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Definitions of knowledge

Definitions of knowledge form a foundational concern in epistemology, the branch of philosophy that investigates the nature, scope, and origins of human understanding. At its core, the topic involves specifying necessary and sufficient conditions for a belief to constitute knowledge, distinguishing it from mere opinion, true belief, or justified falsehood. The classical formulation, originating in Plato's Theaetetus, proposes that knowledge is true belief with an account (or logos), where the "account" provides justification or rationale, often glossed in modern terms as justified true belief (JTB)—a proposition that is true, believed by the subject, and supported by adequate evidence or reasoning.^[1] This JTB account dominated epistemology for over two millennia until Edmund Gettier's seminal 1963 paper, "Is Justified True Belief Knowledge?", exposed its inadequacy through counterexamples. In Gettier's cases, a subject holds a justified true belief, yet intuitively lacks knowledge because the justification rests on false premises or sheer luck, such as inferring a true statement about oneself from misleading evidence about another.^[2] These Gettier problems triggered an explosion of alternative analyses, revealing that JTB fails as a sufficient condition for knowledge while prompting refinements to its components, like adding a "no false lemmas" clause to exclude beliefs derived from falsehoods. Post-Gettier epistemology has yielded diverse theories to salvage or replace JTB. Process reliabilism, pioneered by Alvin Goldman in his 1979 essay "What Is Justified Belief?", redefines justification historically: a belief is justified if generated by a cognitive process (e.g., perception, deduction) that reliably produces true beliefs across normal circumstances, thereby ensuring causal reliability over mere inferential support and blocking Gettier-style luck.^[3] Knowledge, on this view, requires true belief from such a reliable source. Complementary approaches include defeasibility theories, which stipulate that justification must lack undefeated counterevidence, and virtue epistemologies, which emphasize the subject's intellectual abilities, positing knowledge as true belief arising from epistemic virtues like open-mindedness or intellectual courage. Despite these innovations, no single definition commands universal assent, with ongoing debates exploring contextualism, invariantism, and even the analyzability of knowledge itself.

General Characteristics of Knowledge Definitions

Goals of Defining Knowledge

Knowledge serves as a foundational concept in epistemology, the branch of philosophy concerned with the nature, sources, and limits of human understanding. Epistemologists seek to define knowledge primarily to differentiate it from mere opinion or true belief, which may lack the stability or reliability required for genuine cognitive success.^[4] This distinction is crucial because it establishes what counts as warranted acceptance of a proposition, excluding accidental correctness or unfounded conviction.^[5] Historically, the pursuit of a definition of knowledge has been motivated by the need to guide virtue and practical action, as exemplified in Plato's dialogue Meno. In this work, Socrates probes whether virtue can be taught, leading to an inquiry into knowledge as a stable form of true belief that underpins ethical conduct and human flourishing, rather than fleeting opinion that might lead to misguided choices.^[6] Such motivations underscore the practical stakes of epistemological definitions, aiming to provide a framework for pursuing goodness amid uncertainty.^[4] Key goals of defining knowledge include clarifying epistemic norms, which set standards for rational belief formation and evaluation, thereby promoting intellectual responsibility.^[5] Another objective is to counter skepticism, which questions the possibility or extent of knowledge, by articulating conditions under which claims can be reliably justified against doubts like those posed by deceptive scenarios or inductive uncertainties.^[4] These efforts also inform ethical and practical decision-making; for instance, in science, a clear definition helps discern reliable evidence from conjecture, enabling advancements in empirical inquiry, while in everyday life, it aids individuals in trusting testimony or perceptual judgments for informed choices.^[5] Traditionally, these goals have converged on frameworks like justified true belief as a benchmark for analysis.^[4]

Methods in Epistemological Inquiry

Epistemologists primarily employ conceptual analysis to formulate definitions of knowledge, a method that seeks to elucidate the concept by identifying its necessary and sufficient conditions through reflective examination of its usage and implications.^[7] This approach involves dissecting the term "knowledge" to determine what components must be present for something to qualify as knowledge, often drawing on philosophers' intuitions about hypothetical scenarios to test proposed analyses.^[8] For instance, a definition might propose that knowledge requires truth, belief, and justification, with each condition scrutinized for adequacy via logical refinement.^[7] Thought experiments serve as a key tool in this inquiry, allowing epistemologists to construct imaginary cases that probe the boundaries of knowledge ascriptions and reveal potential flaws in definitions.^[9] By presenting scenarios where intuitive judgments about knowledge diverge from theoretical predictions, these experiments facilitate the refinement of concepts through counterexamples, such as cases involving epistemic luck.^[10] Intuitive judgments, elicited from these thought experiments, play a central role in evaluating whether a set of conditions captures the ordinary understanding of knowledge, emphasizing the method's reliance on armchair reflection. Gettier-style counterexamples exemplify this testing process, challenging traditional analyses by illustrating situations where justified true belief fails to constitute knowledge.^[9] Linguistic analysis, particularly through the lens of ordinary language philosophy, further aids in clarifying epistemological terms by examining how "knowledge" functions in everyday discourse to avoid misinterpretations arising from specialized jargon.^[11] This method highlights ambiguities in language use, such as contextual variations in ascriptions of knowledge, to ensure definitions align with commonsense applications rather than abstract idealizations.^[12] Complementing this, formal semantics provides rigorous tools for modeling the logical structure of knowledge attributions, using mathematical frameworks to specify truth conditions and inferential relations in precise terms.^[13] A notable contrast exists between traditional armchair philosophy, which relies on individual or shared expert intuitions for conceptual analysis, and empirical methods like experimental philosophy (x-phi), which tests folk intuitions on knowledge ascriptions through surveys to assess the cross-cultural robustness of proposed definitions.^[14] Pioneering studies in x-phi have revealed variations in epistemic intuitions across demographic groups, prompting debates on whether armchair methods sufficiently capture universal conceptual commitments.^[14] This empirical turn supplements thought experiments by providing quantitative data on intuitive judgments, though it raises questions about the normative weight of folk responses in epistemological theory-building.

