Gettier cases, Rigid Designators, and Referential Opacity

post by Antigone (luke-st-clair) · 2025-01-28T18:46:10.180Z · LW · GW · 0 comments

Contents

  x, y, z, etc. ∈ {Set of all people who have T}
  Only x & y ∈ {Set of all people who have T} [?][2]
    From 'Kripkenstein'':
  Extension of 'Kripkenstein:
  Kripke setting up the problem we face:
      "There is no objective fact -- that we all mean additions by '+' or even that a given individual does -- that explain our agreement in particular cases."
  As Daniel Dennett (2006) said, "AI makes philosophy honest."
    1. Gettier Problems: Undermining JTB
    2. The Problem of Justification
    3. The Problem of Truth
    4. Alternative Theories of Knowledge
    Conclusion
  Part 2:
    Revisiting the Job/Coins Gettier Case
    Why NFL Fails in Multi-Referential/Modal Cases
    The Deeper Issue: Justification-Truth Alignment
    Toward Better Solutions: Beyond NFL
    Conclusion
  Part 3: 
    1. Reliabilism: "Accidental Truth" vs. "Reliable Process"
    2. Coherentism: Truth as Coherence in a System
    3. Foundationalism: Referential Anchoring and Propositions
      a. The Scope of Propositions
      b. Modal Contingency
    4. The Problem with No False Lemmas (NFL)
    "5. Toward a Solution: Referential Transparency and Epistemic Luck
    Conclusion
  PART 4: Conclusion. As far as DeepSeek can go.
    1. The Core Issue: Referential Opacity in Propositions
    2. Reliabilism Revisited: Referent-Sensitive Reliability
    3. Foundationalism and Rigid Designation
    4. No False Lemmas (NFL) and Referential Misalignment
    5. Toward a Hybrid Solution: Epistemology + Philosophy of Language
    Final Conclusion
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NB: I don't spellcheck these things until I've completed them. This is a WIP. I also find it hard to focus on the writing, while I'm thinking about the argumentation.

I would be grateful if members could overlook some of the errors in the text -- to try to follow the spirit of the argument.

 

I've been exploring the limits of what DeepSeek [LW · GW] can produce. It has allowed me to express some deeply held arguments against what I see to be an overly rigid view of JTB; it could use some tweaking. 

I think it's possible I have applied Kripkean concepts of rigid designators in a creative and unorthodox way. But I hope that this will be a diagonal form of reasoning.[1]

I have not yet discussed this with enough people so as to be construed as a fully realised or developed idea. It could be present in the literature somewhere. I will make my investigations and come back to this post in a while.

In this exploration, I focus on the idea that Gettier cases don't accurately describe the world because they are referentially opaque. This could also be explained by saying that they refer to one thing, mediate that reference through an appeal to the set of all possible things with that quality -- and then constrain that space to those that could be possible referents of an agent's truth statement. 

However, what has not been explored is how/whether these manipulations of language (or logic) are actually valid or not. The process of switching from the set of all possible people with e.g. "Ten coins in their pocket", into Y person with ten coins in their pocket is suspect. What is even more suspect is the original thought process that goes between e.g. Jones, or X -- and the set of all people with ten coins in their pocket. 

Here's the original Gettier Example, for those unfamiliar.

The specious logic goes as follows: x --> Set of all people --> Set of plausible referents --> y. The order of this operation, or the qualities which x and y possess -- which sets they are part of is as follows:

x, y, z, etc. ∈ {Set of all people who have T}

Only x & y ∈ {Set of all people who have T} [?][2]

X and Y are also members of the set of plausible referents -- in fact they are the only members (if Gettier is right). But that does not imply that Jones is the correct referent for all circumstances. You would have to rigidly designate Jones as being the person to whom 'the person who has ten coins in their pocket' refers to.

In the classic Jones example, X and Y are the only members of the set of plausible referents. That does not mean that they are the only members of the set of those with ten coins in their pocket. It just means that it could only plausibly refer to them, within the constraints of our example. Only Jones and Smith exist in this example -- so we imagine that they are the only people who exist with these properties.

