Fact

A fact is an occurrence in the real world. The usual test for a statement of fact is verifiability—that is whether it can be demonstrated to correspond to experience. Standard reference works are often used to check facts. Scientific facts are verified by repeatable careful observation or measurement by experiments or other means. 
For example, "This sentence contains words." is a linguistic fact, and "The sun is a star." is an astronomical fact. Further, "Abraham Lincoln was the 16th President of the United States." and "Abraham Lincoln was assassinated." are both historical facts. Generally speaking, facts are independent of belief and of knowledge.
Etymology and usage.
The word "fact" derives from the Latin "factum", and was first used in English with the same meaning: "a thing done or performed" a meaning now obsolete. The common usage of "something that has really occurred or is the case" dates from the middle of the sixteenth century.
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 ...").
Alternatively, "fact" may also indicate an "allegation or stipulation" of something that may or may not be a "true fact", (e.g., "the author's facts are not trustworthy"). This alternate usage, although contested by some, has a long history in standard English.
"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. This use is reflected in the terms "fact-find" and "fact-finder" (e.g., "set up a fact-finding commission").
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."
In philosophy.
In philosophy, the concept "fact" is considered in epistemology and ontology. Questions of objectivity and truth are closely associated with questions of fact. A "fact" can be defined as something that is the case—that is, a state of affairs.
Facts may be understood as information that makes a true sentence true. 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 Jupiter is the largest planet in the solar system.
Correspondence and the slingshot argument.
Pascal Engel's version of the correspondence theory of truth explains that what makes a sentence true is that it "corresponds" to a fact.
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 we reach the counter-intuitive conclusion that there is only one fact—"the truth".
Compound facts.
Any non-trivial true statement about reality is necessarily an abstraction composed of a complex of objects and properties or relations. 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.
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. Those who insist there is a logical gulf between facts and values, such that it is fallacious to attempt to derive values from facts, include G. E. Moore, who called attempting to do so the naturalistic fallacy.
Factual–counterfactual distinction.
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.
In mathematics.
In mathematics, a "fact" is a statement (called a theorem) that can be proven by logical argument from certain axioms and definitions.
In science.
The definition of a "scientific fact" is different from the definition of fact, as it implies knowledge. A scientific fact is 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.
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.
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. Pertinent issues raised by this inquiry include:
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.
The scientific method.
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. Scientific facts are generally believed independent of the observer: no matter who performs a scientific experiment, all observers agree on the outcome.
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.
In history.
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.
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.
In law.
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. Matters of fact have various formal definitions under common law jurisdictions.
These include:
Legal pleadings.
A party to a civil suit generally must clearly state all 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. 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.