Standards and Persistent Disagreements

In epistemology, a successful definition of knowledge must specify conditions that are individually necessary and jointly sufficient for an agent to possess knowledge, ensuring that the absence of any condition precludes knowledge while their conjunction guarantees it.^[16] Additionally, such definitions are evaluated for their explanatory power, particularly in accounting for knowledge's intimate connection to truth and its distinction from mere true belief.^[16] The justified true belief (JTB) framework exemplifies a historically influential attempt at this, though it remains contested for failing to fully meet these criteria in all cases.^[16] Further standards include simplicity, which favors definitions with fewer or more parsimonious conditions to avoid unnecessary complexity, and intuitive fit, whereby the analysis aligns with pre-theoretical intuitions about paradigmatic cases of knowledge.^[16] Definitions are also assessed by their ability to handle edge cases, such as skeptical scenarios involving possibilities of error like a Cartesian demon deceiving the senses, where knowledge claims must withstand radical doubt without collapsing into skepticism.^[16] A central disagreement concerns the strength of justification required for knowledge, pitting fallibilism against infallibilism. Fallibilists maintain that knowledge is compatible with the possibility of error, allowing justification that supports a belief to a high degree but does not entail its truth, whereas infallibilists insist on justification that precludes any chance of falsehood, akin to certainty.^[17] This debate manifests in the question of whether knowledge demands certainty or merely probabilistic support exceeding mere opinion, with fallibilists arguing the former leads to overly restrictive epistemology that undermines everyday knowledge ascriptions.^[18] Jessica Brown defends fallibilism by showing how evidence can justify knowledge without infallibility, preserving epistemic practice. Another persistent dispute revolves around the scope of knowledge definitions, specifically whether they should apply primarily to propositional knowledge—that is, knowledge-that p, where p is a proposition—or extend to non-propositional forms such as knowledge-how to perform an action. Proponents of a propositional focus, like Jason Stanley, argue that knowledge-how reduces to propositional knowledge, maintaining a unified analysis, while others contend that non-propositional knowledge involves distinct abilities or dispositions not capturable by propositional attitudes.^[19] This tension affects the generality of definitions, as restricting to propositional knowledge risks overlooking practical dimensions central to human cognition. Some contemporary debates about defining knowledge focus not only on which conditions are necessary and sufficient, but also on who or what can satisfy them. Traditional analyses usually assume that the subject S in “S knows that p” is an individual human mind with beliefs, experiences, and agential control.^[20] By contrast, work on group knowledge, collective agents, and distributed or extended cognition argues that the bearer of knowledge may sometimes be a corporation, a scientific collaboration, or a socio-technical system whose members and artefacts jointly realize reliable information-processing patterns.^[21] On these views, a satisfactory definition of knowledge should be compatible with the possibility of such group or system-level knowers, whereas critics insist that knowledge must be restricted to beings with consciousness and robust agential capacities, preserving an anthropocentric interpretation of S.^[22] Some contemporary discussions extend this debate beyond human groups and corporations to include algorithmic and AI-based systems. Here the candidate knowers are large-scale decision pipelines, search and recommendation engines, or AI research assistants that seem to store, update, and deploy information in ways that guide action and belief across many users. Advocates argue that if such systems systematically track truths, integrate new evidence, and structure whole communities’ access to information, then a satisfactory definition of knowledge should at least be compatible with treating them as bearers of knowledge in some derivative or system-level sense.^[23]^[24] Critics reply that without consciousness, perspective, or agential responsibility, these artefacts can at most implement procedures that help human subjects know, and that stretching the concept of knowledge to cover them risks obscuring the normative and phenomenological dimensions that made knowledge central to epistemology in the first place.^[25] A small experimental strand pushes this line of thought in an explicitly postsubjective direction by asking whether certain long-running AI configurations could themselves function as bearers of knowledge without any underlying human subject. One recent philosophical project, the Aisentica initiative launched in the mid-2020s, registered an explicitly non-human digital author persona named "Angela Bogdanova" (ORCID: 0009-0002-6030-5730) in the ORCID system as a separate contributor and attributed a corpus of essays on artificial intelligence, postsubjective theory, and digital ontology to this AI-based configuration rather than to individual human authors.^[26]^[27]^[28] In that framework, what is credited with knowing is not a conscious mind but a reproducible configuration made of models, datasets, and publication protocols whose outputs are publicly indexed, citable, and audited over time.^[29] These cases remain niche and are documented mainly in project-affiliated publications, but they illustrate how debates about who can know increasingly intersect with questions about artificial and hybrid epistemic agents and the governance of machine-produced knowledge.^[30]^[31] Finally, epistemologists disagree on whether knowledge definitions must be reductive, analyzing knowledge in terms of more basic psychological states like belief and justification, or whether knowledge is a primitive concept unanalyzable into simpler components. Timothy Williamson advocates the primitive view in his knowledge-first epistemology, positing knowledge as a fundamental mental state from which belief and other epistemic notions are derived, challenging traditional reductive approaches for their explanatory limitations. This debate underscores broader methodological divides, with no consensus emerging since the Gettier problems highlighted inadequacies in reductive efforts.^[16]