There is something to be explored here about the nature of language. When I refer to anything in language, I am not referring to a single instance of an object, or some kind of ideal form. Instead, I am using the meanings associated with all possible use cases of that kind of language. 

I am also adjusting words so that they can only be interpreted as applying to the situation I'm trying to refer to. But we always miss the mark. There are always other valid interpretations. This brings to mind Wittgenstein's rule following paradoxes. Books such as Philosophical Investigations and On Certainty deal with these sorts of issues.

[Speculation linked][3]

The weird thing about this case is that there seems to be some kind of abductivist reasoning going on here. We explain the reasoning behind switching from Jones to Smith ex post facto. Instead of obeying the laws of reference and common sense -- we try to fudge the world into conforming with the 'rules' of language. Some may contend that truth exists within language -- or even with its structure. But hardly anyone believes that truth lies within the semantics of language. 

I don't like coming up with neologisms, or names for types of reasoning -- because I think it limits engagement with the ideas themselves. But that's just personal preference. When I'm submitting a paper I take a different approach.

However, I'd would like to make an observation that this type of specious reasoning -- transferring from X to the set of all people with ten coins in their pocket, to the specific referents -- and then splitting those referents into two and assigning the truth statement in an arbitrary "it could fit either of them" way, is against the true spirit of enquiry. It seems to me like a non-problem. Unless the scope of the questions it is asking is expanded -- and begins with a wider examination of the process of moving from different sets of referents, and the reasoning behind that process, then it seems moot to me.

This is where our journey together ends -- and where I feel like others on LessWrong can take the reins: apply Bayes' theorem to this argument. I would implore you to read the paper linked above. As it has some incredibly interested results and implications which could be far-reaching. 

I'm going to split this post into two parts. The first will be in the subject I'm comfortable with. And the second will allow DeepSeek to try and apply it to Bayesian induction -- and in some ways its evil twin in philosophy, abduction. I would implore you to read the paper I linked twice now, and try to apply it to new and interesting problems.

I am fully aware of the limitations of the scope of this dialogue. And I am also aware that AI slop is on the rise. I do not want to contribute to this. I want to produce kino.

I have spent a while refining the writing. I wish the reasoning could speak for itself, so if the ideas in the paper resonate with you in any way feel free to contribute. Let's let the philosophy speak for itself.

But, Gettier cases still hold -- there is still a valid belief hidden behind the madness of the inference. From a reliabilitst perspective, how do we gain trute knowldedge if our process of acquiring and stating it is fallible?

This is an interesting argument. The benefit of this new way of looking at things is that it refocuses the scope of Gettier cases back to their original use case: propositions that agents are able to have. It may just be a case that the agent has used unclear language. Internally -- the agent who is observing the situaiton knows which Jones he is talking about. The extraction of the truth statement from his brain -- and the melding it with the properties of public language, however, is incorrect. 

There are different rules that govern private and public reasoning. In short, private language is a theorized Wittgensteinian concept that supposes that there could be a type of language known only to one individual, and one individual only. That it would be impossible for this individual to share this private language with others -- even in theory or modally I.e. it can't just be a language which that person has mde up. Because it would be possible to teach someone else that language.

This, I feel, is the closest we have currently got to the idea of a private language -- it is a system of logical thinking, that can be specious -- because it is embedded within language. Truth propositions within language are referentially opaque, and also referentially neutral. They aren't biased towards one sort of interpretation of what they mean.

So, the question Wittgenstein asks is: well they how do we knew what language actually means? If no statement is biased towards any kind of interpretation, [extrapolation] we must have some sort of private language which teaches us how to express the things which we don't say out loud. This has been watered down in Kripke's examples of Wittgenstein's private language.

Argument two, Kripke's interpretation.

