Q14 - Joseph: My encyclopedia says

[megm7267]

Answer choices that include "mistaken" tend to confuse me...Can someone please explain the wording of answer choice (C)?

[geverett]

Here I will diagram out both Joseph and Laura's arguments for you. It might clear up some of the confusion between the arguments.

Joseph basically says "Since no one has been able to prove the theorem it most likely cannot be proved, and since it cannot be proved that most likely Fermat was lying or mistaken." Some pretty bold claims, but here is how this would be diagramed to make finding the core of the argument much simpler.

Theorem not proven -> Prob. can't be proved -> lie or mistake

Laura then counters that recently his theorem was proved and so this shows that Ferman was not lying and he was not mistaken. So she takes Joseph's argument which says this:

Theorem not proven -> Prob. can't be proved -> lie or mistake

And she reaches a conclusion that says this:

Theorem proven ---> ~lying and ~mistaken

If you compare this diagram to the one up top you will see that Laura has taken Joseph's argument and negated the sufficient condition and negated the necessary condition. This is known as a mistaken negation in conditional logic. (If you are not seeing this then take the time to check out pages 61-63 of the manhattan Logical Reasoning guide.)

Now you might ask "Okay, but how does a mistaken negation allow us to come to the answer choice presented in C where it says: "It mistakes something that is necessary for its conclusion to follow for something that ensures that the conclusion follows."

The term ensures is synonymous with sufficient so what the answer choice is saying is that "It mistakes a necessary condition for a sufficient condition." If you put it in the context of the argument it is saying "Laura takes the conditional relationship that Joseph gives us and commits a mistaken reversal with it. A mistaken reversal is the contrapositive or logical equivalent of a mistaken negation which allows us to infer answer choice C.

On another note conditional logic is one of the most frequently tested concepts of this test. Being able to do it backwards, forward, in your sleep, find it in arguments in the newspaper, on NPR, and the myriad other places you can encounter it in daily life will only serve to help you succeed on this test. I highly suggest to anyone to study it inside and out and really internalize it.

Let me know if you need anything clarified in my explanation.

[megm7267]

Thank you, this helps a lot.

Do you think you could provide another example of mistaking a necessary condition for a sufficient condition in layman's terms?

And would it be something along the structure of:

If A then B
If ~A then ~B

It seems like this structure is key to identifying mistaken condition questions.

[mcrittell]

What would example of E's flaw be? Perhaps not a flaw, but would this describe the stim's arg if it didn't say "fails to distinguish"?

[ManhattanPrepLSAT1]

If it were true that Fermat had proven the theorem and yet Joseph believed that Fermat was lying or mistaken, we would have a true claim that was believed to be false.

If it were true that Fermat had not proven the theorem and yet everyone believed that Fermat had proven the theorem, we would have a false claim that was believed to be true.

Answer choice (E) suggests that Laura had confused these two sorts of claims. But the issue is that we aren't certain whether Fermat had proven the theorem, so it's not possible to assert whether the claim was true or false.

Here's an attempt at an example of what answer choice (E) would be referring to:

Joseph: extraterrestrials exist, even though no one believes that they do in fact exist.

Laura: phenomena that do not exist and yet are thought to exist are not independently verified. So the phenomenon of extraterrestrials is not independently verified.

In that case Laura would have confused a claim that is true and yet believed to be false for a claim that is false and yet believed to be true.

Does that answer your question?

[ottoman]

What does answer choice mean?

[nja21]

What does answer choice mean?

I realize this might be to late to answer this question, but someone else might find this helpful.

So what does the A/C say: "It mistakes something that is necessary for its conclusion to follow for something that ensures that the conclusion follows."

First of all "it" refers to the argument, Laura's argument as a whole. "its conclusion" and "conclusion" refers to "your claim-that Fermat was lying or mistaken-clearly is wrong."

Before moving on to the A/C, we can instantly tell where the argument has gone wrong. The fact that the theorem was proven does not ensure that Joseph's Claim is wrong. This is due the the structure of Joseph's argument.

