Does a "fact" have to be true?

Solution 1:

A fact does, in fact, have to be the truth at the time you're using the word.

By 'truth', I mean something you believe to be true (due to any of several possible reasons).¹

Consider: "The number of planets in the solar system is eight." A few years ago, this was not a fact. It is now. (Just an example, don't attack the example.)

[EDIT: Before 1917, people thought it to be a fact that the atom was the smallest particle of matter. Today, it is a fact that it isn't, and we were wrong in thinking it was... I'm including this example to show that in light of the new fact, what we thought was a fact previously, can be rendered untrue for that time too; something @Jay pointed out my previous example didn't specify]

When a jury convicts a man, it's a fact that he's guilty. If he's later acquitted, it's a fact that he is 'not guilty'. (As far as the public is concerned. Individuals who actually saw the crime might know, for a fact, whether it's true or not)

What I'm trying to say is that the word fact is used for what you know (or sincerely believe) to be the truth or what is widely believed to be the truth at the time of speaking. Facts are subject to change.

Something is not a fact if you know/believe it to be untrue or if it can be easily be shown to not be widely believed at the time.

The two can contradict. That's when myth comes into play.

Tom: "Interesting fact: you can see the Great Wall of China from space." (Widely believed).

Neil: "As a matter of fact, you can't. That's a myth." (I went to space. I know better.)

¹ _{Please note that I'm talking exclusively about the cases where you use the word fact. In those cases, I infer you strongly believe it to be true.}

Solution 2:

There are some good answers here. I thought it would be useful to expand on meaning (5) in your list, in case you ever have to deal with it.

In English common law, most matters (criminal or civil) came to be tried by a jury. Over time a rule developed that some questions would be decided by the jury and others by the judge. The jury decided questions of fact whereas the judge decided questions of law.

For example, in the English law of theft, one element of the crime that must be established by the prosecution is that the defendant acted "dishonestly". The meaning of "dishonest" is a question of law, but whether the defendant was dishonest according to that definition is a question of fact.

There are practical consequences of this distinction. In English criminal procedure, you may appeal the judge's decision on questions of law, but not the jury's decision on questions of fact.

In this usage "fact" is used in a slightly technical sense in opposition to the word "law" but it is essentially intended to be restricted to statements that are true, at least that is the hope.