These two come off as contradictory:
1. There are only blocks within the game of building.
2. There is more than language; there certainly are blocks. — Fire Ologist

You have misunderstood.

The bit you miss is that language games and language are not the same.

A language game - moving blocks, counting apples - is not confined to language.

So, "There are only blocks within the game of building" is not confined to language. It directly invovles blocks.

And so a language game involves more than just language.

How will you respond?

To address the form of life in your Gavagai example would require a linguist who is attempting to interpret the language not of a foreign people but of a lion. The lion represents the being with a differing form of life, who, per Wittgenstein's clear statement, we would not understand. The Gavagai example is no different from French to English to German. That is, all those folks share a form of life. We're looking for those who don't. — Hanover

This supposes that the we and the French participate in the same Form of Life...

Are you confident in that? :wink:

Even less so with ChatGPT, since it participates in a form of life in the way of a block or an apple.

So my problem here is that if we're going to say that we're taking as a hinge belief the uniformity of thought processes among various people, why not just make it a hinge belief that we truly have the same beetle metaphysically. — Hanover

That's certainly not something I'm suggesting. "The unity of thought processes" cannot be confirmed in any other way than by what people say and do. It's not a "hinge belief" that brings about any unity. The unity is seen in what is said and done, and that alone.

Hence, we do not have to agree on a hinge belief about gavagai in order to go on the hunt. It;s the doing that counts.

And so a language game involves more than just language. — Banno

I think I see. And thanks for the reply.

Language itself is not the game. Interesting. Because “a language game involves more than just language.”

Does this then make sense:

In the case of building with blocks, we can construct a language game wherein two people work together and one yells “block” and as the other person hears the language and plays the game of building the other then brings the block because he heard “block” and knows the game. The 1. language game of building here involves 2. language and 3. blocks (likely among other things and more language and more complex gaming). But it takes 2 and 3 before 1 can emerge.

And when you say “we are always already in a language” (which I think you said a few times), does that mean we are always sort of given into a language game, already playing by communicating through language, or does it mean something else, like in a language but not in a language game? I took it to mean we are already in a game when we are thinking/communicating in a language about the world.

What do you mean by “already in a language” then?

For instance, I don't think one has the demonstrate that a faculty of noesis exists in order to point out that presupposing as a given that it doesn't seems unwarranted. — Count Timothy von Icarus

You are presupposing that it is a mere presupposition. How about thinking that in the absence of any possibility of demonstrating that a faculty of noesis exists, the conclusion that is does not is warranted? Or more modestly a pragmatic conclusion that if it cannot be demonstrated to exist then it is of no philosophical use?

You are presupposing that it is a mere presupposition. How about thinking that in the absence of any possibility of demonstrating that a faculty of noesis exists, the conclusion that is does not is warranted? Or more modestly a pragmatic conclusion that if it cannot be demonstrated to exist then it is of no philosophical use?

This is what the eliminativist says about consciousness. Of course there are demonstrations, that's why it was the dominant theory. But if one presupposes epistemic standards that remove it by default (much as behaviorism and eliminativism make consciousness epiphenomenal by default) one hasn't done much of anything except beg the question.

And that's not really the point. If such a faculty is accepted as a hinge proposition, it shows that the theory of hinge proposition itself is not presuppositionless, but fails to obtain given certain assumptions.

Where the empiricist tradition has ended up, bottoming out in denying consciousness, denying truth as anything more than a token in "games," etc., along with the radical skepticism engendered by arguments from underdetermination, which are undefeatable given its premises (likewise for Hume's attack on induction), is arguably a reductio conclusion against the initial assumptions.

This is what the eliminativist says about consciousness. — Count Timothy von Icarus

Why change the subject to consciousness. Consciousness is obviously amply demonstrated.

And that's not really the point. If such a faculty is accepted as a hinge proposition, it shows that the theory of hinge proposition itself is not presuppositionless, but fails to obtain given certain assumptions. — Count Timothy von Icarus

Are you suggesting that noesis has been accepted as a hinge proposition? If so, what evidence do you have that that is so?

Noesis has not been demonstrated to exist. If you disagree then show the evidence that it exists. And note, I am treating the belief in noesis as the idea that our metaphysical intuitions can be known to give us, or at least sometimes can be known to give us, a reliable guide to the nature of realty―not reality as sensed, which is obviously intelligible to us, but reality in a purportedly absolute or ultimate sense.

Hume's attack on induction — Count Timothy von Icarus

Hume did not attack induction―he merely pointed out that inductive reasoning is not logically necessary in the way that valid deductive reasoning is.

Much of this has little to do with OC.

This supposes that the we and the French participate in the same Form of Life...

Are you confident in that? :wink:

Even less so with ChatGPT, since it participates in a form of life in the way of a block or an apple. — Banno

So a rabbi and an anthropologist walk into a bar, and Ludwig asks "why are you here?" They each say "it's the right time to be here. " And they don't communicate because their forms of life vary, despite the syntactically correct response, yet the question and answer were entirely different to each.

