I've read all seven of your chapters. Just for workability, I'm going to respond to each chapter separately. This may mean that what I have to say will be a bit disjointed. We'll see.

My biggest overall issue--JTB generally applies to propositions but most of the knowledge we have and use is not really expressible in that form. As an engineer, I usually talked about "conceptual models," which means an overall picture of the situation--in my case it was real estate properties and the soil and groundwater characteristics distributed across the site and at different depths. Models like that will generally be judged and justified as accurate rather than true. As I indicated, as I see it, the way we use knowledge on a daily basis tends to be more like how I've described it rather than just the truth of propositions.

This is highlighted by your discussion of the idea of standards of practice which are used to justify truth. In general, I think that's right, but how standards are applied under JTB (or JTB-U) is different from how various practices apply their standards. How do I apply an engineering standard to a simple declarative statement?

So, I worry that I am going to send your discussion off on a tangent. Now that you've seen some of the substance of my thoughts, should I continue? — T Clark

I don't think this is a tangent, I think it's exactly the kind of stress test that helps clarify my ideas.

On the first point, I agree that a great deal of what we rely on is not best described as a single proposition. Much of it is a competence, a grasp of a situation, a model, or a way of seeing how things hang together. In engineering, the object of assessment is often a conceptual model, and the operative question is whether the model is accurate, robust, and fit for use across the relevant conditions, not whether a sentence is true in isolation.

My reply is that this does not put the JTB family out of business, it forces a clarification of what “truth” and “justification” are doing. A model can be assessed for correctness in the world, it can succeed or fail, it can be refined under error signals, and it can be defeated by counterevidence. In other words, it has correctness conditions even if it's not naturally expressed as a single declarative statement. The “propositional” layer can be treated as a partial extraction from the model, for example, predictions, constraints, and consequences that can be checked. That is often how the model earns and keeps its standing.

On your second point, I agree that we should not imagine applying an engineering standard to an isolated declarative sentence as if that were the primary unit of knowledge. The better way to put it is that standards of practice govern the evaluation of the claim in its proper form, which may be a model, a procedure, a measurement protocol, or a forecast. When I say “public” or “practice-governed,” I mean that there are criteria for correct application, error, and correction that can be articulated and contested within the practice. Engineering seems like a textbook example of this, because the standards include calibration, measurement error, boundary conditions, sensitivity to assumptions, and the discipline of revising the model when it fails.

So, I would welcome you continuing, but with one focusing suggestion so we do not drift. When you respond to a post, pick one concrete engineering example of a conceptual model and say how it is justified in your sense. Then we can map it onto my vocabulary without forcing it into a single sentence: which route of justification is doing the work, what would count as a defeater, where No False Grounds shows up, and what “practice safety” looks like in that domain. If we can do that once, the “propositions versus models” worry will either dissolve or become precise enough to evaluate.

Optional sidebar: Hinges and Gödel, a structural parallel

A brief note for readers interested in foundations. In my paper I suggest a structural parallel between hinge certainties and Gödel style limits. The parallel is not evidential, and it is not a proof of anything in epistemology from mathematics. It is a comparison of structure.

In Gödel’s setting, once a formal system is rich enough, there are truths expressible within the system that cannot be proven by the system’s own resources, and consistency cannot be established from within in the strongest way one might want. The upshot is not that mathematics collapses, but that the practice operates with boundary conditions that are not resolved by the same methods the system makes possible.

In the hinge setting, justificatory practices also have stopping points. Certain things stand fast, not as conclusions of inquiry, but as the background that makes inquiry, doubt, evidence, and correction possible. The upshot is not that justification collapses, but that justification always operates within a framework whose role is not that of an ordinary claim awaiting ordinary support.

So the comparison is this: both domains exhibit limits on what can be achieved from within, and both continue rationally once those limits are acknowledged. That is all I mean by the parallel.

If you want to press on this, I would welcome it, but it will help to keep the debate focused on whether the analogy is illuminating rather than on technical details of Gödel’s proofs.

Much of this is already written out, which is why I can respond quickly sometimes.

Clarifications and terms (so we do not talk past each other)

Before continuing, I want to clarify a few terms that can easily be misunderstood.

What “+U” is and is not. In JTB+U, “Understanding” is not a new ingredient bolted onto JTB. It is a way of making explicit what justification already presupposes in ordinary epistemic practice, the competence to grasp what counts as support, what counts as error, and what would count as correction in the domain.

What I mean by “public.” When I say justification is public, I do not mean popular agreement or institutional permission. I mean that justification has criteria that can, in principle, be articulated, assessed, challenged, and corrected within a shared practice.

Practice Safety is not a demand for infallibility. Practice Safety means that the route by which a belief is held is not fragile or lucky with respect to the mistake conditions the practice recognizes. It is about tracking error signals in the domain, not about achieving certainty in the absolute sense.

What I mean by a defeater. A defeater is not merely disagreement. It is a consideration that, if true, would remove or weaken the support, or would show that the apparent support is misleading. Defeater screening is the discipline of identifying and facing such considerations rather than ignoring them.

Hinges are not reasons. Hinges are not hypotheses supported by evidence. They are background certainties that stand fast and make evidence, doubt, and correction possible in the first place.

Four uses of “certainty.” I distinguish subjective certainty (conviction), hinge certainty (bedrock), epistemic certainty (defeater resistant stability in practice), and absolute certainty (logical or moral necessity). When we disagree, it often helps to say which sense of certainty is in play.

Post 7 of 7:
Gettier, and why “seems justified” can mislead

Gettier cases are designed to make the traditional JTB account look inadequate. The familiar pattern is that a person has a true belief, and can cite what appears to be a justification, yet we hesitate to call it knowledge. The standard moral is that JTB is missing some extra condition. My paper argues that this moral is too quick, because it treats “justification” as if it were exhausted by having a supporting consideration that can be stated.

On the view I am developing, the key distinction is between a belief that looks justified, and a belief that has genuine justificatory standing within a practice. In Gettier style cases, the subject often has support that is either dependent on a false ground, or is insulated from the relevant mistake conditions, or is undermined by an undefeated defeater. In other words, the cases exploit a gap between seeming to meet the justification requirement and actually meeting it once the ordinary constraints on justification are made clear.

This is where the guardrails matter. If a belief depends on a false ground, No False Grounds blocks it. If the route is fragile and the belief is true by luck, Practice Safety blocks it. If there is relevant defeating information that has not been faced, Defeater Screening blocks it. The upshot is not that Gettier reveals a defect in JTB, but that Gettier is trading on an impoverished picture of justification, and once justification is properly described, the cases no longer force an additional condition.

This also brings the “+U” into focus. Understanding is not a decorative addition. It marks the competence by which a person can genuinely track what their support does, what would count against it, and what would require revision. A person can cite a reason and still be out of contact with those mistake conditions. When that happens, the belief can be true and can look justified, yet it lacks the stability we normally require for knowledge.

Upshot: Gettier cases do not show that knowledge needs a mysterious extra ingredient. They show that we should not confuse the appearance of justification with genuine justificatory standing.

Questions for critique:

Do you think Gettier cases still refute JTB even if we build in the guardrails and the “+U” clarification.

Is my diagnosis too dependent on relabeling the justification condition rather than answering the core intuition.

If you have a favorite Gettier case, post it and say which guardrail you think it slips past, if any.

Post 6 of 7:
Hinges and why justification has stopping points

At some point justificatory questions come to an end, not because inquiry has failed, but because the very practice of giving and asking for justification presupposes a background that is not itself justified. If you demand a justification for everything, including the conditions that make justification possible, you do not reach a deeper standard. You undermine the justification.

This is where hinge certainties come in. A hinge is not a hypothesis, not a conclusion, and not a belief held because we have evidence for it. It is something that stands fast in a practice, a bedrock commitment expressed in how we proceed, what we take for granted, what counts as doubt, and what counts as a mistake. Hinges are not the kind of things we arrive at by argument, but they are also not arbitrary. They belong to the inherited background against which reasons, evidence, and defeaters can have their force.

That matters for two reasons. First, it explains why the demand for ultimate proof is misguided. Proof and justification always operate within a framework, and the framework is not itself established by the same tools it makes possible. Second, it explains why skepticism so often feels powerful. Skeptical questions typically target hinges and treat them as if they were ordinary empirical claims. Then, when those hinges cannot be proven in the skeptic’s demanded way, skepticism concludes that nothing can be known. The mistake is grammatical. The skeptic is asking for a kind of justification that cannot apply to the role hinges play.

None of this licenses dogmatism. It is true that some hinges can shift as practices are repaired, methods change, or persistent error signals force a reorientation. But it is equally true that some hinges do not shift, at least not within anything we would still recognize as the same form of life. Their role is constitutive, they are part of what makes inquiry, correction, and assessment possible at all. Where a hinge does shift (e.g. we are objects separate from other objects), the change is usually not a matter of ordinary argument but a deeper reorganization of the practice itself.

Upshot: hinges are not additional reasons. They are the background that makes reasons and defeaters possible, and recognizing this prevents both regress and skeptical distortion.

Questions for critique:

Do you think hinges are real features of our epistemic life, or are they a philosopher’s invention to stop regress.

Does treating skeptical challenges as hinge confusion actually answer skepticism, or does it merely set it aside.

Can you name a hinge you think my framework relies on, and say whether you think it should stand fast or be challenged.

:up:

Post 5 of 7:
Five routes of justification (non exhaustive)

In the paper I lay out five primary routes by which beliefs commonly acquire justificatory standing. The point is not to rank them or claim that every case fits neatly into a single category. The point is to map the main ways we actually come to know, so that we can ask where a claim is getting its support, and what standards and error conditions belong to that route.

Testimony. Most of what we know comes from others, ordinary reports, books, videos, expert claims, historical records, and lived witness. Testimony can confer justificatory standing, but it has its own standards: credibility, independence, competence, convergence, and the absence of relevant defeating information.

Logic (inductive and deductive reasoning). We justify beliefs by inference, sometimes strictly, sometimes probabilistically. Here the relevant standards include valid form where appropriate, good inductive support, sensitivity to base rates, and the ability to identify where an inference is overextended.

Sensory experience. Experience is a central route of support in ordinary life. It has its own error conditions: illusion, distortion, poor conditions, and conflict with other well established checks. Sensory experience does not need to be perfect to justify, but it must be situated within the ordinary corrective practices that make perception reliable in the domain.

Linguistic training. Some things are “known” because we are trained into a practice, trained to use terms correctly, to recognize criteria, to follow rules, and to distinguish correct application from misuse. This route is often invisible because it is basic to how we learn the grammar of our concepts, but it is indispensable for explaining how justification becomes possible at all.

Pure logic (boundary setting only). There are limits that are not empirical discoveries but logical constraints, what is possible, what is coherent, what follows from definitions, what collapses into contradiction. This route does not supply new facts about the world. It sets boundaries, clarifies entailments, and exposes category mistakes.

