First attempt:

Facts, pretences to straightforwardness notwithstanding, are slippery, treacherous beasts. Despite sharing the same name, the members of this vast family are very different. Some social-climbing facts cosy up to truth in an attempt to improve their status; others slum it with cousins like opinion and theory. How does one go about developing a useful classification system for facts?

My first thought was that a simple taxonomy would do: one could deal separately with different categories like:

  • Legal Facts: “The cause of death was a blow to the head with a blunt instrument”;
  • Historical Facts: “The French Revolution took place in 1789”;
  • Scientific Facts: “HIV causes Aids”;
  • Personal Facts: “I dislike pizza”;
  • Geographical Facts: “Everest is the world’s highest mountain”;
  • Economic Facts: “Per capita GDP rose x% in 1999”; which point I realised this could go on a long time and wasn’t going to end up anywhere very interesting. The attempt was enlightening, though: I couldn’t think of a single fact that wasn’t to some extent open to revision or dispute. I also noticed that, in general, the higher the informational content of a statement the more likely it is to be disputed.

So, perhaps we can classify facts according to a) their utility (used in the economist’s broad sense to include usefulness, interest, entertainment value and other things it might be good for a fact to have) and b) their solidity or vulnerability to dispute. A fact like the date of the French Revolution would score high on solidity but low on utility; the fact that CFCs cause ozone layer depletion scores high on utility but a little lower on solidity; the fact that whoever it’s going to be won the 2000 United States presidential election scores high on utility but extremely low on solidity (a definition of “win”, anyone?).

Thinking about facts this way may help to avoid the all-too common confusion between “fact” and “truth” and between “factual” and “objective”. At the low end of the solidity scale facts can be, and frequently are, accused of being mere opinions – but simply naming a statement one way or the other isn’t enough to make it so. Facts are solid in proportion to the quality of the evidence they're based on, regardless of the personal history, beliefs or motivations of those asserting them.

blaaf: Agreed... I feel a certain uneasiness about counting mathematical and logical truths as "facts", though. Maybe this is just a matter of definition: I tend to think of facts as concrete statements about states of affairs in the world that might be otherwise: the moment it couldn't possibly be otherwise it gets lifted into a different realm altogether. To call "-(x and -x)" a mere fact  seems somehow to understate or cheapen it. But that's just me...
Why do you ignore mathematical and logical truth? These would seem to fit what you describe quite well, with physics and the other sciences lagging somewhat behind.

We have found failures in Newton's laws of motion. We know that mass is not necessarily conserved now. We think mass-energy is conserved now. That is an accepted law and an accepted fact, scientifically speaking, but how do we know? We've been wrong before. Matter starts getting wacky at really small scales.

But the beauty of formal mathematics is that it has not been open to revision or dispute, in an important sense. (I use your word "open" loosely.) Yes, a few conjectures have proven wrong and there have been major earthshaking rumbles like Turing's proof about the stopping problem, Godel's incompleteness theorem, and so on.

But the fundamental axioms of mathematics and all the arithmetic, algebra, calculus, geometry, theorems, and proofs built upon them have held up infallibly through the ages. There have been conjectures that have proven wrong, there have been "proofs" that were found to be mistaken. But there has been no failure in mathematics. We haven't found a case where n*0 is not equal to 0. We haven't found a case where the whole is not equal to the sum of its parts. We haven't found a border in the Mandelbrot set where the detail is lost and it smooths out. We haven't found a triangle of more than 180 degrees.

Much of mathematics has been discovered independently by many ancient cultures. These advanced, beautiful theorems have held as true today as they did for cultures thousands of years ago.

This is one reason I love math. It is unreasonably effective. It is beautiful. It is, in a sense, indisputable.

As far as metaphysical, non-scientific, non-mathematical truth... well, what is it?

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