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A fact is a true datum about one or more aspects of a circumstance.[1] Standard reference works are often used to check facts. Scientific facts are verified by repeatable careful observation or measurement by experiments or other means. Generally speaking, facts are independent of belief, knowledge and opinion. Facts are different from inferences, theories, values, and objects.[2]

For example, "This sentence contains words." accurately describes a linguistic fact, and "the Sun is a star" describes an astronomical fact. Further, "Abraham Lincoln was the 16th president of the United States" and "Abraham Lincoln was assassinated" are both historical facts.

Etymology and usage

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The word fact derives from the Latin factum. It was first used in English with the same meaning: "a thing done or performed" – a meaning now obsolete outside the law.[3] The common usage of "something that has really occurred or is the case" dates from the mid-16th century.[3]

Barbara J. Shapiro wrote in her book A Culture of Fact how the concept of a fact evolved, starting within the English legal tradition of the 16th century.[4]

In 1870, Charles Sanders Peirce described in his book The Fixation of Belief four methods which people use to decide what they should believe: tenacity, method of authority, a priori and scientific method.[5]

The term fact also indicates a matter under discussion deemed to be true or correct, such as to emphasize a point or prove a disputed issue; (e.g., "... the fact of the matter is ...").[6][7]

Alternatively, fact may also indicate an allegation or stipulation of something that may or may not be a true fact,[8] (e.g., "the author's facts are not trustworthy"). This alternate usage, although contested by some, has a long history in standard English according to the American Heritage Dictionary of the English Language.[9] The Oxford English Dictionary dates this use to 1729.[10]

Fact may also indicate findings derived through a process of evaluation, including review of testimony, direct observation, or otherwise; as distinguishable from matters of inference or speculation.[11] This use is reflected in the terms "fact-find" and "fact-finder" (e.g., "set up a fact-finding commission").[12]

Facts may be checked by reason, experiment, personal experience, or may be argued from authority. Roger Bacon wrote "If in other sciences we should arrive at certainty without doubt and truth without error, it behooves us to place the foundations of knowledge in mathematics."[13]

In philosophy

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In philosophy, the concept fact is considered in the branch of philosophy concerned with knowledge, called epistemology and ontology, which studies concepts such as existence, being, becoming, and reality. Questions of objectivity and truth are closely associated with questions of fact. A fact can be defined as something that is the case, in other words, a state of affairs.[14][15]

Facts may be understood as information, which makes a true sentence true: "A fact is, traditionally, the worldly correlate of a true proposition, a state of affairs whose obtaining makes that proposition true."[16] Facts may also be understood as those things to which a true sentence refers. The statement "Jupiter is the largest planet in the Solar System" is about the fact that Jupiter is the largest planet in the Solar System.[17]

Correspondence and the slingshot argument

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Pascal Engel's version of the correspondence theory of truth explains that what makes a sentence true is that it corresponds to a fact.[18] This theory presupposes the existence of an objective world.

The Slingshot argument claims to show that all true statements stand for the same thing, the truth value true. If this argument holds, and facts are taken to be what true statements stand for, then one arrives at the counter-intuitive conclusion that there is only one fact: the truth.[19]

Compound facts

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Any non-trivial true statement about reality is necessarily an abstraction composed of a complex of objects and properties or relations. Facts "possess internal structure, being complexes of objects and properties or relations".[16] For example, the fact described by the true statement "Paris is the capital city of France" implies that there is such a place as Paris, there is such a place as France, there are such things as capital cities, as well as that France has a government, that the government of France has the power to define its capital city, and that the French government has chosen Paris to be the capital, that there is such a thing as a place or a government, and so on. The verifiable accuracy of all of these assertions, if facts themselves, may coincide to create the fact, that Paris is the capital of France.

Difficulties arise, however, in attempting to identify the constituent parts of negative, modal, disjunctive, or moral facts.[20]

Fact–value distinction

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Main article: Fact–value distinction

Moral philosophers since David Hume have debated whether values are objective, and thus factual. In A Treatise of Human Nature Hume pointed out there is no obvious way for a series of statements about what ought to be the case to be derived from a series of statements of what is the case. This is called the is–ought distinction. Those who insist there is a logical gulf between facts and values, such that it is fallacious to attempt to derive values (e.g., "it is good to give food to hungry people") from facts (e.g., "people will die if they can't eat"), include G. E. Moore, who called attempting to do so the naturalistic fallacy.

Factual–counterfactual distinction

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Main article: Counterfactual conditional

Factuality—what has occurred—can also be contrasted with counterfactuality: what might have occurred, but did not. A counterfactual conditional or subjunctive conditional is a conditional (or "if–then") statement indicating what would be the case if events had been other than they were. For example, "If Alexander had lived, his empire would have been greater than Rome." This contrasts with an indicative conditional, which indicates what is (in fact) the case if its antecedent is (in fact) true—for example, "If you drink this, it will make you well." Such sentences are important to modal logic, especially since the development of possible world semantics.[citation needed]

In mathematics

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In mathematics, a fact is a statement (called a theorem) that can be proven by logical argument from certain axioms and definitions.[citation needed]

In science

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Further information: Scientific method and Philosophy of science

The definition of a scientific fact is different from the definition of fact, as it implies knowledge. A scientific fact is the result of a repeatable careful observation or measurement by experimentation or other means, also called empirical evidence. These are central to building scientific theories. Various forms of observation and measurement lead to fundamental questions about the scientific method, and the scope and validity of scientific reasoning.