Using geverett's diagramming:

Theorem not proven -> Prob. can't be proved -> lie or mistake

And she reaches a conclusion that says this:

Theorem proven ---> ~lying and ~mistaken

If we take the contrapositive of Joseph's argument we get:
~li and ~mistake -> Theorem Proven. Now it is easy to see that the premise of Laura's argument is actually a necessary condition for her conclusion and not sufficient. This is exactly what A/C says. She is mixing up necessary conditions and sufficient conditions.

Note: Laura is attacking Joseph's premises to obsolete the argument. She is not creating a whole new argument. She says, although implicitly, "structure of joseph's argument is correct and I'm going to use it to attack the conclusion." How? "I just show his premises are not correct."

[mjacob0511]

I don't think all the diagramming is necessary (haha).

Laura points out that Fermat's theory has actually been proven. However, you cannot deduce from the fact that it was proven, that Fermat was not lying or mistaken. Yes, it is necessary that the theorem be proven if you want to say that Joseph's claim was wrong. If the theorem is not provable then we know that Joseph's claim is true and Fermat had to be lying or mistaken, but the fact that the theorem was proven isn't sufficient for that claim.

Why not? Well simply, Fermat died in 1665, maybe a mathematician in 1950 was the one who proved the theorem. It could still be true that Fermat did not prove it and he was either lying or mistaken as Joseph said.

[Mab6q]

I got this question wrong because I decided not to fall for what I thought was a trap in C; I didn't think we had any conditional reasoning in the argument.

After reviewing this question, this is the question that I have, and it applies to all LR questions. Whenever we get a flawed argument on the LSAT, such as the one in this problem where the author assumes the evidence (premise) is enough to justify his conclusion, can that argument in-of-itself be seen as a conditional statement? I say this because the argument assumes that X (the premise) is sufficient to guarantee Y (the conclusion), meaning that it would be a conditional. That is the only was I can see C being the correct answer here.

Otherwise, we cant interpret Joseph's argument {Theorem not proven -> Prob. can't be proved -> lie or mistake} as a conditional, as some of the reviews have done. Although we know that it is a argument, we are not given any indication that a theorem being proven ensures that it is probably that it cant be proved.

I hope i wrote that clear enough. I didn't like answer choice C because the flaw didn't fit my criteria for when an author mistakes a SC for a NC. However, if what I said earlier about the relationship between a premise and conclusion being a conditional is indeed the case, than that would make much more sense. Any help with would be greatly appreciated.

[christine.defenbaugh]

This is really an excellent question, Mab6q, and I think understanding the answer will open up new doors for you in your LR journey.

What you and mjacob0511 above you are getting at it that all flawed arguments assume that their premise is sufficient to guarantee the conclusion. It's not so much that the entire argument is a conditional, but rather that the assumption is a conditional.

The perfect, both-necessary-and-sufficient, assumption for an argument might be thought of as "If the premise is true, then the conclusion is true." This is why so many Sufficient Assumption correct answers are essentially written this way: "If [premise], then [conclusion]."

Given this viewpoint, you can see how some posters above translated Joseph's argument into a conditional - they were actually identifying the assumptions that Joseph had to be making.

However, I actually strongly agree with mjacob0511, that diagramming Joseph's argument is not strictly necessary for determining Laura's flaw. Remember that this is a two part question stem from the olden days, and Q13 was more focused on Joseph's argument. Looking at Laura's argument in a vacuum, we have this:

PREMISE: Fermat's theorem is provable.
CONCLUSION: Therefore, Fermat must have been correct when he claimed that he proved it.

Since, as we said above, authors always assume that their premises are sufficient, we know that Laura is assuming this premise is sufficient. That part is not terribly interesting, since all bad arguments do that.

What is more interesting is that Laura's premise is necessary to prove her conclusion. Lots of authors use random premises that might be wholly unrelated to their conclusions, but Laura has picked up on a piece of evidence that she absolutely cannot do without - that the theorem is provable.

And that's the error that (C) describes: she's identified something she NEEDS for her conclusion, but (like all flawed authors) assumes it is SUFFICIENT for her conclusion.

Please let me know if that helps clear things up a bit! Understanding the relationship between an argument and the implicit conditional assumption will really launch your LR skills into overdrive!

[Mab6q]

This is really an excellent question, Mab6q, and I think understanding the answer will open up new doors for you in your LR journey.

