1. Introduction
The stability of philosophical intuitions has been heavily challenged by experimental philosophy (Negative Xphi), which documents that case-judgments can vary with demographic and cultural factors (see, e.g., Stich and Machery Reference Stich and Machery2022; Machery et al. Reference Machery, Stich, Rose, Chatterjee, Karasawa, Struchiner, Sirker, Usui and Hashimoto2017). In response, a prominent family of “mischaracterization” defenses has emerged. Philosophers such as Cappelen (Reference Cappelen2012), Deutsch (Reference Deutsch2015, Reference Deutsch2016), and Horvath (Reference Horvath2022) argue that the Xphi critique misrepresents philosophical methodology; philosophers do not rely on idiosyncratic case-intuitions as evidence, but rather on arguments (or “Method of Cases-Grounds,” hereafter “MoC-Grounds”) to reach their verdicts. Most recently, Tałasiewicz (Reference Tałasiewicz2025) has expanded this family by proposing a “Quasi-Formal Approach,” arguing that cases demonstrate quasi-logical distinctions rather than eliciting evidential case-judgments.Footnote 1
Sękowski (Reference Sękowski2024a) offers perhaps the most structurally distinct and modern version of this defense. He introduces a strict division between general conceptual judgments (intuitions of intension) and case-application judgments (intuitions of extension). Acknowledging the Xphi threat, Sękowski’s “Concession Strategy” concedes that extensional case-judgments are unreliable. However, he argues that Gettier-style refutations can survive by adopting a revisionary interpretation of the Method of Cases. On this view, thought experiments do not attempt to track the existing folk concept of knowledge; rather, they serve as normative arguments for how experts should revise the concept, relying exclusively on reliable intensional principles. Furthermore, following Deutsch’s (Reference Deutsch2023) recent “infinitist” strategy, if these intensional premises are challenged, they can theoretically be supported by further arguments, avoiding a foundational reliance on raw intuition altogether.
This article takes Sękowski’s framework as the primary case study to challenge the broader family of mischaracterization responses. My central claim is that this Concession Strategy cannot succeed because the elimination of extensional judgments is incomplete. Even if we grant Sękowski his revisionary interpretation, and even if we allow for an infinitist regress of intensional arguments, the Method of Cases cannot get off the ground without concept-application. To make a normative argument revising the concept of knowledge, one must still pump intuitions using a specific vignette. I demonstrate that an ineliminable extensional judgment remains lodged in the thought experiment’s evidential setup – specifically, the premise that “Smith is justified in believing E.” While an author can descriptively stipulate the facts of a scenario, evaluating those facts as instantiating the philosophical concept of “justification” requires a case-directed intuitive judgment.
I further show that plausible attempts to replace these case-sensitive setup premises with general intensional principles (such as standard evidentialism, Conee and Feldman’s evidentialism, or hybrid forms of process reliabilism) fail; they either leave the extensional judgment intact, render the descriptive premises false, or beg the question. Consequently, case-application judgments are inescapable in the Method of Cases. This limited but substantive negative result undermines the claim that mischaracterization-style defenses can fully neutralize the Xphi objection.
The article proceeds as follows. Section 2 reconstructs Gettier’s ten-coins case and sets out the mischaracterization defense, focusing closely on Sękowski’s Concession Strategy and the intension/extension taxonomy. Section 3 identifies the locus of the problematic extensional judgment within the evaluative setup premises. Section 4 examines several families of arguments designed to replace this case-laden premise with general principles, demonstrating why each fails to remove the extensional dependency without significant theoretical cost. Section 5 evaluates recent attempts to bypass this dependency via methodological infinitism and conceptual engineering, arguing that concept-revision logically supervenes on concept-application. Finally, Section 6 outlines the broader implications for epistemological practice given this inescapable reliance on case-judgments.
