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Fallibilism

Fallibilism is the epistemological doctrine that human knowledge is inherently uncertain and provisional, never achieving absolute certainty, as all beliefs remain open to potential revision or falsification through further inquiry.^[1] Coined by the American philosopher Charles Sanders Peirce in the late 19th century, it posits that "our knowledge is never absolute but always swims, as it were, in a continuum of uncertainty and of indeterminacy."^[1] This view emerged as a critique of Cartesian foundationalism, which seeks infallible foundations for knowledge, and skepticism, which doubts the possibility of knowledge altogether, instead advocating a middle path that balances intellectual confidence with humility.^[1] At its core, fallibilism maintains that while conclusive justification is impossible, knowledge can still be attained on the basis of strong but defeasible evidence, allowing agents to justifiably believe propositions even if they could turn out false.^[2] Peirce emphasized the self-corrective nature of scientific inquiry, where doubt initiates investigation and communal effort gradually refines beliefs toward truth, sustained by an epistemic virtue of hope amid uncertainty.^[1] In this framework, no source of knowledge—whether reason, experience, intuition, or revelation—is infallible, yet progress occurs through openness to error and rigorous testing.^[1] Fallibilism thus underpins pragmatism, promoting practical action on tentative beliefs while rejecting dogmatism.^[3] Contemporary defenses of fallibilism address challenges like the value of knowledge, arguing that it serves to identify reliable informants in epistemic communities, thereby preserving its instrumental worth without demanding inconclusiveness-proof justification.^[2] It contrasts with infallibilism, which requires certainty for knowledge attributions, and has influenced fields beyond epistemology, including scientific methodology, by endorsing iterative error correction over static truths.^[3] Key figures extending Peirce's ideas include philosophers like Karl Popper and John Dewey, while critics such as Laurence BonJour have highlighted tensions with commonsense intuitions regarding justification.^[2]

Definition and Historical Development

Core Definition

Fallibilism is the philosophical doctrine that human knowledge is always provisional and subject to potential error, with no belief or theory ever conclusively justified or immune to revision.^[4] This view posits that all claims to knowledge, whether in science, everyday reasoning, or abstract thought, remain tentative due to inherent limitations in human cognition, such as sensory perception, memory, and logical inference.^[4] The core tenets of fallibilism include the rejection of absolute certainty in any belief, the emphasis on ongoing inquiry as a means of error correction, and the acceptance of beliefs as provisionally justified rather than definitively true.^[5] Unlike infallibilism, which holds that certain beliefs can be indubitably known and conclusively justified, fallibilism denies the possibility of such rational certainty, asserting instead that justification is always fallible and open to doubt.^[4] It also differs from relativism, as fallibilism maintains the potential for objective progress toward truth through critical investigation, without implying that all beliefs are equally valid or that truth is merely subjective.^[5] Fallibilism originated in the pragmatism of Charles Sanders Peirce, who formulated its ideal as "the opinion which is fated to be ultimately agreed to by all who investigate," enabling convergence on truth despite the provisional nature of individual beliefs.^[6] In this framework, fallibilism supports a realistic epistemology where knowledge advances through relentless scrutiny and revision, acknowledging human fallibility while affirming the pursuit of reliable understanding.^[4]