The question then is where is this form of life? You say, I don't care where it is, I just need to know that it is. I see it in the way the anthropologist looks at and speaks of evolution and the way the rabbi prays and reads his Talmud.

But my response is it absolutely matters where it is because unlike meaning of language being use, form of life is not in behavior. It is assumed from behavior, but not caused by behavior, meaning a rabbi who mimics an anthropologist to avoid persecution remains a rabbi.

Form of life is inherent in the being. ChatGPT given time will be spoken from the perfect robot, whose behavior will perfectly mimic the human's. I contend it will not use langauge. It is a lion.

A thought experiment: would a community of AI generators that speak publicly create langauge because they all have the same form of life?

Would their language be just as much language as the one we speak?

Yep.

358. Now I would like to regard this certainty, not as something akin to hastiness or superficiality, but as a form of life. (That is very badly expressed and probably badly thought as well.) — OC

This last parenthetical sentence ought give us pause when considering the usefulness of "form of life".

I can't follow your reasoning here, sorry. Was that your point?

The form of life is what we do. It's not here nor there. Consider:

355. A mad-doctor (perhaps) might ask me "Do you know what that is?" and I might reply "I know that it's a chair; I recognize it, it's always been in my room". He says this, possibly, to test not my eyes but my ability to recognize things, to know their names and their functions. What is in question here is a kind of knowing one's way about. Now it would be wrong for me to say "I believe that it's a chair" because that would express my readiness for my statement to be tested. While "I know that it..." implies bewilderment if what I said was not confirmed. — OC

The form of life as "a kind of knowing one's way about".

Are you after something about the supposed missing internal life of a community of AI's? Do you think I am suggesting that there is no "internal life" for the users of "gavagai"? I'm not; I'm just pointing out that you may get your rabbit stew regardless of that internal life. Or not.

Oh, I don't think 'moving blocks' is a language game at all. You can do that without any form of language. That's probably what prompted language to occur - the need to systematize bare action.

I don't think its arguable, either. The use of the words (or, the fact of, i guess) is clearly a language game. Simply moving objects isn't. No?

You are familiar with the example, from PI? There is presumably a difference between moving blocks and moving blocks following an instruction.

Language itself is not the game. Because “a language game involves more than just language.”

Does this then make sense:

In the case of building with blocks, we can construct a language game wherein two people work together and one yells “block” and as the other person hears the language and plays the game of building the other then brings the block because he heard “block” and knows the game. The language game of building here involves language and blocks (likely among other things and more language and more complex gaming). But it takes language and blocks before the language game can emerge. — Fire Ologist

3 distinctions to grapple with? 1. Language, 2. the world to which language is applied, in a 3. language game.

Or

The use of the words (or, the fact of, i guess) is clearly a language game — AmadeusD

This sounds like using language itself is a game (maybe because it comes with syntax, or subject/predicate functioning)? Or is language still not itself a game, and we can talk about language without its gaming application?

I think these are valid questions, no? I certainly don’t know how to address.

This sounds like using language itself is a game (maybe because it comes with syntax, or subject/predicate functioning)? — Fire Ologist

This seems true even without Wittgenstein's insights. We play games with our interlocutors. Some explicit uses would be sarcasm or hyperbole.

Yes, i am familiar. I agree, but the actual moving of the object doesn't seem to me part of the game. Like orange slices at half time.

but the actual moving of the object doesn't seem to me part of the game. — AmadeusD

I don't understand this. If "Block" did not result in the apprentice moving a block, then we have no game. Moving the blocks is constitutive of the block game.

I disagree. There is nothing beyond "I should now do x" contributing to the game, in my view. Moving blocks is not something we do with words (other than to denote what was moved, in the case of a discussion about language games hehehe)

Moving blocks is not something we do with words — AmadeusD

Yeah. The master moves blocks by giving a command as much as by pushing them with their hand. I'm sorry you can't see that. It prevents you participating fully in this discussion.

That's probably a bit too strong. I gather you want something in the mix about agency and instrument? Perhaps we might agree that under a certain description, it's the apprentice who moves the block, yet under another description, it's the master? Adopting the idea that an intention varies with a description, form Davison and Anscombe...

Your first comment: Yes, not only strong, semi-nonsensical. But this second one clarifies, so...

it's the apprentice who moves the block, yet under another description, it's the master? — Banno

I would be hard pressed, but i can certainly see my way to it, yes!

This is an updated version of my paper with corrections. The edits tighten the Gödel side (incompleteness + no from-within proof of consistency) and clarify the analogy as a limit on internal vindication, not “axioms can’t be proved.” That keeps the hinge–Gödel connection exactly as I intended.

