Fact

A Fact is a true statement about a state of affairs that has been obtained, in the world. Facts are contingent: they depend for their truth on what has actually occurred, as opposed to what is possible. Facts make claims that are, in general, independent from our theory. However, human understanding of facts is dependent on our theory: theory laden.

For instance, the fact 'the sun is a star', is independent from theory: theory has no effect on the state of affairs that led to the sun being a star. Understanding this 'fact' requires theory i.e. we need a theory of the: sun, stars, language, etc. Knowledge and beliefs are revisable; facts aren't.

The Factual/Counterfactual distinction

 * the distinction between the indicative conditional and the subjunctive-conditional.
 * Facts can express indicative-conditionals (if-then), which depend for their truth on what is actually the case.
 * Counterfactuals are subjunctive-conditionals, which express (an if-then) which depends for its truth on what would've been the case, if a different state of affairs obtained (a possibility).
 * Facts are about the actual world
 * Counterfactuals are about 'possible worlds'

Examples of fact
The following statements are true:

In relation to maths

 * 2+2=4
 * 9+10≠21

In relation to physics

 * "The Earth is not flat"
 * "Apples fall from trees"

Pseudo-facts from social constructionism

 * "The Sky is Blue" (Or Cyan to be more precise) (or Violet, but our eyes perceive it as blue )

In Logic
The state of affairs a well-formed formula denotes.

As a fallacy
Conspiracy theorists and other alt-right grifters might use "fact" in a fallacious manner. The most well known example among them is Ben Shapiro who once said in a debate "Facts don't care about your feelings".
 * Also, Shapiro commits the 'anti-naturalistic fallacy': he fails to acknowledge that values can influence facts, and feelings significantly affect values.
 * Thus, Shapiro is 'begging the question' since he assumes the 'fact/value' distinction as one of his premises, in order to infer the conclusion that asserts 'said' distinction.
 * "Facts don't care" presupposes the fact/value distinction, Shapiro intentionally uses this rhetoric to make it seem like facts are deliberately indifferent to feelings. However, this anthropomorphises facts, since 'not-caring' presupposes the ability to care, which facts don't have, by definition.
 * Shapiro commits the 'moralistic fallacy': He is not entitled to inferring the factual conclusion "Facts don't care about your feelings", based on a set of assumptions that are evaluative e.g. assumptions about 'caring', 'feelings' etc.

Factualism
The fallacy of 'factualism' occurs when someone inappropriately and excessively relies on facts in an argument i.e. to the detriment of values, possibilities, and beliefs (which are more obviously subject to revision and doubt). For example, over-attention to actual historical languages such as English, to the detriment of possible constructed-languages such as Esperanto. More generally, the neglect of what Carnap called "General Syntax": the study of languages (artificial and natural), in their most general form i.e. not just looking at the historical features of languages, but also, those general features that would make any language possible, period.

As a Rhetorical Device
However, the sentence became less and less effective as a rhetorical device since it started to be viewed as nothing more than a meme and a buzzword. But because it worked once, he tried that at each upcoming debate afterward.

In Science
"Settled Science": once most scientists universally agree on a statement, it becomes a fact. The knowledge and beliefs of the scientists can change; the facts don't. Scientists may change their minds about the knowledge, beliefs, and truth that made up their theories, and thus, what changes, is the theory not the facts. When scientists revise their work, they would say "we thought it was true but it never was", they wouldn't say "the facts were never true to begin with".

To determine whether a statement is true or false, scientists use the scientific method.

In Philosophy
In Philosophy, a fact is a statement that is understood as truthful if the state of affairs allows it. Facts can also be information about those things to which a truthful statement refers.

It questions objectivity.

Personal "facts"
A person may have distorted views of the real world due to beliefs, either mental or physical ailments (Such as color blindness) or other factors. Those "facts" are not viewed as facts since only a limited amount of people consider them to be true.

A person who is color blind will never see the sky in the color blue, it is either completely gray or slightly green to them.

It is worth noting here, a species, of a common cognitive distortion called "emotional reasoning", whereby feelings are perceived as facts. They are not!

Facts vs Concepts
See also Social constructionism.

Since facts are generally bound by pre-defined concepts such as color and the name given to those colors, or the worth of an item (Say, Gold, for example), then it sometimes becomes more complex to define whether a statement is true or false.

An example of that issue would be concerning tomatoes. Based on the definition of 'fruit' or 'vegetable', this made it difficult for people to tell whether tomatoes are a fruit or a vegetable. Another such example that is more complex would be corn. No one has ever managed to say for certain whether corn was a fruit, a vegetable, a grain, or a grass.