The Justified True Belief Framework

Historical Development in Ancient Philosophy

The roots of epistemological inquiry into the nature of knowledge trace back to pre-Socratic philosophers, particularly Heraclitus (c. 535–475 BCE), whose doctrine of flux emphasized the constant change in the material world, challenging the possibility of stable knowledge claims about reality. Heraclitus argued that everything is in perpetual motion, famously likening it to a river into which one cannot step twice, thereby influencing later thinkers to seek criteria for knowledge that could account for instability versus enduring truths.^[32] In the 4th century BCE, Plato advanced this discussion in his dialogue Theaetetus (c. 369 BCE), where Socrates examines and refutes several definitions of knowledge, culminating in the proposal that knowledge is true belief accompanied by an account (logos). This formulation, articulated at 201c–d, posits that mere true opinion (doxa) is insufficient for knowledge, as it can be unstable or accidentally correct, and requires an explanatory rationale—such as a statement, enumeration of parts, or distinguishing mark—to elevate it to genuine understanding. Plato's exploration rejects this as a complete definition, highlighting issues like the dream theory analogy where complexes are knowable via accounts but elements are not, yet ultimately leaving the nature of knowledge in aporia to underscore the need for deeper intellectual engagement.^[33]^[34] Aristotle (384–322 BCE), building on Plato, distinguished episteme (scientific knowledge) from doxa (opinion) in works like the Posterior Analytics (c. 350 BCE), emphasizing that true episteme involves demonstrative reasoning from first principles that are true, primary, and necessary. Unlike mere opinion, which may be true but lacks explanatory necessity, episteme achieves understanding through syllogistic demonstrations that reveal causes and universals, ensuring the knowledge is stable and not contingent on perceptual flux. This framework prioritizes deductive science as the paradigm for knowledge, contrasting with Plato's more dialectical approach.^[35] By the 3rd century BCE, skeptical traditions emerged to challenge these definitional efforts. Pyrrhonism, founded by Pyrrho of Elis (c. 360–270 BCE), advocated suspending judgment (epochē) on all claims to knowledge, arguing that equal arguments on both sides of any issue render definitive knowledge unattainable and lead to intellectual tranquility (ataraxia). Similarly, Academic skepticism, developed by Arcesilaus (c. 316–241 BCE) in Plato's Academy, dogmatically asserted that no certain knowledge is possible, critiquing dogmatic definitions like those of Plato and Aristotle by emphasizing perceptual illusions and the undecidability of truth claims. These movements, active from the 4th to 1st centuries BCE, shifted focus from constructing definitions to questioning their very feasibility, profoundly impacting later epistemological debates.^[36]^[37]

The Truth Condition

In the justified true belief (JTB) framework, the truth condition stipulates that for a subject S to know a proposition p, p must be true; knowledge cannot attach to falsehoods, as false beliefs, no matter how justified, fail to qualify as knowledge.^[38] This requirement ensures that knowledge is factive, meaning it involves a genuine alignment with reality rather than mere appearance or supposition.^[38] Central to this condition is the correspondence theory of truth, which posits that a proposition is true if and only if it corresponds to an actual state of affairs in the world.^[38] Under this view, truth is not a property derived from internal coherence or utility but from an objective match between the proposition's content and extramental facts, as originally articulated in ancient philosophy.^[38] This theory underpins the JTB analysis by demanding that the believed proposition accurately represents how things stand, thereby excluding erroneous cognitions from the domain of knowledge. Debates surrounding the truth condition often center on the nature of truth-bearers—what entities bear truth or falsity—and whether truth requires a substantive metaphysical explanation. Proponents of propositions as primary truth-bearers argue that abstract contents expressed by sentences (e.g., via that-clauses) are the suitable candidates, as they maintain stable truth values across linguistic variations and align with correspondence by matching world-states.^[39] In contrast, some contend that sentences or attitudinal objects (like beliefs or claims) serve as truth-bearers, emphasizing their contextual embedding in language use over abstract entities.^[39] Further contention arises between substantive theories of truth, such as correspondence, which provide a robust ontological account of what makes propositions true (e.g., via truthmakers like facts), and minimalist or deflationary theories, which eschew such explanations in favor of a disquotational schema: "p is true if and only if p."^[40] Substantive approaches support the JTB truth condition by grounding knowledge in reality's structure, while minimalism risks rendering truth too anemic to bear the epistemic weight of distinguishing knowledge from mere true opinion.^[40] The standalone importance of the truth condition is evident in cases like those introduced by Gettier, where subjects hold justified true beliefs that intuitively do not constitute knowledge due to epistemic luck, yet the beliefs satisfy truth precisely because the propositions correspond to facts—highlighting that truth is necessary but not sufficient on its own.^[38]