Wittgenstein's Hinges and Gödel's Unprovable Statements

Abstract

In Ludwig Wittgenstein's final notes, published posthumously as On Certainty (1969), Wittgenstein introduces the concept of hinge propositions as foundational certainties that lie beyond justification and doubt (OC 341-343). These certainties support our language-games and epistemic practices, offering a distinctive perspective on knowledge that challenges traditional epistemology's demand for universal justification. I argue for a structural parallel between Wittgenstein's hinges and Gödel's 1931 incompleteness theorems, demonstrating that any consistent, effectively axiomatized system capable of arithmetic contains arithmetical truths that cannot be proven within the system. Both thinkers uncover fundamental limits to internal justification: Wittgenstein shows that epistemic systems rest on unjustified certainties embedded in our form of life, while Gödel shows that any consistent, effectively axiomatized system strong enough for arithmetic has statements it cannot settle from within and cannot, from within itself, prove its own consistency. Rather than representing failures of reasoning, these ungrounded foundations serve as necessary conditions that make systematic inquiry possible. This parallel suggests that foundational certainties enable rather than undermine knowledge, pointing to a universal structural feature of how such systems must be grounded. This analysis has implications for reconsidering the nature of certainty across epistemology and the philosophy of mathematics.

Introduction

We often perform actions without hesitation, such as sitting on a chair or picking up a pencil, without questioning the existence of either. This unthinking action illustrates Wittgenstein's concept of a hinge proposition, a fundamental certainty that supports our use of language and epistemological language-games. Wittgenstein compares hinge propositions to the hinges that enable a door to function; these certainties provide the underlying support for the structures of language and knowledge, remaining unaffected by the need for justification.

Wittgenstein's hinges bear a remarkable resemblance to Gödel's incompleteness theorems, revealing unprovable mathematical statements. This resemblance points to deeper questions about how both domains handle foundational issues. Both Wittgenstein and Gödel uncover limits to internal justification, a connection I will examine.

Traditional epistemology often misinterprets hinges by forcing them into a true/false propositional role, neglecting their foundational status embedded in our epistemic form of life. These bedrock assumptions precede argument or evidence, forming the foundational elements of our epistemic practices. Similarly, Gödel’s incompleteness theorems show that any consistent, effectively axiomatized system capable of arithmetic contains arithmetical truths unprovable within the system and cannot, from within itself, prove its own consistency.

This connection is significant because it highlights the boundary between what counts as bedrock for epistemic and mathematical systems. Both rest on certainties that lie beyond justification, certainties that are not flaws in reasoning but necessary foundations that make knowledge claims possible. This paper argues that ungrounded certainties enable knowledge, rather than undermining it, and that hinges and Gödel's unprovable statements serve a similar purpose. By examining the parallels between Wittgenstein and Gödel, particularly the role of unprovable foundations and the need for external grounding, this paper sheds light on the nature of certainty in our understanding of both epistemology and mathematics.

Section 1: Hinges and Their Foundational Role

Wittgenstein's concept of hinge propositions is crucial to his thinking, particularly in the context of epistemology. In On Certainty, Wittgenstein introduces the idea of hinges as certainties that ground our epistemic practices. While Wittgenstein never explicitly distinguishes types of hinges, his examples suggest a distinction between nonlinguistic and linguistic varieties, revealing different levels of fundamental certainties.

Nonlinguistic hinges represent the most basic level of certainty, bedrock assumptions that ground our actions and interactions with the world. These are not expressed as propositions subject to justification or doubt but embodied in unreflective action. For instance, the certainty that the ground will support us when we walk is a nonlinguistic hinge that enables movement without hesitation. Similarly, our unthinking confidence that objects will behave predictably, that chairs will hold our weight, that pencils will mark paper, represents this bedrock level of certainty. These hinges operate beneath the level of articulation, forming the silent background against which all conscious thought and language become possible.

Building upon this bedrock foundation, linguistic hinges operate at a more articulated but less fundamental level. These are certainties embedded within our language-games and cultural practices, often taking the form of basic statements like "I have two hands" or "The Earth exists." Unlike nonlinguistic hinges, these can be spoken and seem propositional, yet they resist the usual patterns of justification and doubt. Other examples include statements such as "I am a human being" or "The world has existed for a long time," assertions that appear to convey information but function more as structural supports for discourse than as ordinary claims requiring evidence.

These two types of hinges show how certainty operates at different levels in grounding knowledge. Nonlinguistic hinges form the deepest stratum, revealing the unquestioned backdrop that makes any form of questioning possible. Linguistic hinges, while still foundational, represent a layer above bedrock that anchors shared discourse within specific contexts. Both types resist justification, but their resistance stems from different sources: nonlinguistic hinges from their pre-rational embodiment in action, linguistic hinges from their structural role within our language-games.

Wittgenstein breaks with traditional epistemology here. Rather than viewing these certainties as beliefs requiring justification, he recognizes them as the ungrounded ground that makes justification itself possible. He notes, "There is no why. I simply do not. This is how I act" (OC 148). Doubting these hinges would collapse the very framework within which doubt makes sense, like attempting to saw off the branch on which one sits.