In the most basic sense, a scientific fact is an objective and verifiable observation, in contrast with a hypothesis or theory, which is intended to explain or interpret facts.[21]

Various scholars have offered significant refinements to this basic formulation. Philosophers and scientists are careful to distinguish between: 1) states of affairs in the external world and 2) assertions of fact that may be considered relevant in scientific analysis. The term is used in both senses in the philosophy of science.[22]

Scholars and clinical researchers in both the social and natural sciences have written about numerous questions and theories that arise in the attempt to clarify the fundamental nature of scientific fact.[21] Pertinent issues raised by this inquiry include:

  • the process by which "established fact" becomes recognized and accepted as such;[22]: 182 fn. 1 
  • whether and to what extent "fact" and "theoretic explanation" can be considered truly independent and separable from one another;[22]: 185 [21]: 138 
  • to what extent "facts" are influenced by the mere act of observation;[21]: 138  and
  • to what extent factual conclusions are influenced by history and consensus, rather than a strictly systematic methodology.[21]: 7 

Consistent with the idea of confirmation holism, some scholars assert "fact" to be necessarily "theory-laden" to some degree. Thomas Kuhn points out that knowing what facts to measure, and how to measure them, requires the use of other theories. For example, the age of fossils is based on radiometric dating, which is justified by reasoning that radioactive decay follows a Poisson process rather than a Bernoulli process. Similarly, Percy Williams Bridgman is credited with the methodological position known as operationalism, which asserts that all observations are not only influenced, but necessarily defined, by the means and assumptions used to measure them.[citation needed]

The scientific method

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Apart from the fundamental inquiry into the nature of scientific fact, there remain the practical and social considerations of how fact is investigated, established, and substantiated through the proper application of the scientific method.[22]: 181 ff  Scientific facts are generally believed independent of the observer: no matter who performs a scientific experiment, all observers agree on the outcome.[23] In addition to these considerations, there are the social and institutional measures, such as peer review and accreditation, that are intended to promote factual accuracy among other interests in scientific study.[22]

In history

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Further information: Historiography

A common rhetorical cliché states, "History is written by the winners". This phrase suggests but does not examine the use of facts in the writing of history.[citation needed]

E. H. Carr in his 1961 volume What is History? argues that the inherent biases from the gathering of facts makes the objective truth of any historical perspective idealistic and impossible. Facts are, "like fish in the Ocean", of which we may only happen to catch a few, only an indication of what is below the surface. Even a dragnet cannot tell us for certain what it would be like to live below the Ocean's surface. Even if we do not discard any facts (or fish) presented, we will always miss the majority; the site of our fishing, the methods undertaken, the weather and even luck play a vital role in what we will catch. Additionally, the composition of history is inevitably made up by the compilation of many different biases of fact finding – all compounded over time. He concludes that for a historian to attempt a more objective method, one must accept that history can only aspire to a conversation of the present with the past – and that one's methods of fact gathering should be openly examined. The set of highlighted historical facts, and their interpretations, therefore changes over time, and reflect present consensuses.[citation needed]

In law

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Further information: Evidence (law) and Trier of fact

This section of the article emphasizes common law jurisprudence as primarily represented in Anglo-American–based legal tradition. Nevertheless, the principles described herein have analogous treatment in other legal systems such as civil law systems as well.

In most common law jurisdictions, the general concept and analysis of fact reflects fundamental principles of jurisprudence, and is supported by several well-established standards.[24][25] Matters of fact have various formal definitions under common law jurisdictions.

These include:

  • the determinations of the finder of fact after evaluating admissible evidence produced in a trial or hearing;[28]
  • a potential ground of reversible error forwarded on appeal in an appellate court;[29] and
  • any of various matters subject to investigation by official authority to establish whether a crime has been perpetrated, and to establish culpability.[30]
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Main article: Pleading

A party (e.g., plaintiff) to a civil suit generally must clearly state the relevant allegations of fact that form the basis of a claim. The requisite level of precision and particularity of these allegations varies, depending on the rules of civil procedure and jurisdiction. Parties who face uncertainties regarding facts and circumstances attendant to their side in a dispute may sometimes invoke alternative pleading.[31] In this situation, a party may plead separate sets of facts that when considered together may be contradictory or mutually exclusive. This seemingly logically-inconsistent presentation of facts may be necessary as a safeguard against contingencies such as res judicata that would otherwise preclude presenting a claim or defense that depends on a particular interpretation of the underlying facts and ruling of the court.[32]

See also

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References

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Revisions and contributorsEdit on WikipediaRead on Wikipedia

Fact

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A fact is a state of affairs or aspect of that obtains independently of human beliefs or perceptions, serving as the worldly correlate of a true or statement. In , facts are often understood as truth-makers, meaning they ground the truth of assertions by exemplifying properties or relations in the actual world, such as the undeniable that boils at 100 degrees under standard . This conception distinguishes facts from mere opinions, which are subjective beliefs that may or may not align with , emphasizing that facts exist regardless of whether they are known, disputed, or even knowable. Philosophically, the nature of facts has been central to debates in metaphysics and , where they are viewed not as linguistic strings or psychological states but as objective entities that explain why are justified or true. For instance, factualism posits that all are facts themselves, rather than mental attitudes or abstract contents, ensuring that epistemic justification rests on explanatory connections to , as in the case where the fact of wet streets provides it rained. Epistemologically, facts underpin by forming the basis of justified true , contrasting with truth as the agreement between a and a fact, where facts are , testable realities that resist . In scientific contexts, facts are categorized into brute facts—events occurring independently of —and interpreted scientific facts, which emerge through experimental, theoretical, and frameworks but remain anchored in objective occurrences. This theory-laden quality highlights that while facts are independent, their ascertainment involves human constructs, yet they retain an objective core, as seen in established observations like the . Overall, the of fact underscores the pursuit of objective truth across disciplines, influencing everything from everyday assertions to profound ethical and existential inquiries.

