one feels pain when stung by a wasp. It is not the pain that is true.

The truth is that hinges are beyond doubt. It is not the hinge that is true.

Language alone cannot reveal the whole structure of the world. — Corvus

But is what Wittgenstein believed?

Is it not the case that Wittgenstein believed that our language "is" our world, where the world is embedded in language through the hinge proposition?

Part of the difficulty is translating experience, the anecdotal and intuition into the formula of philosophy arguments. — Jack Cummins

Introduction, Body, Conclusion.

Perhaps a Body of four sections.

In support:
Section one of 400 words - Ghandi. "There is no path to peace; peace is the path."
Section two of 400 words - Erasmus of Rotterdam. Perhaps the foremost humanist writer of the Renaissance, and arguably also one of the foremost philosophers of peace.
Section three of 400 words - Bertrand Russell. Established the Bertrand Russell Peace Foundation. Launched in 1963, the Foundation was established to carry forward Russell's work for peace, human rights and social justice.

Counterargument:
Section four of 400 words - Nietzsche. Controversially valorizes struggle and war as necessary ingredients of human flourishing.

Section one as typical:
20 words as introduction
180 words just describing Ghandi's approach to peace. See https://www.mkgandhi.org/articles/fighting-for-peace-the-Gandhian-way.php
180 words giving your personal reasons why Ghandi was right. Here you include your own experiences and thoughts.
20 words as summary

This would make up an academic philosophical essay

There is this impossible epistemic and thus ontological distance between knowledge and the world, until, that is, this distance is closed. — Astrophel

But how can it be closed?

Our only direct knowledge is that of the sensations in our five senses.

We perceives shapes and colours, relations and quantities, which are clearly not the thing in the world.

From these sensations alone we infer a world that has caused these sensations

We can only make inferences when moving from the epistemology of our sensations to the ontology of a presumed world, but inference is not knowledge

Even though we only know our own sensations, there is an intersubjective agreement about things like the Moon, but is this public agreement about our intersubjective sensations or about a thing in the world causing these sensations?

Jack, you know you are one of my favorite people, but civilization as we know it may collapse — Athena

The good thing about a philosophical essay is that the author needs to defend their thesis using a clear and well structured argument, critically analyse the evidence and show that their premises are true and that their argument is valid.

Like the formal logic cannot capture or cope with the whole reality, language alone cannot capture or understand the world. — Corvus

Yes, but perhaps for a different reason.

There is language and there is the world.

For the Direct and Indirect Realist, there is a world that exists independently of any human observer. It would seem that for the Direct and Indirect Realist, language alone cannot fully capture or understand the world.

But for Wittgenstein, what is the relation between language and the world?

It seems to me that for Wittgenstein, language "is" the world.

It is not the case that the proposition "here is one hand" is a representation of a world or corresponds to a world, but rather the world is embodied in "here is one hand".

In a sense, a similar concept to that of the Indirect Realist who doesn't perceive a representation of the colour red but directly perceives the colour red.

374. We teach a child "that is your hand", not "that is perhaps (or "probably") your hand". That is how a child learns the innumerable language-games that are concerned with his hand. An investigation or question, 'whether this is really a hand' never occurs to him. Nor, on the other hand, does he learn that he knows that this is a hand.

There is nothing the other side of a world embodied in language.

"Here is one hand" is a hinge proposition not because it is needed to enable a language game that can represent or correspond with a world, but because the world is embodied in the hinge proposition.

What are the implications? We can only understand the world using language. But if the world is our language, and language cannot understand itself, then this inevitably puts a limit on our understanding of the world.

Above is not a hinge proposition, but it is the absolute true fact (which is verified via the logical reasoning and reality), and I don't doubt it at all. It is exempt from doubting. — Corvus

Wittgenstein defines what we call the hinge proposition as being a proposition that is exempt from doubt.

OC 341. That is to say, 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.

For Wittgenstein, if "here is one hand" is a hinge proposition and therefore exempt from doubt, there is no reason why "here is no hand" must also be a hinge proposition and therefore exempt from doubt.