A crucial distinction emerges between subjective and objective dimensions of these certainties. While our relationship to hinges involves unquestioning acceptance, this certainty is not merely psychological. These assumptions are shaped by our interactions with a world that both constrains and enables our practices. The certainty reflected in our actions has an objective component, as it emerges from our shared engagement with reality and proves itself through the successful functioning of our practices.

This interpretation of hinges as operating at different foundational levels finds support in recent Wittgenstein scholarship, though it diverges from some prominent readings. Danièle Moyal-Sharrock argues that hinges are fundamentally non-propositional, existing as lived certainties rather than beliefs or knowledge claims (Moyal-Sharrock 2004). While my distinction between nonlinguistic and linguistic hinges aligns with her emphasis on the embodied, pre-propositional character of our most basic certainties, I suggest that some hinges do function at a more articulated level within language-games, even if they resist standard justification patterns.

Duncan Pritchard's interpretation emphasizes hinges as commitment-constituting rather than knowledge-constituting, arguing they represent a distinct epistemic category that enables rather than constitutes knowledge (Pritchard 2016). This view supports the parallel with mathematical axioms: both hinges and mathematical axioms function as enabling commitments that make systematic inquiry possible without themselves being objects of that inquiry. The mathematical case strengthens Pritchard's insight by showing how even formal domains require such commitment-constituting foundations.

This analysis extends beyond epistemology to reveal a striking parallel with Gödel's incompleteness theorems, which demonstrate analogous limits within formal mathematical systems. Just as Gödel showed that sufficiently strong systems face statements they cannot settle and cannot prove their own consistency from within, Wittgenstein's hinges reveal that epistemic systems rest on certainties that cannot be justified internally. This comparison suggests a fundamental structural limitation in rational grounding, whether in mathematics or human knowledge, and invites reconsideration of what it means for knowledge to be properly grounded.


Section 2: Gödel’s Unprovable Statements and a Hinge-Like Limit

Gödel’s incompleteness theorems (1931) mark hard limits within formal theories. In any consistent, effectively axiomatized system strong enough for arithmetic, there are arithmetical statements that are true under the standard interpretation but not provable by the system’s own rules; and no such system can, from within itself, prove its own consistency. These are structural limits, not defects of a particular axiom set, and they persist under extension: add new axioms to settle an undecidable statement and—so long as the strengthened theory remains consistent and comparably strong—new undecidable statements arise in turn.

This limitation mirrors Wittgenstein’s hinges in an important way. Just as hinges are certainties that are not justified by the very practices they enable, Gödel identifies a limit on internal vindication: even very strong formal systems have truths they cannot prove and cannot establish their own consistency from within. The point is not that axioms ought to be proven (axioms are adopted), but that every practice—including mathematics—runs on enabling commitments that do not receive their warrant from the inferential moves they make possible.

Independently of Gödel, formal theories begin with axioms that are adopted rather than proved. Gödel’s results then add a further limit: even once the axioms are fixed, some truths remain unprovable and the theory cannot certify its own consistency from within. Wittgenstein’s hinges play an analogous enabling role in our epistemic life: background certainties we do not arrive at by inference but that make inference possible.

Yet there is an important difference here: mathematical axioms are typically chosen for their elegance, consistency, and power to generate interesting mathematics, while hinges appear more embedded in contingent cultural and biological practices. Yet this difference strengthens rather than weakens the parallel. If even mathematics, often considered the paradigm of rigorous proof, requires unjustified foundational elements, how much more must everyday understanding rely on unexamined certainties? The universality of this structural requirement across domains as different as formal mathematics and lived experience suggests a fundamental feature of how systems of thought must be organized.

Both domains thus reveal that functioning without such foundational elements is implausible. Mathematical systems risk incoherence without axiomatic starting points, just as epistemic practices risk collapse without the bedrock certainties that Wittgenstein identifies. The parallel illuminates a shared structural necessity: systematic thought requires ungrounded foundations that enable rather than undermine the possibility of reasoning within those systems.


Section 3: Beyond Internal Justification: A Cross-Domain Analysis

Both Wittgenstein and Gödel reveal that justification operates within boundaries, where certain elements serve as foundations that cannot be further justified within their respective systems. Both thinkers expose a basic structural feature of systematic thought: the impossibility of a complete system of justification in either domain.

Traditional approaches to knowledge often assume that proper justification requires tracing claims back to secure foundations that are themselves justified. This assumption generates the classical problem of infinite regress: any attempt to justify foundational elements through further reasoning creates an endless chain of justification that never reaches secure ground. Both Wittgenstein's hinges and Gödel’s incompleteness results reveal why this demand for complete internal justification is not merely difficult but impossible in principle.

