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Logic Problems at the Court II.

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Logic Problems at the Court II. - Back to the Logic Problems

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 not true!”

Did the attorney help his client?

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Logic Problems at the Court II. - solution

The statement of plaintiff is a lie only if the hypothesis (or antecedent) is true and conclusion (or consequent) is not true. So the solicitor did not help his client at all. He actually said that his client was guilty and there was no accomplice.

Answer presented by Naruki (for explanation see below):

The correct answer is either "not enough information" or "invalid question".

Two lawyers had the following conversation.

Plaintiff: "If the prisoner is guilty, then he had an accomplice."

Solicitor: "That's not true!"

Did the solicitor help his client?h

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• 1 month later...

I don't like this one; the word "that" in "That's not true!" is ambiguous. Regardless, the prisoner can't be guilty, so the Solicitor helped him. There are three ways to look at it:

1. "That" refers to the If statement as a whole. In this case, the Solicitor says the Plaintiff lies, which can't be true. But if it's not true, the Solicitor can't say it, so "that" can't refer to the entire If statement.

2. "That" refers to the prisoner having an accomplice. If the prisoner was guilty, but there was no accomplice, the Plaintiff is incorrect which can't happen. So the prisoner has to be not guilty and no accomplice.

3. "That" refers to the prisoner being guilty. Nobody else matters at this point, because the Solicitor is telling the truth and the prisoner isn't guilty.

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• 3 weeks later...

Indeed, you can't have two truthtellers with one saying that the other uttered an untruth.

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Two truthful lawyers had the following conversation.

Plaintiff: "If the prisoner is guilty, then he had an accomplice."

Solicitor: "That's not true!"

Did the solicitor help his client?

This can only have a solution if a truthful lawyer may be mistaken.

If the solicitor thought his client was innocent, he would not respond that way. Only if he thought his client was guilty would he have an opinion on whether or not the plaintiff's statement was true or false.

Therefore, the solicitor did not help his client because he made it obvious that he believes his client is guilty.

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• 1 month later...

So, to solve this, we are to assume that the two lawyers are truthful...HA!

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Plaintiff: "If the prisoner is guilty, then he had an accomplice."

Solicitor: "That's not true!"

...

The statement of plaintiff is a lie only if the hypothesis (or antecedent) is true and conclusion (or consequent) is not true.

I think you need to look up the definition of "lie". A lie is when you communicate (what you believe are) false facts as though they are true.

They might _actually_ be true, but you believe they are false. The key feature is that you are trying to make your listener believe something that (you think) is false.

If you are making an incorrect (or untrue, or false, etc.) statement from incompetence, that is not a lie - it is just incorrect. This is most likely the case in the Plaintiff's statement. He asserts that guilt requires an accomplice, regardless of circumstances (circumstances were not considered relevant to this problem, so they cannot be part of that equation). Such a statement is logically absurd. Thus, the Plaintiff has apparently uttered a non sequitur.

Had this been a practical (i.e., real life) scenario, the context of that statement would have been crucially important. For example, if the crime involved lifting an object too heavy for one man, we would understand the statement to mean "if the suspect committed the crime, he must have had an accomplice to help lift".

In such a case, the Defense could logically argue that is not true, as anyone with a forklift, a pulley system, or a lever could have managed the feat alone.

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.

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This is another poorly designed logic problem.

feel free to reword any puzzle posted by me ... post your puzzles ... criticize ... but don't forget to come up with a suggestion - improvement (corrected wording)

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feel free to reword any puzzle posted by me ... post your puzzles ... criticize ... but don't forget to come up with a suggestion - improvement (corrected wording)

Fair enough, but...

It would be easier for me to fix the answer instead of trying to improve the question. The correct answer is either "not enough information" or "invalid question". (It's also important to replace "lie" with "false", but the explanation isn't needed in the fixed answer.)

I don't know how to reword that question to make it achieve the desired outcome (accidentally implicated his client) without being fatally flawed.

Those who can, do. Those who can't join the Peanut Gallery.

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I agree with Naruki on this one. When I read the teaser, the Solicitor actually did nothing for the client. I didn't think for one minute that the Solicitor implicated his client.

If you read the stimulus again, the Plaintiff states a principle, an "if...then" statement. All the Solicitor said was that this particular principle is incorrect. Let's examine this more closely.

"If A, then B". The logical opposite (and what the Solicitor is claiming) is "If A, then B OR not B" or "If A occurs, B does not necessarily have to occur". In this light, the Solicitor is saying that his client could be guilty without having an accomplice. Note that this does not allow us to make any inference as to whether A has happened or not (whether the client is guilty or not). If the client is not guilty, then the lawyers are arguing over a principle is irrelevant to the case. We must KNOW that the client is guilty in order to make a valid conclusion about having an accomplice. We CANNOT use this principle to determine guilt (condition A).

My answer to the teaser would be "No, he did not help the client." The more complete answer is that the Solicitor neither aided nor harmed his client's case. He only refuted a principle put forth by opposing counsel.

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• 2 months later...
Logic Problems at the Court II. - Back to the Logic Problems

Two lawyers had the following conversation.