2. Reconstructing the ten-coins case and the mischaracterization defense
2.1. Gettier’s ten-coins case and the evaluative setup
Gettier (Reference Gettier1963) offers two short vignettes designed to show that justified true belief (JTB) is not a sufficient condition for knowledge. The first – the ten-coins case – can be presented compactly as follows: Smith and Jones apply for a job. Smith has strong evidence for the conjunctive proposition: (d) “Jones will get the job, and Jones has ten coins in his pocket.” Smith’s evidence is: (i) the company president assured Smith that Jones would be selected; and (ii) Smith counted ten coins in Jones’s pocket 10 min earlier. From (d) Smith infers (e) “The man who will get the job has ten coins in his pocket.” Unknown to Smith, Jones will not get the job; Smith will. Unknown also to Smith, Smith himself has ten coins in his pocket. Thus (e) is true, Smith believes (e), and Smith is, by Gettier’s account, justified in believing (e); yet it seems wrong to say Smith knows (e).
To make the structure explicit, the dialectical core of Gettier’s refutation can be reconstructed as a deductive argument:Footnote 2
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(1) E is true. [E = “the man who will get the job has ten coins in his pocket”] (descriptive)
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(2) Smith believes E. (descriptive)
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(3) Smith has strong evidence for E (the president’s assurance; counting the coins). (descriptive/evaluative)
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(4) If one has strong evidence for p, then one is justified in believing p. (general conceptual principle)Footnote 3
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(5) Therefore, Smith is justified in believing E. (from 3 and 4)
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(6) Therefore, Smith has a justified true belief (JTB) that E. (from 1, 2, and 5)
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(7) If JTBs were sufficient for knowledge, then Smith would know E. (conceptual)
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(8) But Smith does not know E. (target conclusion/case verdict)
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(9) Therefore, JTB is not sufficient for knowledge. (from 6–8)
Much of the metaphilosophical debate focuses on supporting Premise 8 – the verdict that “Smith does not know E.” Those supporting arguments are what Deutsch Reference Deutsch(2010) and others in the mischaracterization family call “G-Grounds.” Philosophers have proposed several families of G-Grounds to underwrite this conclusion without relying on raw intuition, such as the Epistemic-Luck G-Ground, the No-Defeaters G-Ground, and the Disconnect G-Ground.
Each G-Ground carries advantages and costs. As critics have noted, attempts to introduce neutral principles often risk reintroducing the very intuition-sensitivity that experimental philosophy highlights, or they simply restate contested intuitions under another label (e.g., Landes Reference Landes2023; Horvath Reference Horvath2022).
Furthermore, it is crucial to clarify the epistemic status of the vignette’s “setup” (Premises 1–3). Although an author is perfectly entitled to stipulate the descriptive facts of a thought experiment (e.g., that the president spoke to Smith, or that Smith counted the coins), the categorization of those stipulated facts as constituting “strong evidence” or “justification” cannot be merely stipulated without begging the question. Evaluating whether the specific actions in the vignette successfully instantiate the philosophical concept of justification requires an active, case-directed intuitive judgment.
2.2. The mischaracterization family and Sękowski’s concession strategy
Sękowski (Reference Sękowski2024a) offers a highly sophisticated, strategic response to the Negative Xphi challenge on behalf of the mischaracterization family. Drawing on Craig (Reference Craig1990) and Spicer (Reference Spicer2008, Reference Spicer2010), he introduces a strict distinction between intuitions of intension and intuitions of extension:
Intuitions of intension: Judgments concerning the general properties of a concept (e.g., “knowledge should involve a nonaccidental connection to the truth”).
Intuitions of extension: Judgments about the epistemic state of an agent in a particular situation (e.g., “Given this vignette, Smith does not know E”).