As Wittgenstein observes, "There is no why. I simply do not. This is how I act" (OC 148). This insight captures something crucial about the nature of foundational certainties: they are pre-rational in the sense that they precede and enable rational discourse rather than emerging from it. Hinges are not conclusions we reach through reasoning but lived realities that make reasoning possible. Similarly, mathematical axioms are not theorems we prove but starting points we adopt to make proof possible.

There is an important difference between these domains. Hinges emerge from contingent practices embedded in particular forms of life, while mathematical axioms are selected through systematic considerations within formal contexts. Hinges reflect the biological and cultural circumstances of human existence, whereas axioms reflect choices made for their mathematical power and elegance. If anything, this difference makes the parallel more compelling by demonstrating its scope: if even the most rigorous formal disciplines require unjustified starting points, the necessity of such foundations in everyday knowledge becomes even more apparent.

This cross-domain similarity reveals what appears to be a universal structural requirement. Systems of thought, whether formal mathematical theories or practical epistemic frameworks, cannot achieve complete self-justification. They require external elements that are not justified within the system but make systematic inquiry within that framework possible. Rather than representing failures or limitations, these unjustified foundations function as enabling conditions that make coherent thought and practice possible.

Recognizing this structural necessity transforms how we understand the relationship between certainty and knowledge. Instead of viewing unjustified elements as epistemological problems to be solved, we can understand them as necessary features that allow knowledge systems to function. Both mathematical proof and everyday understanding depend on foundations that lie beyond their internal capacity for justification, yet this dependence enables rather than undermines their respective forms of systematic inquiry.


Conclusion

I have argued for a fundamental parallel between Wittgenstein's hinges and Gödel's incompleteness results: both demonstrate that systematic thought requires ungrounded foundations. By examining how epistemic and mathematical systems share this structural feature, we gain insight into the nature of foundational certainties across domains of human understanding.

The parallel between these seemingly distinct philosophical insights suggests that the limits of internal justification are not accidental features of particular systems but necessary conditions for systematic thought. Recognizing this gives us a more realistic picture of how knowledge functions, not through endless chains of justification reaching some ultimate ground, but through practices and formal systems that rest on foundations lying beyond their internal scope.

Rather than treating these limits as problems in need of a cure, we should take them as structural conditions of inquiry. Wittgenstein’s hinges anchor our epistemic practices in the lived background of a form of life; in mathematics, axiomatic choices provide the starting points of a theory. Gödel’s incompleteness results mark the corresponding boundary on internal vindication: even with the axioms fixed, a system strong enough for arithmetic has statements it cannot settle and cannot, from within itself, prove its own consistency. Both lessons show that the demand for a completely self-grounding system is not merely difficult but misconceived.

I believe this perspective has broader implications for understanding certainty and knowledge. It suggests that the interplay between grounded and ungrounded elements is not a flaw in human reasoning, but a fundamental feature of how systematic understanding must be structured. By recognizing this necessity, we can develop more nuanced approaches to foundational questions in epistemology, philosophy of mathematics, and potentially other domains where the relationship between systematic inquiry and its enabling conditions remains philosophically significant.




References

Gödel, K. (1931). Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I. Monatshefte für Mathematik und Physik, 38, 173-198.

Moyal-Sharrock, D. (2004). Understanding Wittgenstein's On Certainty. Palgrave Macmillan.

Pritchard, D. (2016). Epistemic Angst: Radical Skepticism and the Groundlessness of Our Believing. Princeton University Press.

Wittgenstein, L. (1969). On Certainty (G. E. M. Anscombe & G. H. von Wright, Eds.; D. Paul & G. E. M. Anscombe, Trans.). Basil Blackwell.

I have argued for a fundamental parallel between Wittgenstein's hinges and Gödel's incompleteness results: both demonstrate that systematic thought requires ungrounded foundations. By examining how epistemic and mathematical systems share this structural feature, we gain insight into the nature of foundational certainties across domains of human understanding — Sam26

I have argued that this parallel is more metaphorical than substantive, because the two concepts operate in fundamentally different domains and address different kinds of problems. To claim a direct parallel between the mechanics of hinges and incompleteness is to make a category error. There is only a broad formal similarity between the two. Gödel saw his results not as a reason to abandon formalism but as a guide to discovering new, intuitive axioms from set theory that could extend our mathematical knowledge. He was a mathematical Platonist who believed we had access to mathematical truth beyond formal systems. For Wittgenstein, the problem of skepticism is dissolved, not solved. The response is to stop looking for a philosophical foundation and recognize the foundation in our ordinary practices.

I have argued that this parallel is more metaphorical than substantive, because the two concepts operate in fundamentally different domains and address different kinds of problems. To claim a direct parallel between the mechanics of hinges and incompleteness is to make a category error. There is only a broad formal similarity between the two. Gödel saw his results not as a reason to abandon formalism but as a guide to discovering new, intuitive axioms from set theory that could extend our mathematical knowledge. He was a mathematical Platonist who believed we had access to mathematical truth beyond formal systems. For Wittgenstein, the problem of skepticism is dissolved, not solved. The response is to stop looking for a philosophical foundation and recognize the foundation in our ordinary practices. — Joshs

Thank you for the response. I am not claiming that hinges and incompleteness are the same thing; I am arguing that they share a structural feature, a limit on internal vindication, that clarifies why both epistemic practice and formal mathematics proceed as they do. By “foundational,” I do not mean an inferential base that justifies the rest; I mean constitutive certainties that enable assessment and inquiry without themselves being earned by inference.