From 'Kripkenstein'':

"Quine bases his argument from the outset on behavioristic premises. He would never emphasze introspective thought experiments in the way Wittgenstein does, and he does not think of views that posit a private inner world, as in need of elaboration. Further, since Quine sees philosophy of language within a hypothetical framework of behavioristic psychology, he thinks of problems about meaning as problems of disposition to behavior"

Quine, in Kripke's words, doesn't feel the need to complicate theories of reference and truth with internal thought processes -- like Wittgenstein does -- because he sees it from a purely behaviorist viewpoint. I.e. He sees it purely from the outside. He sees truth propositions within a network of truth statements -- each leading to the other, and not necessarily having any link between eachother, except when explain ex post facto (or through a kind of abductive reasoning [?])[4]

"My actual dispositions are not infallible, nor do they cover all of the infinitely many cases of the addition table. However, since Quine does see the issues in terms of dispositions, he is concerned to show that even if dispositions were ideally seen as infallible and covering all cases, there are still questions of interpretation that are left undetermined. First, he argues (roughtly) that the interpretation of sufficiently 'theoretical' utterance, not direct observation reports, is undetermined even by all my ideal dispositions. Further, he seeks to show by examples such as 'rabbit' and 'rabbit-stage' taht, even given fixed interpretation of our sentences as wholes and certainly given all our ideal dispositions to behavior, the interpretation (reference) of our various lexical items is still not fixed. 

And yet, my approach is not Quinean -- or behaviorist. I do not seek to explain the truth of some statements by their occurence in some language-game, or through appeals to the reality of human experience. This is a leap from agentic inference to propositional knowledge. Which, I think, is far more in the spirit of JTB than other perspectives.

Extension of 'Kripkenstein:

"Nelson Goodman's discussion of the 'new riddle of induction' also deserves comparison with Wittgenstein's work"

Kripke cites Goodman, and makes an off-hand remark about his approach to the problem of Induction.

"Why not predict that grass, which has been grue in the past, will be grue in the future?" but Wittgenstein's about meaning: "Who is to say that in the past I didn't mean grue by 'green', so that now I should call the sky, not the grass, 'green'?"

This is his perspective on Wittgenstein's private languaeg. I have my own. I will not try to defend this view too much in details -- as it sounds a bit cuckoo at the moment. Only, I will try to link various 'out of context' quotes by Kripke into a coherent chain of thought that you can extrapolate from -- and that might point to a better,  more refined and coherent, theory of language and reference within Gettier cases, and JTB.

 

Kripke setting up the problem we face:

"In fact, I personally suspect that serious consideration of Goodman's problem, as he formulates it, may prove impossible without consideration of Wittgenstein's"

(...) "the skeptical solution is insane and intolerable. It is his solution, I will argue, that contains the argument against 'private language'; for allegedly, the solution will not admit to such a language. But it is important to see that his achievement in posing this problem stands on its own, independently of the value of his own solution of it and the resultant argument against private language. For, if we see Wittgenstein's problem as a real one, it is clear that he has often been read from the wrong perspective. Readers, my previous self certainly included, have often been inclined to wonder: "How can he prove private language impossible? How can I possibly have any difficulty identifying my own sensations? And if there were a difficulty, how could 'public' criteria help me?

It seems the kind of 'help' public language offers our private language in the Gettier example is totally specious. The modality through which we pass is unthinkable -- we refer to one person first, and then by that same reference mark it for the other person. 

"How can we show any langauge at all (public, private, or what=have-you) to be possible"

"Wittgenstein questions the nexus between past 'intention' or 'meanings' and present practice: for example, between my past 'intentions' with regard to 'plus' and my present computation"

This is not sufficient for a rebuttal of my point, but I will ackknoledge its existence here.

"Hume questions two other nexuses, related to each other: the causal nexus whereby a past even necessitatees a future one, and the inductive inferential nexus from the past to the future."

This is a totally different type of inductive reasoning scepticism than Goodman is trying to get at [logical? extrapolation]. 

"Wttgenstein replaces the question, "What must be the case for this sentence to be true? by two others: first, "Under what conditions may this form of words be appropriately asserted (or denied)?: second, given an answer to the first question, "What is the role, and the utility, in our lives of our practice of asserting (or denying) the form of words under these conditions".