Plaintiff: "If the prisoner is guilty, then he had an accomplice."

Solicitor: "That's not true!"

Did the solicitor help his client?

If the prisoner is innocent, what would he have needed an accomplice for? Not for any crime he didn't commit. Anyway, the Plaintiff made a statement the truth of which would only matter IF THE PRISONER IS GUILTY.

If the prisoner is innocent, Plaintiff's comment was irrelevant, and the Solicitor would not have any reason to refute it.

If the prisoner is guilty, it may or may not matter if he worked on his own. What Plaintiff said could ONLY be untrue, if the prisoner was guilty and worked alone. So the solicitor's claim would immediately implicate that this is actually the case. That's not really helping his client, if you ask me

BoilingOil

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If the prisoner is guilty, it may or may not matter if he worked on his own. What Plaintiff said could ONLY be untrue, if the prisoner was guilty and worked alone. So the solicitor's claim would immediately implicate that this is actually the case. That's not really helping his client, if you ask me

The original statement implied a false causal relationship: that guilt in that case required an accomplice. The statement is untrue because no such relationship exists. It matters not whether the defendent is actually guilty or not.

"If the sky is blue, then you are a raspberry."

That statement is untrue, EVEN IF you actually are a raspberry. The reason it is untrue is because it implies a false causal relationship. The color of the sky cannot cause you to be a particular type of fruit.

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• 2 weeks later...

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• 2 months later...

The answer is 'the solicitor did not help his client'. The answer provided firstly is incorrect because the word 'lie' is used, what should be used is 'false'.

Naruki's answer of "not enough information" or "invalid" question is incorrect for

the mere fact that this question deals with logic, as in formal logic. There is enough information for a logic problem.

If Q > P is not a true statement, then that means that Q is true and P is false. The conclusion from the original answer is correct (minus 'lie'). I know this has all been said, but after having been said it was concluded that there is something wrong with the question itself, and that is not the case.

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• 2 weeks later...

I agree with a fake mustache. There is really no need to humour anyone who says that there is not enough information.

At the heart of this logic problem is the phenomenon which occurs when you deny a conditional statement. A conditional statement says so little that to deny one actually says a lot. In this case it says all this: that there was no accomplice and that the client is guilty. It's just hard to get your head around how it could be that the solicitor is saying so much with such a simple statement, which is probably what is stumping most people and causing them to fixate on issues about the exact meaning of "lie", whether the lawyers are telling the truth or not and so on.

This shows formally how the solicitor said so much. Let, G mean 'the client is guilty', and A mean 'the client had an accomplice':

The solicitor said: not ( if G then A )

which is equivalent to: not( not G or A ) [material implication]

which is equivalent to: not not G and not A [demorgan's theorem]

which is equivalent to: G and not A [double negation]

which expands to: 'the client is guilty' and not 'the client had an accomplice'

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• 2 months later...

no

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• 4 weeks later...

I don't believe the solicitor helped, no hindered, his client.

It's an if and then statement.

If the first thing happens, then the second thing will...

IE: If Tommy studies for his test, then he will get an A.

The fact that he says, That's(that is) not true!, means to say that he is in fact claimed innocent, as in the face of the Lawyer by his statement. Yet, this is only heresay by the solicitor and will not hold up in court without solid evidence behind it.

Believe me, I work for lawyers. "

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• 2 months later...

no offense to any attorneys reading this

the question is an oxymoron citing "two truthful lawyers". both are swindlecants as they are lawyers

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• 9 months later...

This is my thought... it is not as pretty and filled with logical jargon like everyone else's posts... but I like to K.I.S.S. (Keep It Simple Stupid). ...and I am mighty stupid most of the time.

Yes, he did help his client. If either part of the statement is not true, the accused cannot have done the crime. If he had no accomplice then according to the accuser, he did not do the crime and if he did not do the crime he obviously did not have a accomplice.

Edited by jhyatt455
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• 4 weeks later...
Logic Problems at the Court II. - Back to the Logic Problems

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 not true!”

Did the attorney help his client?

Logic Problems at the Court II. - solution

The statement of plaintiff is a lie only if the hypothesis (or antecedent) is true and conclusion (or consequent) is not true. So the solicitor did not help his client at all. He actually said that his client was guilty and there was no accomplice.

Answer presented by Naruki (for explanation see below):

The correct answer is either "not enough information" or "invalid question".

Two lawyers had the following conversation.

Plaintiff: "If the prisoner is guilty, then he had an accomplice."

Solicitor: "That's not true!"

Did the solicitor help his client?h

it didn't necessarily help his client, but it also didn't necessarily NOT help him either. It could mean one of two things:

one, if he did the crime, he did it alone,

or two, he did not do the crime with an accomplice, as he didn't do it at all.

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If we take the prosecuters statement as truth, than the defence attorney did help his client by saying that he did not have an accomplis, and therefore did not commit the crime.

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• 5 months later...

Not only did the attorney not help his client, he accused him of being guilty.

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."

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• 6 months later...

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.

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• 9 months later...

I know this post is old, but I just had to put in my two cents. Both answers are true with the way the question is stated. Since that makes for a crappy logic problem, I offer an alternative.

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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