On the charge of “mere metaphor” or category error, my claim is second-order. Hinges are arational certainties that do not get their warrant from the very inferences they enable; they are part of the background that makes asking for reasons possible. Gödel’s results show that any consistent, effectively axiomatized system strong enough for arithmetic contains arithmetical truths it cannot prove, and cannot, from within itself, prove its own consistency. In both domains, there is a principled limit on what counts as from-within justification, that is the level at which I am drawing the parallel.

Gödel’s own Platonism is not essential to this point. Whether one seeks new axioms on intuitive grounds or not, incompleteness and the second theorem still mark the same internal limit. Extending a theory yields only relative vindication, inside the stronger framework undecidable truths reappear, and consistency still lacks a proof from within.

On Wittgenstein and skepticism, I agree that the problem is dissolved rather than solved. That is exactly why calling hinges “foundational” in a non-traditional sense matters, they are enabling conditions rooted in our form of life, not premises that do evidential work. The analogy respects this, it does not revive a search for ultimate grounds, it explains why the demand for a self-grounding system misfires.

There are important disanalogies, and I acknowledge them. Gödel sentences are ordinary propositions with determinate truth conditions, many basic hinges are enacted and often non-propositional. Mathematics is deliberately revisable and pluralistic; hinge certainties are far more stubborn and pre-theoretical. These differences do not touch the structural point. My thesis is modest and substantive; both domains exhibit a limit on internal justification, and seeing that parallel helps explain why the quest for a completely self-grounding system is not merely difficult, it is misconceived.

I transferred this post to epistemology, removing the NDE connection.

Part 2 of my book (a subsection):
Chapter 6: Epistemology and the Nature of Knowledge—A Deeper Dive

We often talk as if knowing were simple. I say I know my car is in the driveway, I know my closest friend’s name, I know the sun will rise tomorrow. Such claims feel immovable in ordinary life, and the confidence that accompanies them belongs to how these judgments function for us. Yet, when we press the matter, when we ask what gives that assurance its footing, we find that certainty is not a free-standing monument but part of a wider practice in which reasons, entitlements, and background certainties cooperate. The appearance of simplicity is instructive: it invites us to pause, examine the ground under our feet, and say what must already stand fast for talk of reasons, proof, and mistake to make sense at all.

The same tension frames NDE reports. A patient describes vivid perceptions while clinically near death—voices, instruments, exchanges among staff—and later offers a detailed account that seems to match the room and the timeline. The narrative arrives with conviction, sometimes with life-altering force and moral seriousness. But conviction alone does not settle what we are entitled to say we know, nor does it show how such reports fit the language-games of evidence. Our task is to sort conviction from warranted belief, and warranted belief from truth, without ignoring the human weight of these experiences or the public criteria by which claims are assessed.

In Chapter 2 I set out a four-condition account of knowledge that I will use here, call it JTB+U. Knowledge requires the truth of the proposition, the believer’s commitment to it, publicly assessable justification, and a further condition: conceptual understanding. Without that competence, words misfire, and what looks like a belief becomes a misuse of grammar rather than a contentful claim. With JTB+U in view, we can approach testimony with standards that respect ordinary practice while guarding against lucky alignment. In what follows, I treat justification as practice-indexed: reasons count within our language-games, the ordinary practices that supply public criteria for correct use (see Glossary: “Language-games”).

1. Truth — accords with how things are in reality; reality makes it true, not our confidence.
2. Belief — the subject takes the claim to be true, not merely recites the sentence or entertains it as a hypothesis.
3. Public Justification — the belief is supported by reasons others can in principle inspect, check, and contest; the support is not private.
4. Conceptual Understanding — the subject competently grasps the concepts at issue and can use the relevant terms correctly within the practice. Mastery shows in application: recognizing what counts as a correct move, spotting misuse, and explaining the ordinary tests. This is not a matter of private introspection but of publicly trainable rule-following within our language-games (see Glossary: “Rule-following,” “Language-games”).

The tripartite model reaches back to Plato’s Theaetetus and has endured because it captures something right about knowledge: true belief is not yet knowledge unless it is properly grounded. At the same time, lived inquiry is messier than tidy definitions suggest. “Justification” can become an empty placeholder if we detach it from the practices that supply criteria, error-signals, and standards of success. That detachment is what the “+U” is designed to prevent.

