A fact was information which was considered as true. It could be verified with evidence. Facts might be exaggerated, influenced by biased opinion, and might lead an individual to wrong conclusions. (TOS: "Where No Man Has Gone Before"; TNG: "The Defector")
It was a fact that one of Spock's ancestorsmarried a Humanfemale. (TOS: "Where No Man Has Gone Before")
It was a fact that, by 2265, studies into ESP in Humans had discovered some had the ability of sensing future happenings or reading the backs of playing cards; however, the esper capacity was always quite limited. (TOS: "Where No Man Has Gone Before")
The only sure fact recovered from the SS Valiant's disaster recorder was that the ship had been destroyed. CaptainJames T. Kirk saw this as the "best argument" for continuing the probe of the galaxy's edge, because he reasoned that other vessels might come this way and they would need to know what dangers they might encounter. (TOS: "Where No Man Has Gone Before")
In 2266, after being informed by Ben Childress, the representative of the Rigel XIIminers, that he could either accept the terms of a swap for lithium crystals or the crystals would be hidden in a place that a USS Enterpriselanding party could never locate, Kirk responded, "You're a long way out in space, gentlemen. You'll need medical help, cargo runs, starshipprotection. You want to consider those facts too?" (TOS: "Mudd's Women")
In 2366, after the androidData had been sent by Starfleet to the colonyplanetTau Cygna V, inhabitants had been discussing why he came and Gosheven called a meeting to replace misinformation with fact. (TNG: "The Ensigns of Command")