Logical ReasoningDifficulty: Hard

PT112 S4 Q14 Explanation

Joseph: My encyclopedia says

A free, expert breakdown of this official LSAT Logical Reasoning question.

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Stimulus

Joseph: My encyclopedia says that the mathematician Pierre de Fermat died in 1665 without leaving behind any written proof for a theorem that he claimed nonetheless to have proved. Probably this alleged theorem simply cannot be proved, since—as the article points out—no one else has been able to prove lying or else mistaken when he made his claim.

Laura: Your encyclopedia is out of date. Recently someone has in fact proved Fermat’s theorem. And since the theorem is provable, your or mistaken—clearly is wrong.

What this question is testing

Flaw

Conclusion (Laura)

Laura is pushing back at Joseph:

Evidence

Her only evidence is that someone, recently, proved the theorem.

Evaluate

Here's the gap. For Fermat to have actually proved the theorem in the 1600s, the theorem had to be provable — that is necessary. But the theorem being provable does not guarantee that Fermat proved it. He could still have been bluffing or mistaken, and centuries later somebody else figures it out.

Think of it this way: to win an Olympic gold, the event has to actually exist. But the event existing does not prove that you won gold. Laura is treating a "the prize is winnable" fact as if it settled "this person won the prize."

Goal

The right answer will say Laura confuses something necessary for her conclusion with something that would actually guarantee it.

Reading along? Open the full official question in LawHub — we show a fragment here and keep the reasoning in our own words.

The question
14.

Which one of the following most accurately describes a reasoning error in

Answer choices

  1. Self-Contradiction10% picked this

    It purports to establish its conclusion by making a claim that, if true, would actually

    This answer accuses Laura of using a claim that, if true, would contradict her conclusion. Nothing about "the theorem has been proved" contradicts "Fermat was not lying or mistaken." If anything, it is offered as support — weak support, but not contradictory. The flaw is overreach, not self-contradiction.

  2. Bad Description3% picked this

    It mistakenly assumes that the quality of a person’s character can legitimately be taken to guarantee the accuracy of the

    Laura never appeals to Fermat's character to vouch for his claim. Her evidence is purely about whether the theorem itself is provable, not whether Fermat was the kind of person who would tell the truth. This describes an entirely different argument.

  3. Correct63% picked this

    It mistakes something that is necessary for its conclusion to follow for something that ensures

    Why this is right

    This is the move precisely. For Fermat to have legitimately proved the theorem, the theorem had to be provable — that is necessary. But provability alone does not guarantee that Fermat himself produced a valid proof. Laura takes the necessary condition (the theorem is provable, as established by today's proof) and treats it as sufficient to conclude that Fermat was not lying or mistaken. He could still have been wrong about having a proof; provability and Fermat's actual proof are two different things.

    Skill tested: Flaw · how this choice captures the argument's function is the move to repeat next time.

  4. Bad Description1% picked this

    It uses the term “provable” without

    The word "provable" is used in its ordinary mathematical sense — capable of being proved — and Laura's argument does not turn on a hidden ambiguity in that term. The flaw is logical (necessary vs. sufficient), not linguistic. Demanding a definition would not fix anything.

  5. Bad Description23% picked this

    It fails to distinguish between a true claim that has mistakenly been believed to be false and a false claim that has

    This is a fancy-sounding distinction that does not match the argument. Laura is not confusing two kinds of mistaken belief. She is treating one fact (the theorem is provable) as proof of a different claim (Fermat himself produced the proof). That is a necessary-vs.-sufficient slip, not a true/false confusion about the theorem's status.

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