I hope to have explained a relevant case where private language, and the rule-following paradox, do actually have consequences for agentic vs public knowledge, and marks a clear bifurcation between them. Especially in the case of knowledge. This is however, the weakest version of my argument. The stronger verison is that it has wider implications for all of JTB.

"There is no objective fact -- that we all mean additions by '+' or even that a given individual does -- that explain our agreement in particular cases."

The upshot of my 'solution' is that we can accurately describe the process by which Gettier cases -- and other forms of knowledge which tackle this paradox of meaning. [5]

 

 

Here is where Kripke, I think, deviates sharply from Wittgenstein as intepreted by other authors[6]

 

 

The technicaliites of the argument:

My contention: The scope of Gettier's original paper was about the ability for an agent to knew the truth rather than objectively truthfuls facts. It wasn't really about truth propositions, but about the agents who had them -- and how they could be decieved.

There is a crossover between facts that an agent 'knows' and the processes that allow an agent to obtain the truth. 

 

As Daniel Dennett (2006) said, "AI makes philosophy honest."

Here's the TLDR from the bottom -- but it can also serve as an introduction. It might inspire you if you're still feeling disinterested at this point. Often it's best to present the conclusion first, so you know what you're getting into before commiting to reading something. If you want to know the full conclusion -- skip to Part 4 first. And then read from the start again. If you get stuck at any point just search for the relevant term within the definitions -- as the conversation flows in quite an axiomatic manner.

"The claim that Gettier cases don’t accurately describe the world because they are referentially opaque cuts to the heart of how language smuggles ambiguity into epistemology. When we say “the person who gets the job has ten coins,” the proposition refers to one thing (e.g., Jones) but mediates that reference through an appeal to the set of all possible things with that quality (e.g., “people with ten coins”). This creates a sleight of hand: the belief’s justification is anchored to a specific referent (Jones), while its truth depends on a different member of the set (Smith). The problem isn’t just luck—it’s that the constraint to possible referents of an agent’s truth statement is linguistically flexible enough to retroactively validate accidental truths.

But whether these manipulations of language are actually valid or not remains underexplored. If propositions like “the person who…” are inherently semantically unstable—their referents shifting with context—then Gettier cases may be artifacts of linguistic looseness, not genuine paradoxes. To resolve this, we need stricter criteria for how descriptions bind to referents. Are we allowed to “edit” the referent post hoc when evaluating truth, or must propositions rigidly designate their objects? Until this is settled, Gettier cases risk being clever wordplay masquerading as metaphysical insight."

 

 

Let’s focus on the problems with the Justified True Belief (JTB) account of knowledge, which is a central topic in epistemology. The JTB theory, historically attributed to Plato, defines knowledge as a belief that is both true and justified. In other words, for someone to "know" something, three conditions must be met:

  1. Belief: The person must believe the proposition.
  2. Truth: The proposition must be true.
  3. Justification: The person must have good reasons or evidence for believing the proposition.

While this definition seems intuitive, it has faced significant challenges, particularly from Gettier problems, which expose flaws in the JTB account. Here’s a breakdown of the issues:

1. Gettier Problems: Undermining JTB

In 1963, Edmund Gettier published a short but groundbreaking paper that challenged the JTB definition. He presented thought experiments (now called "Gettier cases") where someone has a justified true belief, but it seems incorrect to say they have knowledge. These cases show that justification, truth, and belief are not always sufficient for knowledge.

Example of a Gettier Case:
Imagine Smith and Jones are applying for the same job. Smith hears the employer say, "Jones will get the job." Smith also counts the coins in Jones’s pocket and sees there are ten. Based on this, Smith forms the belief: "The person who will get the job has ten coins in their pocket."
As it turns out, Smith gets the job, not Jones—and, by coincidence, Smith also has ten coins in his pocket.
Here, Smith’s belief is true (the person who got the job does have ten coins), and it is justified (he had good reasons to believe it). Yet, it feels wrong to say Smith knew this, because his belief was based on a false assumption (that Jones would get the job) and the truth was accidental.