Sękowski concedes that extensional case-judgments are vulnerable to demographic variation, rendering them an unreliable source of evidence. However, he insists that the justificatory grounds for thought experiments – what we might generally call MoC-Grounds – can and should be formulated strictly in terms of intensional principles. Returning specifically to the ten-coins vignette, Sękowski’s favored move is to construe the Disconnect G-Ground as relying entirely on an intensional expectation: “For each X, if X knows that p, then some facts that led X to acquire the belief that p are truth-makers for p.” His Disconnect G-Ground goes as:
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8a. Smith believes E on the basis of believing (i) Jones has ten coins and (ii) Jones will get the job. (descriptive)
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8b. The facts that make E true are (i*) Smith has ten coins and (ii*) Smith gets the job. (descriptive)
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8c. For any X: if X knows p, then some facts that led X to acquire the belief that p are truth-makers for p. (intensional principle)
Smith does not know E. (From 8a–8c)
The attractiveness of this reconstruction, as Sękowski sees it, is that 8c is an intensional principle – a general principle about the property of knowledge that does not depend on case-application judgments – and 8a–8b are descriptive facts one takes from the vignette. Thus, Sękowski claims, the G-Ground is not hostage to the vagaries of intuitions of extension.Footnote 4
Sękowski (Reference Sękowski2024a), at the same time (and the later Reference Sękowski2024b, Sękowski and Landes Reference Sękowski and Landes2026), crucially pairs this specific G-Ground with a broader revisionary interpretation of the Method of Cases. On his view, MoC-Grounds in general are not attempting to describe an everyday folk concept; they are normative, concept-revision arguments dictating what conditions should be imposed on the target concept by experts immersed in the discourse. Moreover, following Deutsch’s (Reference Deutsch2023) infinitist strategy, if these intensional premises are challenged, philosophers can simply supply further arguments, creating a dialectical chain that never necessarily terminates in a raw, unjustified intuition. By coupling concept-revision with intensional premises, Sękowski contends the Xphi attack is defused.
I concede Sękowski’s main moves for the sake of argument. I will assume the Disconnect reconstruction is acceptable, I will grant the revisionary interpretation of the Method of Cases, and I will allow for the infinitist regress of intensional arguments. Even granting all of these, the Concession Strategy does not succeed.
The strategy fails because the premises that establish the setup of the thought experiment – specifically the claim that “Smith is justified in believing E” (Premises 3 and 4, and the inference to 5) – inescapably depend on extensional judgments. One cannot make a normative argument revising a concept using a specific vignette without first applying concepts to that vignette to establish its parameters. Eliminating extensional judgments from the conclusion (the G-Grounds for Premise 8) does not guarantee their elimination from the setup.
This localized diagnosis identifies the strategic gap the mischaracterization family must still close. They must show not only that the G-Grounds are intension-based, but also that every premise supplying the evaluative setup (e.g., that Smith has “strong evidence”) can be justified without smuggling back the disputed extensional judgments or rendering the descriptive premises false.Footnote 5 Sections 3 and 4 examine this fatal locus in detail.
3. Identifying extensional judgments in the evaluative setup
Recall the reconstruction from §2. Although Sękowski successfully anchors the conclusion of the thought experiment in general conceptual principles (intensional judgments), the evaluative setup of the vignette – specifically the premises justifying the claim that “Smith is justified in believing E” – inescapably relies on case-judgments (extensional judgments). This section isolates those premises and demonstrates why they remain vulnerable to the Negative Xphi critique.
3.1. The target premises and the evaluative gap
Consider the relevant subargument identified in §2.1:
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(3) Smith has strong evidence for E (the president’s assurance; counting the coins). (descriptive/evaluative)
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(4) If one has strong evidence for p, then one is justified in believing p. (general conceptual principle)
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(5) Therefore, Smith is justified in believing E. (from 3 and 4)
As discussed regarding the dialectical nature of thought experiments, Premise 3 is not merely a stipulated fact; it is a case-application judgment. It attributes an evaluative epistemic status (“has strong evidence”) to the raw facts of the vignette. Deciding whether the president’s testimony combined with Smith’s observation successfully reaches the threshold of “strong evidence” is precisely the kind of extensional judgment vulnerable to demographic variation.
Even if we accept Premise 4 as a universally true intensional principle, the inference to Premise 5 only succeeds if the reader intuitively accepts the case-application in Premise 3. Endorsing Premise 3 requires the reader to evaluate the specific evidence provided and categorize it as “strong.” Thus, the inference hides a reliance on an extensional judgment in its descriptive antecedent. An intensional rule cannot neutralize an extensional application.