Etymology and General Usage

Origins of the Term

The word "fact" derives from the Latin factum, the neuter past participle of facere meaning "to do" or "to make," signifying "a thing done," "deed," or "act." This term entered English through Old French fait (or fet), where it retained connotations of an action or accomplishment, and its earliest attestations as a noun in English appear in the 15th century, initially denoting "a thing done" or performed. By the early 16th century, such as in 1539 according to the Oxford English Dictionary, the word was commonly used to describe an event or deed, often in a moral or narrative sense rather than as an objective truth. In its initial English usage, "fact" frequently carried negative implications, particularly in legal and literary contexts, where it referred to a criminal act or , as seen in 16th-century texts describing misdeeds or offenses. This sense aligned with medieval and early modern legal traditions, where "fact" or "matter of fact" emerged in the within proceedings to distinguish evidentiary claims about events from interpretive law, becoming a standard element by the mid-16th century. Early modern English literature and documents, such as legal treatises and chronicles, employed the term to recount specific actions or occurrences, emphasizing deeds over abstract veracity. During the 16th and 17th centuries, the meaning of "fact" began to shift toward verifiable events, influenced by humanism's revival of classical inquiry and emphasis on empirical observation, alongside evolving legal practices that prioritized and tangible over authority or rumor. Humanist scholars, through the dissemination of printed texts, fostered toward unverified claims, promoting "facts" as reliable, contingent happenings that could be confirmed through direct experience. In legal spheres, this evolution solidified "fact" as something provable in court, laying groundwork for its later adoption in philosophical and scientific discourses on truth, though such extensions remained nascent at this stage.

Contemporary Definitions and Applications

In contemporary usage, a fact is defined as a thing that is known or proved to be true and verifiable through , distinguishing it from subjective opinions or unproven beliefs. This core concept emphasizes verifiability, often requiring empirical support or logical proof to confirm its truth, rather than reliance on personal interpretation. Major dictionaries reinforce this definition with slight variations in emphasis. The describes a fact as "a thing that is known or proved to be true," highlighting the role of provability in establishing . Similarly, defines it as "something that actually exists or occurs," with a strong focus on to differentiate verifiable realities from speculative claims. These definitions underscore facts as building blocks of reliable , applicable across everyday and formal . In education, facts serve as foundational knowledge, providing the essential facts, terms, and concepts that students must internalize to develop higher-order skills like critical thinking and analysis. Educational models, such as Dee Fink's taxonomy of significant learning, identify foundational knowledge—including basic facts—as a prerequisite for deeper understanding and application in academic disciplines. This approach ensures curricula prioritize verifiable information to build a solid base for lifelong learning. In policy-making, facts enable evidence-based decisions by supplying verified data and research outcomes to guide effective . The U.S. Foundations for Evidence-Based Policymaking Act of 2018 mandates federal agencies to use such facts—defined as systematically collected information on program needs and —to inform development and . This integration promotes accountability and resource allocation based on proven results rather than assumptions.

Philosophical Foundations

Correspondence Theory of Truth

The posits that a proposition or is true it corresponds to a fact or state of affairs in the world. This view holds that facts serve as the truth-makers for propositions, meaning truth arises from an accurate matching between what is asserted and the objective it describes. Originating in , the theory traces its roots to , who in his Metaphysics articulated a foundational idea: "To say of what is that it is, and of what is not that it is not, is true," implying that truth involves a correspondence between language or thought and the way things are. further suggested in works like Categories and De Interpretatione that truth resembles a likeness to facts, such as the proposition "He is sitting" aligning with the actual situation of someone sitting. In the early 20th century, Bertrand Russell advanced and formalized the theory within his framework of logical atomism, arguing that "a belief is true when there is a corresponding fact" and that atomic facts—simple, independent states of affairs—underpin the truth of corresponding atomic propositions. Russell's approach emphasized a structural isomorphism between propositions and facts, where the components of a true statement mirror the elements of the reality they depict, thereby establishing facts as existent entities that verify truth claims. For instance, the proposition "Snow is white" qualifies as a fact and is true precisely because it corresponds to the observable state of affairs in which snow possesses the property of whiteness. This correspondence ensures that facts are not merely linguistic constructs but objective anchors for truth, independent of human cognition in realist interpretations. The theory has faced significant criticisms, particularly from idealist philosophers who contend that facts and truth are mind-dependent rather than corresponding to an external, mind-independent reality. Idealists like F.H. Bradley and H.H. Joachim rejected strict correspondence in favor of a coherence theory, arguing that truth emerges from the internal consistency of a system of beliefs rather than alignment with purportedly independent facts; for Joachim, in The Nature of Truth, truth cannot be isolated correspondence but requires harmony within a comprehensive web of coherent propositions, rendering facts as projections of thought rather than objective entities. Bradley similarly viewed truth as an aspect of the holistic unity of experience, challenging the notion of discrete facts as truth-makers by emphasizing that reality is an interconnected whole inaccessible to atomistic matching. Such critiques highlight potential relativism, where truth becomes dependent on subjective belief structures, undermining the theory's claim to objectivity. Additionally, challenges like the slingshot argument suggest that distinct true propositions might collapse into correspondence with a single undifferentiated fact, complicating the theory's account of fact pluralism.