This five route map is not meant to replace the earlier guardrails. The guardrails discipline justification. The routes describe where justification is coming from. In any concrete case, the question becomes: which route is in play, what are its standards, and do the guardrails hold.

Upshot: the routes give us a practical way to locate a claim in the space of support, standards, and error conditions, without turning epistemology into a single method.

Questions for critique:

Are these five routes a helpful map, or do you think the categories blur in a way that makes the list misleading.

Do you think “linguistic training” deserves to be a distinct route, or is it better treated as part of the background of the other routes.

Is my use of “pure logic” as boundary setting clear, or does it need a different label.

Post 4 of 7:
Three guardrails that discipline justification

If justification is a standing within a practice, it still needs discipline. Not every chain of support confers standing, and not every true belief that happens to be well supported counts as knowledge. In the paper I use three guardrails to mark common ways justification fails, even when a belief looks respectable.

No False Grounds (NFG). A belief cannot have genuine justificatory standing if the support it depends on is false, or if it is being carried by a false presupposition that is doing the real work. The point is simple: if the ground is false, whatever looks like support is a counterfeit support.

Practice Safety. A belief is practice safe when it is formed and maintained in a way that reliably tracks the mistake conditions recognized by the practice. This is not infallibility. It is the idea that the route by which the belief is held is not fragile, lucky, or insulated from the ordinary error signals that would count against it in a particular domain.

Defeater Screening. Even when the grounds look good, justificatory standing is undermined when there are live defeaters that have not been faced. A defeater is not merely a contrary opinion. It is a consideration that, if true, would remove or weaken the support, or would show that the apparent support is misleading. Defeater screening is the discipline of identifying and addressing such considerations, rather than ignoring them.

These are not meant as extra conditions stapled onto JTB. They are ways of making explicit the constraints that ordinary epistemic practice already applies when it distinguishes genuine support from luck, from illusion, and from rationalization.

Upshot: the guardrails do not add a new theory of knowledge, they articulate the failure modes that explain why “seeming justified” can diverge from genuine justificatory standing.

Questions for critique:

Do you think these guardrails capture real failure modes, or do they smuggle in something stronger than ordinary justification.

Is Practice Safety a useful idea, or does it collapse into defeater screening or into reliability talk.

Can you think of a case where a belief meets these guardrails and still intuitively fails to count as knowledge.

Yes, it makes sense for you to participate, and I think your pragmatic approach can fit naturally with mine, as long as we keep the different uses of “certainty” from sliding into each other.

I divide certainty into different uses:

Subjective certainty, conviction, how settled a claim feels.

Hinge certainty, the bedrock that stands fast and makes inquiry and doubt possible at all.

Epistemic certainty, defeater resistant stability in practice, the kind of standing we treat as enough for responsible action within a domain.

Absolute certainty, logical or moral necessity.

With that in view, your “adequate certainty about outcome” sounds closest to what I call epistemic certainty, not absolute certainty, and not merely subjective certainty. In other words, it is not infallibility, and it is not just confidence. It is a claim having the right kind of stability under the relevant checks, given the stakes and the standards of the practice you are operating in.

Where our approaches might meet is that both of us think justiification is disciplined by standards. Where we might differ is that I frame those standards in terms of justificatory standing within a practice, including what would count as a mistake, what would count as a defeater, and what would count as a responsible correction. Practical stakes can raise the bar, but they do so by tightening what counts as adequate support, not by demanding absolute certainty.

So yes, participate. If you want a clean point of contact, tell me what your “adequacy” standards are in a concrete case, and we can ask how they relate to defeater resistance, false grounds, and practice safety, and which sense of certainty they are aiming at.

Post 3 of 7:
What “Understanding” is doing in JTB+U

In JTB+U, “Understanding” is not a new mental ingredient added on top of truth, belief, and justification. It names a feature already at work in justification, the grasp of the concepts and inferential roles that make justificatory standards applicable at all. If justification is a standing within a practice, then understanding is the competence by which a person can genuinely participate in that practice, not merely mimic its conclusions.

Someone can hold a true belief and even cite a correct supporting data, while still failing to grasp what that support is doing, what would count against it, what would defeat it, and what would count as a relevant correction. In that situation the belief can look justified from the outside, and even to the person themselves, but the justificatory standing is fragile, because the person does not reliably track the mistake-conditions that the practice treats as decisive. Understanding, in this sense, is the operative structure of justification, the competence that makes justificatory standards genuinely operative rather than merely repeatable.

This is also why I resist treating “justification” as if it were only a list of supporting propositions. A list can be repeated by rote. Understanding is what makes the support more than a recitation, it is the ability to locate the claim within the space of reasons, objections, defeaters, and revisions that the practice recognizes. That is not infallibility, and it is not an impossible demand. It is simply the difference between having a standing and merely borrowing one.

Upshot: “+U” marks the competence that makes justificatory standards operative, it is not a separate add on.

Questions for critique:

Is this notion of understanding genuinely distinct from justification, or does it collapse into it.

Does tying understanding to error signals, defeaters, and correction make the account clearer, or does it over intellectualize ordinary knowing.

Can you think of a counterexample, a case where someone lacks this competence but still seems to have genuine justificatory standing.

Post 2 of 7:
What I mean by “justification”

When I use the word “justification,” I am not talking about something private, a feeling of confidence, or a mere report of how things seem from a subjective point of view. I mean justificatory standing, the sort of standing a belief has when it is supported by the standards that govern a practice, standards for what counts as evidence, what counts as error, and what counts as correction.

That is why I sometimes describe justification in terms of grammar (Wittgensteinian grammar). The point is not that knowledge is “only language,” but that the difference between being entitled and merely thinking one is entitled is built into how our practices work. We learn what it is to justify by learning how claims are checked, challenged, repaired, and sometimes withdrawn. Those norms are not optional decorations added after the fact. They are part of what makes the idea of justification intelligible.

This is also why I emphasize the public character of justification. “Public” here does not mean popular agreement or institutional permission. It means that justification has criteria that can, in principle, be articulated, assessed, and disputed within a shared practice. A belief can be held with sincerity and conviction and still fail to have justificatory standing.

Upshot: justification is a normative standing within a practice, not an inner endorsement, and that is the background against which the “+U” move makes sense.

Questions for critique:

Do you think justificatory standing can be explained without appeal to shared criteria, or does that collapse into a purely psychological picture.

Is my use of “grammar” illuminating here, or does it obscure what is really going on.

Does “public in this sense” capture what we need for justification, or does it leave out something essential.

You can comment as I go along, but many of the questions about what I mean by this or that will be explained in later posts.

The spine of my paper will be covered in seven posts.

1. What JTB+U is claiming

2. What I mean by justification as practice grammar

3. What “Understanding” is doing

4. The guardrails (No False Grounds, Practice Safety, Defeater Screening)

5. The five routes of justification

6. Hinges as non-epistemic background

7. Gettier diagnosis and upshot

Post #1
What JTB+U is claiming

My paper defends a practice-oriented refinement of the traditional JTB account. I call it JTB+U: “justified true belief” plus Understanding. My point is not to add a new requirement onto JTB as if we had discovered a fourth ingredient. My point is to make explicit something justification already presupposes in everyday epistemology, i.e., the competence to grasp what counts as support, what counts as error, and what would count as correction within a practice.

On this view, many familiar puzzles arise when we picture justification as something essentially private, an inward sense of being entitled (e.g. the use of know as an expression of a conviction), as if the fact that a belief feels well supported could stand in for the standards by which it is actually assessed. But in ordinary epistemic life, justificatory standing is not conferred by confidence or by an internal impression of rightness. It depends on the grammar of our practices, the criteria by which we count something as evidence, the ways we identify error, and the norms by which we correct it. When we bring that grammar into view, Gettier cases lose much of their force because many depend on a mismatch between seeming justified and having justificatory standing.

Upshot: I am not replacing JTB, I am strengthening it by making explicit the Understanding that is already doing quiet work inside justification.

Questions for critique:

Does the “+U” clarify anything real, or is it a relabeling.

Where would you draw the boundary between justification and understanding, if you think there is one.

What is your strongest reason to think Gettier still bites even after this move.

Morality from a secular position is necessarily subjective. — Ram

This premise isn't true. The key is that you said necessarily. To counter a necessity claim, I do not need to show that all morality is objective, or even that all harm is objective, I only need one counterexample. For example, suppose I cut off someone’s arm for no good reason. The harm in that case is not a matter of opinion or private feeling. It is publicly observable, i.e., objective: an arm on the ground, blood loss, shock, the screams of the one harmed, the reactions of witnesses, the lasting impairment. Anyone can see what has happened, and anyone can see that nothing about this depends on my personal preferences.

Now you might say, “Fine, the harm is objective, but calling it wrong is still subjective.” But that is exactly where the word necessarily overreaches. In ordinary moral judgment, severe harm functions as a public defeater: if you cannot give reasons that others can evaluate as sufficient, the act is not merely “disliked,” it is impermissible. You can reject that grammar if you want, but then you are no longer describing morality so much as evacuating it. So, at a minimum, this one case shows that a secular moral judgment can be anchored in objective features of the world and in publicly assessable justification, which is enough to refute the claim that secular morality is necessarily subjective.

I say this as someone who is not a secularist, but as someone who allows for an expanded metaphysics.

Hello everyone,

I'm writing to share that this will be my final post for a few months. I need a break.

Sam

My general impression of your narrative says, "You want to pair the metaphysics of knowledge relationships (p →q), as dynamically governed by an emergent and energetic inter-relation, viz., truth, with empirical experience. Dynamical, energetic identity transformations across space and time forming symmetries that conserve identity and support an enduring POV embody the living experience of truth. — ucarr

In other words, truth isn’t some hidden essence, it’s what happens when our justified beliefs line up with the facts of the world, or the way the world is. We test truth through shared practices (Wittgenstein's language games, which are governed by implicit rules), our forms of life, where we check, correct, and agree on what counts as evidence. In some cases, like science or mapping, truth can be pictured or measured, but even there it works only because we understand what the picture means and how it connects to reality. Understanding (JTB+U) isn’t optional; it’s what lets us tell genuine truth from lucky coincidence.

Formal theories of truth, like those used in logic, capture a structure but not its lived reality. They can show when a statement fits certain conditions but can’t explain how truth operates in lived reality, how it shapes belief, correction, and meaning. Truth, as we actually experience it, isn’t a Tarski formula (“p” is true iff p.) but a practice. There's a philosophical bridge between ontology and epistemology: the world has its own structure (what obtains), and we have our structures of reason, language, and justification. Truth is the point where those two orders (the world and epistemology) align.