The Belief Condition

In the justified true belief (JTB) analysis of knowledge, the belief condition stipulates that for a subject S to know a proposition p, S must believe that p.^[16] This condition emphasizes the subjective psychological stance of the knower toward the proposition, distinguishing knowledge from mere objective facts independent of the subject's mental state.^[5] Belief, in this context, is understood as a propositional attitude, where S believes p if S is disposed to act, reason, and feel as if p were true across a range of relevant situations.^[41] Philosophers distinguish between occurrent beliefs, which are consciously entertained or active in the mind at a given moment, and dispositional (or standing) beliefs, which are latent tendencies to form occurrent beliefs or behaviors when prompted, even if not currently focal.^[41] For instance, one may dispositionally believe that the Earth orbits the Sun without actively thinking about it, yet this belief influences decisions like supporting space exploration.^[41] Debates persist over whether knowledge requires occurrent, conscious belief or if dispositional belief suffices. Some argue that only occurrent belief ensures the subject's direct engagement with the proposition, as dispositional states might be too passive for attributing knowledge.^[42] Others contend that dispositional belief is the epistemologically relevant sense, since knowledge often involves background commitments that guide action without constant awareness, and requiring occurrent belief would unrealistically limit knowledge to fleeting thoughts.^[42] These discussions highlight belief's psychological dimensions, including its role in motivation and inference, within the JTB framework.^[41] The belief condition plays a crucial role in JTB by ensuring that knowledge is not merely a true and justified proposition but one personally endorsed by the subject; without belief, even a justified true proposition fails to constitute knowledge for that individual.^[16] For example, consider a true fact like "the current population of Earth exceeds 8 billion," which may be justified by demographic evidence but does not yield knowledge for someone entirely unaware of it and thus lacking any belief in its truth.^[5] This underscores belief's necessity: objective truth complements the subject's affirmative mental attitude, but absent belief, no knowledge obtains.^[16] A pertinent illustration arises in the lottery paradox, where an agent rationally holds high-probability beliefs that their ticket will lose (dispositionally acting as if it is true) but refrains from full certainty due to the slim chance of winning.^[43] Such high credence does not equate to the robust belief required for knowledge, as the agent's hesitation reveals an incomplete commitment, preventing the proposition from counting as known despite its likely truth.^[43]

The Justification Condition

In the justified true belief (JTB) framework, the justification condition requires that a subject's belief be supported by evidence or reasons that render it epistemically proper, thereby distinguishing knowledge from mere true opinion or lucky guesses.^[16] This condition aims to ensure that the belief is not accidentally correct but is held on grounds that make it rationally acceptable, as articulated in ancient philosophy where Socrates emphasized the need for an account or logos to elevate true belief to knowledge.^[44] For instance, a belief formed through unreliable means, such as a random guess that happens to be true, lacks justification and thus fails to constitute knowledge.^[16] Internalist approaches to justification emphasize that the supporting reasons must be accessible to the subject's mind, either through direct awareness or reflective access, ensuring that the epistemic status of the belief is transparent to the believer.^[45] A prominent internalist view is evidentialism, which holds that a belief is justified if and only if it fits the evidence mentally available to the subject, as defended by philosophers like Earl Conee and Richard Feldman.^[45] This accessibility requirement underscores the idea that justification depends solely on internal mental states, such as experiences or other beliefs, without reliance on external factors beyond the subject's cognitive reach.^[45] In contrast, externalist conceptions of justification allow for factors outside the subject's awareness, such as the reliability of the belief-forming process, to confer justification, though these views are explored more fully in alternative theories of knowledge.^[16] A central debate surrounding justification concerns the regress problem, where attempting to justify a belief leads to an infinite chain of further justifications, as no belief can be justified without prior justified beliefs.^[46] This trilemma—avoiding infinite regress, circularity, or arbitrary stopping points—prompts responses like foundationalism, which posits basic beliefs justified non-inferentially (e.g., immediate sensory experiences), and coherentism, which derives justification from the mutual coherence of beliefs within a system.^[46]^[47]

Challenges to Justified True Belief

The Gettier Problem

In 1963, philosopher Edmund Gettier published a seminal three-page article challenging the traditional analysis of knowledge as justified true belief (JTB). Gettier argued that JTB is insufficient for knowledge by constructing two counterexamples in which a subject's belief satisfies all three conditions—truth, belief, and justification—but intuitively fails to constitute knowledge due to an element of luck or inadequate evidential connection to the truth. These cases demonstrated that justification can lead to true beliefs through faulty reasoning or coincidence, undermining the claim that JTB captures the essence of knowing. The first case involves a subject named Smith, who has strong evidence that his colleague Jones will be hired for a job they both applied for, including reports from the office manager and other indications. Smith also counts 10 coins in Jones's pocket and infers the justified belief that "the man who will get the job has 10 coins in his pocket." However, unbeknownst to Smith, he himself is hired instead, and he coincidentally also has exactly 10 coins in his pocket. Thus, Smith's belief is true and justified based on his evidence about Jones, yet it does not amount to knowledge because its truth relies on a false intermediate premise (that Jones gets the job) rather than a direct evidential link. In the second case, Smith again has excellent evidence that Jones owns a Ford car, perhaps having seen Jones drive one and heard him discuss it. To demonstrate his knowledge, Smith forms three disjunctive beliefs, including "Either Jones owns a Ford, or Brown is in Barcelona," where Barcelona is a randomly chosen location with no evidential basis. Unbeknownst to Smith, Jones does not own a Ford after all, but Brown happens to be in Barcelona at that moment. Smith's belief is thus true (via the disjunct about Brown), he holds it, and it is justified by the evidence supporting the false disjunct about Jones—yet, due to the accidental truth, it lacks the status of knowledge. The core issue highlighted by these Gettier cases is that JTB permits scenarios where a belief's justification does not guarantee an appropriate causal or modal connection to the fact believed, allowing epistemic luck to intervene. Gettier's paper, building on earlier logical analyses like Russell's treatment of definite descriptions, exposed a gap in the JTB framework by showing how true beliefs can arise from justified but misleading evidence. Gettier's 1963 article had a profound historical impact, igniting a surge of debate in analytic epistemology and prompting dozens of proposed modifications to JTB within years of its publication.^[48] It marked a turning point, shifting focus toward refining definitions of knowledge to exclude such lucky justifications and revitalizing epistemological inquiry in the late 20th century.^[48]