Origins and Key Figures

The roots of fallibilism can be traced to ancient philosophical traditions, where ideas resembling the recognition of human knowledge's inherent limitations emerged as precursors. Socrates, through his famous admission of ignorance articulated in Plato's dialogues, exemplified a proto-fallibilist stance by emphasizing that true wisdom lies in acknowledging one's lack of certain knowledge, thereby challenging dogmatic claims to absolute truth.^[7] Similarly, Arcesilaus, leader of the Middle Academy in the 3rd century BCE, advanced Academic skepticism by arguing that no belief could achieve indubitable certainty, advocating instead for a fallibilistic approach where judgments are provisional and subject to suspension based on equipollence of arguments. Fallibilism as a distinct epistemological doctrine gained formal articulation in the 19th century through the work of American philosopher Charles Sanders Peirce. In his essays from the 1860s and later developments, such as the 1892 article "The Doctrine of Necessity Examined," Peirce introduced fallibilism as the view that all human knowledge is inherently uncertain and revisable, linking it intrinsically to pragmatism and the iterative nature of scientific inquiry.^[1] Peirce's formulation emphasized that even the most well-established beliefs remain open to potential refutation through future evidence, positioning fallibilism as a corrective to Cartesian foundationalism.^[8] The 20th century saw significant expansion of fallibilist ideas, particularly through Karl Popper's philosophy of science. In his 1934 book Logik der Forschung (published in English as The Logic of Scientific Discovery in 1959), Popper integrated fallibilism by prioritizing falsifiability over verifiability, asserting that scientific theories are conjectures that can never be conclusively proven but only corroborated or refuted, thus underscoring the provisional status of all empirical knowledge.^[9] This approach profoundly influenced post-World War II philosophy, promoting a critical rationalism where error elimination drives progress. Other influential figures further developed fallibilism within pragmatist and scientific contexts. William James, in his 1907 lectures compiled as Pragmatism, provided pragmatic support by portraying truth as a process of verification through experience, inherently fallible and adaptable to new contexts, thereby extending Peirce's ideas to emphasize practical consequences over absolute certainty.^[10] Imre Lakatos, in the 1976 edition of Proofs and Refutations, applied fallibilism to mathematics, demonstrating through historical case studies like Euler's theorem that mathematical knowledge evolves through a quasi-empirical process of proof, counterexample, and revision rather than infallible deduction. In contemporary philosophy, Bas van Fraassen's constructive empiricism, outlined in his 1980 book The Scientific Image, incorporates fallibilist elements by advocating that scientific acceptance aims at empirical adequacy rather than truth, acknowledging the limits of unobservable theoretical commitments.^[11] This timeline—from Peirce's late-19th-century foundations through his 1890s lectures on the subject, to Popper's mid-20th-century synthesis and its widespread adoption in scientific methodology—illustrates fallibilism's evolution from ancient skeptical intuitions to a cornerstone of modern epistemology.^[1]

Epistemological Aspects

Infinite Regress and Justification

The problem of infinite regress arises in foundationalist epistemologies, where attempts to justify a belief lead to a chain of reasons that either loops circularly, halts at unjustified axioms assumed to be certain, or extends infinitely without providing ultimate certainty for any belief.^[12] In such views, foundational beliefs are posited as self-evident or indubitable to terminate the regress, but critics argue this undermines genuine justification by relying on unproven starting points.^[13] Fallibilism addresses this challenge by rejecting the need for infallible foundations, instead endorsing approaches like coherentism or infinitism that permit holistic or progressive justification without requiring absolute certainty.^[14] In coherentism, beliefs gain justification through mutual support within a web of interconnected propositions, allowing circularity as a feature rather than a flaw, while infinitism accepts an infinite chain of reasons as non-vicious, providing ever-increasing evidential support.^[15] These strategies align with fallibilism's core tenet that all justifications are provisional and open to error, enabling epistemic progress without foundational anchors.^[1] A key aspect of fallibilist justification is the notion of infinite progress, where knowledge advances through ongoing correction and refinement, converging toward truth over time without ever achieving finality.^[14] Charles Sanders Peirce, a foundational figure in fallibilism, described this as the "long run" convergence of inquiry, in which iterative self-correction by a community of inquirers approximates reality asymptotically. Unlike pure coherentism, which might stabilize at a static equilibrium of mutual consistency, fallibilism emphasizes the inherent error-proneness of all beliefs, mandating perpetual openness to revision and ensuring that coherence remains dynamic and testable.^[14]