The Slingshot Argument

Versions of the slingshot argument, with earlier formulations by Alonzo Church, Kurt Gödel, and W.V. Quine and famously employed by Donald Davidson against the ontological status of facts, demonstrate that, under certain plausible assumptions, all true sentences must correspond to a single, undifferentiated "big fact," thereby undermining the notion of distinct, independent facts as entities to which sentences relate. Davidson presents this argument to critique theories that treat facts as objects of reference or correspondence, particularly in semantics and truth theory. The argument's structure relies on two key principles: first, that substituting co-referring singular terms in sentences reporting facts preserves the identity of the fact denoted; second, that substituting logically equivalent sentences within the scope of a (such as "the fact that") also preserves the reference. To illustrate, consider two distinct true propositions, such as f1f_1: "Snow is white" and f2f_2: "Grass is green." Let aa be an arbitrary particular, like a specific . The argument begins with the tautological identity: the fact that f1f_1 is identical to the fact that f1f_1. Next, Davidson employs definite descriptions to bridge the propositions. The description "the xx such that x=ax = a" refers to aa, and logically equivalent reformulations allow substitution: "the fact that f1f_1" is equivalent to "the fact that the xx such that x=ax = a is to the xx such that x=ax = a and f1f_1." Similarly, "the fact that f2f_2" equates to "the fact that the xx such that x=ax = a is to the xx such that x=ax = a and f2f_2." The definite descriptions "the xx such that x=ax = a and f1f_1" and "the xx such that x=ax = a and f2f_2" are co-referential because both uniquely pick out aa, given the truth of f1f_1 and f2f_2. Applying the substitution principles iteratively, the fact denoted by f1f_1 is shown to be to the fact denoted by f2f_2. Since f1f_1 and f2f_2 are arbitrary true propositions, all true sentences denote the same fact. This reductio implies that positing facts as discrete ontological entities leads to , as it collapses the multiplicity of truths into one monolithic fact. Ontologically, the argument suggests that facts should not be viewed as independent objects but rather as relations between (or ) and the world, aligning with Davidson's broader semantic program where truth is explicated through Tarskian conventions without invoking fact-entities. The thus targets correspondence theories by showing that if true sentences correspond to facts, there can be only one such fact, rendering the theory untenable in its standard form.

Fact-Value Distinction

The fact-value distinction, also known as the is-ought distinction, posits a fundamental separation between descriptive statements about what is the case (facts) and normative statements about what ought to be the case (values). This philosophical divide was articulated by in his (1739), where he observed that often transitions abruptly from factual to evaluative conclusions without justification, arguing that no imperative can be logically derived from indicative statements alone without bridging . Hume emphasized that "is" propositions, grounded in empirical observation, cannot entail "ought" propositions, which involve or moral direction, highlighting a gap in rational that requires additional non-factual elements to cross. In ethical theory, this distinction underscores how facts provide the descriptive basis for moral deliberation but do not themselves prescribe actions or judgments. For instance, the factual claim that " causes " describes observable consequences, yet it does not logically imply the value judgment that " is wrong," which requires an evaluative commitment to minimizing as inherently undesirable. This separation influences by challenging attempts to ground moral norms solely in empirical or natural properties, insisting that values emerge from sentiments, conventions, or additional rational principles rather than pure description. Debates surrounding the distinction intensified with G.E. Moore's critique in (1903), where he introduced the concept of the to denote the erroneous reduction of ethical terms like "good" to factual or natural properties, such as pleasure or evolutionary fitness. Moore argued that defining "good" in descriptive terms commits this fallacy because it equivocates on the non-natural, indefinable nature of goodness, rendering such definitions analytically false and open to the "open question argument"—wherein substituting a factual predicate for "good" leaves a meaningful query about whether it truly is good. This critique reinforced Hume's gap by targeting , though it sparked further contention over whether values can ever be objectively derived from facts without fallacy.

Factual and Counterfactual Realms

In , the factual realm encompasses events and states of affairs that have actually occurred or obtained in the actual world, serving as the basis for empirical and historical knowledge. These are realized possibilities, grounded in verifiable occurrences such as the in 1963. In contrast, the counterfactual realm involves unrealized possibilities—hypothetical scenarios that did not transpire but could have under altered circumstances, often expressed through subjunctive conditionals like "If Kennedy had not been assassinated, he might have pursued different policies." This distinction highlights the boundary between what is and what might have been, enabling analysis of contingency without conflating hypotheticals with established truths. Counterfactuals play a central role in philosophical analyses of causation, particularly through David Lewis's seminal counterfactual theory. Lewis posits that an event cc causes an event ee if, in the closest where cc does not occur, ee also does not occur, establishing causation as a relation of counterfactual dependence rather than mere correlation. This framework, introduced in his 1973 work Counterfactuals and refined in subsequent papers, differentiates factual causation—rooted in actual sequences—from counterfactual alternatives that reveal causal structures by imagining minimal deviations from reality. In , counterfactuals similarly underpin causal decision theory, where agents evaluate choices by considering the outcomes that would arise from hypothetical actions in possible worlds, guiding rational deliberation beyond mere evidential probabilities. Historiographical applications of counterfactuals exemplify their utility in exploring unrealized possibilities, such as "" scenarios that probe historical contingencies without asserting their factual status. For instance, scholars might examine whether the American Civil War's outcome hinged on pivotal battles, imagining alternative paths to assess the fragility of events like the Confederate defeat at Gettysburg, thereby illuminating causal chains in history. These exercises emphasize that counterfactuals are tools for understanding factual realms' contingency, not claims to alternative truths. Moral counterfactuals, in turn, extend this to ethical evaluations, such as pondering the value implications of averted harms in hypothetical scenarios.