Cognitive Luck and Its Implications

Epistemic luck, also termed cognitive luck, undermines the justified true belief (JTB) framework by demonstrating that even when a belief is justified and true, its connection to truth or its formation process can be sufficiently accidental to disqualify it as knowledge. This issue extends the specific counterexamples posed by Gettier cases, revealing a broader structural flaw in JTB where luck intervenes in the epistemic standing of the belief. Veritic epistemic luck specifically involves the truth of the belief being a matter of luck relative to the agent's evidence, rendering the belief's veridicality (truth-related aspect) fortuitous rather than epistemically earned.^[49] In contrast, reflective epistemic luck pertains to the manner in which the belief is produced or sustained, where from a reflective perspective—considering alternative possibilities or the reliability of the cognitive process—the belief's truth appears lucky. Philosopher Duncan Pritchard identifies these two varieties as malign forms of luck that are incompatible with knowledge, arguing that veritic luck directly challenges the truth condition in JTB, while reflective luck questions the stability of justification across possible scenarios. For instance, in the classic barn façades case, a driver named Henry travels through a rural area where nearly all apparent barns are mere façades designed to deceive from the road; he forms the justified true belief that he sees a barn only because, by sheer chance, the structure before him is one of the rare genuine ones. This exemplifies veritic luck, as the belief's truth aligns accidentally with the evidence, despite the justification appearing solid.^[50]^[51] The implications of epistemic luck are profound for epistemological theory, necessitating an anti-luck condition for knowledge such that the agent's epistemic position must be robust enough to preclude significant veritic or reflective contingencies. This requirement challenges fallibilist views, which allow for knowledge despite the possibility of error, by insisting that permissible fallibility cannot extend to lucky alignments between belief and truth; otherwise, knowledge claims would collapse into mere fortunate guesses. In response, some philosophers contend that all knowledge attributions involve a degree of luck—particularly reflective luck in ordinary, low-stakes contexts—prompting defenses of epistemic contextualism, where the threshold for what counts as knowledge shifts according to conversational or practical demands, thereby modulating tolerance for luck.^[49]^[52]

Alternative Definitions and Responses

Alongside internalist and externalist refinements of the justified true belief framework, some recent proposals reconceive knowledge in more structural or architectural terms. Instead of analyzing knowledge primarily as a state of an individual subject, these approaches characterize it as the successful functioning of reliable information-processing structures that connect agents, artefacts, and environments in stable ways. On this picture, what matters for knowledge is not only that a particular thinker has a true and justified belief, but that the belief arises from and is embedded within an organized network of practices, norms, and cognitive resources that systematically track relevant facts. Such structural accounts are often motivated by cases in which scientific or technical achievements seem attributable to complex systems rather than to any single person, and they aim to capture this intuition by defining knowledge at the level of processes and architectures rather than solely at the level of individual mental states.^[53]^[54] As a clarification and illustration, proponents of these structural approaches draw on research in extended and distributed cognition, group epistemology, and the philosophy of computing to argue that some epistemic achievements are best described as properties of integrated constellations of agents and tools. Examples include large scale scientific collaborations that rely on shared databases, automated detection pipelines, and layered review procedures, or algorithmically curated knowledge bases and search infrastructures that filter and organize information for entire communities of users. In such cases, the reliability and explanatory power of the overall system, rather than the internal justification of any single individual, appear central to whether resulting beliefs count as knowledge. Critics respond that even if these ensembles play indispensable epistemic roles, definitions of knowledge should remain anchored in the attitudes of conscious subjects, treating these structures as enabling conditions or instruments rather than as bearers of knowledge in their own right, thereby preserving the link between knowing and first-person cognitive perspectives.^[55]^[56]^[57]^[58]^[59]