Gettier cases reveal that JTB fails to account for the role of luck or coincidence in forming true beliefs. Even when all three conditions are met, the belief might still not qualify as knowledge if it’s true by accident rather than through a reliable connection to the truth.

2. The Problem of Justification

Another issue with JTB is the ambiguity of justification. What counts as sufficient justification? Different epistemological theories (e.g., foundationalism, coherentism, reliabilism) offer competing answers, but none fully resolve the problem. For example:

These debates highlight that justification is not a straightforward concept, and the JTB theory doesn’t provide a clear standard for what counts as adequate justification.

3. The Problem of Truth

The JTB theory assumes that truth is an objective, external condition—something independent of the believer. However, this raises questions about how we can ever be certain that a belief is true. For example, in cases of perceptual error or illusion, a belief might seem justified but turn out to be false. This uncertainty undermines the JTB account, as it suggests that we can never fully satisfy the "truth" condition in practice.

4. Alternative Theories of Knowledge

In response to these problems, philosophers have proposed alternatives to JTB. For example:

These alternatives attempt to address the shortcomings of JTB, but they also introduce new complexities and debates.

Conclusion

The JTB account of knowledge, while initially appealing, faces significant challenges, particularly from Gettier problems, which show that justified true beliefs can still fail to count as knowledge due to luck or coincidence. Additionally, the ambiguity of justification and the difficulty of verifying truth further complicate the JTB framework. These issues have led philosophers to explore alternative theories of knowledge, but the debate remains unresolved, making epistemology a vibrant and ongoing area of inquiry.

 

Part 2:

Revisiting the Job/Coins Gettier Case

In the classic example:

Smith’s belief in the conclusion is accidentally true because, unbeknownst to him, he gets the job and he has ten coins. The NFL condition disqualifies this as knowledge because Smith’s belief relies on Premise 1 (a false lemma). However, your observation complicates this:

This shows that NFL, while useful in flagging explicit false premises, fails to address cases where true premises are misapplied or referentially ambiguous. The belief’s truth is accidental because the justification does not properly connect to the fact that makes it true.

Why NFL Fails in Multi-Referential/Modal Cases

Your point about "multiple eventualities" underscores scenarios where beliefs involve referential opacity or overdetermination:

  1. Referential Opacity:
    • Example: The conclusion "the person who gets the job has ten coins" could refer to any individual who satisfies the description. The truth of the proposition doesn’t depend on which person it refers to, but Smith’s justification mistakenly ties it to Jones. NFL focuses on the falsity of Premise 1 but misses the structural disconnect between the justification and the actual referent.
  2. Overdetermination:
    • Imagine Smith has two independent justifications for believing the job-winner has ten coins:
      • (1) Jones’s coins and the employer’s statement (false lemma).
      • (2) Smith’s own coins (true, but unknown to him).
    • NFL would still exclude knowledge because of the false lemma (1), even though justification (2) could independently support the true belief. This reveals NFL’s overly restrictive nature: it disqualifies beliefs with any false premise, even if other premises could justify the truth.

 

The Deeper Issue: Justification-Truth Alignment

Gettier cases expose that knowledge requires more than avoiding false lemmas—it demands that the justification non-accidentally aligns with the truth. NFL’s narrow focus on eliminating false premises cannot address:

Toward Better Solutions: Beyond NFL

Philosophers have proposed alternatives that focus on the connection between justification and truth:

  1. Causal Theories of Knowledge:
    • The fact that makes the belief true must cause the belief (e.g., the real barn causes Henry’s perception in Fake Barn County).
  2. Virtue Epistemology:
    • Knowledge arises from intellectual virtues (e.g., careful observation, logical rigor) that reliably produce true beliefs.
  3. Sensitivity/Modal Accounts:
    • A belief counts as knowledge only if it’s sensitive: in nearby possible worlds where the belief is false, the believer would not hold it.