Mathematical Conceptions

Theorems as Facts

In , a is defined as a statement that has been rigorously proven true based on a set of axioms and previously established results, thereby constituting an indisputable fact within the it inhabits. This proof process transforms a into a permanent truth, applicable universally without reliance on empirical verification. A classic example is the , which asserts that in a right-angled triangle, the square of the equals the sum of the squares of the other two sides, expressed as a2+b2=c2a^2 + b^2 = c^2, and was formally proven as Proposition 47 in Book I of Euclid's Elements around 300 BCE. The establishment of theorems as facts relies on deductive reasoning, a method that proceeds from general axioms to specific conclusions through logical deduction, ensuring the theorem's validity holds for all cases within the axiomatic framework. This deductive approach guarantees universality and necessity, as each step follows inescapably from prior premises, rendering the resulting fact immune to counterexamples or revision based on observation. In contrast to fields like physics, where facts may evolve with new data, mathematical theorems, once proven, remain eternally true within their system. This process builds upon axiomatic foundations, as detailed in the section on axioms and proof structures. A prominent illustration of a theorem's enduring status as a fact is , which states that there are no positive integers aa, bb, and cc satisfying an+bn=cna^n + b^n = c^n for any integer n>2n > 2. Conjectured by in 1637, it was proven by in 1995 through a groundbreaking demonstration linking elliptic curves and modular forms, solidifying it as an immutable mathematical truth. Wiles's proof, spanning over 100 pages, exemplifies how complex deductive chains can resolve long-standing problems into facts of absolute certainty.

Axioms and Proof Structures

In , axioms serve as foundational statements that are accepted without proof, forming the unproven starting points from which all other truths, or theorems, are logically derived within a . These axioms are chosen for their self-evident nature or utility in constructing a consistent framework, enabling the systematic exploration of mathematical structures. For instance, Euclid's , one of the five postulates in his Elements, asserts that given a straight line and a point not on it, exactly one line through the point is parallel to the given line, meaning it never intersects it. This postulate, while seemingly intuitive, exemplifies how axioms establish the basic rules governing geometric facts. Proofs provide the rigorous mechanisms for deriving facts from axioms, ensuring that each step follows logically from prior ones. Direct proofs proceed by assuming the premises and deducing the conclusion through a chain of implications, maintaining straightforward logical flow. Proofs by contradiction, also known as , assume the of the statement to be proved and demonstrate that this leads to a logical inconsistency, thereby affirming the original claim. Mathematical induction, particularly useful for statements about natural numbers, involves verifying a base case and showing that if the statement holds for some k, it also holds for k+1, thus establishing it for all such numbers. These proof types operate within axiomatic structures, where formal systems—such as those based on —define precise rules for symbol manipulation and inference. However, the completeness of such systems is limited, as revealed by Kurt Gödel's incompleteness theorems in 1931. The first theorem states that in any consistent powerful enough to describe the arithmetic of natural numbers, there exist true statements that cannot be proved or disproved within the system itself. The second theorem extends this by showing that such a system cannot prove its own consistency. These results highlight inherent boundaries in axiomatic frameworks, underscoring that not all mathematical facts are provable from a given set of axioms, and some truths remain independent. A pivotal historical shift occurred in the with the emergence of non-Euclidean geometries, which demonstrated the contingency of axiomatic facts. While Euclid's had long been treated as an indubitable foundation for plane , mathematicians including , János Bolyai, and explored alternatives by rejecting or modifying it. In , for example, through a given point not on a line, infinitely many parallels can be drawn; in , none exist. This development revealed that different sets could yield equally consistent yet distinct geometric facts, transforming the conception of axioms from universal truths to selectable foundations. Such structures ultimately support the derivation of theorems as established facts within their respective systems.

Scientific Dimensions

Empirical Observations

Empirical observations form the cornerstone of scientific facts, defined as information acquired through sensory perception or experimentation that can be repeatedly verified under consistent conditions. These facts emphasize repeatability, allowing independent researchers to confirm results and build collective knowledge. A classic example is the of at , which consistently reaches 100°C under standard of 1 , as measured in controlled settings. Measurement and instrumentation have profoundly expanded the capacity to generate empirical facts, evolving from rudimentary tools to sophisticated devices that extend human senses. Galileo's refinement of the in 1609 enabled precise astronomical observations, such as the discovery of Jupiter's four largest moons, providing direct visual evidence of celestial motions that supported heliocentric models. In modern contexts, particle detectors like those in CERN's ATLAS and CMS experiments record empirical data on subatomic particles, tracking their paths and energies to establish facts about fundamental interactions, such as the Higgs boson's decay patterns. These empirical facts, while foundational, retain a provisional character, liable to falsification by subsequent observations, as outlined in Karl Popper's criterion of demarcation for scientific theories. Popper posited that scientific knowledge advances through bold conjectures tested against reality, where facts are corroborated but never conclusively proven, ensuring ongoing scrutiny and refinement. Corroborated empirical observations thus achieve robustness through replication, yet their tentativeness drives scientific progress by accommodating potential refutations.