3.2. The case-sensitivity of “strong evidence”
Gettier uses the phrase “strong evidence” to indicate that Smith has a prima facie reason to accept E. However, “strong evidence” is an open-ended evaluative predicate. Agents can reasonably disagree about the force of testimony in the absence of corroboration, or whether a single observation (counting ten coins) is decisive. These are paradigmatic case-to-concept categorizations. Concrete alternative readings of the vignette illustrate this variability:
The skeptical reading: A respondent who believes that corporate executives frequently mislead applicants might treat the president’s assurance as weak evidence. For this respondent, Premise 3 is false, and the justificatory chain to Premise 5 collapses.
The trusting reading: A respondent who treats authoritative corporate testimony as definitive will easily accept Premise 3.
Framing effects: Altering the presentation of the vignette can shift a respondent’s willingness to endorse the evaluative label. For example, presenting the descriptive facts before labeling them “strong evidence” may cause respondents to evaluate the evidence more critically than if the author preemptively declares the evidence to be “strong.”Footnote 6
Experimental philosophy provides direct empirical support for this expected divergence. Studies demonstrate that case-application judgments about epistemic scenarios vary significantly based on demographic factors, cultural norms regarding authority, and experimental framing (Swain et al., Reference Swain, Alexander and Weinberg2008; Stich and Machery Reference Stich and Machery2022; Machery et al. Reference Machery, Stich, Rose, Chatterjee, Karasawa, Struchiner, Sirker, Usui and Hashimoto2017). Because the acceptance of Premise 3 depends on these highly variable factors, it remains a critical locus of extensional vulnerability.
3.3. Why general principles cannot bridge the gap
One might hope that deploying a highly robust intensional principle – a rigorous epistemological rule equating specific evidential conditions with justification – might dissolve the need for an extensional judgment. However, formalizing the rule does not eliminate the need to evaluate the antecedent.
Any principle of the form “If S meets conditions xyz, then S is justified” still requires the reader to judge that the specific agent in the vignette actually meets conditions xyz, which serves as a critical bridging premise. The generality of the rule does not alter the case-sensitivity of its application. Furthermore, introducing more sophisticated intensional principles of justification (such as Conee and Feldman-style evidentialism, which requires the absence of defeaters) creates a new dilemma. If the vignette contains elements that a respondent intuitively views as a defeater, the intensional rule renders Premise 3 false. In that case, using the general principle to justify Premise 5 will either fail entirely, or it will only succeed if the philosopher secretly alters the vignette’s factual content to force the premise to be true – a move that fundamentally begs the question.
Consequently, even if Sękowski can recast the overarching MoC-Grounds for a thought experiment’s final verdict as intension-based, extensional judgments remain inescapably lodged in the supporting setup premises.
4. Attempts to replace the extensional judgment in the evaluative setup
Recall the problem identified in §3; the premise that Smith “has strong evidence for E” requires an extensional, case-application judgment. To fully protect the mischaracterization defense from the Xphi challenge, one must show how to secure the inference to the claim that “Smith is justified in believing E” using strictly general, intensional principles without relying on contested case-judgments.
In this section, I examine four prominent families of “J-Arguments” – general epistemological theories intended to justify the step from the vignette’s descriptive facts to the evaluative claim that Smith is justified.Footnote 7 I argue that none succeeds in eliminating the extensional dependency without unacceptable theoretical costs. For each family, I state the general intensional principle, demonstrate how it would be applied to the vignette, and explain why the move either leaves the extensional vulnerability intact, renders the descriptive premises false, or begs the question.
4.1. Standard evidentialism
Standard evidentialism (SE) posits a general principle of justification: For any subject S and proposition p, if S’s evidence makes p highly probable (or is overwhelmingly supportive), then S is justified in believing p. Footnote 8 SE is a purely intensional rule. When applied to Gettier’s vignette, the argument proceeds as follows:
J-Argument 1 (SE-applied):
Descriptive setup: Smith’s evidence consists of (i) the company president’s assurance that Jones will get the job, and (ii) Smith’s observation of ten coins in Jones’s pocket.
