LSAT Explanation PT 30, S4, Q13: Joseph: My encyclopedia says that the

LSAT Question Stem

Joseph's statement that "this alleged theorem simply cannot be proved" plays which one of the following roles in his argument? 

Logical Reasoning Question Type

This is an Argument Part question. 

Correct Answer

The correct answer to this question is B. 

LSAT Question Complete Explanation

Let's first analyze the argument in the passage. Joseph states that since Fermat died without leaving any written proof for his theorem and no one else has been able to prove it, it's likely that the theorem cannot be proved. Based on this, he concludes that Fermat was either lying or mistaken when he claimed to have proved the theorem. Laura, on the other hand, argues that Joseph's encyclopedia is out of date and that Fermat's theorem has been recently proved. She concludes that Joseph's claim that Fermat was lying or mistaken is wrong.

In Joseph's argument, the statement "this alleged theorem simply cannot be proved" is a subsidiary conclusion that supports his main conclusion that Fermat was either lying or mistaken. The premise supporting this subsidiary conclusion is that no one else has been able to prove the theorem.

Now let's identify the question type and discuss the answer choices. The question type is Argument Part, asking us to identify the role played by Joseph's statement in his argument.

a) an assumption for which no support is offered: This is incorrect because an assumption is always unstated, and Joseph's statement is explicitly stated. Moreover, his statement is supported by the fact that no one else has been able to prove the theorem.

b) a subsidiary conclusion on which his argument's main conclusion is based: This is the correct answer. Joseph's statement serves as a subsidiary conclusion that supports his main conclusion that Fermat was either lying or mistaken.

c) a potential objection that his argument anticipates and attempts to answer before it is raised: This is incorrect because Joseph's statement is not addressing a potential objection but rather supporting his main conclusion.

d) the principal claim that his argument is structured to refute: This is incorrect because Joseph's statement is not the main conclusion that his argument is trying to refute; it is a subsidiary conclusion that supports his main conclusion.

e) background information that neither supports nor undermines his argument's conclusion: This is incorrect because Joseph's statement is not merely background information but serves as a subsidiary conclusion that supports his main conclusion.

In summary, Joseph's statement that "this alleged theorem simply cannot be proved" plays the role of a subsidiary conclusion on which his argument's main conclusion is based, making answer choice B the correct one.