In the framework I use, truth is not a metaphysical essence but a relation intrinsic to our practices of justification. To say a proposition is true is to claim that it holds up under the public criteria of a form of life, viz., that it connects belief with what obtains in the world. Truth marks the point where our language intersects with reality and is further illuminated by understanding: not merely that the world is as the proposition says, but that we can see how and why this is the case. The correspondence is real and, in some language-games, legitimately pictorial, e.g., where mapping, modeling, or measurement aim to reproduce structure or proportion. Yet even there, “picturing” works only because it is guided by understanding: without grasping how the representation functions, no degree of accuracy would amount to knowledge. Understanding is easily overlooked because it seems built in, but it is what allows us to apply the criteria of truth, to distinguish success from coincidence, evidence from echo. What makes a proposition true is the state of affairs that obtains; what makes that truth knowable is the grammar of our interaction with it, governed throughout by understanding. In this sense, truth is both discovered and articulated, anchored in reality and shown through our capacity to comprehend its order.

Formal definitions of truth, though indispensable in logic, leave this fuller picture out. Tarskian or semantic schemas (“‘p’ is true if and only if p”) capture the structure of truth but not its life. They specify conditions of equivalence but remain silent about how truth functions within inquiry, how it guides belief, sustains correction, and grounds public justification. Formal accounts strip truth of human context: they can model consistency but not meaning, accuracy but not understanding. What they describe is the form of truth’s operation, not its practice. Truth, as lived and recognized, is not a symbol in a metalanguage but what’s embodied in our forms of life (our language games), the point where the world’s order and our conceptual order momentarily coincide.

Can you name a few of those "forward-looking thinkers"? — Janus

There are those who view AI as an epistemic tool, something that extends, rather than replaces human inquiry. There's a long list of people who fit the bill. For example, Nick Bostrom and Luciano Floridi have been working on the conceptual implications of AI for ethics, cognition, and the philosophy of information. Vincent Müller and Mariarosaria Taddeo have been exploring how AI reshapes the logic of justification and responsibility in scientific reasoning. On the cognitive side, Joscha Bach treats AI systems as experimental models of mind, ways to probe the nature of understanding. Even researchers outside philosophy, in fields like computational linguistics and mathematical discovery, are beginning to treat AI as a genuine collaborator capable of generating new proofs and hypothesis.

Maybe we use books, dictionaries, philosophical papers, editors, and scientific discoveries to make us look smarter than we are. You see this all the time in forums, even without AI, so it's nothing new. Besides do you really care about the psychology of someone who's writing about what they think?

I won't comment on the political part of your post because I think we're very far apart. However, in the future I can see where humans will merge with AI, so we'll probably become one with machines, probably biological machines.

The objective in thinking for yourself is to take every idea you hear from others with a grain of salt, and to even question your own ideas constantly. — Harry Hindu

If you take every idea with a grain of salt, you’ll never move beyond hesitation. Critical thinking isn’t about doubting everything, it’s about knowing when doubt is justified. In logic, mathematics, or physics, for instance, constant suspicion would paralyze learning; you suspend doubt provisionally because the framework itself has earned trust through rigor.

In a philosophy forum, though, caution makes sense. Most participants lack grounding in epistemology, logic, or linguistic analysis, so what passes for argument is often just speculation dressed up as insight. Honestly, you could gain more from interacting with a well-trained AI than from sifting through most of what appears here, it would at least give you arguments that hold together.

Much of what all of us do is "parrot." Not many people can come up with an original idea to save their life.

It's already helped me expand my thinking on epistemology, and it gave me good ideas on my book. However, you do have to have prior knowledge because it does make mistakes. The next two iterations of ChatGPT and Grok 5 have a good chance to reach AGI.

AI models from OpenAI and Google DeepMind reached gold medal-level performance at the 2025 International Mathematical Olympiad (IMO), one of the most prestigious math competitions in the world. It's also better at diagnosing than many doctors. So, I don't know where you're getting your information.

I've come to see anything that is not based on rigorous analysis or scientific understanding as intellectual wankery—mental masturbation—and I have no problem with people enjoying that, but the idea that it is of any real significance is, for me, merely delusory. — Janus

Don't mistake the speculative misuse of ideas for the ideas themselves. AI is no longer in the realm of “mental masturbation,” it’s already reshaping science, mathematics, and even philosophy by generating proofs, modeling complex systems, and revealing previously inaccessible patterns of thought. To dismiss that as delusory is to confuse ignorance of a subject with the absence of rigor within it.

The irony is that the very kind of “rigorous analysis” you claim to prize is being accelerated by AI. The most forward-looking thinkers are not treating it as a toy but as a new instrument of inquiry, a tool that extends human reasoning rather than replacing it. Those who ignore this development are not guarding intellectual integrity; they’re opting out of the next phase of it.

Truth is an emergent feature of linguistic and conceptual frameworks; it depends on the existence of propositions and shared criteria of correctness.

The fact is that if you don't know what you're doing, the result will be a mess. I've used AI for programming before and you really have to guide it and pay close attention to everything it does and constantly question its decisions. — Jamal

I wholeheartedly agree with your assessment. I used AI extensively while writing my book on NDEs and my work on epistemology. It was helpful for editing and idea generation, but it also made frequent errors, enough that I often wondered if it was creating more work than it saved. You have to know the material well to catch the subtle mistakes. Philosophical reasoning is especially difficult for AI: unlike programming or mathematics, it depends less on fixed rules and more on conceptual precision and contextual understanding. I don't think there is any doubt that it will help refine our thinking, but I'm not sure that it will replace humans in this area, but who knows.

I think we agree, unless I've misunderstood. Epistemology is about justification, truth of beliefs, i.e., when a belief counts as knowledge or as rationally warranted.

Abduction, on the other hand, concerns how hypotheses arise. It’s more about possibilities, not their justification. So, it belongs to the context of discovery, not the context of justification. Abduction is pre-epistemic, it produces candidates for knowledge but doesn’t by itself confer warrant. It’s how we start to think, not how we come to know.

I started by feeding all the material from my thread on NDEs into an AI tool to help compile and organize it into a coherent outline. From there, I used AI to assist with drafting the book—it’s incredibly useful for structuring ideas and generating momentum. That said, it does require constant oversight; AI still makes plenty of mistakes, so I had to correct and refine as I went. About a week ago, I handed the manuscript off to a human editor, since AI isn’t quite ready for the precision and nuance required in final edits. I’m now applying the same process to my work on epistemology. So yes—AI is absolutely part of my workflow, but it’s a tool, not a replacement.

Your response does not belong in a thread on epistemology.

Post #9 Conclusion

Justified True Belief Plus Understanding: A Wittgensteinian Extension

Samuel L. Naccarato

XIII. Conclusion — Epistemology Renewed
The question that began this inquiry—how we can still speak meaningfully of knowledge—has led back to the lived conditions that make such speech possible. The classical structure of justified true belief remains sound, but its adequacy depends on what had always been implicit within it: understanding. The addition of +U does not modify JTB’s logic; it completes its grammar. It makes explicit that justification is a human practice sustained by comprehension, correction, and shared criteria rather than by mechanical rule or private conviction.

Structured by hinges, disciplined by guardrails, and expressed through distinct routes of justification, JTB+U shows that knowledge is neither arbitrary nor—apart from the domains of logical, mathematical, grammatical, and moral necessity—absolute. It stands between skepticism and dogmatism, holding firm where reasons meet life. The framework’s strength lies not in closing inquiry but in keeping it open under discipline: it teaches how belief becomes accountable without demanding infallibility. In matters of fact we justify through evidence; in matters of value we infer from what experience shows to be harmful or life-giving. Knowledge thus joins observation to reason without confusing them. Its humility is its rigor.

In a world flooded with information and simulation, this distinction matters more than ever. Data can be multiplied indefinitely, but understanding cannot be automated. To know is not merely to process information but to stand within a practice whose meanings are lived. JTB+U therefore provides not only a philosophical model but a civic necessity: a grammar for preserving discernment in an age that confuses coherence with truth and confidence with warrant. The challenge is not to collect more facts but to cultivate the forms of life that make facts meaningful.

Epistemology, once dismissed as abstract, returns here as the discipline of intellectual survival. It asks what must remain in place for our practices of reasoning, testing, and trust to endure amid complexity. The answer is not another foundation but an attitude: to see what stands fast, to correct what drifts, and to understand what our words commit us to when we claim to know. That is what the framework of JTB+U restores—a picture of knowledge at once demanding and humane.

If philosophy’s task is to clarify what we already know in use, then epistemology’s renewal lies in remembering that use itself is layered, corrigible, and alive. Knowledge does not transcend life; it belongs to it. To know, in the fullest sense, is to participate intelligently in the world that gives knowing its possibility. The work of epistemology is therefore ongoing, not to end doubt but to keep sense intact—to ensure that understanding remains possible as our language, our tools, and our world continue to change.

Post #8 Continuing with paper...

Justified True Belief Plus Understanding: A Wittgensteinian Extension

Samuel L. Naccarato

XI. Progress, Regression, and Cultural Error
If individual error reveals the need for epistemic guardrails, cultural error shows why those guardrails must endure over time. Communities, like persons, can mistake conviction for knowledge. History offers many examples of beliefs once held with confidence—about astronomy, medicine, or morality—that now stand as reminders of how justification can be distorted by authority or habit. Yet the fact of revision does not imply that knowledge is relative or progress illusory. It shows instead that justification is a living practice: it matures as understanding deepens, even as it occasionally loses its way.

To call a change “progress” is to imply a standard by which improvement can be judged. JTB+U provides such a standard without appealing to timeless dogma. A belief counts as progress when it strengthens public justification—when it expands the range of reliable evidence, refines the criteria of testing, or clarifies the meanings that guide inquiry. A change that merely replaces one unexamined conviction with another is not progress but rotation. Epistemic improvement is measured not by novelty but by the steadiness of the connection between belief and truth under conditions of shared scrutiny.

Regression occurs when that connection weakens—when social or ideological forces detach belief from its justificatory routes. This can happen through political coercion, technological manipulation, or the seductive ease of untested consensus. In such moments, the form of knowledge may persist while its function decays. People continue to “believe,” “know,” and “explain,” but the grammar of those words no longer aligns with the practices that once gave them meaning. Wittgenstein’s warning about the “craving for generality” applies here: when a community elevates its own favored picture of truth to the status of an essence, it loses sight of the diversity of practices that give “knowing” its sense.

Examples abound. The moral insight that slavery is wrong did not arise from moral relativism but from the correction of moral reasoning. When thinkers like Gregory of Nyssa or, later, abolitionists challenged the institution, they appealed not to new emotions but to deeper coherence within existing moral grammar: the recognition that treating persons as property violates the very criteria by which moral justification operates. Progress here meant recovering what had been implicit all along—an expansion of understanding that reconnected moral belief with the truths it professed to serve.

Science, too, advances by oscillation between error and correction. The movement from Newtonian mechanics to relativity did not overthrow the structure of justification but refined it, showing that reliability lies in responsiveness, not rigidity. What endures through such revolutions is not a single theory but the hinge of methodological honesty: the willingness to let observation, logic, and replication override preference. Cultural progress follows the same rhythm. The strength of a civilization’s epistemic life is measured not by how seldom it errs, but by how readily it can recognize and amend those errors.

