Surely that also depends on the domain you are reasoning about? For example, when debugging computer programs it seems that I am eliminating the impossible all the time. "Hm, this function is not returning the answer I expect. Am I calling it with the wrong argument? (Printf -- no.) Are the calculations right up to this point? (Printf -- yes). Aha, this must be the line that's wrong!"
True! However, I know I've had times in program debugging (though I can't remember a specific one) when I eliminated something "impossible" and it turned out not to be. I think there was usually a flaw in my reasoning though, rather than a flaw in my knowledge of what's possible. (In other words, I overlooked some simple possibility.) Anyway, when I feel like I'm at the end of my debugging rope, I just start from the beginning with an eye towards stuff I could have missed the first time around, including stuff that I disregarded as "impossible".
Related: "select" Isn't Broken".
Here's the new quotes thread.
Rules: