LSAT Question Stem

The conclusion follows logically if which one of the following is assumed? 

Logical Reasoning Question Type

This is a Sufficient Assumption question. 

Correct Answer

The correct answer to this question is E. 

LSAT Question Complete Explanation

First, let's analyze the argument in the passage. The passage states:

Premise: No mathematical proposition can be proven true by observation.

Conclusion: It is impossible to know any mathematical proposition to be true.

Now, let's simplify this argument using a relatable example. Imagine you have a box of different shapes, and you can only identify a shape by touching it (observation). The argument states that you cannot prove a mathematical proposition (e.g., a specific shape) to be true just by touching it. Therefore, it is impossible to know for certain what shape you have in your hand.

The question type is a Sufficient Assumption question, which asks us to find an answer choice that, if assumed, would make the conclusion logically follow from the premise.

Before discussing the answer choices, let's create an "Evaluate" question for the argument: "Is observation the only way to know a mathematical proposition to be true?"

Now, let's analyze each answer choice:

a) Only propositions that can be proven true can be known to be true.

This answer choice is not sufficient because it does not specify that observation is required to prove a proposition true. It is too broad and does not address the specific method of proving mathematical propositions true.

b) Observation alone cannot be used to prove the truth of any proposition.

This answer choice weakens the argument as it implies that observation cannot be used for any proposition, not just mathematical ones. It does not help in establishing a connection between observation and knowing mathematical propositions to be true.

c) If a proposition can be proven true by observation, then it can be known to be true.

This answer choice reverses the logic of the argument. It states that observation is sufficient for knowing a proposition to be true, but it does not address the necessity of observation for knowing mathematical propositions to be true.

d) Knowing a proposition to be true is impossible only if it cannot be proven true by observation.

This answer choice is a mistaken negation of the correct answer. It implies that the only situation in which knowing a proposition to be true is impossible is when it cannot be proven true by observation. This does not help establish the necessity of observation for knowing mathematical propositions to be true.

e) Knowing a proposition to be true requires proving it true by observation.

This is the correct answer. It establishes that observation is necessary for knowing a proposition to be true, thus connecting the premise and conclusion of the argument.

In conclusion, the correct answer is E, as it provides the necessary assumption that observation is required for knowing a mathematical proposition to be true, making the conclusion logically follow from the premise.