General principle (SE): If S’s evidence makes p highly probable, then S is justified in believing p.
Evidential assessment premise (EAP): The combination of (i) and (ii) makes E (“the man who will get the job has ten coins”) highly probable.
Conclusion: Therefore, Smith is justified in believing E.
This argument is deductively valid, and the SE principle itself is stable. However, the EAP – the crucial bridging premise determining whether the vignette actually satisfies the antecedent of the rule – remains an extensional case-judgment. People reasonably differ on how much weight to give uncorroborated testimonial assurance or a single observation. As Xphi studies demonstrate, these assessments are highly sensitive to pragmatic and cultural background assumptions. Thus, the SE argument relocates the extensional judgment rather than removing it. To truly neutralize the Xphi critique, one would need an independent intensional rule that entails the EAP from purely descriptive facts – a resource unavailable within standard evidentialist bounds.
4.2. Conee and Feldman’s evidentialism
Conee and Feldman (Reference Conee and Feldman2004) advocate an evidentialist schema featuring an explicit defeater condition (CFE): S is justified in believing p iff (i) S’s total evidence supports p, and (ii) there are no undefeated defeaters that undercut or rebut that support. Applying CFE yields the following argument:
J-Argument 2 (CFE-applied):
Descriptive setup: Smith’s evidence = president’s assurance + observation of coins.
General principle (CFE): Justification requires evidential support plus the absence of undefeated defeaters.
No-defeater premise (NDP): There are no undefeated defeaters in the vignette that would undermine Smith’s evidence for E.
Conclusion: Therefore, Smith is justified in believing E.
The critical step here is the NDP, which again requires a case-application judgment. Different readers construe the president’s assurance differently – perhaps as reliable testimony, or perhaps as a manipulative, defeasible corporate test. Therefore, CFE preserves the extensional vulnerability unless the author simply stipulates that no defeaters exist.
However, stipulation begs the question. It imposes a contested evaluative conclusion on readers who might reasonably think otherwise. Conversely, if we refuse to stipulate the absence of defeaters, the factual reality of the vignette (that Smith himself ultimately gets the job) acts as an obvious defeater to Smith’s primary evidence (the president’s assurance regarding Jones). In that scenario, the bridging premise (NDP) becomes false, and the justificatory argument collapses. Hence, CFE either leaves the extensional judgment intact, renders the bridging premise false, or relies on an illegitimate stipulation.
4.3. Classic process reliabilism
We might instead turn to a principle from Process Reliabilism (PR); S is justified in believing p if S’s belief that p is produced by a reliable cognitive process (one that tends to produce true beliefs). Footnote 9 Applying PR generates the following argument:
J-Argument 3 (PR-applied):
Descriptive setup: Smith’s belief was produced by cognitive processes including accepting testimony, visual observation, and logical inference.
General principle (PR): If a belief is produced by reliably truth-conducive processes, the belief is justified.
Reliability assessment premise (RAP): These processes, in the relevant environment described in the vignette, are reliable.
Conclusion: Therefore, Smith is justified in believing E.
Determining whether the relevant process is reliable in the vignette’s specific context (the RAP) requires empirical, case-directed judgments about how often executives give truthful assurances or how reliable brief observations are. These are highly case-sensitive categorizations. One respondent’s assessment of the process as “reliable” will inevitably differ from another’s, displacing the extensional vulnerability directly into the reliability assessment.
4.4. Goldman’s revised reliabilism
Goldman (Reference Goldman1998) and others have proposed revised or hybrid accounts that incorporate additional constraints to handle Gettier-style problems. Call this revised principle GR: S is justified in believing p iff S’s belief is produced by a reliable process and the process-output is appropriately connected to the truth (no relevant epistemic luck), with suitable auxiliary conditions.
