[rookie1ja]

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?

Spoiler for Solution:

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".

Spoiler for old wording:

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

[fosley]

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.

[Canon]

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

[jmull747]

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.

[csp0104]

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

[Naruki]

Quote

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.

[rookie1ja]

Quote

Quote

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)

[Naruki]

Quote

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.

[SickDelirium]

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.

[BoilingOil]

Quote

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