Thus, the persistence of misunderstanding is not evidence against truth but a sign of how deeply the human condition depends on interpretation. The point is not to transcend fallibility but to inhabit it wisely—to build systems of belief that can bend without breaking. JTB+U models this attitude: it joins conviction to correction, belief to discipline, and knowledge to the humility of what stands fast. Cultures regress when they forget that distinction; they progress when they recover it.

Epistemology, in this light, becomes a study of cultural memory: how communities retain the habits that keep belief answerable to the world. The test of any intellectual tradition is whether it can renew that discipline in changing conditions. A society that confuses persuasion with proof, or sentiment with reason, may thrive rhetorically but will falter epistemically. Progress is not measured by information gained but by understanding maintained—the ability to keep justification alive amid the noise of conviction.

XII. Beyond JTB+U — Layered Hinges and the Ultimate Background
Every inquiry ends where explanation meets its own conditions. Having traced justification through its routes and guardrails, we reach the level where even those depend on something deeper: the conscious background that allows epistemic activity to occur at all. To speak of an “ultimate hinge” is not to posit a new metaphysical entity but to notice the condition that makes any belief or proof intelligible. Consciousness is not an object of knowledge but the horizon within which that knowledge appears.

Hinges are layered. At the base lie bodily hinges—the sensorimotor regularities that orient perception. Above them, linguistic hinges stabilize communication and memory, making shared criteria possible. Higher still are conceptual hinges: the methodological norms that govern inquiry in science, ethics, and art. Each layer rests on the one beneath it, yet all presuppose the field of awareness in which appearing, judging, and meaning unfold. Consciousness, in this sense, is not another hinge but the ground of all hinge-dependence—the background in which every act of knowing takes place.

To recognize this is not to drift into metaphysics but to extend Wittgenstein’s method beyond therapy into description. Language clarifies meaning only because life already discloses a field in which meaning matters. The point is grammatical, not doctrinal: the form of life that makes epistemology possible is given in awareness itself. JTB+U, disciplined by its guardrails and grounded in hinges, ultimately leads back to this awareness—knowledge as a relation between conscious life and the world it inhabits.

Epistemology thus returns to ontology. To understand what it means to know is to glimpse what it means to be the kind of creature for whom knowledge is possible. The final humility of JTB+U is to see that even our most rigorous justifications rest within this unprovable background. The task is not to escape it but to live wisely within it—to let understanding mirror the layered depth of the reality it seeks to comprehend.

Post #7 Continuing with paper...

Justified True Belief Plus Understanding: A Wittgensteinian Extension

Samuel L. Naccarato

IX. Certainty and Probability
Few words have caused more confusion in epistemology than certainty. It has been treated as the mark of knowledge, the goal of justification, or the unattainable ideal we must renounce. The trouble is grammatical: certainty is used in several distinct ways, and philosophy has often blurred them together. To recover clarity, we must separate these uses and see how each belongs to a different layer of our epistemic life.

The first is subjective certainty—the conviction one feels when doubt no longer presses. It is the inner firmness of belief, the sense that “I just know.” This is a psychological state, not a justification. It may accompany knowledge, but it can also accompany error; history is full of confident mistakes. Subjective certainty belongs to the domain of belief, not knowledge. Within JTB+U, it marks the affective side of commitment but carries no epistemic weight unless joined to public justification and understanding.

The second is hinge certainty—the arational stability that makes doubt and justification possible. These are the propositions, practices, and bodily expectations that stand fast within a form of life: the sense that the world exists, that words retain their meaning, that memory and perception generally hold. Such hinges are not derived from proof but constitute the background that gives proof its sense. They are not known in the ordinary way but shown in our ongoing confidence. To call them certain is to describe their role, not their epistemic status: they belong to the grammar of inquiry, not to its conclusions.

The third is epistemic certainty, which arises when a belief is so well grounded that no available defeater remains. It is the practical summit of justification: defeater-resistant, publicly testable, and secure enough for action. Epistemic certainty is what science and law aim for when they speak of confidence “beyond reasonable doubt.” It is not infallibility but closure within current bounds of evidence. Under JTB+U, epistemic certainty reflects a state in which belief, truth, justification, and understanding converge under active guardrails.

The fourth is absolute certainty, encompassing logical, mathematical, grammatical, and moral necessity—the kinds of truth that define the boundaries of sense itself. “A triangle has three sides,” “Two plus two equals four,” and “All bachelors are unmarried” express such certainty: each is non-empirical, though different in source. Absolute certainty, in the logical and grammatical sense, is conceptual rather than empirical—it belongs to the structure of meaning, not to the flux of experience. Mathematical certainties share this role within a formal grammar of symbols, exhibiting necessity through rule rather than observation. Moral certainties, however, join experience to reasoning. From observed facts—harm, benefit, justice, deprivation—we infer the principles that ought to govern conduct. This knowledge is empirical in origin but normative in conclusion: it rests on evidence about human flourishing and the goods that sustain it. To call murder wrong, for example, is to draw a rational inference from the visible destruction of life’s basic good. Logical and grammatical certainty frame thought; mathematical certainty orders formal reasoning; moral certainty directs action. Each has its own domain, and clarity about their relation preserves both reason and moral sense.

When these four uses blur together, skepticism flourishes. If all knowledge required infallibility or absolute proof, none would survive; if all conviction counted as knowledge, none would be trustworthy. The strength of JTB+U lies in maintaining their distinctions: it grounds knowledge in what is publicly justifiable while acknowledging the deeper hinge-structure that allows justification to function. We act with epistemic certainty against a backdrop of hinge stability, tempered by the awareness that both remain fallible in practice.

Probability enters here as the grammar of humility. To think probabilistically is not to weaken knowledge but to situate it: to treat degrees of confidence as reflections of evidence, not as confessions of doubt. Probability quantifies what understanding already senses—the difference between stronger and weaker grounds. It disciplines belief without surrendering the concept of truth. When properly used, probability expresses the same modesty that hinge awareness teaches: that knowledge is never absolute, yet it can be reliable enough for life.

In this light, certainty and probability are not opposites but coordinates on the same epistemic map. Certainty describes where justification holds firm; probability marks where it shades into openness. The work of epistemology is not to abolish either but to keep them aligned—to preserve confidence without arrogance, and humility without paralysis. Under JTB+U, that alignment becomes a form of understanding: the ability to know how far one’s knowledge reaches and where it must give way to further inquiry.

This structure is already visible in the sciences, which embody JTB+U’s grammar in practice. Observation supplies the sensory route; mathematical and experimental reasoning exemplify logic; replication and peer review enforce public justification; and conceptual understanding binds the whole system together. Scientific progress depends on defeater sensitivity, practice-safety, and the correction of false grounds—the very guardrails that make knowledge reliable across contexts. JTB+U therefore does not compete with science; it clarifies what science has always done. It reveals that the same discipline of justification runs through every field where truth is pursued under shared criteria.

X. Framework vs. Application — The Problem of Error
No epistemic framework is immune to misuse. The failures of individuals or cultures to reason well do not refute the grammar of reasoning itself. Just as a player may blunder without discrediting the rules of chess, the misapplication of justification does not invalidate the structure of JTB+U. It shows only that fallibility is built into the game. A framework can be sound even when its players are not. The proper question is therefore not whether error occurs, but what kind of system allows its recognition and repair.

JTB+U holds precisely because it expects correction. Its guardrails—No-False-Grounds, Practice-Safety, and Defeater Screening—were never meant to guarantee infallibility but to sustain reliability in the long run. They turn epistemology from a search for perfect certainty into a practice of continual calibration. What counts is not that mistakes never happen, but that they can be identified, traced to their source, and rectified without abandoning the pursuit of truth. A theory that cannot accommodate error is not a theory of knowledge but of denial.

Confusion arises when apparent defeaters are mistaken for genuine ones. A discovery that revises a belief does not always falsify the method that produced it. The refinement of scientific models, for example, is not epistemic collapse but epistemic health: the self-correction of a method capable of learning from its own limits. Likewise, moral and cultural progress depends on practices of justification that outgrow their earlier boundaries while preserving the standards that made such revision intelligible. Error, in this sense, is not the opposite of knowledge but its price—the cost of operating in a world that resists simplification.

Framework stability differs from application success. The grammar of JTB+U remains intact even when its users fail to meet its demands. A community may mistake tradition for justification or ideology for truth, yet the failure lies in neglecting the framework, not in the framework itself. To say that a culture “knew” something false is to misuse the word know; knowledge cannot rest on what fails its own criteria. JTB+U retains its authority precisely by excluding such cases—it defines knowledge by the discipline that distinguishes warranted belief from collective conviction.

Reliability, then, is statistical rather than absolute. Knowledge need not work always; it must work more often than not. A belief-forming process counts as reliable when its success rate exceeds chance by the margin of disciplined attention. That threshold varies by context: science demands reproducibility, law demands consistency, ordinary life demands functionality. What unites them is the same structure of public accountability. When those standards erode, justification becomes a gesture without content—a language-game played with empty pieces.

To understand error in this way is to see why epistemology remains indispensable. It teaches how to recognize when reasoning has left its track and how to return without despair. The possibility of error is not a threat to knowledge but its enabling condition: it defines what it means for a belief to stand fast in a world that does not guarantee us success. JTB+U embodies that humility. It neither denies fallibility nor accepts confusion as fate. It makes knowledge corrigible rather than fragile—strong enough to endure mistake, and honest enough to admit it.

Post #6 Continuing with paper...

Justified True Belief Plus Understanding: A Wittgensteinian Extension

Samuel L. Naccarato

VII. Guardrails and Routes of Justification
If hinges show the background that makes justification possible, guardrails describe the boundaries that keep it responsible. All knowing occurs within shared practices; the question is not what the ultimate foundations are, but what prevents justification from drifting once the game has begun. Classical epistemology often sought safety in certainty; JTB+U seeks it in discipline. Knowing is not guaranteed by indubitable premises but safeguarded by procedures that prevent collapse—rules of use that maintain coherence within the practice itself.

Hinges are layered, and each layer calls for its own kind of vigilance. Bodily and perceptual hinges secure our immediate commerce with the world; linguistic and social hinges stabilize meaning and coordination; conceptual hinges structure inquiry within specialized domains such as science or law. None of these layers is absolute, yet each provides the stability within which justification has sense. The guardrails of JTB+U operate across these layers, translating hinge-dependence into practical norms that keep reasoning from losing its footing.

Three guardrails mark this discipline: No-False-Grounds (NFG), Practice-Safety, and Defeater Screening. Each preserves the integrity of justification without appealing to unshakeable foundations. NFG bars a claim from counting as knowledge if it rests on a false or corrupted premise; Practice-Safety requires that the route by which a belief is formed remain reliable under normal conditions of use; Defeater Screening demands that a knower remain alert to evidence or context that would undermine the claim. Together they form a framework of epistemic balance—flexible enough to apply across language-games, firm enough to distinguish knowledge from conviction.
The same vigilance that keeps guardrails firm extends into the particular routes by which justification travels.