JTB, then, is a helpful starting point, not a final resting place. We sharpen it by situating reasons in use—within specific language-games—by marking the public criteria that govern correct application, and by acknowledging the hinge background that makes justificatory moves possible at all. With JTB+U in view, we can now state how justification works in practice and why that shift dissolves much of the apparent puzzle about luck and knowledge.

Enter Wittgenstein. He shifts meaning from inner pictures to use and relocates philosophical grip in our public, rule-governed activities. In On Certainty, he brings into view hinge propositions: arational certainties that are not hypotheses to test or theses to prove, but the conditions that let testing and proving count as such. We do not justify them; they stand fast for us, and because they do, reasons can be weighed. This vantage also clarifies the grammar of “know,” separating the epistemic use—answerable to criteria—from the convictional use that simply voices assurance. Set within this frame, JTB gains depth; adding conceptual understanding makes it a tool situated inside the practices it is meant to illuminate.

In the notes collected as On Certainty, Wittgenstein traces the limits of doubt and shows why a wholesale challenge to the background ends the very language-game of giving and asking for reasons. Some certainties lie in the river-bed, shifting slowly if at all; some are cultural-historical or personal-practical; still others are embodied and prelinguistic, displayed in how we move through a familiar room without inner consultation. These layers of bedrock make inquiry possible. They are not theses to defend; they are what allows defense and criticism to be recognizable practices. Acknowledging this bedrock does not canonize it; it clarifies the conditions under which revision has sense.

Before drawing a method from these insights, a brief orienting note about testimony’s place in the framework is in order.

Testimony is both a primary route to justification and, at a higher level, a proving ground for method. Because it is social, it depends on public criteria: access to the facts, competence in the relevant domain, sincerity, independence of sources, convergence over time, and resilience under attempted disconfirmation. Throughout this chapter, I will treat testimony, logic (inductive & deductive), sensory experience, linguistic training, and pure logic as principal routes rather than an exhaustive catalog. The ordering is fixed for clarity, not to signal rank. Testimonial claims will serve as a running case, precisely because they are rich, contested, and guided by public standards while remaining open to defeat by further evidence.

With JTB+U in view, and with hinges and testimony on the table, the task now is to lay out a method for evaluating knowledge claims in practice. The aim is modest and disciplined: identify the route, check the grammar of the claim, scan for hinge background, apply route-specific criteria, and screen for defeaters. Along the way, we will distinguish the epistemic use of “I know,” which is answerable to criteria, from the convictional use that merely voices assurance.


I certainly wouldn't propose that Wittgenstein would agree with everything I'm proposing. I'm merely extending what I think follows from Wittgenstein.

Edited 8/24/2025

More on JTB+U with a twist

I have always been skeptical of Gettier problems, even back when I subscribed to the classical Justified True Belief (JTB) model of knowledge. To me, those examples never quite landed as genuine counterexamples; they seemed more like confusions in how we apply the concept of justification. In the standard Gettier case, like the one where Smith believes "Jones owns a Ford or Brown is in Barcelona" based on misleading evidence about Jones, the belief ends up true by accident via Brown. It's true, believed, and apparently justified—but it doesn't feel like knowledge. Critics say this breaks JTB, demanding fixes like no-false-lemmas or tracking conditions. But I saw it differently: Smith isn't truly justified; he's just thinking he is, relying on premises that don't hold up under scrutiny.

This intuition fits seamlessly into my JTB+U framework, which extends JTB with a Wittgensteinian twist. Knowledge still requires truth (the proposition matches reality), belief (genuine conviction, not mere recitation), and justification (supported by publicly assessable reasons via paths like testimony or logic). But we add Conceptual Understanding (+U): competent grasp of the key terms, demonstrated through correct use in the relevant language-game. Without this, claims misfire as grammatical errors, not valid epistemic moves.

In Gettier scenarios, +U reveals the flaw: the subject misapplies "justification," treating lucky or false-based reasons as a competent warrant. Smith's inference conflates private seeming (convictional assurance) with public criteria—his reasons are defeasible and hinge on a mismatch with reality. Hinge propositions, those arational certainties from Wittgenstein's On Certainty that "stand fast" (like "Evidence should track truth without coincidence"), ground genuine justification. Gettier cases dissolve therapeutically: they're not failures of JTB but calls to clarify usage in practice. We don't need to redefine knowledge; we need to see that "thinking one is justified" isn't the same as being justified in the shared stream of life.

This approach honors Wittgenstein's insight that philosophical puzzles often stem from misusing language. It keeps evaluation pragmatic: warrant emerges from public reasons and competent grasp, respecting conviction's human weight without equating it to knowledge. In the end, Gettier cases, rooted in misunderstandings of justification, underscore the value of JTB+U: knowledge as a practice in our forms of life, where genuine warrant leaves no space for luck.

While I believe JTB+U offers a fresh way forward in epistemology, blending classical JTB with Wittgenstein's later ideas on hinges and language-games, I hesitate to call it entirely new; philosophy builds on what came before, after all. It's more an extension or refinement, with some original touches like the layered hinges and the Gödel parallel, but grounded firmly in existing traditions. If it sparks clearer thinking, that's enough for me.