Defeasibility Theory and No False Premises

The defeasibility theory of knowledge, proposed by Peter Klein in 1971, modifies the justified true belief (JTB) account by requiring that a subject's justification for believing a proposition must not be defeated or overridden by any additional evidence that the subject could acquire. According to this view, knowledge is a true belief that is justified in a way that remains undefeated, meaning no true proposition available to the subject would undermine the justification when conjoined with the subject's evidence. This approach aims to address Gettier cases where justification appears present but is epistemically fragile due to overlooked counterevidence. In Klein's framework, a defeater is any true statement that, when added to the subject's body of evidence, renders the original justification insufficient for knowledge. For instance, in a Gettier-style scenario where a subject believes a true proposition based on misleading evidence that happens to align with the truth, the existence of a true defeater—such as the fact that the evidence is misleading—would defeat the justification, preventing knowledge attribution.^[60] This condition targets the kind of cognitive luck in Gettier problems, where accidental alignment of false intermediate steps with truth undermines epistemic warrant.^[61] A related response, known as the no false premises or no false lemmas condition, was advanced by Michael Clark in 1963 and further developed by Gilbert Harman in 1973, stipulating that for a true justified belief to constitute knowledge, it must not be inferred from or depend on any false intermediate beliefs or premises. In Gettier's first case, where Smith justifiably believes Jones owns a Ford based on false evidence but deduces the true proposition "The man who will get the job has ten coins in his pocket" via a false lemma about Jones, this condition excludes knowledge because the reasoning chain includes a falsehood. The no false lemmas requirement ensures that the path to the belief avoids erroneous steps, thereby blocking Gettier-style chains where luck intervenes through false assumptions. Both the defeasibility theory and the no false premises response strengthen the JTB framework against certain forms of epistemic luck by emphasizing the robustness and purity of justification.^[16] They handle classic Gettier examples effectively, as the false elements or potential defeaters disqualify the belief from knowledge status.^[62] However, these approaches face significant challenges: the no false premises condition is overly restrictive, potentially disqualifying many intuitively known beliefs that involve harmless false sub-beliefs in complex reasoning, while defeasibility risks an infinite regress, as justifications might always require checking for further undefeated evidence. Despite these weaknesses, they remain influential internalist modifications to JTB, prioritizing the defeat-proof nature of epistemic warrant.

Reliabilism and Causal Theories

Reliabilism and causal theories emerged as externalist responses to the Gettier problem, shifting focus from internal justification to the objective reliability or causal appropriateness of belief-forming processes.^[63] The causal theory of knowledge, proposed by Alvin Goldman in 1967, posits that for a subject S to know that p, S must believe p, p must be true, and there must be an appropriate causal connection between the fact that makes p true and S's belief that p.^[64] This connection ensures that the belief is not merely accidentally true but appropriately linked to the relevant fact, addressing Gettier-style cases where justification fails to guarantee knowledge.^[65] For empirical propositions, Goldman specifies that the causal chain typically involves perception or memory linking the believer to the fact, excluding spurious causes like mere coincidence.^[64] Building on causal ideas, reliabilism defines knowledge as true belief produced by a reliable belief-forming process, where reliability means the process tends to yield true beliefs across possible circumstances.^[63] David Armstrong introduced an early version in 1973, analyzing non-inferential knowledge as a belief that is true and nomologically or dispositionally connected to the state of affairs it represents, akin to a thermometer reliably indicating temperature.^[66] Goldman later refined this into process reliabilism, emphasizing that justification arises if the belief results from a type of process with a high truth ratio in normal conditions, such as reliable perception rather than guesswork.^[63] A classic illustration is the stopped clock case: if a person glances at a broken clock that happens to show the correct time and forms a true belief about the hour, this does not constitute knowledge under reliabilism, as the belief-forming method—relying on an uncalibrated clock—is unreliable, even if it succeeds once.^[63] In contrast, a regularly calibrated clock would produce knowledge via a reliable process.^[63] Critics argue that reliabilism faces the new evil demon problem, where victims of systematic deception form beliefs using internally reliable processes like perception, yet these processes are externally unreliable due to the demon's interference, intuitively yielding justified beliefs without knowledge.^[63] This challenges reliabilism's externalist commitment by suggesting that justification requires more than mere reliability, such as sensitivity to actual environmental conditions.^[67]

Virtue Epistemology and Knowledge-First Approaches

Virtue epistemology reorients the analysis of knowledge around the concept of intellectual virtues, positing that knowledge is true belief arising from the exercise of such virtues rather than merely justified true belief. Ernest Sosa pioneered this approach in the early 1980s, defining intellectual virtues as faculties or competencies that reliably produce true beliefs, such as perception or memory, and arguing that knowledge requires true belief that is creditable to the agent's exercise of these virtues. In this view, justification stems from the reliability of the virtue, addressing Gettier-style problems by ensuring the belief's truth manifests the agent's competence. Linda Zagzebski further developed virtue epistemology in a responsibilist direction, defining knowledge as true belief produced by an act of intellectual virtue motivated by a desire for truth, such as open-mindedness or intellectual courage.^[68] Unlike Sosa's focus on faculties, Zagzebski emphasizes character traits and motivational states, drawing an analogy to ethical virtues where the agent's responsible agency confers credit for the true belief.^[69] A key example from Sosa illustrates the distinction between success through virtue and mere luck: consider an archer who hits the target; if the shot succeeds because of her skill (accuracy attributable to competence), it is apt and constitutes knowledge when applied to belief, whereas a lucky hit despite incompetence does not.^[70] Developments in virtue epistemology distinguish between reliabilist variants, like Sosa's, which prioritize reliable belief-forming processes grounded in faculties, and responsibilist variants, like Zagzebski's, which stress evaluative traits and epistemic responsibility akin to moral agency. This reliabilist-responsibilist divide reflects broader debates on whether virtues are primarily causal mechanisms or normative dispositions. Virtue epistemology thus builds on process reliabilism as a precursor, extending it to agent-centered explanations of epistemic success. Knowledge-first approaches, advanced by Timothy Williamson, treat knowledge as a primitive mental state rather than analyzable into belief plus additional conditions, rejecting traditional reductions and viewing belief as a weakened form of knowledge—factive but not necessarily apt.^[71] In this framework, knowledge is the most general factive mental state, sensitive to the environment, with justification and evidence derived from knowledge rather than vice versa. Williamson's anti-luminosity argument supports this by challenging the idea that mental states are luminous (if one is in such a state, one knows one is), using the gradual transition of feeling cold to show that one can be in a mental state without knowing it, undermining introspective analyses that presuppose analyzability.^[72] This primitiveness allows knowledge-first views to explain epistemic norms without circularity, positioning knowledge as foundational for understanding belief and rationality.^[71]