The force of these guardrails appears most clearly in practice. No-False-Grounds is what prevents us from counting a conclusion as knowledge when its evidence is tainted—when, for instance, a medical finding rests on miscalibrated instruments or a historical claim depends on forged documents. Practice-Safety protects reasoning from self-defeat: a belief is justified only if the process that produced it would still yield truth under the normal circumstances of its use. The surgeon’s judgment, the pilot’s checklists, the scientist’s controls—all illustrate this principle. They show that knowledge is not an accident of success but a discipline of reliability.

Just as hinges define what stands fast, guardrails mark the limits within which we can move securely. They do not replace understanding but sustain it, ensuring that justification remains responsive to correction and anchored in the background practices that give it sense. Under JTB+U, knowledge becomes not a static possession but a maintained equilibrium: a way of navigating error while preserving contact with truth. The guardrails provide the grammar of that navigation—the habits of self-monitoring that make justification a living process rather than a frozen credential.

The next task is to see how these guardrails interact with the five primary routes of justification through which knowledge is ordinarily secured—Testimony, Logic, Sensory Experience, Linguistic Training, and Pure Logic. Having outlined the framework’s safeguards, we can now trace its operation within those routes.

VIII. Routes of Justification
Having outlined the guardrails that preserve epistemic integrity, we can now examine the main routes through which justification ordinarily proceeds. Each represents a distinct way in which belief becomes answerable to public criteria—paths by which knowledge maintains its contact with truth. The five routes are not competing theories but complementary dimensions of one practice: the human effort to test, verify, and sustain claims within shared forms of life. They are Testimony, Logic, Sensory Experience, Linguistic Training, and Pure Logic. Together they show how JTB+U functions as a living grammar of knowledge, operating across contexts yet anchored in use.

1. Testimony
Most of what anyone knows comes from others. Testimony is not a secondary or inferior route of justification but the default medium of social knowledge. The reliability of testimony depends on the same guardrails that govern all epistemic practice: its sources must be free of false grounds, its claims must hold under the normal conditions of communication, and its credibility must withstand potential defeaters. In law, we cross-examine; in science, we replicate; in daily life, we corroborate. Each procedure exemplifies the same structure: trust qualified by testability. What makes testimony a route of justification is not blind acceptance but public accountability—a pattern of speech in which reasons can be requested and errors exposed.

2. Logic (Inductive and Deductive Reasoning)
Reasoning transforms belief into structure. Logic provides the skeleton of justification: the rules by which claims connect coherently. Deductive reasoning secures necessity within formal systems, while inductive reasoning extends confidence through patterns of experience. Both operate under the same discipline—No-False-Grounds in premises, Practice-Safety in application, and Defeater Screening in the ongoing readiness to revise. Logic shows that justification is not a private intuition but a rule-governed practice: a grammar of inference that binds participants who share its norms. When applied well, it does not remove uncertainty but gives it proportion and direction.

3. Sensory Experience
Perception anchors the web of belief to the world. Sensory experience is the route by which language meets reality, the ongoing test that keeps our reasoning from floating free of what it claims to describe. Yet experience is not self-certifying; it requires the interpretive frame supplied by language-games and forms of life. A red patch on the retina becomes red only within a community that has learned to distinguish and name it. Sensory justification, therefore, is not raw data but disciplined perception—an interplay between what appears and what our training allows us to see. The guardrails keep this route honest: they prevent us from mistaking illusion for observation or correlation for causation.

4. Linguistic Training
Every act of justification presupposes fluency in the practices that give words their sense. We learn not only vocabulary but the criteria for using it correctly. Linguistic training is a route of justification because it grounds knowledge in shared grammar. To understand know, reason, see, or prove is to have mastered their use within a community. Without that background, even true statements can fail to count as knowledge. Language itself thus functions as an epistemic discipline: it transmits both the content and the method of justification. The guardrails operate here as norms of correctness—what makes a use right or wrong, what counts as a reason rather than a mere association.

5. Pure Logic (Boundary-Setting)
At the outer edge of justification lies what might be called pure logic—the clarification of boundaries rather than the discovery of new truths. It does not supply new truths but delineates the conditions under which any truth-claim makes sense. This route corresponds to the hinge-layer of our rational practices: the axioms, definitions, and inferential rules we accept to make reasoning possible. Their justification is not empirical but grammatical—they set the stage on which justification itself occurs. In JTB+U, pure logic functions as a regulative ideal: it reminds us that even the most abstract reasoning depends on tacit agreements about sense and rule-following.

These five routes are not exhaustive, but they mark the principal ways justification remains public, corrigible, and embodied. Each relies on understanding to interpret its own standards, and each gains reliability from the guardrails that keep it tethered to practice. Together they show that knowledge is neither atomistic nor monolithic: it is a network of disciplined activities that preserve our contact with reality while allowing revision within it.

Post #5 Continuing with paper...

Justified True Belief Plus Understanding: A Wittgensteinian Extension

Samuel L. Naccarato

VI. Grounding JTB+U: Hinges and the Limits of Explanation
Having made explicit what JTB always presupposed, we can now ask what even understanding itself presupposes. If justification depends on understanding, and understanding on the ability to “go on rightly” within a practice, then our inquiry turns toward the background that makes such going-on possible at all. Here we reach the level of what Wittgenstein calls hinge propositions: the certainties that do not stand as conclusions but as the framework within which conclusions have sense. These are not hypotheses or theories but the quiet conditions that give justification its grammar.

A hinge is not known, doubted, or inferred; it is shown. When I check the clock to see if my train leaves at 8:15, I do not also doubt the existence of clocks, the reliability of numbers, or the fact that trains normally run on tracks. These stand fast; they form the river-bed against which all reasoning flows. To treat them as ordinary beliefs would dissolve the very distinction between doubt and knowledge that makes reasoning possible. Wittgenstein treats them as hinges—commitments that stand fast and underwrite the use of reasons.

We misunderstand hinges when we look for them in the wrong logical space. They are not hidden propositions waiting to be uncovered but the background conditions that make propositional exchange possible. In Wittgenstein’s terms, they belong to the grammar of our language-games, not to their content. The certainty that there is an external world, that memories usually persist, or that words keep their meaning from one moment to the next does not arise from inference; it is built into our way of acting and speaking. To question such things would not be to doubt within the game but to suspend the game itself. Hinges, then, mark the limits of meaningful doubt.

Because hinges are shown rather than stated, they resist direct articulation. We notice them only when they shift or fail—when something we took for granted ceases to hold and the practice stumbles. A child learning to tell time, for instance, must acquire not only the vocabulary of numbers but the hinge-certainty that the clock’s face represents a continuous and reliable system. Only within that certainty does the instruction “the train leaves at 8:15” make sense. Likewise, the scientist who checks her instruments does not begin by questioning whether instruments can measure; she works within that bedrock confidence until evidence forces revision. Hinges are thus the tacit limits within which understanding operates, the background from which justification and belief draw their meaning.

Hinges therefore mark the final limit of explanation. They are not conclusions reached by argument but the inherited background that allows argument to begin. Each form of life has its own pattern of such certainties—its ways of acting, measuring, and trusting that make its language-games coherent. Some are bodily and perceptual, such as our confidence that the floor will bear our weight; others are linguistic and communal, such as the expectation that words retain their meaning from one moment to the next. These are not propositions waiting for proof but the bedrock regularities that give “proof” any sense at all.

These hinges also differ in depth and scope. Some belong to our immediate bodily orientation, others to the linguistic and social patterns that stabilize meaning, and still others to the conceptual frameworks that structure inquiry within specialized domains. They form a layered background rather than a single foundation. Each layer depends on the one beneath it but can evolve within its own field of stability. Recognizing this stratification will matter later, when we consider how the entire structure of justification ultimately rests within consciousness itself—the horizon that makes hinge-dependence intelligible, not a foundation that explains it.

To grasp the role of hinges is to see why justification must have an endpoint that is neither arbitrary nor absolute. The search for reasons cannot proceed forever, yet to stop anywhere seems dogmatic. Hinges resolve this tension. They are the stopping points that are not chosen but inherited—the certainties into which we are trained by participation in a form of life. Their authority is not imposed by argument but conferred by practice. In this sense, they halt regress without appeal to foundations in the traditional sense. The chain of reasons stops, but it stops in what everyone already shows through action: in looking, measuring, speaking, and trusting where trust is the very grammar of the activity.

This structure avoids both extremes that have long haunted epistemology. Against skepticism, hinges show that not everything needs proof for knowledge to be possible; some things must stand fast if proof is to count as proof. Against dogmatism, hinges remain open to revision—not by refutation but by transformation of the practice itself. When the background shifts, the hinges shift with it, and new patterns of justification emerge. That is how scientific revolutions, moral realignments, and linguistic innovations occur: not by overthrowing all hinges, but by slowly reconstituting the bedrock upon which justification rests.

Hinges therefore give epistemology its shape. They delineate the limit of what can be doubted without rendering doubt meaningless, and they ground understanding in a world that is already shared before it is analyzed. JTB+U finds its ultimate stability here: justification ends not in an axiom but in a lived form of certainty that makes reasoning possible. To know is to move within a practice whose hinges hold—to rely, often silently, on what stands fast while thought and language do their work.

The same pattern that Wittgenstein exposes in language reappears, in a different key, within logic itself. Gödel’s incompleteness theorems demonstrate that any consistent formal system rich enough for arithmetic will contain true statements that cannot be proved from within that system’s own rules. Each coherent structure thus depends on truths it cannot generate—propositions that serve as the system’s own hinges. What Wittgenstein shows from the side of practice, Gödel shows from the side of form: both reveal that intelligibility depends on limits that cannot be removed without dissolving the very activity they sustain.

This parallel does not reduce hinges to mathematics, nor Gödel’s limit to psychology. It marks a shared architecture of dependence: reason requires an outside it cannot grasp. The mathematician must assume the reliability of symbolic operations just as the speaker must assume the stability of language. Both inhabit a framework that is not itself derivable but is continuously shown through use. In each case, the impossibility of total self-grounding is not a defect but a condition of meaning.

Seeing this restores epistemology to its proper scale. The point is not to seek absolute foundations but to understand how knowledge coheres within the boundaries of sense. JTB+U names that coherence at the level of practice; Wittgenstein and Gödel show the horizon that holds it in place. What lies beyond that horizon is not another proposition to discover but the silent background that allows discovery to occur. To recognize that limit is not to retreat from knowledge but to acknowledge the modesty built into knowing itself.

Post #4 Continuing with paper...

Justified True Belief Plus Understanding: A Wittgensteinian Extension

Samuel L. Naccarato

V. JTB+U: Adding Understanding
The regress of justification need not end in skepticism. It ends, rather, in recognition that justification always presupposes a grasp of how reasons connect—a background fluency that cannot itself be justified propositionally. Wittgenstein’s hinges show where reasons stop; understanding shows how they continue to make sense. The classical triad of truth, belief, and justification captures the outward form of knowledge, but its stability depends on an inner relation that binds these elements together. To make that relation explicit is the task of JTB+U.