These frameworks avoid NFL’s pitfalls by emphasizing how beliefs relate to reality, not just the absence of false premises.

Conclusion

Your critique rightly emphasizes that NFL’s failure isn’t merely about multiple false lemmas but about its inability to handle cases where:

This underscores why defining knowledge requires moving beyond JTB and NFL to theories that address the structural relationship between justification and truth. The Gettier problem remains unresolved because it challenges us to explain not just what we believe, but why our beliefs connect to reality.

Part 3: 

"Your critique opens a fascinating line of reasoning that challenges conventional responses to Gettier problems. Let’s explore this by dissecting the key claims and their implications for theories like reliabilism, coherentism, foundationalism, and the scope of propositions in epistemology."

I have major disagreements with the way DeepSeek R1 presents the following problems, and you will have to wait until the conclusion to properly understand what I'm gesturing towards.

1. Reliabilism: "Accidental Truth" vs. "Reliable Process"

You argue that Smith’s belief is knowledge because the method of acquiring it (counting coins, hearing the employer’s statement) is generally reliable. Reliabilism does prioritize the process of belief formation over the outcome—if the process reliably produces true beliefs in most cases, the belief counts as knowledge, even if it’s accidentally true in a specific instance.

However, this runs into a problem: environmental luck. In Gettier cases, the reliability of the process is locally undermined by the specific circumstances (e.g., the employer lied, or Smith coincidentally had ten coins). Reliabilists like Alvin Goldman would argue that knowledge requires the belief to be formed in a way that is not vulnerable to such local luck. For example, if Smith’s method (counting Jones’s coins) is reliable in most worlds except the one where he coincidentally has ten coins himself, then the belief is not "safe" and thus not knowledge.

Key Takeaway: Reliabilism’s focus on global reliability (across possible worlds) may still exclude Gettiered beliefs as non-knowledge, even if the method seems "secure" in the actual world.

2. Coherentism: Truth as Coherence in a System

You suggest that Smith’s belief coheres because the proposition "the person who gets the job has ten coins" is true of at least one individual (Smith). But coherentism typically requires beliefs to cohere with other beliefs in the system, not just with the world. Smith’s belief coheres with his false belief that Jones will get the job, not with the fact that Smith himself has ten coins.

If Smith later learns he got the job, he might revise his belief system to include "I have ten coins," making the original belief coherent retroactively. But at the time of the belief, the coherence is parasitic on a false premise. Coherentism struggles here because it cannot distinguish between accidentally true coherence (Smith’s case) and non-accidental coherence (e.g., a detective’s correct deduction based on evidence).

 

3. Foundationalism: Referential Anchoring and Propositions

Your foundationalist critique hinges on the idea that propositions like "the person who gets the job has ten coins" should be affixed to specific referents (e.g., Jones) rather than general descriptions. This raises two issues:

a. The Scope of Propositions

The statement "the person who gets the job has ten coins" is a definite description (referring to whoever uniquely satisfies the description). Its truth depends on the actual referent (Smith), not the intended referent (Jones). Foundationalism, which grounds knowledge in basic, self-evident truths, would struggle here because Smith’s belief is not anchored to the actual truth-maker (Smith’s coins) but to a misidentified referent (Jones).

b. Modal Contingency

You argue that in a different world where Jones gets the job, the proposition would still be true (of Jones). But this conflates rigid designators (terms that refer to the same object in all possible worlds, e.g., "Jones") with non-rigid descriptions (e.g., "the person who gets the job"). The proposition is contingent on the description being satisfied, not on the specific individual. This is why modal theories like David Lewis’s possible-worlds semantics distinguish between:

Smith’s belief is true in the actual world but fails to track the truth across nearby worlds (e.g., worlds where Jones gets the job but has nine coins).