Integration in the Scientific Method

In the scientific method, facts emerge through a structured sequence of steps that transform initial s into validated knowledge. The process begins with careful of phenomena, which identifies patterns or anomalies warranting further investigation. These observations inform the formulation of a testable , a proposed explanation that predicts outcomes under specific conditions. The is then subjected to experimentation, involving controlled tests designed to gather that either support or contradict it. Finally, of experimental results leads to fact validation, where consistent evidence across multiple tests establishes a as a reliable fact, subject to ongoing refinement. A historical illustration of this integration is Isaac Newton's development of his laws of motion and universal gravitation in the late 17th century, building directly on Johannes Kepler's empirical laws of planetary motion derived from observational data. Kepler's laws—describing elliptical orbits, equal areas in equal times, and harmonic periods—served as the observational foundation; Newton demonstrated through mathematical derivation that these facts implied an of gravitational attraction, unifying disparate observations into a broader factual framework. This progression exemplifies how the refines raw empirical data into enduring facts. Peer review and replication function as essential post-experimentation mechanisms to confirm and solidify scientific facts. involves independent experts evaluating a study's , , and conclusions prior to , identifying errors or biases that could undermine factual claims. Replication entails independent researchers repeating under similar conditions to verify results, with successful reproductions increasing in the fact's robustness while failures prompt revisions or rejections. Together, these processes mitigate individual biases and ensure that only well-substantiated facts enter the scientific corpus. Despite these safeguards, science has encountered a since the 2010s, particularly in fields like , , and social sciences, where large-scale efforts to reproduce published findings have succeeded in only about 40-50% of cases as of 2025. For example, a 2025 involving 97 attempts across 47 biomedical experiments found many original results non-replicable, highlighting issues such as , p-hacking, and underpowered studies that inflate false positives. This crisis underscores the fragility of some scientific facts and has spurred reforms including preregistration of hypotheses, mandatory , and incentives for replication studies to bolster the verifiability and reliability of empirical knowledge. The integration of facts in the has evolved from Francis Bacon's 17th-century inductive approach, which advocated systematic accumulation of observations to eliminate false generalizations and derive true axioms, to contemporary Bayesian methods that quantify factual probabilities. In Baconian induction, facts were built incrementally through exhaustive and exclusion of alternatives, laying the groundwork for empirical rigor. Modern Bayesian updating refines this by incorporating prior knowledge as probability distributions, iteratively revising them with new evidence to yield posterior probabilities that represent updated factual confidence, particularly in fields like clinical trials and data-intensive research. This probabilistic framework enhances the method's adaptability to complex, uncertain data while preserving the commitment to evidence-based validation.

Historical Interpretations

Establishing Historical Facts

Establishing historical facts involves rigorous verification processes to distinguish verifiable events from or , relying on systematic of to construct reliable narratives of the past. Historians prioritize primary sources as the foundation for this endeavor, as these materials offer direct, unfiltered insights into events as they unfolded. By examining such sources through established criteria and quantitative techniques, scholars can affirm the occurrence, timing, and details of historical events with a high degree of confidence. Primary sources form the core of historical verification, encompassing documents like letters, treaties, and official records; artifacts such as tools, inscriptions, or artworks; and eyewitness accounts from diaries, chronicles, or oral testimonies produced contemporaneously by participants or observers. For instance, the , an embroidered cloth created around 1070, serves as a key for verifying the , depicting the invasion of by and pinpointing the decisive clash to October 14, 1066, through its sequential illustrations of the campaign. This artifact corroborates textual accounts from Norman and Anglo-Saxon chroniclers, providing visual evidence of , participants, and the battle's outcome that transformed English history. Eyewitness accounts, such as those in the , further support the tapestry's narrative by recording the invasion's timeline and Harold Godwinson's defeat, though they must be cross-checked for potential biases inherent to their authors. To assess the reliability of these sources, historians apply key criteria: corroboration, , and . Corroboration entails comparing multiple independent sources to identify consistencies in details, thereby strengthening the evidential weight of an event; discrepancies, when present, prompt further scrutiny to resolve contradictions. evaluation requires situating the source within its broader historical, social, and cultural milieu to discern influences like political motivations or societal norms that might affect its accuracy or intent. traces the and uninterrupted ownership history of a or artifact from creation to modern preservation, ensuring no tampering or fabrication has occurred; for example, archival records detailing transfers of custody help authenticate medieval manuscripts. These criteria collectively mitigate risks of , enabling historians to build factual assertions on converging lines of rather than isolated claims. Quantitative methods enhance precision in establishing facts, particularly for dating and cross-verification. Carbon dating, or radiocarbon analysis, measures the decay of isotopes in organic remains to provide calendar ages for artifacts up to about 50,000 years old, offering empirical confirmation of timelines; it has, for instance, validated the sequence of Egypt's Old, Middle, and New Kingdoms by dating wooden samples from tombs and structures. Archival cross-referencing involves systematically comparing records across disparate collections—such as diplomatic correspondences in —to align dates, locations, and participants, thereby refining historical chronologies with greater accuracy. These techniques, when integrated with qualitative assessment, yield robust factual foundations, distinguishing established from speculative counterfactual scenarios.

