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There are a few meanings and uses for fact.
In the scientific world, you can perhaps exchange the word "facts" for "data", and "truth" for conclusion, or even hypothesis. I.E. to adapt that approach back into the nonscientific world, facts are what you reason with to make conclusions (truth).
I think the legal system works the same way.(?)
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ultimate fact n. in a trial, a conclusion of fact which is logically
deduced from evidence ("evidentiary facts"). Example: the evidentiary
facts were that driver Larry Leadfoot a) exceeded the speed limit, b)
drove over the double-line, c) skidded and lost control of his car; the
ultimate fact was, therefore, Leadfoot was negligent. It is essential to
introduce the evidentiary facts during the trial in order to prove the
ultimate fact. A mere statement by a witness that "Leadfoot was
negligent" is not sufficient, since it is an opinion of the witness and is
not evidence.(See: evidence)