The classic explanation of counterfactuals begins with this distinction:
- If Lee Harvey Oswald didn’t shoot John F. Kennedy, then someone else did.
- If Lee Harvey Oswald hadn’t shot John F. Kennedy, someone else would have.
In ordinary usage we would agree with the first statement, but not the second (I hope).
If, somehow, we learn the definite fact that Oswald did not shoot Kennedy, then someone else must have done so, since Kennedy was in fact shot.
But if we went back in time and removed Oswald, while leaving everything else the same, then—unless you believe there was a conspiracy—there’s no particular reason to believe Kennedy would be shot.
Some counterfactuals seem definitely wrong, like “If Lee Harvey Oswald hadn’t shot John F. Kennedy, the earth would have been destroyed.”
But how can we know what counterfactuals are right? You may say that counterfactuals exist only in your mind and therefore are completely arbitrary.
Yudkowsky however believes that you can, with the help of the mighty Judea Pearl, “compute a counterfactual, given only your beliefs about the actual world.”
I don’t know how relevant this stuff is but here is a good introduction to Judea Pearl’s theory of causal inference, which is of course pretty technical.
I am quite confident that the statement 2 + 3 = 5 is true; I am far less confident of what it means for a mathematical statement to be true.
2+3 =5 ;regardless of what anyone thinks.
“Okay, so it’s possible for something that appears thought-independent, to actually be thought-independent. But why do you think that 2 + 3 = 5, in particular, has some kind of existence independently of the dots you imagine?”
Because two sheep plus three sheep equals five sheep, and this appears to be true in every mountain and every island, every swamp and every plain and every forest.
And moreover, it is also true of two rocks plus three rocks.
…”But my dear sir, if the fact of 2 + 3 = 5 exists somewhere outside your brain… then where is it?”
Damned if I know.