Continuing remarks on JTB+U

I begin where our practices begin. Before I argue for anything, I stand on what already stands fast: there is a shared world, words keep their uses from one moment to the next, memory and instruments ordinarily work, and other people are real partners in inquiry. I do not prove these each time I make a claim; I rely on them so that giving and asking for reasons can even get started. I call these fixed points hinges. They are not conclusions; they are the bedrock on which conclusions are drawn.

This starting floor matters because the old problems of regress and circularity never go away. If every reason needed a further reason, I would never begin; if I tried to justify the starting floor with the very tools it enables, I would move in a circle. Hinges stop both temptations. They are not secret premises and not dogmas; they are the background of our forms of life. They can shift when our ways of checking change, but within a given practice, they are the background that lets reasons count.

With that in view, I can say what I mean by knowing. To know is to accept something as true, to be able to give reasons that others can check, and to understand the claim well enough to use it correctly and to see where it does not apply. The public side is essential: justification is not a private feeling; it is an earned standing inside shared procedures. In my view, JTB is further strengthened by grounding it in this background, rather than weakened by its dependence on what stands fast.

The word “know” itself does two jobs, and conflating them generates confusion. Sometimes “I know” functions as an expression of conviction, as in “I know this is my hand.” No one expects evidence there; it points to the floor we act from. At other times, “I know” signals epistemic standing, where doubt makes sense and a route of checking is available, as in “I know the train leaves at 6:18,” backed by a timetable and ordinary procedures. My model keeps these uses apart: the first marks hinge-level certainty, the second belongs to justification.

Public justification runs along five familiar routes, none sovereign on its own: testimony, logic in both inductive and deductive reasoning, sensory experience, linguistic training, and pure logic understood as formal structure only, for example “X or not X.” Different questions call for different mixes, but the rule of thumb is simple: give the kind of reason a competent other could in principle verify from where they stand.

To keep the routes honest, I rely on three guardrails. First, No-False-Grounds: do not build on a mistake, so check the provenance of what you take for granted in the case at hand. Second, practice safety: use methods that fit the practice, so chemistry is not settled by a poll and character is not read off a voltmeter. Third, defeater screening: actively look for counter-evidence and better explanations that would undercut the claim. These do not replace reasons; they discipline how reasons are gathered, weighed, and held.

Understanding the “U” in JTB+U is not an ornament. It shows in competent use: the ability to extend a concept to new instances, to draw the inferences that go with it, and to recognize its limits without special prompting. Someone who repeats a medical note yet cannot tell a pulse from an oxygen reading does not, in the relevant sense, know. Understanding ties reasons to the grammar of the claim within the practice.

Taken together, the picture is spare. Hinges give us a place to stand, so regress and circularity do not paralyze inquiry. Within that space, knowledge is true belief with reasons others can check, further strengthened by grounding it in what stands fast. The five routes say what counts as a reason here, the three guardrails keep the routes from drifting, and the two uses of “know” keep our language clear. The aim is not a clever definition; it is a workable method for telling knowledge from its near-neighbors in ordinary cases and in the cases that matter most.

JTB+U

I start by fixing the background, and the chess analogy helps: you do not prove the board, pieces, or rules before you move; you stand on them so that a move can be a move at all. Inquiry works the same way. I rely on a shared world, on words keeping their uses from moment to moment, on memory and instruments ordinarily working, on other minds as partners in checking. These are fixed-point hinges. They are not conclusions we reach; they are what let giving and asking for reasons get started.

This starting floor matters because the old problems of regress and circularity never go away. If every reason needed a further reason, I would never begin; if I tried to justify the starting floor with the very tools it enables, I would move in a circle. Hinges stop both temptations. They are not secret premises and not dogmas; they are the background of our forms of life. They can shift when our ways of checking change, but within a given practice, they are the background that lets reasons count.

The analogy also marks the limits of doubt. In chess you doubt a move, not the existence of the board mid-game; in inquiry you doubt a reading, an inference, a report, not the bare possibility of language working while you are using it to doubt. Skepticism belongs inside the game, where there are procedures for checking. That is the sense in which hinges preempt the regress: they do not win an argument by force; they make argument possible.

Hinges are not chosen by whim and not certified by theory. We inherit them in our training and reveal them in what we count as a check. Over time, whole practices can change, new instruments, new techniques, new standards, and with them, some hinges may move. But the movement is slow and public, like learning a variant of the game rather than making a special move. Day to day, the hinges stand fast so that reasons can be given, tested, and corrected.

With this in view, the next step is straightforward: when I say “know,” I mean a true belief, backed by reasons a competent other could in principle check, held with enough understanding to use the claim correctly and see where it does not apply. The hinge background does not replace those reasons; it frames them. In my view, JTB is further strengthened by grounding it in what stands fast.