Some may object that understanding is already contained in justification, that no one can justify a belief without some degree of comprehension. I agree, but the very fact that this dimension remains unarticulated has allowed epistemology to treat justification as if it were purely propositional. Naming +U does not add a new condition; it restores to view the conceptual hinge that justification already turns upon.

Understanding is already implicit in JTB. The classical model could never function without it, for to justify a belief is already to grasp the connection between reasons and conclusion. Yet in most philosophical treatments this grasp is left unarticulated, as though understanding were guaranteed whenever justification appears. My point in making it explicit is not to alter the structure of JTB but to bring to light what it silently depends on.

Understanding functions analogously to a hinge—not arational in the Wittgensteinian sense, but structural in the epistemic sense; it keeps justification in motion—the capacity to follow reasons as reasons, to see how evidence supports a claim rather than merely to repeat that it does. Without that inner relation, justification becomes mechanical and belief drifts toward imitation. When we examine how the word know functions in our language-games, we see that understanding is built into its grammar. To say “I know that p” normally implies that I can use p rightly in related contexts—that I see its sense and can extend it coherently.

We withdraw the word know when this fluency is missing, as when someone parrots a theorem or repeats an argument they do not comprehend. Thus, understanding is not an optional embellishment but part of what gives the concept of knowledge its life. JTB has always assumed it, much as a door presupposes its hinge even when the hinge is unseen. Making that hinge explicit matters because it prevents epistemology from mistaking outward form for inner mastery.

Classical analyses of justification tend to focus on external adequacy: the quality of reasons, the truth of premises, the logical connection among propositions. But none of these suffice if the knower lacks comprehension of how those reasons work. The +U draws attention to this internal dimension, protecting JTB from its own abstraction. It ensures that the model remains tied to lived competence rather than to formal correctness alone.

From a Wittgensteinian perspective, this move simply applies his method to epistemology itself. By describing how know operates in our practices, we notice that understanding is already part of its use. Knowledge is shown in one’s ability to go on rightly when the explicit rule runs out, to recognize when an argument holds and when it does not. The philosopher’s task is not to add new parts to the machine but to illuminate what makes it run.

In this light, JTB+U is not a new engine but a clearer description of the one we have always been using. Naming understanding thus gives epistemology self-awareness. It acknowledges the quiet condition that makes justification possible and holds belief in contact with truth. To call the model JTB+U is to make explicit the hinge on which it already turns. The addition changes nothing in principle, yet it changes everything in practice: it restores to the concept of knowledge the depth and accountability that modern epistemology, in its fixation on external form, too easily neglects.

Philosophers often distinguish knowing that from knowing how. The first concerns propositions, beliefs that can be stated and assessed for truth. The second concerns abilities, skills displayed in doing rather than saying. Yet in practice, the two are intertwined. To know that the Earth has one moon is to hold a justified true belief; to know how to count is to participate in a rule-governed practice that gives such propositions meaning. Understanding bridges these domains. It is what allows one to move from proposition to application, from rule to use, from explicit statement to competent action.

Gilbert Ryle drew this distinction to resist the idea that all knowledge is propositional, but the point can be carried further: understanding is not reducible to either kind. It is the fluency that lets us go on rightly when explicit instruction ends—the ability to see what follows, to extend a pattern without mechanical repetition. In this sense, +U names the skill within belief, the practical mastery that turns justification from recitation into insight. Where knowing that gives structure, knowing how gives life; understanding unites them in a single epistemic posture.

Understanding gives the classical framework its working strength. It prevents justification from collapsing into rote conformity and keeps belief in contact with the practices that confer meaning. In JTB+U, understanding performs a stabilizing function: it disciplines justification, grounds belief, and keeps truth from becoming an abstraction. To understand is to know when justification applies, when it fails, and when further inquiry is needed. It is the tacit mastery that lets us recognize a defeater before it destroys confidence, and to adjust reasons when new evidence appears.

This functional role can be described in three interlocking features. First, understanding is defeater-sensitive: it detects when a justification no longer holds because the context has shifted or the evidence has been undermined. Second, it is publicly oriented: understanding moves within language-games that allow others to test and correct what we claim. Third, it is practice-safe: it operates within the bounds of skills, tools, and norms that keep error recognizable rather than catastrophic. These are the guardrails that make justification resilient instead of brittle.

In this way, +U transforms the classical model without altering its structure. Truth, belief, and justification remain, but their coherence now depends on a living capacity to follow reasons rightly. A community that shares this capacity can correct itself without abandoning realism; a thinker who possesses it can doubt responsibly without falling into skepticism. The model becomes self-monitoring rather than self-sealed. JTB+U thus unites epistemic rigor with Wittgensteinian humility: justification is never final, yet it can be secure enough for action because understanding continuously interprets, tests, and re-grounds it in practice.

Because justification depends on public criteria, the framework of JTB+U is inherently democratic. Knowledge does not belong to experts alone but to any participant trained in the grammar of reasons. Public justification levels the epistemic field: it allows disagreement to become inquiry rather than authority. What distinguishes good reasoning from mere assertion is not who speaks but how claims can be examined, corrected, and improved. The addition of understanding restores this shared capacity to its proper place—it ensures that justification remains a communal achievement rather than a private performance.

Consider a familiar academic scene. A student can recite the steps of a proof in formal logic, yet when asked to apply the same principles in a new example, the reasoning collapses. The difficulty is not with memory but with understanding. The student’s belief that the proof is valid may be true and even accompanied by justification in the narrow sense—citations, derivations, and the correct symbolic form—but the grasp of why those steps hold is missing. By contrast, another student who genuinely understands the proof can adapt it, recognize where an inference fails, and explain its scope. The difference lies not in propositional content but in the mastery that unites rule and use.

This contrast illuminates what +U contributes. Without understanding, justification can mimic knowledge while remaining hollow. With understanding, the connection between truth and belief becomes internally visible: the knower can not only assert the conclusion but trace its sense within a broader practice. In scientific inquiry, this difference distinguishes the technician who repeats a method from the researcher who knows when and why to revise it. In ordinary life, it separates parroting from comprehension, rote conformity from intelligent trust. Understanding gives epistemology a human shape; it turns the abstract structure of JTB into a lived capacity for discernment. The same distinction explains why artificial systems, however advanced their pattern recognition, simulate justification without displaying understanding. They produce correct outputs without the grasp that links rule to use—a difference that exposes, rather than closes, the human horizon of epistemology.

The same distinction appears in our encounter with artificial intelligence. A large language model can reproduce the surface grammar of comprehension—it can extend a discussion, follow contextual cues, and generate reasons that sound plausible—but it does not inhabit the life-grammar that gives those moves their weight. It has no background of risk, training, or embodied continuity. What we call a feeling for context in human understanding is not a private emotion but a readiness to respond grounded in shared forms of life. Machines can simulate coherence, yet simulation is not participation. The +U in JTB+U names precisely this difference: the grasp of meaning that lives in practice and cannot be replaced by correlation.

JTB+U restores the living grammar of knowledge. By making understanding explicit, it completes rather than revises the classical model: truth, belief, and justification now cohere through the grasp that keeps reasons intelligible within practice. The framework is thus strengthened from within—defeater-sensitive, publicly testable, and responsive to context without surrendering objectivity. Yet this clarification raises a deeper question: if understanding binds justification to truth, what binds understanding itself? To answer that, we must look beneath reasons to what makes reasoning possible—the background certainties that stand fast when inquiry begins. It is there, at the level of hinges, that the structure of knowledge finds its ground.

Post #3 Continuing with paper...

Justified True Belief Plus Understanding: A Wittgensteinian Extension

Samuel L. Naccarato

IV. The Limits of Classical JTB
For all its durability, the classical model of knowledge conceals internal strains. It describes our epistemic grammar but does not explain how justification itself is secured. If every reason calls for a further reason, the regress of justification seems endless; if the chain simply stops, it risks arbitrariness. JTB thus oscillates between two unsatisfactory poles: infinite regress or dogmatic halt. The problem is not that justification fails, but that its ground is misunderstood. We treat it as though reasons could stand alone, detached from the forms of life that give them sense. To move beyond this impasse, we must examine what makes justification possible at all—how it arises within practices, why it cannot be fully propositional, and what happens when it tries to explain itself.

When justification is pressed for its own warrant, philosophy turns in a circle. Each appeal to evidence, perception, or logic depends on background practices that it cannot itself justify. We trust our senses because they have worked; we rely on induction because it continues to deliver; we accept inference because our community has trained us to do so. None of these rests on proof in the narrow sense. Both Wittgenstein and Gödel expose this structural limit from different directions: the first by showing that justification must end in what “stands fast,” the second by showing that no consistent, effectively axiomatized formal system strong enough for arithmetic can prove all of the arithmetical statements that are true in its standard interpretation. In each case, the search for ultimate justification reveals a boundary built into the practice of reasoning itself.

This boundary is not a defect but a condition of intelligibility. To say that justification depends on what is not justified is not to surrender reason but to recognize its grammar. The chain of reasons stops not in an arbitrary assertion but in action—in the regularities of life that give words and proofs their sense. These are our hinges: arational certainties expressed in doing rather than saying, in counting, measuring, speaking, and trusting testimony. Some are nonlinguistic—bodily and perceptual orientations that make language possible; others are linguistic—rules and criteria we inherit without explicit proof. Together they form the bedrock upon which propositional knowledge rests.

The same structure appears in logic itself. Gödel’s incompleteness theorems show that any consistent, sufficiently strong formal system cannot, from within its own axioms and rules, prove all the truths it expresses. The undecidable sentences of mathematics play a role analogous to Wittgenstein’s hinges: they delineate what can be shown without being themselves derivable. In both cases, the limit is not an obstacle but an architecture—an edge condition that makes meaningful proof and meaningful doubt possible. Recognizing this shifts the philosophical task from seeking absolute justification to describing the frameworks that silently enable it.

Post #2 Continuing with paper...

Justified True Belief Plus Understanding: A Wittgensteinian Extension

Samuel L. Naccarato



III. JTB in Practice—Strengths and Durability
With this toolkit in hand, we can now return to JTB itself, no longer as an abstract formula but as a practice embedded in forms of life. The next section examines how the triad of truth, belief, and justification operates within science, law, and ordinary reasoning, showing why it has endured across centuries of intellectual change. JTB persists because our language-games still require the grammar it names.

The endurance of the classical triad lies not in philosophical inertia but in functional necessity. Wherever human beings act together, we rely—often without notice—on the grammar that JTB names. Truth secures contact with reality; belief marks personal assent; justification connects the two through publicly defensible reasons. Remove any one element and the practice collapses. The model persists because its logic is lived before it is theorized. Science, law, and ordinary life all enact its pattern, however differently they speak.

To dismiss testimony out of hand is to practice a selective skepticism that defeats itself. Every belief, even in science, relies on others’ reports—records, measurements, observations, and reasoning transmitted through language. The issue is not whether testimony can yield knowledge but under what conditions it does. When sources are transparent, independent, and open to challenge, testimony functions as a public route of justification, not a private appeal to authority. A framework that denied this would unravel its own basis, for even the principles of logic and experiment reach us through human transmission.