Relation to Skepticism

Fallibilism engages with philosophical skepticism by offering a moderate epistemological stance that acknowledges the possibility of error in all beliefs while still permitting the rational acceptance of knowledge claims on a provisional basis. Unlike radical forms of skepticism that undermine the pursuit of truth, fallibilism treats doubt as a constructive element in inquiry rather than a paralyzing force. This positioning distinguishes it from both Pyrrhonian skepticism, which advocates for the complete suspension of judgment (epoché) to achieve mental tranquility, and Academic skepticism, which permits probable beliefs based on the weight of evidence but stops short of certainty. Fallibilism aligns more closely with the latter tradition, as seen in the work of Philo of Larissa, the last head of Plato's Academy, who in the late 1st century BCE developed a fallibilist view that allowed for knowledge as true impressions appropriately caused, without requiring infallibility, thereby evolving Academic skepticism into a framework for fallible yet justifiable beliefs.^[16] A key distinction between fallibilism and skepticism lies in their attitudes toward doubt and inquiry. Skepticism, particularly in its Pyrrhonian form, often halts intellectual progress by inducing equipollence—equal arguments on both sides of any issue—leading to the suspension of belief and avoidance of dogmatic commitments. In contrast, fallibilism harnesses doubt as a tool for ongoing error-correction and advancement, enabling provisional acceptance of beliefs that best withstand critical scrutiny while remaining open to revision. This approach echoes the historical interplay with René Descartes' method of hyperbolic doubt, outlined in his 1641 Meditations on First Philosophy, where extreme skeptical scenarios are employed not to endorse global unbelief but to identify indubitable foundations; fallibilists extend this by rejecting the quest for absolute certainty and instead emphasizing iterative testing and refinement of knowledge claims.^[4]^[17] In modern epistemology, fallibilism critiques global skepticism—such as scenarios like the brain-in-a-vat hypothesis, where one's experiences might be simulated by a deceptive entity—by prioritizing actionable, contextually justified beliefs over unattainable indubitability. While global skeptics argue that such possibilities render all empirical knowledge uncertain to the point of unknowability, fallibilists maintain that we can possess knowledge if our beliefs are reliably formed and defeaters are absent, even if error remains theoretically possible; this allows for practical engagement with the world without succumbing to paralyzing doubt.^[18]

Applications in Science and Rationalism

Critical Rationalism

Critical rationalism, as developed by Karl Popper, represents a key application of fallibilism in the philosophy of science, where knowledge is advanced not through confirmation but through the critical scrutiny and potential falsification of conjectural theories. Popper's framework posits that scientific theories are bold guesses or conjectures that must withstand rigorous testing to eliminate errors, acknowledging the inherent fallibility of human cognition and the provisional nature of all claims to truth. This approach underscores that no theory can be conclusively verified, but it can be corroborated by surviving attempts at refutation, thereby approximating truth more closely over time.^[19] Central to Popper's critical rationalism is the rejection of inductive logic, which fallibilism deems unreliable for establishing secure knowledge since past observations cannot guarantee future outcomes. Instead, progress arises from inventing imaginative hypotheses and subjecting them to severe, potentially refuting tests, with scientific merit lying in a theory's exposure to criticism rather than its accumulation of supportive evidence. Popper elaborated this in Conjectures and Refutations: The Growth of Scientific Knowledge (1963), asserting that "the growth of knowledge is a process of learning from our mistakes" through error elimination.^[20] He further formalized the emphasis on falsification in The Logic of Scientific Discovery (1934/1959), where deductive testing replaces induction as the engine of scientific rationality.^[9] Popper's demarcation criterion delineates science from pseudoscience by requiring theories to be falsifiable—capable of being contradicted by empirical evidence—thus aligning with fallibilist principles of error-prone inquiry and iterative improvement. Scientific advancement occurs as theories survive refutations, weeding out falsehoods and enhancing verisimilitude, the degree of closeness to truth. This criterion has shaped modern philosophy of science by prioritizing testable predictions over unfalsifiable dogmas.^[19] The influence of critical rationalism extends beyond methodology to broader philosophical and social domains, rejecting historicism's deterministic view of history and advocating for an "open society" sustained by critical rational debate and institutional checks against authoritarianism. In The Open Society and Its Enemies (1945), Popper defended liberal democracy as a fallibilist framework where policies are treated as experiments open to revision through criticism, countering totalitarian ideologies that claim infallible knowledge.^[21] An illustrative example is Einstein's general theory of relativity, which exemplifies a highly falsifiable scientific theory: its prediction of gravitational light deflection during a solar eclipse in 1919 offered a clear empirical test that could have refuted it, contrasting sharply with the unfalsifiable assertions of pseudosciences like Marxism or psychoanalysis, which evade decisive refutation.^[22]