J-Argument 4 (GR-applied):
Descriptive setup: Smith’s belief is produced by processes functioning in the environment described in the vignette.
General principle (GR): Justification requires reliable processes appropriately connected to the truth (excluding relevant epistemic luck or defeaters).
Auxiliary assessment premise (AAP): In the vignette, the processes are reliable and appropriately connected to the truth (i.e., no relevant epistemic luck or undercutting).
Conclusion: Therefore, Smith is justified in believing E.
The AAP is once again a contested case-judgment. Assessing whether Smith’s situation exhibits the forbidden kind of “epistemic luck” depends entirely on whether the observer classifies the initial testimony and observation as ordinary or as structurally misleading.
To ensure that the theory handles the thought experiment cleanly, defenders may be tempted to craft ad hoc auxiliary conditions tailored specifically to preclude problematic readings. However, this effectively encodes the desired verdict into the theory’s stipulations, rather than deriving it transparently from general intensional principles. And, exactly as with CFE, if we refuse ad hoc stipulations regarding epistemic luck or disconnected truth-makers, the descriptive facts of the case (Smith getting the job) sever the appropriate connection to the truth, rendering the AAP false.
4.5. The inescapability of concept-application
A clear pattern emerges from the failure of these four J-Arguments. (i) Although intensional principles themselves are general and stable, they always require factual antecedents (e.g., “S has strong evidence,” “there are no defeaters,” “the process is reliable”) that function as case-application judgments. (ii) Determining whether those antecedents hold in a specific vignette depends on background assumptions, cultural norms regarding testimony, and context – precisely the factors experimental philosophy has shown to produce demographic variation. (iii) Attempts to bypass this variation by simply stipulating the evaluative antecedents beg the question; attempts to apply the rules without stipulation often render the bridging premises false in light of the vignette’s descriptive twists.
Therefore, none of the leading families of epistemological arguments successfully eliminates the reliance on extensional case-judgments in the evaluative setup without incurring fatal theoretical costs.
5. The limits of infinitism and concept-revision
Defenders of the mischaracterization strategy might attempt to bypass the failure of the J-Arguments by deploying two advanced metaphilosophical maneuvers: methodological infinitism and conceptual engineering. Although both offer sophisticated defenses of philosophical methodology in the abstract, neither can rescue the Method of Cases from its reliance on extensional case-judgments in practice.
5.1. The “bottoming-out” of methodological infinitism
Recognizing that premises must be justified, and seeking to avoid a foundational reliance on raw intuition, Deutsch (Reference Deutsch2023) proposes “methodological infinitism” (or “arguments all the way down”). On this view, philosophers do not need their arguments to terminate in an unjustified intuitive premise. Whenever a premise is challenged, the philosopher simply supplies a further argument for it, creating a dialectical chain of justification that never needs to reach an intuitive bedrock.
If we apply this to the ten-coins case, a defender might argue that the intensional rules governing justification (like standard evidentialism) do not rest on intuition, but are themselves supported by deeper epistemological arguments.
The fatal flaw in applying infinitism to the Method of Cases is a category mistake regarding the nature of thought experiments. Although it is theoretically possible to have an infinite regress of general intensional principles (where Rule A is justified by Rule B, which is justified by Rule C), a thought experiment is not merely a system of general rules. It is an argument anchored to a specific, concrete scenario.
To have any dialectical force against a target theory (like JTB), the infinite chain of general rules must eventually “touch down” on the descriptive facts of the vignette. The philosopher must establish that the specific agent (Smith) successfully satisfies the conditions of the general rule. This “touchdown point” is an evaluative categorization of a particular scenario – an inescapable extensional judgment. Infinitism can indefinitely postpone the justification of the rule, but it does absolutely nothing to bridge the gap between the rule and its application to the case.