Philosophers have long distinguished between knowledge by acquaintance—the direct familiarity one has with a person, color, or sensation—and knowledge by description, which depends on propositions or reports. The former is immediate and non-inferential; the latter mediated and linguistic. Both fit naturally within the JTB grammar: acquaintance anchors belief in perception and experience, while description anchors belief in testimony and reasoning. What Wittgenstein’s method adds is the reminder that these are not competing species but overlapping uses of know, each governed by its own criteria of justification within a form of life.

Consider science first, not as an institution but as a disciplined form of life. A physicist claims to know that a certain particle has a particular charge. What makes that claim knowledge rather than opinion is not conviction but the convergence of truth and justification. The statement corresponds to how the world behaves; the methods used to reach it—calibration, replication, peer review—provide the warrant that secures belief against mere luck. The scientist’s belief, her internal assent, is indispensable but not decisive. If later evidence overturns the finding, we say that the community was mistaken, not that belief altered truth. This readiness to correct itself shows the health of the practice: knowledge here is corrigible without being arbitrary.

In science, JTB functions as a structure of accountability. Truth guards against fantasy; justification institutionalizes humility. A result that cannot be checked or replicated fails the justificatory test no matter how confidently it is asserted. Likewise, a correct result reached by accident—a lucky guess or an uncalibrated instrument—fails the epistemic test because justification is missing. These boundaries mirror the grammar that JTB codifies: luck without reason is not knowledge, and reason without truth is illusion. The laboratory simply dramatizes what ordinary cognition already presupposes.

The same structure governs law, though expressed in another language-game. A jury must decide whether an accused person committed a crime. The verdict involves belief, but that belief counts as knowledge only when tethered to evidence that meets public standards—cross-examination, corroboration, admissibility. Truth is represented by the facts as they occurred; belief is the jurors’ collective assent; justification is the process that links the two—the rules of evidence and reasoning that make the verdict intelligible. The system acknowledges the fallibility of justification through appeals and retrials, mechanisms that reflect the same epistemic humility found in science. Even where human judgment replaces experiment, the grammar remains constant: knowledge requires a claim to be both true and justifiable to others.

Legal reasoning also shows why knowledge must be public to be binding. The witness who swears to tell the truth invokes all three conditions. Truth corresponds to what occurred; belief is the sincerity of the witness; justification is the evidentiary frame that renders the testimony credible. A statement may be true yet unjustified if it cannot be corroborated, or justified yet false if the witness is mistaken. These permutations display the interlocking checks that give the concept its durability. We could abolish juries or rewrite evidentiary codes, but any workable system of accountability would still presuppose the same triad.

Outside formal institutions, JTB continues to guide everyday reasoning. When I say that I know the bus leaves at eight fifteen, I am implicitly asserting that the schedule is accurate (truth), that I believe it (assent), and that I have grounds—experience, confirmation, or testimony—to warrant the claim. If the bus departs at eight thirty, I was mistaken, not lying. The grammar of correction—“I thought I knew”—shows that knowledge is a normative status, not a psychological state. We retract know precisely when one of its components fails.

Such examples reveal that JTB is not a theoretical invention but a description of how epistemic life is already organized. Each time we distinguish between “He believes it” and “He knows it,” we invoke this grammar. Justification serves as the hinge between subjective conviction and objective warrant, allowing communities to coordinate understanding without collapsing into solipsism. The continuity of this pattern across domains explains its longevity. Cultures differ in what they treat as good evidence, yet all maintain a distinction between reliable and unreliable belief. That constancy points to a deep pragmatic truth: societies cannot act coherently without a shared grammar of epistemic accountability.

The triad’s durability also shows its resilience to technological change. Algorithms, like humans, are judged by truth, belief-analogues, and justification. A predictive model that forecasts rain tomorrow is evaluated by whether it rains (truth), how confidently the system assigned probability (belief-analogue), and whether the reasoning behind the prediction—its data and parameters—holds up (justification). We demand these checks even of machines because they mark the boundary between information and knowledge. The form of life shifts, but the grammar remains.

Durability here should not be confused with rigidity. Each component balances and corrects the others. Truth disciplines belief; belief animates truth; justification mediates between them. Remove truth and we drift into relativism; remove belief and we are left with sterile description; remove justification and we lapse into dogma. The triad functions as a self-correcting system, not a closed one. It remains stable precisely because it allows error to be recognized and remedied within practice.

This balance can be seen in education, medicine, and ordinary trust. In education, to know a theorem is not merely to recite it but to understand its proof and application—a glimpse of the +U that will later enter our model. In medicine, to know a diagnosis is to link symptoms to mechanisms through reasoning that others can review. In friendship, to know someone’s character is to form a belief responsive to evidence and revised by experience. Across these contexts, the same triadic structure persists: truth as correspondence, belief as personal assent, justification as the publicly defensible bridge between them.

Wittgenstein’s contribution is to make this structure visible rather than reinvent it. He shows that the power of JTB comes from its embeddedness in language-games. The standards of justification differ between a physicist and a parent, yet both belong to forms of life where reasons can be given and challenged. By examining those practices, we see that the grammar of know is stable not because it is timeless but because it is lived. When philosophers attempt to replace JTB, they usually reintroduce it under another name. Even coherence theories and reliabilism preserve its skeleton: truth as target, belief as stance, justification as route. The differences lie in emphasis, not in structure.

The persistence of JTB across changing practices is therefore a mark of its depth. It names the minimal conditions under which knowledge remains intelligible. Even when justification fails or belief wavers, we appeal back to this framework to make sense of the failure. It functions like the grammar of a language: rarely noticed when used well, instantly felt when violated. To reject JTB entirely would be to forfeit the distinction between knowledge and luck, between reasoned warrant and accidental truth.

For this reason the model endures. It does not demand perfection but provides a standard by which imperfection can be recognized. Its durability comes from its fit with the rhythms of human reasoning, from the fact that it mirrors the way we already keep our words in contact with the world. In this light, JTB is not a relic but a record of the conditions that make rational discourse possible. We can now examine its limits—the ambiguities of justification and the regress of reasons—and prepare for the Wittgensteinian insight that will dissolve those tensions without abandoning realism.

I just finished my paper on epistemology which I'll post in here a section or two at a time.

Post #1

Justified True Belief Plus Understanding: A Wittgensteinian Extension

Samuel L. Naccarato

Abstract
This paper reexamines the classical model of knowledge as Justified True Belief (JTB) and argues for its refinement through the addition of Understanding (+U). Drawing on Wittgenstein’s later philosophy—especially the concepts of language-games, grammar, and hinge propositions—it shows that justification operates within shared forms of life rather than in isolation. The JTB+U framework retains truth, belief, and justification but grounds them in public criteria and interpretive competence: knowing is not only having reasons but grasping how reasons function within practice. Three guardrails (No-False-Grounds, Practice-Safety, and Defeater Screening) and five justificatory routes (Testimony, Logic, Sensory Experience, Linguistic Training, Pure Logic) formalize this discipline of reliability. The analysis situates epistemology amid today’s information landscape, where distinguishing knowledge from persuasion has become urgent. By integrating Wittgenstein’s insights with modern concerns about data, AI, and scientific reasoning, the paper presents an epistemology that is self-correcting, communal, and humane. JTB+U preserves realism without dogmatism, acknowledging that understanding is both the hinge of justification and the safeguard of discernment in an age of unmoored information.

I. Why Epistemology Still Matters
It is fashionable to treat epistemology as an exhausted discipline—an inheritance of an earlier age, once useful for justifying science or theology but now displaced by data and probability. Yet the problem of knowledge has not vanished; it has multiplied. In a world where opinion spreads faster than evidence and conviction can be engineered by algorithms, the need to distinguish knowing from believing has never been greater. We inhabit a culture that prizes information but neglects understanding; it equates confidence with competence. Epistemology, properly understood, is not a relic but the grammar of orientation—our means of finding footing amid proliferating claims to truth.

We are entering an age in which the very conditions of knowing are being rewritten. Information now multiplies faster than human understanding can absorb it, and systems that simulate reasoning already shape what most people take to be true. The problem is no longer access to data but the loss of criteria for weighing it. Algorithms can imitate justification, narratives can mimic coherence, and conviction can be manufactured at scale. In such an environment, epistemology becomes a public necessity, not an academic luxury. To know what knowledge is—to see how truth, belief, justification, and understanding interlock—is the only safeguard against a world where persuasion replaces reason and where the grammar of “knowing” itself is quietly altered. Clarifying that grammar is the task before us.

To speak of knowledge presupposes an order of assessment. We do not call every opinion knowledge, nor every true remark knowledgeable. The distinction is not moral but functional: society, law, and science depend on reliable ways of sorting appearance from reality. When a court accepts testimony, when a physician interprets a scan, when a citizen evaluates a headline, the same question arises in different dress: what warrants belief? Epistemology matters because these decisions, repeated daily, determine whether our shared practices remain rational or collapse into echo.

The classical model—Justified True Belief—still captures the skeleton of these practices. Truth ensures contact with reality; belief marks the personal uptake of that contact; justification provides the public warrant. Each condition blocks a familiar failure: without truth, we cling to illusion; without belief, we mouth what we do not hold; without justification, we risk luck or hearsay. The triad endures not because Plato decreed it but because human life still relies on the difference between being right and merely happening to be right. JTB describes, in grammatical form, the criteria by which we hold one another epistemically accountable.

The word know itself does not wear a single face. We use it to express both epistemic and non-epistemic relations: I know the capital of France, I know how you feel, You should know better than that. Some of these are claims to justification; others are gestures of familiarity, empathy, or expectation. Wittgenstein reminds us that meaning follows use: the epistemic sense of know is only one branch within a broader family of uses. Clarifying that branch—seeing how it functions within our language-games—prevents us from mistaking conviction, or mere agreement, for knowledge. JTB+U is concerned solely with the epistemic use, where truth, belief, justification, and understanding converge within a form of life.

Yet the simplicity of JTB conceals a difficulty sharpened by modernity. One can satisfy its letter without satisfying its spirit. A belief may be true and even justified by available evidence yet still lack the kind of grasp that distinguishes genuine knowledge from the echo of authority. Students can recite correct answers; machines can compute them; neither necessarily understands what they affirm. The missing element is not another reason but an internal relation—the capacity to use, extend, and situate what one claims to know. This fourth component, understanding (U), restores life to the classical framework and reconnects epistemology with practice.

Understanding bridges knowing that and knowing how. It is not a separate species of knowledge but a measure of conceptual uptake: one understands when one can move fluently within the logical and practical consequences of a claim. To say “I know how a lever works” or “I know what justice requires” is to claim competence beyond the recital of propositions. This element of grasp allows knowledge to resist mere imitation. Adding U to JTB does not alter the structure of knowledge; it clarifies the dimension tacitly presupposed whenever philosophers spoke of insight, judgment, or wisdom—the ability to navigate a concept’s grammar, not merely repeat it.

