This is a usage question. Seriously.
Folks use both words with great confidence, which leads me to believe they know what they're talking about.
We are assured that on EL&U questions must not be posted whose answers can only be opinion-based. And - if your answer isn't factual, it'll be closed immediately. Yes. We know the drill.
So it came to me as a shock today when someone with a rep of more than 50K (a fellow whom I like, incidentally) began answering a question with "I think ..."
Personally I have nothing against it. Opinions are superior to facts - in Decartes' ... opinion ... anyway. The word opinion is a derivative of the word opine, which means "to think" in Latin. Had Decartes thought ... damn it ! ... had he thought it was the other way around, he would have said "I've got some facts here, therefore ..." But he didn't.
According to the standard definition, a fact is something that can be proven right. (They usually leave it at that; however, an honest person should hasten to add " ... or wrong").
An opinion is something that cannot be proven right, nor wrong for that matter.
Or so they say.
A long, long time ago scientists took it as a matter of course that the Earth was the center of the Universe. To them and their groupies this was a fact. At the same time other scientists protested that the Sun, and not the Earth, was in the center, or slightly off-center. The two schools of thought continued to prove their rivals wrong and their own theory right. This went on for many centuries. Geocentric, heliocentric.
(There was, to be sure, Nicholas of Cusa, who explained that the Universe as we know it cannot have a geometrical center, but he was pointedly ignored).
Then, many centuries later, someone demonstrated, or thought he did, that neither the Sun nor the Earth were in the middle. Today's scientists believe in the almighty singularity that appeared out of nowhere and detonated itself with such vim and vigor that space, time, matter and energy suddenly appeared and began rapidly to expand in all directions centerlessly. That is now a fact, while the older ideas are no longer viewed as facts: they're outdated opinions. (Facts cannot be outdated: facts are forever, as Cleopatra used to say).
"What is the source of this?" demands the skeptical Mr. X squeamishly when he encounters information that doesn't quite fit into his well-adjusted outlook.
The ancient Romans thought the story of Troy was fiction. Troy? Fiction. Of course. It's a fact. Only ignorant people believe it might be true.
Folks continued to hold this ... op ... whoa. Folks continued to view the fictional nature of Troy as a fact until someone somewhere developed a different ... opinion ... damn it ... Eventually, an amateur named Schliemann dug up something that definitely wasn't Troy. Then, reluctantly, some folks began to agree that it was ... well ... kind of ... Troy.
Now we know for a fact that the Trojan War took place sometime in the 12th Century B.C. Look it up if you don't believe me. What's my source? I've got many. Wikipedia is one. Britannica Encyclopedia is another. There are countless books and essays.
Yes, but all those encyclopedia entries, all those textbook chapters - they didn't just magically appear, did they? No. They were written by, well, people. Reputable and scholarly, but still human. What was their source? Evidence? What evidence? Homer and Schliemann?
But no one questions Troy anymore. There's just no need. Too many entries. Too many books, well-indexed and cross-referenced. Consensus. Part of the paradigm.
But. Someone was first. The pioneer. The trailblazer. The idea's only champion at the time. At some point in the past that someone said, "Homer's account was based on actual historical events."
They called him a moron and told him to keep his uninteresting opinions to himself. Until ...
As it turns out, a fact is an opinion agreed on by many. Evidence or no evidence. An opinion is a unit of information someone believes in. A fact is a unit of information many reputable people believe in.
When you're stating a fact, it does help if your ... uh ... "source" ... is "reputable," i.e. the person whose essay or book you're so cavalierly alluding to is properly certified (has the stamp of approval, a.k.a. "the Sign of the Beast").
Am I right? ...
Now comes the comical part. I'm pretty sure a whole bunch of folks will want to close this question because "it is primarily opinion-based." Which is to say that, while we only consider facts, and never opinions, here on EL&U, what a fact or an opinion actually is is a matter of opinion, not fact.
If not, please give me your definition of those two words.