Similarly, "here is the Jackpot", "here is no Jackpot", "here are winnings" and "here are no winnings" must also all be hinge propositions and therefore exempt from doubt.

These hinge propositions may be combined into language games:
1) "here is the Jackpot" and "here are winnings"
2) "here is the Jackpot" and "here are no winnings"
3) "here is no Jackpot" and "here are winnings"
4) "here is no Jackpot" and "here are no winnings"

Your particular case is 2) "I didn't win the jackpot"

It is true that your proposition "I didn't win the jackpot" is exempt from doubt.

But I assume that combining two hinge propositions doesn't form a single new hinge proposition.

This is perhaps why "I didn't win the Jackpot" is not a hinge proposition, even though exempt from doubt, as it is a combination of hinge propositons.

As I understand it:

A hinge proposition enables a language game.

A hinge proposition must be exempt from doubt in order to ground the language game.

A language game is contingent because it describes how the world is.

In the mind of the user of the language game, it would be wrong to say that this language game either represents or corresponds with the world. It would be more accurate to say that this language game "is" their world, meaning that there is no other world outside the language game itself.

In other words, we use the language game to understand the world, and this world is nothing other than the language game itself.

To clarify, this event is about 'Philosophy Writing'. So, that is the 'broad category'. — Amity

You are saying that rule 4 should have read "must fall under the broad category of philosophy writing"?

Moreover, we can't forget OC 206, where Wittgenstein points out that if someone asked, "but is that true" (referring to hinges), we might respond "yes," — Sam26

There is a difference between asking is it true that "here is one hand" and asking "is it true that here is one hand".

Asking is it true that "here is one hand"
See OC 204
"Here is one hand" is a hinge proposition because it is a rule that constitutes the language game. The end is not a certain proposition that strikes us as true, it is our acting.


Asking "is it true that here is one hand".
See OC 206
If someone asks us "is it true that here is one hand", we may answer "yes, but I cannot give you any grounds". The expression "here is one hand" in this instance is not being used as a hinge proposition. It is not being used as a rule that constitutes the language game but is being used as a part of the language game.

To my understanding, "here is one hand" can be used both as a rule that constitutes a language game and as an expression within a language game. The first is not truth-apt, but the second is.

So the world is what is said by true sentences. — Banno

Hence, they are not propositions that set out how things are in the world, but propositions that set out how we are to talk about the world. They are the rules that set up and constitute our language games. They don't represent the world; they set the terms on which representation takes place. — Banno

How does Wittgenstein overcome what seems to be a circularity?

1) Hinge propositions are the rules that constitute our language game.

2) Within this language game there can be representations of the world.

3) The world is what is said by true sentences.

Removing any reference to "world"

4) Hinge propositions are the rules that constitute a language game that can represent what is said by true sentences.

It seems that such a language game is self-referential.

However, perhaps the OP could be improved to lessen confusion. — Amity

@Moliere

As rule 4 says "must fall under the broad category of a philosophical essay", this seems to suggest that what is required is a philosophical essay.

There are many examples of how to write a philosophical essay on the internet, but taking University College Cork as an example.

Note 1: "philosophy paper" is synonymous with "philosophical essay"
Note 2: a philosophical essay is not about flowery language or story-telling technique.
Note 3: start with a proposition to be proved

Writing a Philosophical Essay: A Brief Tutorial

II. What is a philosophy paper?

Philosophical essays prove some point through the use of rational argument. A philosophical essay is not about flowery language, story-telling techniques, or surprising the reader. The beauty of a philosophical essay is found in your ideas; the language that you use is only a tool for conveying these ideas to the reader. The art is in proving one’s point clearly.

The philosophical essay generally follows a very simple structure:

1. State the proposition to be proved.
2. Give the argument for that proposition.
3. Show that the argument is valid.
4. Show that the premises are true.
5. Consider an objection to your argument and respond to that objection.
6. State the upshot of what has been proven. (Martinich, A.P. (1996) Philosophical
Writing. Oxford: Blackwell Publishing. p. 53.)