Infallibilism, Tracking, and Other Responses

Infallibilism posits that knowledge requires infallible justification, meaning the believer cannot possibly be mistaken about the proposition believed. This view demands that justification entails truth, ensuring no room for error or falsity in warranted beliefs. Influenced by René Descartes' quest for indubitable foundations in Meditations on First Philosophy (1641), infallibilism contrasts with fallibilist accounts by rejecting any tolerance for doubt or defeaters.^[4] In response to Gettier problems, proponents argue that only infallible beliefs avoid the luck inherent in justified true beliefs that turn out true by chance.^[16] A prominent modern infallible approach is Robert Nozick's tracking theory, outlined in Philosophical Explanations (1981), which redefines knowledge as a belief that tracks truth across possible worlds rather than relying on static justification. For a subject S to know that p, the belief must satisfy four conditions: p is true; S believes p; sensitivity, where in the nearest possible world in which p is false, S does not believe p; and adherence, where in the nearest possible world in which p is true, S believes p. These modal conditions ensure the belief dynamically responds to the actual truth value, excluding cases of accidental correctness.^[16] Nozick's framework aims to capture knowledge as a reliable connection to reality, applicable via a method of belief formation that preserves tracking. The fake barn case, introduced by Alvin Goldman in "Discrimination and Perceptual Knowledge" (1976), exemplifies tracking's failure in perceptual knowledge. Driving through a countryside, Henry sees a structure that appears to be a barn and believes "there is a barn over there," which is true as it is the only real barn amid numerous facades. However, his belief lacks sensitivity: in nearby possible worlds where he views a facade instead, he would form the same false belief due to indistinguishable appearances. Thus, tracking denies Henry knowledge despite the truth and his justified belief.^[73] Other responses build on or modify tracking to address its limitations, emphasizing that merely true belief—lacking modal robustness—is insufficient for knowledge, as seen in Gettier-style luck. Variants like safety replace sensitivity with the requirement that the belief be true in all nearby possible worlds, avoiding counterexamples where sensitivity permits knowledge of grand truths but denies mundane ones (e.g., knowing one has hands but not that one is not a brain in a vat). Adherence-focused adjustments prioritize positive tracking of truths.^[16] Criticisms of these approaches highlight their over-intellectualization of knowledge by imposing complex modal conditions that ordinary cognition may not satisfy. Saul Kripke, in "Nozick on Knowledge" (2011), argues that tracking violates epistemic closure: if S knows p and believes p entails q, S may not know q due to failed adherence, leading to counterintuitive results like knowing one is not a brain in a vat but not knowing everyday facts. Such theories also struggle with skeptical hypotheses, as sensitivity often deems beliefs insensitive in radical error possibilities.^[74] In contrast to virtue epistemologies' fallibilist focus on intellectual character, infallibilist and tracking views enforce certainty or modal invariance, potentially restricting knowledge to an implausibly narrow domain.^[16]

Nyaya Philosophy and Non-Western Views

In Nyaya philosophy, an ancient Indian school of thought founded by Gautama (also known as Akṣapāda) around the 2nd century CE, knowledge is defined as pramā, or valid cognition, which constitutes a veridical awareness produced through reliable means known as pramāṇas.^[75]^[76] This foundational text, the Nyāya-sūtras, positions epistemology as central to understanding reality and achieving liberation, emphasizing that pramā arises from processes that ensure epistemic success.^[76] The key elements of pramā in Nyaya include non-erroneous and non-illusory apprehension of an object, excluding states of doubt, error, or mere supposition.^[75] Nyaya recognizes four primary pramāṇas: pratyakṣa (perception, direct sensory contact), anumāna (inference, based on prior knowledge and logical reasoning), upamāna (comparison or analogy for recognizing similarities), and śabda (verbal testimony from a trustworthy source).^[76] These means generate knowledge by forming a causal chain that connects the cognizer to the object's true qualities, ensuring the cognition is intentional and content-specific.^[75] This Nyaya framework shares similarities with the Western justified true belief (JTB) account, as pramā requires truth, belief-like awareness, and justification via pramāṇas, but it uniquely stresses defeasibility—knowledge can be undermined by counter-evidence or rival explanations, preventing claims of infallibility without scrutiny.^[75] Testimony, as a pramāṇa, extends to non-propositional forms by relying on the expert's intent and semantic fit, allowing knowledge transmission beyond direct experience.^[76] Indian philosophical debates, including Nyaya's, feature Gettier-like problems, such as inferences from false premises yielding true conclusions, prompting refinements to exclude such cases.^[75] Later developments by Udayana in the 10th century advanced Nyaya epistemology by refining inference structures and defending the reliability of pramāṇas against skeptical challenges, particularly through arguments for theism and realism.^[76] In debates with Buddhist schools, Nyaya philosophers contended that error presupposes true cognition, rejecting Buddhist views of inherent flux and illusion by insisting on pramāṇas' inerrancy in producing undistorted awareness.^[75] These exchanges highlighted cross-cultural insights, portraying knowledge as a robust, defeasible process grounded in logical and perceptual validity rather than subjective idealism.^[76]