The urgency of this refinement becomes clear when justification falters under the weight of information. In an age of machine learning, deepfakes, and algorithmic persuasion, justification alone cannot guarantee comprehension. We can outsource calculation but not understanding. Even a flawless predictive system, if it cannot recognize the bounds of its certainty or the hinges on which its reasoning turns, mistakes correlation for truth. JTB+U therefore serves both as an epistemic model and as a moral warning: intelligence without understanding is cleverness without orientation.

The revival of epistemology thus requires a shift in emphasis—from metaphysical speculation to grammatical description. Wittgenstein’s later philosophy provides the tools for that shift. His method was not to invent new theories of knowledge but to examine how the word know functions within our language-games. In doing so, he showed that justification is always contextual, embedded in the forms of life that sustain meaning, and that doubt operates only against a background of what stands fast. Our standards of justification are not free-floating; they draw their authority from these inherited practices. JTB+U continues this line by formalizing what Wittgenstein left implicit: that understanding is active mastery of a grammar, not possession of a mental state. Knowledge is not a mysterious substance but a practice: moving rightly within the space of reasons.

This also clarifies why epistemology cannot be replaced by psychology or neuroscience. No scan or algorithm can decide whether a belief is justified; that judgment belongs to the public web of reasons in which meaning is maintained. To know something is to occupy a position within that web—to give and ask for reasons intelligibly to others. Epistemology names the effort to keep that web intact, to prevent private conviction from masquerading as objective warrant. When those boundaries collapse, language loses traction and communities lose trust.

This project is conservative in spirit but progressive in aim. It seeks not to discard the classical framework but to ground it more deeply in lived practice. Adding understanding acknowledges that knowledge is never exhausted by propositions; using Wittgenstein’s methods locates those propositions within the activities that give them sense. The result is an epistemology both stricter and more humane: strict because it demands defeater-sensitivity and conceptual clarity, humane because it recognizes that justification is always conducted within a form of life.

Although the framework I develop here is not metaphysical in method, it is not divorced from metaphysical depth. JTB+U does not appeal to a single essence or hidden ontology to give knowledge its meaning, yet it presupposes that justification and understanding unfold within a reality intelligible to mind. Metaphysics, in this sense, forms a horizon rather than a foundation: it shapes what can be meant without dictating how meaning is given. The grammar of knowledge may be clarified without invoking ultimate reality, but such clarity need not deny that a deeper order exists—what I later call the ultimate hinge of consciousness, the background that makes any grammar of understanding possible.

If epistemology is to remain a living discipline, it must show how understanding anchors responsible judgment across domains—from the sciences and ethics to education and emerging forms of artificial intelligence. Only by refining what it means to know can we preserve a shared orientation toward truth in an age increasingly shaped by uncertainty.

In what follows, I review why the JTB framework remains the most durable articulation of knowledge in practice, then trace its internal tensions—especially the ambiguity of justification and the regress of reasons—and show how Wittgenstein’s notion of hinges dissolves them without skepticism. From there, I introduce the +U element, outline the guardrails that keep justification reliable, and distinguish the several uses of certainty that reveal where knowledge properly resides. The paper concludes by showing how this Wittgensteinian extension preserves knowledge as a corrigible yet indispensable concept—one capable of guiding both human and artificial intelligence toward a more responsible understanding of truth.

II. The Wittgensteinian Toolkit—Clarifying Our Grammar of Knowledge
If metaphysics provides the horizon of intelligibility, Wittgenstein’s later philosophy supplies the instruments for navigating within it. His method is therapeutic rather than speculative: instead of offering new theories of knowledge, it clarifies how the word know functions in the practices where sense and doubt are learned. The tools are deceptively simple—language-games, grammar, forms of life, family resemblance, and hinges—but they work together, reinforced by the ideas of rule-following, public criteria, and the river-bed imagery of On Certainty. Taken as a whole, this toolkit grounds epistemology not in metaphysical essence but in lived intelligibility.

Language-games: where “know” has meaning
Wittgenstein begins with the recognition that meaning arises from use. Words are not labels for private entities but moves within human activities. To call something knowledge is not to identify a mysterious inner state but to perform a specific act inside a game with shared rules—asserting, challenging, correcting, teaching. Each domain has its own grammar of knowing: the scientist cites data, the witness swears an oath, the child repeats a lesson. There is no single essence of know; the unity lies in family likeness across these games. By examining language-games, we shift the epistemological question from “What is knowledge?” to “How do we use ‘know’ here?” The philosopher’s task becomes descriptive rather than legislative.

Grammar: the logical order that frames sense and doubt
Grammar, for Wittgenstein, is not syntax but the underlying logic that determines what counts as sense. It tells us what it means to justify, to verify, to doubt. Grammar sets the boundaries of intelligible talk: we can meaningfully say “I know this is a hand,” but not “I know I am in pain.” The latter confuses private experience with public criteria. Grammar thus replaces the metaphysician’s search for foundations with attention to rule-governed use. To grasp a concept grammatically is to know what would count as applying it correctly, what would make its application nonsensical, and how mistakes show themselves. Epistemology becomes a study of conceptual grammar—the order that lets sense and error exist at all.

Forms of life: the public foundations of justification
Every grammar stands on a background of practices, gestures, and agreements that are not themselves justified but simply enacted. These are our forms of life: the biological and cultural patterns within which reasoning has meaning. Justification presupposes such a background. We can question a witness, but not the practice of questioning itself; we can test a thermometer, but not the institution of measurement that makes testing possible. Forms of life are not propositions but the lived matrix of criteria. They explain how justification can be public without being infinite: our shared ways of acting already contain the standards that make giving reasons possible. Language-games and forms of life are mutually defining: our forms of life give stability to our games, and the games, in turn, articulate the forms of life they express.

Rule-following and public criteria
Within a form of life, rules acquire authority through training and correction. To follow a rule is not to consult an inner diagram but to participate competently in a practice where others can see and correct our moves. This dissolves the picture of justification as an internal state of certainty. What shows that I understand a rule is not introspection but my ability to go on correctly when circumstances vary. Knowledge therefore carries a social dimension: it is demonstrated in action and confirmed by public criteria. Wittgenstein’s reminder—there is no inner pointing to meaning—cuts against the Cartesian idea that knowing is primarily a private event. The grammar of know is visible in use, not hidden in consciousness.

Family resemblance: unity without essence
Philosophers often seek the single property that makes all instances of knowledge what they are. Wittgenstein advises a different posture: notice the overlapping similarities among uses instead of chasing a universal definition. Just as “games” share no one essence but display a network of resemblances—competition, rules, play—so too “knowledge” unites diverse activities by kinship rather than identity. This insight loosens the grip of essentialism that has haunted epistemology since Plato. It allows JTB, later extended to JTB+U, to function as a grammatical model rather than as a metaphysical claim. Its durability lies in family likeness across contexts, not in a timeless form.

Hinges and the river-bed: the arational background of reason
On Certainty adds the final and most radical instrument. Every act of justification presupposes propositions that stand fast—hinges that make doubt meaningful. These are not beliefs we know but certainties we act from. They form the river-bed in which the current of reasons flows. To question them all at once would be to lose the very distinction between sense and nonsense. Examples include “There is an external world,” “Objects persist,” “Words have stable meanings,” and, in your metaphysical horizon, “Consciousness is the condition for any appearing at all.” Hinges are arational, not irrational; they lie beneath justification, providing the stage upon which justification can occur.
This insight explains why epistemic regress ends without circularity. When reasons run out, we do not reach an arbitrary stopping point but the practical background that makes reasoning possible. To call something a hinge is to mark the transition from saying to doing, from proposition to practice. Wittgenstein’s point is grammatical: the verb to know presupposes a contrast with possible doubt; remove that contrast, and the word loses its function. Hinges, then, are the conditions of meaningful knowledge, not propositions we could ever justify or refute.

Doubt as practice-bound
Because hinges define the limits of intelligible doubt, skepticism must itself be seen as a language-game. Doubting that the external world exists or that one has a body is not a deeper form of inquiry but a misuse of grammar—like playing chess without a board. Doubt has sense only where the framework of certainty stands fast. This reframes epistemology: instead of searching for indubitable foundations, we describe the hinges that already stabilize our reasoning. Certainty here is not a psychological feeling but a logical role. It anchors rather than concludes.

The toolkit as re-grounding for epistemology
When these instruments work together, they convert epistemology from a quest for absolute justification into a grammar of responsible use. Language-games reveal diversity; grammar maps the logic of sense; forms of life show why justification is public; rule-following and criteria keep meaning from collapsing into subjectivity; family resemblance preserves unity without essence; and hinges secure the background that makes any of this possible. The result is an epistemology both humbler and stronger: humbler because it recognizes limits, stronger because it grounds knowledge in the lived regularities that precede theory.

Wittgenstein’s method thus complements rather than replaces the classical JTB framework. JTB describes the explicit structure of epistemic accountability; the toolkit shows the soil in which that structure grows. Together they transform the question of knowledge from a search for metaphysical foundations into an examination of the practices that sustain sense. When we later add understanding as the fourth component, the +U will draw directly on these insights: understanding is nothing other than fluency in a language-game, mastery of its grammar, and attunement to its hinges.

Someone could parrot an explanation of how a belief is justified without really 'getting' the explanation. It is very difficult, though, to say just what "getting" an explanation consists in other than the feeling or sense of getting it.

In What Computers Can't Do and What Computers Still Can't Do Hubert Dreyfus argued that computers will never be genuinely intelligent because they cannot understand context.

Yet the LLMs do seem to be able to do that, even though I cannot imagine how it would possible that they do that. Is it just a matter of parroting so sophisticated as to be able to fool us into thinking they do understand context?

It begs the question as to how we grasp context, and I don't have an answer for that, but can only think that it must somehow be a matter of feeling. I can't imagine a computer having a feeling for context—but then what do I know? — Janus

That’s a fair point, and an important point. When I say that someone can parrot an explanation without getting it, I don’t mean that “getting” is a hidden mental glow or some private feeling that accompanies comprehension. I mean that understanding shows itself in how a person can go on rightly — how they use what they’ve learned in new circumstances, recognize when it breaks down, and repair it. It’s not the presence of a sensation but the manifestation of mastery within a shared practice.

That’s where I think the difference lies between human understanding and what large language models are doing. They can reproduce the surface grammar of context, the statistical pattern of what normally follows what, but they don’t inhabit the life-grammar that gives those patterns weight. They have no stake, no risk, no embodied continuity of experience. Our grasp of context isn’t just cognitive; it’s lived. It shows up as what I’d call a feeling for relevance: a readiness to respond that draws on our bodily attunement to the world and to one another.

So yes, LLMs can simulate contextual understanding impressively, but simulation isn’t participation. Their outputs can mirror what understanding looks like, yet nothing in them corresponds to the hinge-layer that makes sense possible in the first place. Our “feeling for context” isn’t a mysterious extra — it’s the human way the background of meaning becomes visible in use.