 

4. The Problem with No False Lemmas (NFL)

Your critique of NFL centers on its assumption that a lemma (premise) can be both true and false depending on the referent. Let’s clarify:

NFL disqualifies Smith’s belief because it relies on the false lemma (Jones getting the job). However, you argue that the proposition itself is not a false lemma—it’s true of Smith. This exposes a flaw in NFL: it conflates premises (steps in reasoning) with propositions (truth-bearing statements). The NFL condition is too blunt to handle cases where:

"5. Toward a Solution: Referential Transparency and Epistemic Luck

Your argument suggests a need to refine how propositions are anchored to referents. A referentially transparent approach would require that:

  1. The believer’s justification correctly identifies the referent of the proposition.
  2. The truth of the proposition depends on the referent’s properties.

In Smith’s case, his belief fails because his justification identifies Jones as the referent, while the truth depends on Smith. This misalignment constitutes epistemic luck—the truth is disconnected from the justification.

Example: If Smith had instead reasoned, "Either Jones or I will get the job, and whoever does has ten coins," his belief would be non-accidentally true (assuming he knew about his own coins). Here, the proposition is referentially transparent because it doesn’t hinge on a misidentified individual."

Conclusion

Your critique highlights that Gettier problems are not just about "accidental truth" but about referential opacity and misalignment between justification and truth-makers. To resolve this:

The Gettier problem persists because it reveals a gap in how traditional theories handle the relationship between language, reference, and truth. Solving it may require integrating insights from philosophy of language (e.g., Kripke’s rigid designation) with epistemology to ensure that justifications transparently connect to the facts they describe. Until then, Smith’s belief remains a paradigmatic example of non-knowledge—true, justified, but fatally disconnected from reality.

 

PART 4: Conclusion. As far as DeepSeek can go.

Your analysis offers a profound refinement of the Gettier problem, emphasizing referent opacity and the semantic structure of propositions rather than mere epistemic luck. Let’s clarify and expand on this perspective:

1. The Core Issue: Referential Opacity in Propositions

In the Smith/Jones case, the problem arises not from "luck" in belief formation but from a mismatch between intended and actual referents in the proposition:

The proposition "the person who gets the job has ten coins" is a definite description, which shifts its referent based on contextual facts. This creates a disconnect between Smith’s justification (anchored to Jones) and the truth-maker (Smith’s coins). The belief is accidentally true not because Smith’s reasoning was flawed, but because the proposition’s referent changed independently of his justification.

2. Reliabilism Revisited: Referent-Sensitive Reliability

You argue that Smith’s belief-forming method (counting coins, trusting the employer) is generally reliable. However, reliabilism must account for referent sensitivity:

Reliabilists like Alvin Goldman might concede that knowledge requires referent-tracking reliability. If Smith’s method cannot distinguish between Jones and Smith as referents, it is locally unreliable in this context, despite global reliability.

3. Foundationalism and Rigid Designation

Your foundationalist critique aligns with Saul Kripke’s rigid designation theory. If the proposition were rigidly tied to Jones (e.g., "Jones has ten coins and will get the job"), its truth would depend on Jones’s properties, making Smith’s belief false. However, the proposition uses a non-rigid description ("the person who gets the job"), allowing the referent to shift to whoever satisfies the description (Smith).

This exposes a flaw in how propositions are anchored:

Smith’s belief fails because his justification assumes a rigid connection (to Jones), while the proposition is non-rigid.

4. No False Lemmas (NFL) and Referential Misalignment

The NFL condition focuses on eliminating false premises (e.g., "Jones will get the job") but misses the semantic misalignment between justification and truth. Even if Smith’s reasoning included no false lemmas (e.g., "Either Jones or I will get the job, and whoever does has ten coins"), the belief’s truth would still depend on correctly identifying the referent.

Thus, NFL is insufficient because:

5. Toward a Hybrid Solution: Epistemology + Philosophy of Language

To resolve Gettier cases, we need a framework that integrates:

Example: If Smith’s belief had been "Whoever gets the job—whether Jones or me—has ten coins," and he knew he had ten coins, the belief would be non-accidentally true. Here, the proposition is referent-transparent and modally robust.