5.2. Concept-revision supervenes on concept-application
Alternatively, mischaracterization defenders often retreat to a normative, revisionary interpretation of philosophy. As Sękowski (Reference Sękowski2024a, Reference Sękowski2024b) and Sękowski and Landes (Reference Sękowski and Landes2026) explore, the Method of Cases can be understood through the lens of conceptual engineering. On this reading, Gettier is not attempting to passively describe the folk concept of “knowledge,” but is instead actively advocating for how experts should revise the concept. Because it is a normative project, defenders argue that it is immune to the Xphi critique; the fact that folk extensional judgments vary does not invalidate the expert’s normative proposal.Footnote 10
However, this defense fundamentally misunderstands the mechanics of using a thought experiment as an engineering tool. Concept-revision logically supervenes on concept-application. To persuade an audience that the concept of “knowledge” requires revision based on Smith’s situation, the philosopher must first successfully build the situation. Building the situation requires applying foundational background concepts – like “justification,” “strong evidence,” or “defeaters” – to the raw descriptive facts of the story. If the application of these foundational setup concepts is vulnerable to demographic variation (as demonstrated in §§3 and 4), the entire engineering project lacks a stable launchpad.
In short, one cannot successfully engineer a target concept using a hypothetical vignette if the audience does not intuitively agree on the epistemic reality of the vignette itself. Even as a tool of conceptual engineering, the Method of Cases remains parasitically dependent on extensional case-judgments to establish its parameters, leaving the mischaracterization defense permanently exposed to the negative findings of experimental philosophy.
6. Conclusion
The mischaracterization family – and Sękowski’s (Reference Sękowski2024a) sophisticated Concession Strategy in particular – makes an attractive and important move by attempting to recast the evidential grounds of thought experiments in strictly general, intensional terms. I granted this move for the sake of argument and reconstructed the target MoC-Grounds as relying entirely on conceptual principles. Nevertheless, this analysis demonstrates that this maneuver does not remove the vulnerability to experimental philosophy from the Method of Cases as a whole.Footnote 11
The evaluative setup of these vignettes – specifically the subargument establishing that “Smith is justified in believing E” – inescapably depends on a descriptive antecedent that functions as an extensional case-application judgment. Leading epistemological theories designed to replace or underpin that antecedent with general principles (standard evidentialism, Conee and Feldman’s evidentialism, classic process reliabilism, and revised hybrid forms) either leave the case-dependency intact, render the needed bridging premises false, or secure the conclusion only through question-begging stipulations. Furthermore, retreating to methodological infinitism or normative conceptual engineering fails to rescue the method, because the revision of a concept logically supervenes on the successful, stable application of baseline concepts to the vignette. Thus, extensional case-judgments are inescapable in the Method of Cases unless one accepts ad-hoc stipulations or artificially narrows one’s audience.Footnote 12
If the reliance on case-application judgments in Gettier-style thought experiments is taken seriously, several implications follow for epistemological practice. First, although Gettier’s core negative result remains conceptually important, the persuasive force of specific brief vignettes is highly contingent on background evidential judgments; discussions relying on such cases should explicitly acknowledge this contingency. Second, philosophers who use case-based arguments must either make their contested evidential bridging judgments explicit or supply independent support for them (e.g., by expanding the vignette’s details or adducing empirical claims about testimonial reliability), as leaving those bridging premises implicit invites demographic and interpretive dispute. Third, attempts to repair JTB by adding auxiliary conditions must be evaluated not only for their theoretical virtues, but also for whether they covertly encode the desired verdict as a theoretical stipulation. Finally, debates about knowledge that rest heavily on a small set of intuitions would benefit from combining careful case construction with argumentation that appeals to broader empirical evidence, reducing reliance on background-sensitive classifications and making the dialectic more accessible to diverse audiences.Footnote 13
Acknowledgments
I am deeply grateful to my supervisor, Professor Shuyi Feng, whose courses in philosophical methodology provided the initial inspiration for this research. Her invaluable guidance, support, and meticulous feedback throughout the preparation and revision of this manuscript have been instrumental. I would also like to extend my sincere thanks to Zhengchuan Li and Ziwen Zhou for our illuminating discussions, which significantly helped refine the arguments presented here during the two rounds of manuscript revision.