Challenges in Historiography

Historiography encounters profound obstacles in ascertaining historical facts, primarily stemming from biases inherent in sources and the incompleteness of records. Primary sources, such as diaries, official documents, and eyewitness accounts, are often produced by individuals or institutions with vested interests, resulting in selective reporting or deliberate distortions that skew interpretations of events. For example, colonial records from European powers in the frequently minimized atrocities against indigenous populations to justify imperial expansion, thereby complicating efforts to reconstruct unbiased timelines. Incomplete records exacerbate this issue, as vast portions of the past—particularly from non-elite or marginalized groups—have been lost to time, destruction, or neglect, leaving historians to piece together fragmentary evidence that may never yield a comprehensive picture. This scarcity forces reliance on indirect inferences, increasing the risk of erroneous conclusions about causal relationships or event sequences. Historical revisionism further complicates fact determination by challenging established narratives, often through ideological motivations rather than new evidence. A stark example is the ongoing debates over the scale of , where revisionists like have denied the systematic extermination of six million Jews, asserting that gas chambers were nonexistent and Nazi policies aimed merely at emigration. Despite overwhelming archival proof—including Nazi transportation logs, survivor testimonies, and perpetrator confessions such as those from Auschwitz commandant —these claims persist, alleging a vast conspiracy to fabricate evidence. Scholars counter that such revisionism ignores irrefutable documents, like the 1942 protocols outlining , and dismisses the logistical impossibility of a global hoax involving millions of witnesses. French historians, in a 1978 Le Monde declaration signed by 34 experts, affirmed that the existence of gas chambers is "obvious" and beyond legitimate debate, underscoring how revisionism undermines factual consensus even amid robust evidence. Postmodern critiques intensify these challenges by questioning the very nature of historical facts as objective truths, portraying them instead as constructed narratives shaped by power dynamics and language. , in (1979), defined as "incredulity toward metanarratives," arguing that grand historical explanations—such as linear progress or —legitimize through totalizing stories that suppress alternative voices. For , this implies that facts emerge not from neutral observation but from "phrase regimens" or discourse games, where events like the Shoah resist full representation due to their traumatic unpresentability. Lyotard's framework highlights "differends," situations where competing narratives cannot be reconciled, as in versus empirical testimony, yet he maintains that facts remain anchored in verifiable evidence rather than pure invention. This perspective urges historians to acknowledge narrative contingency while prioritizing empirical grounding to avoid . Case studies illustrate these ambiguities vividly. The "lost years" of Jesus, spanning roughly ages 12 to 30, exemplify gaps in ancient records that fuel scholarly uncertainty; the Gospels provide no details on this period, leading to debates over whether Jesus engaged in typical Jewish life in or traveled elsewhere, with sources like the apocryphal dismissed as legendary. Modern quests for the , drawing on sparse Synoptic accounts and archaeological context, yield diverse portraits—from to apocalyptic —due to theological biases in the texts and the absence of contemporary non-Christian corroboration. Similarly, the remain contested, with ambiguities in diplomatic intentions and secret alliances complicating blame attribution. Fritz Fischer's 1961 thesis portrayed Germany as aggressively expansionist, driven by domestic pressures, but critics like emphasized systemic European rivalries, including imperialism and , as shared faults; centenary analyses by further highlight contingency in events like the 1914 , where incomplete archival releases perpetuate interpretive disputes over premeditation versus escalation.

Facts in Evidence and Testimony

In legal proceedings, facts are established primarily through evidence presented in court, which includes testimony and tangible materials that courts evaluate to determine the truth of disputed matters. serves as the factual foundation for judicial decisions, distinguishing verifiable assertions from mere allegations. The process emphasizes reliability, relevance, and procedural fairness to ensure that only credible facts influence outcomes. Physical evidence, such as documents, objects, or biological samples, provides direct or circumstantial support for facts by linking events to specific individuals or occurrences. For instance, DNA evidence extracted from crime scenes has become a cornerstone of factual proof in trials, offering probabilistic matches that can conclusively identify perpetrators or exonerate the innocent with high accuracy when properly analyzed. Witness testimony, another key type, consists of oral statements under oath from eyewitnesses or parties involved, recounting observed events to establish factual sequences. Expert opinions, rendered by qualified specialists, interpret complex evidence—like forensic analysis or medical reports—to opine on factual implications, such as the cause of an injury or the authenticity of a signature, provided the expert's methodology meets scientific standards. The burden of proof dictates the level of certainty required to affirm facts as true, varying by case type to balance individual rights against societal interests. In criminal trials, the prosecution must prove guilt beyond a , meaning the leaves no logical alternative explanation for the facts, a standard rooted in protecting against wrongful convictions. Civil cases, by contrast, require only a preponderance of the , where facts are deemed established if more likely true than not—typically interpreted as over 50% probability—to resolve disputes efficiently. These standards guide juries and judges in weighing without quantifying doubt precisely. Admissibility rules ensure that only reliable evidence contributes to factual determinations, excluding unreliable or prejudicial material. The hearsay rule, for example, bars out-of-court statements offered to prove the truth of the matter asserted, as they lack and oath safeguards, unless falling under exceptions like excited utterances or business records that demonstrate inherent trustworthiness. Courts apply tests alongside these rules to filter evidence, preventing speculative facts from entering the record while allowing robust presentation of and exhibits. This framework upholds the integrity of facts in and , though it may briefly intersect with requirements in formal filings. In legal pleadings, parties formally assert facts to frame the issues in a civil dispute, primarily through complaints filed by plaintiffs and answers submitted by defendants. Under the U.S. , Rule 8 requires a to include a short and plain statement of the claim showing entitlement to relief, which typically involves alleging material facts supporting , the , and requested remedies. Similarly, an answer must admit or deny each in the , with specific denials addressing individual paragraphs to avoid general denials that could be deemed insufficient. These pleadings establish the factual foundation of the case without requiring exhaustive detail, emphasizing notice to the opposing party over evidentiary proof at this stage. A key distinction in pleadings arises between admitted and disputed facts, which directly influences the scope of . Facts that a explicitly admits in the answer are treated as established, narrowing the controversy to only those allegations that are denied or disputed, as per Rule 8(d), which deems undenied averments admitted unless the pleader intends a different response. This mechanism streamlines proceedings by identifying uncontested elements, allowing courts to focus judicial resources on genuine factual conflicts that require resolution through evidence presented later in the litigation process. The structure and role of facts in pleadings have evolved significantly from the rigid common law system to contemporary procedures designed for efficiency. In early English , pleadings revolved around technical writs and formal declarations that demanded precise formulation of facts to select the appropriate remedy, often leading to dismissals for minor errors in phrasing. This formalism persisted in American courts until reforms like the 1848 New York Field Code introduced simpler, fact-based pleadings, paving the way for the 1938 , which adopted "notice pleading" to prioritize substantive justice over procedural technicalities. A pivotal modern development is the mechanism under Rule 56, which allows courts to resolve cases pretrial if there is no genuine dispute over material facts, supported by affidavits or discovery, thereby preventing unnecessary trials on undisputed issues.