Fallibilism in Scientific Method

Fallibilism integrates with empiricism by viewing science as an inherently fallible enterprise, where theories function as provisional hypotheses open to continuous empirical revision rather than absolute truths.^[1] This perspective underscores that scientific knowledge advances through the tentative acceptance of ideas that withstand scrutiny, acknowledging the limitations of human observation and inference. Thomas Kuhn's analysis in The Structure of Scientific Revolutions (1962) exemplifies this by describing scientific progress as occurring through paradigm shifts, where dominant frameworks are replaced when anomalies accumulate, tempering empiricist optimism with fallibilist realism that no paradigm is immune to future overthrow.^[23] Charles Sanders Peirce's influence on fallibilism in the scientific method emphasizes abduction as a fallible form of inference for hypothesis formation, complementing deduction and induction in the inquiry process.^[24] Peirce argued that scientific method involves generating conjectures through abduction, which are inherently uncertain and subject to testing, thereby embedding fallibilism as a core principle that all conclusions remain provisional and revisable based on new evidence.^[25] This triadic logic promotes an iterative approach where errors are anticipated and corrected, fostering scientific self-correction over dogmatic certainty. Error-correction mechanisms in science embody fallibilist principles through practices like peer review, which scrutinizes claims for potential flaws, and responses to replication crises, such as the post-2010 reforms in psychology that prioritized preregistration and open data to mitigate biases and enhance reliability.^[26] These reforms arose from large-scale replication efforts revealing low reproducibility rates, prompting a cultural shift toward viewing non-replications not as failures but as opportunities for refinement, aligning with fallibilism's emphasis on error detection.^[27] Bayesian updating serves as another fallibilist tool, allowing scientists to revise probabilities of hypotheses incrementally as new data emerges, treating beliefs as degrees of confidence rather than certainties.^[28] In contemporary applications, fallibilism manifests in climate science, where models project future scenarios amid substantial uncertainties from internal variability, incomplete data, and scenario assumptions, necessitating provisional interpretations and ongoing validation.^[29] Similarly, in AI ethics, ethical frameworks for alignment are treated as fallible and provisional, subject to revision through iterative testing and interdisciplinary input to address biases and unintended consequences in machine learning systems.^[30] These fields highlight fallibilism's role in managing uncertainty by promoting adaptive, evidence-based adjustments rather than fixed doctrines. A representative example is Darwinian evolution, proposed as a fallible theory in On the Origin of Species (1859), which has been strengthened by accumulating genetic, fossil, and observational evidence without ever being conclusively proven, remaining open to refinement or falsification through future discoveries.^[31]

Fallibilism in Mathematics

Mathematical Foundations

Fallibilism in mathematics challenges the traditional view of proofs and axioms as providing absolute certainty, positing instead that mathematical knowledge is provisional and subject to revision. Kurt Gödel's incompleteness theorems, published in 1931, demonstrate that in any consistent formal system capable of expressing basic arithmetic, there are true statements that cannot be proved within the system, and the system's consistency cannot be proved internally.^[32] These results undermine the Euclidean ideal of mathematics as a complete and infallible deductive structure, supporting a fallibilist perspective where formal systems are inherently limited and require ongoing extension or modification to encompass more truths.^[33] Imre Lakatos further developed this fallibilist approach in his 1976 book Proofs and Refutations: The Logic of Mathematical Discovery, portraying mathematical progress as a dialectical process akin to scientific inquiry. Through historical analysis, such as the evolution of Euler's polyhedral formula, Lakatos illustrates how theorems emerge via "quasi-rigid" proofs that are tested against counterexamples, leading to refinements like "monster-barring" (excluding anomalous cases) or concept-stretching (adjusting definitions).^[34] This methodology rejects formalist notions of timeless proofs, emphasizing instead that mathematical theorems are conjectural and fallible, evolving through criticism and refutation rather than achieving finality. In axiomatic systems, fallibilism manifests as the recognition that foundational frameworks like Zermelo-Fraenkel set theory (ZF), often augmented with the axiom of choice (ZFC), serve as provisional bases rather than absolute truths. While ZFC provides a consistent foundation for most mathematics, Gödel's theorems imply its incompleteness, necessitating potential additions such as axioms for large cardinals to resolve undecidable propositions like the continuum hypothesis.^[35] Moreover, alternatives like intuitionistic mathematics, which rejects the law of excluded middle, highlight the revisability of axioms, as no single system commands unquestioned authority. Fallibilism aligns mathematics with quasi-empiricism, a view advanced by Lakatos, treating proofs and axioms as hypotheses testable through logical exploration and counterexamples, much like empirical conjectures in science. This perspective underscores mathematics as a human endeavor prone to error and improvement, where certainty is illusory and progress depends on fallible intuition and communal scrutiny.^[34] A historical exemplar is the 19th-century revision of Euclidean geometry's parallel postulate, which posits a unique parallel line through a point not on a given line; its replacement yielded consistent non-Euclidean geometries by Lobachevsky and Bolyai, demonstrating that even core axioms can be altered without contradiction, thus exemplifying mathematical revisability.^[36]