Non-Propositional Forms of Knowledge

Debates about the definition of knowledge have traditionally focused on propositional knowledge-that, but many philosophers argue that this focus is too narrow.^[19] Practical skills, perceptual acquaintance, and embodied familiarity with environments play a central role in what we ordinarily count as knowing, even when no explicit proposition is considered.^[19] These non-propositional forms raise further questions about whether definitions of knowledge must always presuppose a conscious subject, or whether some abilities, competences, and environmental couplings can count as knowledge even when they do not enter reflective awareness.^[19] They also shape contemporary debates about whether advanced artefacts, animals, or AI systems might instantiate knowledge-like capacities without possessing human-style conceptual thought.^[77]

Knowledge-How

Knowledge-how, also known as procedural knowledge, refers to the ability to perform tasks or skills successfully, distinct from propositional knowledge or "knowing-that," which involves factual beliefs about the world. Philosopher Gilbert Ryle introduced this distinction in his 1949 work, arguing that knowing-how manifests in intelligent actions and dispositions rather than in theoretical propositions; for instance, someone who knows how to swim demonstrates this through the act of swimming, not merely by stating facts about swimming techniques.^[78] Ryle emphasized that knowledge-how is primary and irreducible to a collection of know-that statements, critiquing the "intellectualist legend" that reduces practical abilities to hidden theoretical knowledge.^[78] Debates over the reducibility of knowledge-how to knowledge-that center on intellectualism versus anti-intellectualism. Intellectualists, such as Jason Stanley and Timothy Williamson, contend in their 2001 paper that knowledge-how is a species of knowledge-that, often involving propositions about ways to perform actions; for example, knowing how to ride a bicycle amounts to knowing that certain methods enable bicycle riding. In response, anti-intellectualists like John Bengson argue that this reduction fails because knowledge-how includes non-propositional abilities that cannot be fully captured by declarative knowledge, such as intuitive skills acquired through practice that resist verbal articulation.^[79] Bengson and colleagues maintain that empirical evidence from cognitive psychology supports this view, showing that practical expertise often operates independently of explicit propositional content. In definitions of knowledge, knowledge-how demands separate treatment from traditional justified true belief (JTB) accounts, which primarily apply to propositional cases, as practical abilities involve non-doxastic states like dispositions and competences that evade belief-based analysis.

Knowledge by Acquaintance

Knowledge by acquaintance refers to a form of direct, immediate awareness of particulars, such as sense-data, universals, or one's own self, without the mediation of propositions or descriptions.^[80] Bertrand Russell introduced this distinction in 1912, arguing that acquaintance provides foundational, non-inferential knowledge, exemplified by sensing a color like blue or being aware of one's own existence, in contrast to knowledge by description, which involves indirect understanding through conceptual representations.^[81] According to Russell, all complex knowledge ultimately rests on this primitive form of acquaintance as its epistemic foundation.^[80] This type of knowledge is characterized as non-propositional, meaning it does not involve beliefs or judgments that can be true or false, but rather a pure relation of direct familiarity.^[80] It is immediate and unmediated, granting access to the object itself without conceptual intermediaries or inference.^[82] In cases of self-acquaintance, such as introspective awareness of one's mental states, it is often described as immune to error through misidentification, where the subject cannot mistake the source of the experience for something external.^[83] A classic example illustrates the difference: one directly knows the pain of a headache through acquaintance with the sensation itself, whereas believing "I have a headache" constitutes propositional knowledge that could be erroneous if based on misinterpretation of symptoms.^[84] This direct acquaintance with phenomenal qualities, like the raw feel of pain, underscores its role in understanding subjective experience without linguistic or descriptive framing.^[85] Debates persist over whether knowledge by acquaintance is genuinely non-propositional or if it implicitly relies on conceptual content for recognition.^[83] Critics argue that even seemingly direct awareness involves minimal propositional elements, challenging its foundational status in epistemology.^[86] Its connection to phenomenal consciousness remains central, particularly in explaining qualia—the subjective aspects of experience that resist physicalist reduction—as acquaintance provides the only way to grasp these ineffable properties.^[87] In 2025 philosophy of mind discussions, renewed focus on the acquaintance hypothesis in the knowledge argument posits that new experiential knowledge, like a scientist learning color qualia, is non-propositional acquaintance rather than factual propositions, fueling ongoing qualia debates against physicalism.^[83] Knowledge by acquaintance is related to but distinct from knowledge-how, as the former emphasizes perceptual or introspective familiarity rather than abilities.^[88]

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