What you and mjacob0511 above you are getting at it that all flawed arguments assume that their premise is sufficient to guarantee the conclusion. It's not so much that the entire argument is a conditional, but rather that the assumption is a conditional.

The perfect, both-necessary-and-sufficient, assumption for an argument might be thought of as "If the premise is true, then the conclusion is true." This is why so many Sufficient Assumption correct answers are essentially written this way: "If [premise], then [conclusion]."

Given this viewpoint, you can see how some posters above translated Joseph's argument into a conditional - they were actually identifying the assumptions that Joseph had to be making.

However, I actually strongly agree with mjacob0511, that diagramming Joseph's argument is not strictly necessary for determining Laura's flaw. Remember that this is a two part question stem from the olden days, and Q13 was more focused on Joseph's argument. Looking at Laura's argument in a vacuum, we have this:

PREMISE: Fermat's theorem is provable.
CONCLUSION: Therefore, Fermat must have been correct when he claimed that he proved it.

Since, as we said above, authors always assume that their premises are sufficient, we know that Laura is assuming this premise is sufficient. That part is not terribly interesting, since all bad arguments do that.

What is more interesting is that Laura's premise is necessary to prove her conclusion. Lots of authors use random premises that might be wholly unrelated to their conclusions, but Laura has picked up on a piece of evidence that she absolutely cannot do without - that the theorem is provable.

And that's the error that (C) describes: she's identified something she NEEDS for her conclusion, but (like all flawed authors) assumes it is SUFFICIENT for her conclusion.

Please let me know if that helps clear things up a bit! Understanding the relationship between an argument and the implicit conditional assumption will really launch your LR skills into overdrive!

That was extremely helpful Christine!

[seychelles1718]

Can anyone give me some advice on how to first approach questions like this? I got this wrong at first but after I diagrammed the arguments, I could easily go through answer choices. But during the timed PT, I first read the stimulus, couldn't find out how Laura's argument was flawed, panicked, and skipped the question, without trying diagramming... Do you guys diagram as soon as you start reading stimulus for flaw questions?

[maryadkins]

I think that I, and I'll go ahead and say most of the LSAT instructors I know, would NOT diagram this question.

I'd approach Q14 by eliminating answers I know are wrong: (A), (B) and (D) and (E) strike me as not what Laura is actually doing. So I would, honestly, probably reach (C) by process of elimination, then verify it (assuming I have time).

Remember, eliminating wrong answer choices even if you can only eliminate 1-2 increases your chances of guessing correctly. So even if you aren't confident you have the time/understanding to reach the correct answer, that does not mean it is not worth your time figuring out a couple that are definitely wrong before guessing.

[AbhistD667]

I don't understand why the statements are seen as conditional logic when there is no "If" and "Then" or "only IF". Do we have to see every argument in this way or is there something else I am missing? Please let me know

[Misti Duvall]

I don't understand why the statements are seen as conditional logic when there is no "If" and "Then" or "only IF". Do we have to see every argument in this way or is there something else I am missing? Please let me know

Sure! Sometimes conditional logic statements have clear indicator words like "if" and "then" and sometimes they can be a little trickier. Chapter 8 of the Logical Reasoning Strategy Guide is a great place to review for different ways conditional logic statements can be written.

[YufeiR103]

Hi, I would like to share my view of this question here.

It: refers to Laura's argument
your claim: Joseph's claim, which is "Fermat was lying or mistaken"

by combining these two, it refers to "since Fermat's theorem is provable, 'Fermat was lying or mistaken' is wrong".

C is right, and the "something" in C refers to the evidence "Fermat's theorem is provable",
By negating it, we can see that if "Fermat's theorem is not provable", clearly, Fermat is either lying or mistaken, and it is inconsistent with Laura's conclusion. So "something" is necessary for Laura's conclusion; however, it is not sufficient for the conclusion, since Fermat could be lying about that he had proved the theorem, for it is only recently someone has proved it. That is saying that Laura's evidence, "something", isn't sufficient itself to support her conclusion.

As a result, Laura's argument mistakenly taken a necessary evidence as a sufficient evidence. Hence, C is correct.