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The phrase "a fact exists" is correct and usable in written English.
It can be used when stating the presence or reality of a particular fact in a discussion or argument.
Example: "In the debate about climate change, it is important to acknowledge that a fact exists: the planet is warming due to human activity."
Alternatives: "a fact is present" or "a fact is true".
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The Supreme Court's recent decision in Global-Tech Appliances v. SAB found two requirements to prove someone was willfully blind: "(1) the defendant must subjectively believe that there is a high probability that a fact exists and (2) the defendant must take deliberate actions to avoid learning of that fact".
If a state of affairs obtains, then an obtaining state of affairs exists, a fact exists.
Similar(58)
A theory should be considered inaccurate if a single fact exists that contradicts that theory 23.5 30.6 9.2 19.4 17.3 A theory can still be useful even if one or more facts contradict that theory 20.
For, in many cases, whether or not a structural fact exists depends not only on the existence of its constituent facts but also on the absence of certain others (Armstrong 1997, 34ff).
Individuals composing society do not directly cause suicide: suicide, as a social fact, exists independently in society, and is caused by other social facts (such as rules governing behavior and group attachment), whether an individual likes it or not.
This is too great a price to pay for judicial incrementalism, especially after seven of the justices had concluded that such a right in fact exists.
An Armstrongian state of affairs (or fact) exists "if an only if a particular (at a later point to be dubbed a thin particular) has a property or, instead, a relation holds between two or more particulars.
He ruled that "a triable issue of fact exists as to whether Jahi currently satisfies the statutory definition of 'dead.' " In a trial expected to last a month, a jury will decide if Jahi is alive.
The city's arguments, she wrote, "do not withstand the overwhelming evidence that there, in fact, exists a centralized stop-and-frisk program that has led to thousands of unlawful stops".
The patient will die without a treatment that in fact exists to cure her.
Samples tended to be small, risking Type II errors (i.e. not detecting a relationship which in fact exists).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com