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Logic Problems at the Court II.
Posted 05 October 2009 - 09:51 PM
People seem to be confused on who's telling the truth. The prosecutor merely stated "if the accused committed the crime, he had an accomplice." He did not indicate whether it's true or not, it's just a conditional statement. The defender, this attorney, marks this as a fallacy, stating it is not true. Now if you know your logic, or if you have read oranfry's post, the negation of statement P -> Q, is P and ~Q, or in this case, th accused committed the crime, and there is no accomplice. So by stating "that is not true", he basically confirms that the negation is true. So he just screwed his client.
Many people have mistaken the negation of P -> Q as ~Q -> ~P. That is incorrect. As a matter of fact, they are equivalent. In this case, if we agree to the prosecutor about his statement, the defender can just prove there is no accomplice, and set his client free.
The right way to reply to such statements from the prosecutor should be "there is no ground to that statement."
Posted 09 April 2010 - 02:12 AM
The Plaintiff's statement has absolutely no bearing on the suspect's guilt, and declaring it true or false likewise has absolutely no bearing on the suspect's guilt.
This is another poorly designed logic problem.
It depends on whether you look at the problem through the eyes of natural English or literal logic.
Naruki is right that the statement "if the prisoner is guilty, he had an accomplice" implies "the guilty party had an accomplice". Then, when the attorney says that this is false (which is taken as indisputable truth by the court) it means that whoever committed the crime could have done so on his own, with a forklift truck or whatever.
However, this is not what the prosecutor said. He said "if the prisoner is guilty, he had an accomplice." Through the eyes of logic, the only way this logical implication can be false is if the prisoner is guilty and did not have an accomplice.
Arguably, both points of view are valid, but only the literal view gives an answer. As far as the court is concerned, the prisoner's guilt is now an indisputable truth, and the answer to the question is no.
Of course, nowhere does it say that the attorney cannot lie; he could now say "My client is innocent", creating a paradox in the minds of the courtspeople, thus causing the entire situation to collapse into a huge hypothetical vortex of nothingness.
I like these puzzles.
Posted 01 February 2011 - 10:16 AM
I think the problem can be fixed by changing what the lawyer says to, "That is a lie!" instead of, "That is not true!" This addresses what all the natural English people are saying.
If he were to call it a lie, instead of simply not true, he places the blame on the prosecutor. It means that the prosecutor's knowingly made a false statement, and as many pointed out, creates p and ~q. Calling it not true can be interpreted to mean the prosecutor is unwittingly wrong, and the client could have committed the crime without an accomplice (forklift, pulley, etc.) but did not, necessarily, commit the crime.
I posit that the problem he restated thus:
A man accused of a crime, hired an attorney whose statements were always admitted by the court as undisputable truth. The following exchange took place in court.
Prosecutor: “If the accused committed the crime, he had an accomplice.”
Defender: “That is A LIE!”
Did the attorney help his client?
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