However, this June event is wider. It is about philosophy writing. — Amity

I agree that there is a difference between philosophy writing and a philosophy essay, but rule 4) does say it must fall under the broad category of a philosophical essay.

4) Must fall under the broad category of a philosophical essay. The Essay's Title and Topic are chosen by the author. The philosophical viewpoint can be academic or less formal. It should be systematic with an Introduction, Main Body and Conclusion. This is non-fiction. Poetic expression is allowed if it completes or supports the philosophical exploration.

@Moliere does conclude by saying "Resources were requested for help on what exactly an academic philosophy essay should look like, and provided by @Amity so I've appended them here:

The first link is "How to write a crap philosophy essay"
The second link "Guidelines on writing a Philosophy Paper" notes "don't try to establish any earth shattering conclusions in your 5-6 page paper."
The third link is "An academic guide to planning essays"

All this suggests that this writing challenge is looking for a philosophy essay rather than philosophy writing.

Remember, it's all a story...with or without a definite conclusion. Open ended...for further exploration. Philosophy is a Conversation. Here, writers and readers can be in close dialogue or a wild dance — Amity

Yes, but I am not sure about "with or without a definite conclusion".

A philosophy essay is about making a claim and then defending it.

There must be a thesis, such as "I intend to argue that J.J.C. Smart’s criticism of rule utilitarianism is correct because, as he argues, there are clearly some cases where it is optimific to break a generally optimific rule"

There must be a conclusion, such as "I have argued that J.J.C. Smart’s criticisms of rule utilitarianism are correct"

They believe that doubts are also simulation — Corvus

I cannot doubt that I doubt, even if I am a simulation.

Folks who believe life could be simulation could doubt if the Earth exists. — Corvus

True, but they don't doubt that they have the doubt as to whether the Earth exists.

I have heard about "lived experience", but not "lived truths". What is "lived truths"? — Corvus

That was my question to @Sam26 who wrote "hinges are about lived truths".

Maybe I am misunderstanding the point here. It seems to me that we misunderstand and misuse words all the time...When Descartes starts doubting away in the Meditations, he doesn't stop writing in French. — Count Timothy von Icarus

As a starting position, Wittgenstein in On Certainty did write that some propositions are exempt from doubt.

OC 341 That is to say, 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.

You point out that in ordinary language we do doubt the meaning of some words all the time, so where in ordinary language are those propositions that are exempt from doubt?

In the Meditations, Descartes was discarding all beliefs that were not absolutely certain. He was not discarding all words about which he was not absolutely certain. I can doubt ever getting a good meal in Paris without doubting the meaning of the words "I can doubt ever getting a good meal in Paris". I can use words whose meaning I am certain about to express ideas about which I am not certain.

We may doubt the meaning of some words all the time but we never doubt the meaning of all the words all the time.

As an example consider the sentence "it seems to me that we misunderstand and misuse words all the time."

If I doubted the meaning of every expression within the sentence, the sentence as a whole would be meaningless to me, making it impossible for me to respond to it. But I am responding to it, meaning that in practice I am certain as to the meaning of the words used.

If I doubted the meaning of every expression within the sentence, language as a means of communication would be impossible.

For example, in the sentence "Inaonekana kwangu kwamba hatuelewi na kutumia vibaya maneno kila wakati." there is not a single expression whose meaning is exempt from doubt in my mind

But we know that language does work in enabling communication, therefore there must be some expressions within our language exempt from doubt, as Wittgenstein wrote.

It may be the case that in a sentence there are words whose meaning I am not certain about,
but in that situation I can refer to a dictionary, which may then remove any uncertainty as to its meaning.

If I find the meaning of a word uncertain, I would reach for the Dictionary, not stop writing.

Hinges are about lived truths, — Sam26

Wittgenstein wrote that some propositions are exempt from doubt.

OC 341 That is to say, 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.