Facts in Language and Communication

Assertions and Verifiability

In , assertions are speech acts performed primarily through declarative sentences, which express propositions that the speaker claims to be true. For instance, the sentence "The Earth orbits the Sun" functions as an assertion by presenting a factual claim about a state of affairs in the world. Unlike interrogative sentences, which seek , or imperative sentences, which direct actions, declarative sentences commit the speaker to the truth of the proposition they convey, thereby distinguishing assertions as vehicles for stating facts. The verifiability principle, a cornerstone of , further delineates the role of facts in assertions by requiring that meaningful statements about facts be empirically confirmable. Articulated by in his 1936 book Language, Truth and Logic, the principle holds that a is factually significant only if it can be verified through direct or indirect sensory experience, or if it is analytically true by . Ayer's emphasizes that assertions purporting to describe facts must be testable against observable evidence, rendering unverifiable metaphysical claims nonsensical rather than factual. This criterion underscores the testability inherent in factual assertions, linking linguistic expression to empirical validation. Linguistic analysis reveals nuances in how assertions encode facts through verb types, particularly factive and non-factive predicates. Factive verbs, such as "know" or "realize," presuppose the truth of their complement clauses, embedding a factual commitment that persists even under , questioning, or modal embedding—for example, "John does not know that the meeting is canceled" still implies the meeting's cancellation as a fact. In contrast, non-factive verbs like "believe" or "think" do not entail truth, allowing the complement to remain an rather than an established fact, as in "John believes that the meeting is canceled," which carries no such . This distinction, first systematically explored by Paul Kiparsky and Carol Kiparsky in their 1970 paper "Fact," highlights how factives reinforce the verifiability of assertions by projecting truth assumptions across syntactic contexts.

Facts in Journalism and Media

In journalism, fact-checking serves as a systematic process to verify the accuracy of claims made by public figures, organizations, and news sources, ensuring that reported information aligns with verifiable evidence. Organizations like , founded in 2007 by the , evaluate statements using a scale from "True" to "Pants on Fire," drawing on primary sources, expert consultations, and public records to assess truthfulness. This practice gained heightened prominence following the 2016 U.S. , when concerns over ""—deliberately fabricated stories mimicking legitimate —prompted to declare it the "2016 Lie of the Year," highlighting how such content influenced voter perceptions and eroded trust in media. Ethical standards in emphasize the pursuit of truth through rigorous verification and contextual presentation, as outlined in the (SPJ) Code of Ethics, revised in 2014. The code mandates that journalists "test the accuracy of information from all sources and exercise care to avoid inadvertent error," while also requiring them to "provide context for the events and issues they cover" to prevent misleading interpretations. It further instructs reporters to "gather, update and correct information throughout the life of a story," underscoring for ongoing accuracy in dynamic reporting environments. These principles aim to uphold by distinguishing factual reporting from opinion or unverified assertions. The digital era has amplified challenges to factual reporting, with spreading rapidly on platforms due to algorithmic amplification and user-sharing behaviors, often outpacing traditional news cycles. Studies indicate that false information diffuses faster than accurate content on these networks, fueled by bots and echo chambers that prioritize over verification. To counter this, platforms like and X (formerly ) have implemented algorithmic fact-labeling, where automated systems flag potentially misleading posts and append warnings based on third-party fact-checker assessments, such as those from or . As of 2023, research shows these labels effectively reduce engagement with flagged content without suppressing overall platform use, though public perceptions of such interventions remain mixed, with concerns over . By 2025, features like X's have further evolved crowd-sourced , with studies showing significant reductions in reposts, likes, and views for flagged . Recent advancements also include AI-assisted tools by platforms like Meta and for detecting and labeling , particularly in response to events like the 2024 U.S. elections, aiming to bolster media trust amid ongoing challenges.

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