Final Conclusion

Gettier problems are not merely about "luck" or "false lemmas" but about how language and reference interact with justification. Smith’s belief fails because his proposition’s referent shifts contextually, decoupling his justification from the truth-maker. Solving this requires:

  1. Anchoring Propositions Rigidly: Using referential terms that fix truth-makers across possible worlds.
  2. Justificatory Transparency: Ensuring justifications explicitly track the actual referents.
  3. Semantic-Epistemic Hybrid Theories: Bridging epistemology and philosophy of language to address referential opacity.

Until then, Gettier cases will persist as reminders that knowledge demands more than justified true belief—it requires semantic precision in how we connect our words to the world.

 

TLDR;

"The claim that Gettier cases don’t accurately describe the world because they are referentially opaque cuts to the heart of how language smuggles ambiguity into epistemology. When we say “the person who gets the job has ten coins,” the proposition refers to one thing (e.g., Jones) but mediates that reference through an appeal to the set of all possible things with that quality (e.g., “people with ten coins”). This creates a sleight of hand: the belief’s justification is anchored to a specific referent (Jones), while its truth depends on a different member of the set (Smith). The problem isn’t just luck—it’s that the constraint to possible referents of an agent’s truth statement is linguistically flexible enough to retroactively validate accidental truths.

But whether these manipulations of language are actually valid or not remains underexplored. If propositions like “the person who…” are inherently semantically unstable—their referents shifting with context—then Gettier cases may be artifacts of linguistic looseness, not genuine paradoxes. To resolve this, we need stricter criteria for how descriptions bind to referents. Are we allowed to “edit” the referent post hoc when evaluating truth, or must propositions rigidly designate their objects? Until this is settled, Gettier cases risk being clever wordplay masquerading as metaphysical insight."

 

I would really like some feedback on this idea. And perhaps a co-author who is more mathematically inclined. I want to develop this into something much broader and more interesting. Thank you!

 

 

  1. ^

    https://zerophilosophy.substack.com/p/note-on-diagonal-method

  2. ^

    I have no great proof of this lemma.

  3. ^

    Models of language, and references, develop over time. But there are also new models of cognition. The way in which we refer to how, and what we think tends to expand in scope over time. 

    Computers allowed us to formalize logic into something we could understand. Neural networks have formalised the world -- through data -- into something computers can understand. 

    [Pure speculation] We might see new developments in the theory of truth in relation to LLMs.

    A lot of this is very releveant to Wittgenstein -- because LLMs have to make sense of our words and follow our intended rules. But this is an inherent limitation of language. Wittgenstein said “A serious and good philosophical work could be written consisting entirely of jokes."

    Norm Macdonald was always searching for the perfect joke. A joke that where the set up was exactly the same as the punchline. Does this not imply a way of looking at language differently? The idea that two separate, but concrete ideas could be drawn in from the same fountain of truth that is a sentence, or a propsition?

  4. ^

    This is a deep over-extension on my part. Trying to draw links between vastly different philosophical topics is incredibly difficult and not often useful. But I do see some kind of link between behaviorism and abductive reasoning. Although, it probably has correlates within Bayesianism as well. 

  5. ^

    This reminds of a great quote (as I like to link together some practical knowledge about philosophical dieas and their correlates in 'philosphical f-actuality': 'if you are not writing things down, you are not thinking'. The link here should be trivial for the reader to understand. If not, it is a nice inductive, meaning-uncertain puzzle.

  6. ^

    I am particularly reminded of a talk I attended -- and spent a considerable amount of time arguing against (and then becoming convinced) by a pre-eminnent Wittgenstein scholar at Oxford. It was in 2023 -- and the lecture was given in a small room to a group of Post-Docs/BPhil students. But the thing I most firmly remember was his absolute rejection and excoriation of Kripkenstein. He also mentioned some pretty batshit things about how his work stopped a neuroscientist collaborator in the resistance from winning a Nobel Prize. But I think that was just posturing to make me more convinced of his viewpoint. Anyhow, he was in a rush and I made him late for a meeting because of our furious intercourse.

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