Where does Wittgenstein write that those propositions which are exempt from doubt are "lived truths"?

But all language games are embedded in the world; the counting of apples involves apples and charts, the building involves blocks and slabs. It is not peculiar to hinge propositions to be about how things are - all propositions do that. — Banno

The language game that includes the sentence "Sherlock Holmes lives at 221B Baker Street" is embedded in a world of literature rather than a world outside literature.

It seems that Wittgenstein agrees that there is a world but never specifies exactly where this world exists.

My understanding is that in a sentence such as "here is one hand and in the hand is a mug and in the mug is an elephant", not only is every part a hinge proposition but also every part can form a T-sentence.

Each part, i) "Here is one hand", ii) "in the hand is a mug" and iii) "in the mug is an elephant" has to be a hinge proposition in order to allow the rest of the language game to take place.

That a language game is embedded in the world means that there is a correspondence between the language game and the world. If the language game was not embedded in the world, then there could be no correspondence between the language game and the world.

That there is a correspondence means that the T-sentence can be formed from each part, i) "here is one hand" is true IFF here is one hand. ii) "in the hand is a mug" is true IFF in the hand is a mug, iii) "in the mug is an elephant" is true IFF in the mug is an elephant.

In a T-sentence, what does "true" mean? It seems to mean that in the event that something is the case in the world, something does obtain in the world or something is a fact in the world, then that fact can be described by language.

What are the philosophical / epistemological / logical grounds for hinge propositions being exempt from doubt? — Corvus

What does "hapa kuna mkono mmoja na katika mkono huu kuna kikombe" mean?

I can tell you that this is a coherent language, where each part is fully in context with all the other parts of the sentence.

The question is, where is the key that unlocks the meaning of the whole?

Can the key be found inside the text, or can it only be found outside the text?

Only if the meaning of each part was exempt from doubt in your mind could you understand the meaning of the whole.

Any part whose meaning is exempt from doubt in your mind can be called a hinge proposition.

We treat hinges as true for practical reasons. And the fact that they're not doubted demonstrates they don't play the true/false game. We accept them as true, period. — Sam26

There are many different definitions of "truth" (SEP - Truth)

Wittgenstein did not consider the hinge proposition as being true.

OC 204 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, not yet false.

What definition of truth are you using when you say that hinge propositions are "true"?

So far, I've referenced only one philosopher on the subject, which has not been of general interest to philosophers, and I'm hard put to find a rebuttal. — Vera Mont

Can you slightly adjust the wording of your thesis such that you can find three philosophers that support it and one philosopher that opposes it?

If you can, then:

Write the 200 word Introduction in the future tense after you have written the Body.

Write the 200 word Conclusion in the past tense after you have written the Body.

Imagine a Body of four sections, each of 400 words. The first three sections based on three philosophers that support your thesis. The fourth section based on a philosopher that opposes your thesis.

Consider a typical 400 word section. An introduction of 20 words written after you have written the body of the section. A summary of 20 words also written after you have written the body of the section.

This leaves 360 words for the body of the section. The first 180 words describing the philosopher's position regarding your thesis. The second 180 words giving your thoughts about the philosopher's position, including why you think their argument is valid and where you think their argument can be improved.

Would this work?

Both what makes hypothesis and any possible experience that could validate or falsify it intelligible are already framed by the hinge conviction. — Joshs

:up: Continuing:

For example, in a language game, "here is one hand and the hand is holding a mug of coffee", "here is one hand" is the hinge proposition and "the hand is holding a mug of coffee" is the ordinary (non-hinge) proposition.

Being an ordinary proposition, "the hand is holding a mug of coffee " can be true or false, depending on whether or not it corresponds with what is actually the case in the world.

But the truth-aptness of this ordinary proposition is only intelligible if the language game has been founded on a hinge proposition.

Because, if a language game was not founded on a hinge proposition, and there were no hinge propositions, then the meaning of each expression would depend on its context within the language game.

