What is a fact, exactly? A table, for instance, is an object located within a particular region of space. But what about facts? Are they one kind of object, and if so, what kind of objects are they?
(1) History tells facts, novels do not.
Here, fact means true event.
(2) Scientific facts differ from historical facts.
The fact that water freezes at 0° C is a fact but not an event; it is, at best, an event type of which each freezing of water at 0° C is a token. Sometimes scientific facts are called "phenomenon".
(3) Science does not study facts but consequences; only history (natural or civil) studies facts (Hobbes, Leviathan).
A fact corresponds to a categorical sentence ("The Earth rotates about its N - S axis"); a consequence corresponds to a conditional statement ("if no net force acts on a movng body, then this body will continue its movement in a straight line at a constant speed").
(4) A fact is whatever denotes a true proposition. Truth is adequation of a sentence to a fact.
But in that case, a false sentence denotes nothing; in such a way that there is no meaningful false sentence? (Russell's critique in Problems of Philosophy).
(5) A fact is nothing else than a true proposition, the fregean "sense" (of a true sentence).
(6) A fact is an obtaining state of affairs, a fact is "what is the case".
A state of affairs is a complex entity involving a particular and a universal (property or relation) . Some states of affairs do not obtain; only those which obtain are facts.
A fact is not an event: that the Earth is (roughly) round is a fact, but it is not something that "happens" in whatever way. That mother Theresa never married is a fact; again, no assiciated event.
"The world is the totality of facts, not of things". (Wittgenstein, Tractatus, 1.1)
(7) A fact is a contingent obtaining state of affairs. (Hume)
That 2+2 = 4 is not a fact, but a "relation of ideas".
The philosophical notion of facts is "sentence-like slices of reality" (Quine). Basically, when we look at things, like a red sky, do we only directly think "a red sky" or do we think, "The sky here is red right now"? If we think the latter, do we think it into the sky, or from it?
This is sort of obscure but it underwrites the classical notion of substance. An object was said to be a substance if it was a sort of "subject that can't be a predicate" objectively. Of course we could invert the orders of words so that any subject becomes a predicate, so here, substances are things themselves conforming to the notion of facts.
This is what Wittgenstein is claiming about the world itself, then: that if the world is like a book, the book isn't a list of noun phrases but of full sentences.
Karl Popper holds that facts are the hypotheses that we have sufficient confidence in to build other hypotheses upon. IE -- the things we know about the world are all inferences, and none are certain or objective. "Facts" are just the most reliable of those inferences.
As hypotheses are abstract objects, inhabiting world 3, so are all facts. They are abstract objects.