Examples and Implications

One prominent historical example of fallibilism in mathematics is the prolonged development of Fermat's Last Theorem, conjectured by Pierre de Fermat around 1637 in a marginal note in Diophantus's Arithmetica, stating that no positive integers a, b, and c satisfy a^n + b^n = c^n for integer n > 2. The theorem remained unproven for 358 years until Andrew Wiles presented a correct proof in 1995, after his initial 1993 attempt contained a subtle error in the Euler system that required collaborative correction. This journey involved numerous fallible intermediate results, such as Gabriel Lamé's 1847 announcement of a general proof using unique factorization in complex integers, which Joseph Liouville swiftly refuted due to the failure of unique factorization in those rings. Similarly, Ernst Kummer's 19th-century partial proofs for "regular" primes relied on idealized number theory that later proved incomplete, highlighting how even rigorous-seeming advancements can harbor undetected flaws. A modern illustration arises in the Four Color Theorem, proved in 1976 by Kenneth Appel and Wolfgang Haken, which asserts that any planar map can be colored with at most four colors such that no adjacent regions share the same color. Their proof reduced the problem to checking 1,936 configurations via computer assistance, a process that took over 1,200 hours of computation on an IBM 370. This reliance on computational verification sparked fallibilist concerns, as the sheer volume of cases made independent human checking infeasible, raising questions about potential software errors or overlooked assumptions in the reduction process.^[37] Subsequent efforts, such as Georges Gonthier's 2005 formalization in Coq, addressed these issues but underscored the provisional nature of computer-aided results until fully mechanized.^[38] Fallibilism also manifests in inherently undecided problems like the Continuum Hypothesis (CH), which posits that there is no set whose cardinality strictly exceeds that of the natural numbers but is less than that of the real numbers.^[39] Kurt Gödel demonstrated in 1940 that CH is consistent with the Zermelo-Fraenkel set theory with the Axiom of Choice (ZFC), meaning its adoption leads to no contradictions. Paul Cohen then proved in 1963, using his forcing technique, that the negation of CH is also consistent with ZFC, establishing its independence and thus its undecidability within standard foundations.^[39] This independence exemplifies fallibilism by showing that core mathematical questions may resist definitive resolution, depending instead on axiomatic choices. These examples carry significant implications for mathematical practice. Fallibilism encourages pluralism in foundations, accommodating multiple logics and set theories—such as ZFC versus New Foundations—without privileging one as absolutely true, as seen in responses to CH's independence.^[40] In education, it promotes viewing mathematics as an evolving discipline, where students engage with historical errors like Lamé's to develop critical evaluation skills, aligning with constructivist pedagogies that emphasize argument refinement over rote certainty.^[41] In computer science, it influences automated theorem proving, where tools like Lean or Coq produce fallible outputs susceptible to bugs, prompting hybrid human-machine verification to mitigate risks in proofs like the Four Color Theorem.^[42] Overall, fallibilism transforms mathematics from a pursuit of dogmatic certainty into a creative, error-correcting enterprise, as briefly captured in Imre Lakatos's method of proofs and refutations, which treats theorems as provisional amid counterexamples and revisions.