IE, the meaning of "the hand" would depend on its context "the hand is holding a mug of coffee", and the meaning of "holding a mug of coffee" would depend on its context "the hand is holding a mug of coffee". Although this language game might be perfectly coherent, it would be ultimately be nonsensical.

For a language game to make sense, within the language game there must be something extra-linguistic that founds the language game within the world, and these things are the hinge propositions.

Hinge propositions are extra-linguistic, even they they are part of the language game.

My idea is that you can doubt on anything and everything if you choose to do so. Even the fact "Paris in France." could be doubted under the simple syllogism. — Corvus

"Exempt" is normally used for the situation where an object is free from liability, duty or restriction. Hence it seems not a proper word to use for doubt. — Corvus

In a language game are ordinary propositions such as "it is raining" and hinge propositions such as "here is one hand".

All ordinary propositions can be doubted. I say "it is raining". You say "are you sure?"

The whole point of a hinge proposition is that it is exempt from being doubted. Doubting a hinge proposition cannot even be considered.

Hinge propositions, like the earth has existed for more than ten minutes or "I have two hands” —aren’t true in the way we typically think of propositions being true (i.e., through evidence, justification, or correspondence to reality). — Sam26

"It is raining" is true1 IFF it is raining

You say that hinge propositions are true2, where true1 and true2 are different.

But how have true1 and true2 been defined? A proposition that corresponds with a fact is true1. A proposition that is exempt from doubt is true2 (OC 341)

The definition of true1 is well established, and there are many references in the literature. However, the definition of true2 does not seem to be established at all, and I haven't found any references to it in the literature.

It seems that true2 is your personal definition. There is nothing wrong with inventing definitions, in fact I invented the definition "peffel". However, no-one other than me uses it.
===============================================================================

Someone might ask you "Is it true that bishops move diagonally?" and you reply, "Yes," but does this mean that it's true in an epistemological sense? No, — Sam26

In other words, "bishops move diagonally" is true IFF bishops move diagonally.

Truth is the relation between the proposition and the fact.

Truth is neither the proposition nor the fact.

Seems to be delicate nuance in the uses, but the gist of the claim seems it is impossible to doubt? — Corvus

Not really. "Impossible to doubt" has a different meaning to "exempt from doubt" OC 341

For example, "food is exempt from vat".

How would you replace "exempt" by "impossible" in the above sentence?

What is the illocutionary difference between the two expressions? — Corvus

Cannot doubt vs exempt from doubt

My previous example was:

i) That Paris is in France cannot be doubted means that we started with a doubt and then concluded that our doubt was baseless.
ii) That Paris is in France is exempt from doubt means that we are not even allowed to doubt at all.

But in addition - cannot could mean:
i) not allowed - as in you cannot speak in an exam
ii) not able - as in you cannot climb Mount Everest because you are unfit

Exempt could mean
i) not applied - as in food is exempt from vat
ii) not present - as in summer nights are exempt from frost

I understand W said that hinge propositions / certainties cannot be doubted or not allowed doubting — Corvus

In OC 341 Wittgenstein writes "That is to say, 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."

"Exempt from doubt" has a different meaning to "cannot be doubted."

Is there anywhere in On Certainty where Wittgenstein writes that hinge propositions cannot be doubted?

There are different types of doubts too i.e. rational doubts based on reasoning, and psychological doubts based on feelings, emotions and beliefs. — Corvus

True, but on a thread about Wittgenstein's On Certainty, the question is, how did Wittgenstein describe doubt?

The other language game of truth is one of foundational convictions. The latter convictions are accepted as true and cannot be sensibly doubted. — Sam26

There is a difference in meaning between i) hinge propositions cannot be doubted and ii) hinge propositions are exempt from doubt

Wittgenstein says "exempt from doubt"

OC 341 That is to say, 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.

For example:
i) That Paris is in France cannot be doubted means that we started with a doubt and then concluded that our doubt was baseless.
ii) That Paris is in France is exempt from doubt means that we are not even allowed to doubt at all.