Here is an amusing sporting fact that resonates with our puzzle in which a decision that is the same under conditions of A true and A false, may not be the right decision when the truth status of A is unknown.
John Howard (London School of Economics) tells me that in cricket it can happen that a batsman attempts to drive the ball but appears to miss (or he may have snicked it). The ball then hits his pad, bounces off, and is caught by a slip fielder. There is an appeal for lbw (leg before wicket). The umpire would have given him out "lbw" if he was sure he had not hit the ball. He would be out "caught" if he had hit the ball. But a batsman cannot be given out unless a definite reason is given, and if the umpire is not sure which of these two it was, then batsman is not out.
I am told that a similar incident happened in the recently concluded India-Australia Test, where the bowler appealed for lbw or caught, the umpire upheld the appeal for lbw, but the batsman was upset thinking he was given caught out as he had not edged the ball.
You can read more about this in the article, Ricky Ponting and the Judges, by Ian Rumfitt, who writes:
"In the first innings of the final Ashes Test of 2009, Ricky Ponting faced a ball which was deflected, off something, into the wicket-keeper’s hands. The English XI appealed, and in the agonizingly long time that it took Asad Rauf to decide, Jonathan Agnew (commentating on Test Match Special) reasoned as follows: ‘Either the ball hit Ponting’s bat or it hit his pads. If it hit his bat, he is out caught behind. If it hit his pads, he is out lbw. So, either way, he is out’. Rauf, however, appeared to disagree with Agnew’s reasoning, and Ponting stayed at the wicket."
John Howard (London School of Economics) tells me that in cricket it can happen that a batsman attempts to drive the ball but appears to miss (or he may have snicked it). The ball then hits his pad, bounces off, and is caught by a slip fielder. There is an appeal for lbw (leg before wicket). The umpire would have given him out "lbw" if he was sure he had not hit the ball. He would be out "caught" if he had hit the ball. But a batsman cannot be given out unless a definite reason is given, and if the umpire is not sure which of these two it was, then batsman is not out.
I am told that a similar incident happened in the recently concluded India-Australia Test, where the bowler appealed for lbw or caught, the umpire upheld the appeal for lbw, but the batsman was upset thinking he was given caught out as he had not edged the ball.
You can read more about this in the article, Ricky Ponting and the Judges, by Ian Rumfitt, who writes:
"In the first innings of the final Ashes Test of 2009, Ricky Ponting faced a ball which was deflected, off something, into the wicket-keeper’s hands. The English XI appealed, and in the agonizingly long time that it took Asad Rauf to decide, Jonathan Agnew (commentating on Test Match Special) reasoned as follows: ‘Either the ball hit Ponting’s bat or it hit his pads. If it hit his bat, he is out caught behind. If it hit his pads, he is out lbw. So, either way, he is out’. Rauf, however, appeared to disagree with Agnew’s reasoning, and Ponting stayed at the wicket."