Criticisms and Contemporary Debates

Primary Criticisms

One major objection to fallibilism arises from foundationalist perspectives, which maintain that certain basic beliefs possess infallible justification immune to rational revision. Proponents of reformed epistemology, such as Alvin Plantinga in his 1980s works, contend that fallibilism's denial of conclusive warrant for any belief erodes the reliability of these foundational elements, thereby opening the door to skepticism by implying that no knowledge claim can be securely held.^[4] Fallibilism also faces the charge of fostering relativism, particularly in its association with pragmatist thinkers like Richard Rorty, who emphasize inquiry's contingency and reject absolute representational truth. Critics argue that this approach, while Rorty denies outright relativism, effectively relativizes truth to communal practices and historical contexts, undermining any universal standard of objectivity and allowing beliefs to be equally valid based on their utility rather than correspondence to reality.^[43] On practical grounds, fallibilism is criticized for complicating decision-making under uncertainty, as the perpetual possibility of error in all judgments may induce hesitation or paralysis in situations requiring prompt action. For instance, in Blaise Pascal's Wager, where belief in God is framed as a rational bet due to infinite stakes, fallibilism's provisional epistemology could deter commitment by perpetually questioning the reliability of evidence about divine existence, thus hindering decisive ethical or existential choices.^[44] In mathematics, traditionalists adhering to programs like David Hilbert's formalist initiative sought to establish the discipline's claim to apodictic certainty through absolute demonstrability. Hilbert's 1920s effort to prove the consistency of axiomatic systems through finitistic means aimed to secure mathematics against doubt. This contrasts with later fallibilist approaches, such as those developed by Imre Lakatos, which portray theorems as provisional and subject to revision.^[45]^[34]

Modern Responses and Developments

In response to criticisms of foundationalism, which posits indubitable basic beliefs as the bedrock of knowledge, Susan Haack developed foundherentism as a hybrid theory that integrates elements of foundationalism and coherentism while embracing fallibilist principles of ongoing revision and error correction.^[46] Haack's approach, articulated in her 1993 book Evidence and Inquiry: Towards Reconstruction in Epistemology, treats justification as a "double-aspect" process where experiential evidence provides a foundational anchor but is evaluated through coherent interconnections among beliefs, allowing for the fallible nature of all epistemic claims without rigid hierarchies.^[47] This framework counters foundationalist dogmatism by permitting beliefs to be strengthened or weakened dynamically based on emerging evidence, thus aligning with fallibilism's rejection of certainty.^[48] Bayesian epistemology offers another modern defense of fallibilism by modeling belief revision as probabilistic updates to prior degrees of confidence in light of new evidence, thereby avoiding the relativism charged against some coherentist views. Colin Howson and Peter Urbach's 1989 work Scientific Reasoning: The Bayesian Approach exemplifies this by formalizing confirmation through Bayes' theorem, where hypotheses are never conclusively verified but gain or lose support incrementally, embodying fallibilist humility in the face of incomplete information.^[49] This method promotes rational inquiry without absolute foundations, as subjective priors converge toward objective posteriors over time through repeated testing, providing a tool to refute charges of epistemic relativism by grounding updates in evidential probability rather than arbitrary coherence.^[50] In recent developments within feminist epistemology, fallibilism has been extended to emphasize situated knowledges that acknowledge the partial and error-prone nature of perspectives shaped by social position, fostering inclusive mechanisms for collective error correction. Donna Haraway's 1988 essay "Situated Knowledges: The Science Question in Feminism and the Privilege of Partial Perspective" argues for an objectivity rooted in fallible, embodied viewpoints that challenge god-trick illusions of transcendence, enabling marginalized voices to contribute to knowledge revision through dialogic accountability.^[51] Similarly, in decolonial thought, fallibilism supports epistemic pluriversality by promoting the ongoing critique and integration of diverse knowledge systems, countering colonial epistemologies' claims to universality and encouraging error-correction across cultural boundaries to build more equitable inquiry processes.^[52] Twenty-first-century applications of fallibilism have emerged in debates over AI reliability, particularly post-2020 discussions framing machine learning models as inherently fallible systems that align with the Peircean-Popperian tradition of conjectural knowledge subject to refutation. In contexts like generative AI, fallibilism underscores the provisionality of algorithmic outputs, which depend on biased training data and can propagate errors unless subjected to rigorous, iterative falsification akin to scientific hypotheses.^[53] This perspective, as explored in philosophical analyses of AI rationality, treats machine intelligence not as infallible but as a tool for fallible human cognition, emphasizing the need for transparent error-detection protocols to mitigate risks in high-stakes applications.^[28] Ongoing debates, such as those surrounding climate denialism, increasingly invoke fallibilist principles in science communication to highlight the self-correcting nature of empirical inquiry while countering demands for unattainable certainty. A fallibilist approach, as applied to climate science amid misinformation campaigns, stresses that consensus on anthropogenic warming emerges from provisional evidence accumulation and potential revision, not dogmatic proof, thereby inoculating public discourse against skepticism that exploits science's inherent tentativeness.^[54] This strategy reframes denialist tactics—like impossible expectations of perfection—as misunderstandings of fallibilism's strength in enabling robust, adaptive responses to global challenges.^[29]

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Apr 4, 2016 · Imre Lakatos (1922–1974) was a Hungarian-born philosopher of mathematics and science who rose to prominence in Britain.Life · Lakatos's Big Ideas · Against Formalism in... · Proofs and Refutations (1963...
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Philosophy of Mathematics (Stanford Encyclopedia of Philosophy)
Summary of each segment:
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article2 - University of Exeter
The opposing is view often called 'fallibilist' and this sees mathematics as an incomplete and everlasting 'work-in-progress'. It is corrigible, revisable, ...
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The Colorful Problem That Has Long Frustrated Mathematicians
Mar 29, 2023 · The four-color problem is simple to explain, but its complex proof continues to be both celebrated and despised.
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[PDF] A computer-checked proof of the Four Color Theorem - Hal-Inria
Mar 17, 2023 · This report gives an account of a successful formalization of the proof of the Four Color. Theorem, which was fully checked by the Coq ...Missing: fallibilism | Show results with:fallibilism
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THE INDEPENDENCE OF THE CONTINUUM HYPOTHESIS | PNAS
### Summary of Paul Cohen's 1963 Paper on the Independence of the Continuum Hypothesis
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Geoffrey Hellman, Pluralism and the Foundations of Mathematics
A plurality of approaches to foundational aspects of mathematics is a fact of life. Two loci of this are discussed here, the classicism/constructivism ...Missing: fallibilism | Show results with:fallibilism
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[PDF] Why Not Philosophy? Problematizing the Philosophy of Mathematics ...
The fallibilist view of mathematics aligns itself with pedagogy consistent with constructivist theories, utilizing problem-based learning, real world ...
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https://plato.stanford.edu/entries/pascal-wager/
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What Is at Stake Between Putnam and Rorty?1 - jstor
Putnam, intuitions about criticism and fallibilism must be explained by re- course to a limit notion of truth. For Rorty, it is our intuitions about the.
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Pascal's Wager - Stanford Encyclopedia of Philosophy
May 2, 1998 · “Pascal's Wager” is the name given to an argument due to Blaise Pascal for believing, or for at least taking steps to believe, in God.Missing: fallibilism | Show results with:fallibilism
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Hilbert's Program - Stanford Encyclopedia of Philosophy
Jul 31, 2003 · The question of what Hilbert thought the epistemological status of the objects of finitism was is equally difficult. In order to carry out the ...
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[PDF] ESTUDIOSFILOSÓFICOS
Resumen: En este artículo relaciono los primeros trabajos de. Susan Haack sobre el faliblismo con la génesis de su fundheren-.
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Double-aspect foundherentism: A new theory of empirical justification
Haack, Susan (1993). Double-aspect foundherentism: A new theory of empirical ... Haack's foundherentism is a foundationalism.Peter Tramel - 2008 ...Missing: fallibilism | Show results with:fallibilism
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Haack's Foundherentism Is a Foundationalism - jstor
Abstract Susan Haack has always maintained that her unquestionably important foundherentist theory of epistemic justification is not a foundationalism.Missing: fallibilism | Show results with:fallibilism
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Scientific reasoning: the Bayesian approach - PhilPapers
Scientific reasoning: the Bayesian approach · Peter Urbach & Colin Howson. Chicago: Open Court. Edited by Peter Urbach (1993).
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[PDF] Bayesianism, Convergence and Social Epistemology - PhilArchive
Sep 22, 2010 · Subjective Bayesian epistemology is a thoroughly fallibilist ... Again, following Howson and Urbach (1993), the Principle of. Bayesian ...
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Fallibilism and Generative AI in Cartography: Some Fundamental ...
Feb 12, 2025 · Epistemological fallibilism emphasizes that all knowledge, whether human or machine-generated, is always provisional and revisable. For ...
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A Fallibilist Approach in the Age of COVID-19 and Climate Change
Request PDF | A Fallibilist Approach in the Age of COVID-19 and Climate Change ... Fallibilism and pentecostal theological epistemology. Article. Sep 2025.