Lesson 2.2: Assumptions and the Logical Gap

Introduction

In this lesson, we will explore the critical concepts of assumptions within arguments and how they create logical gaps between premises and conclusions. Understanding assumptions is essential for developing strong analytical skills, particularly as they relate to Logical Reasoning on the LSAT. We will thoroughly examine what an assumption is, how to identify it, and how to distinguish between necessary and sufficient assumptions. By the end of this lesson, you will be equipped to assess arguments effectively and improve your critical reasoning skills.

Learning Objectives

Understand what an assumption is and how to find the gap between premises and conclusions.
Differentiate between necessary assumptions and sufficient assumptions.
Identify the unstated assumptions upon which arguments depend.
Distinguish a necessary assumption from a sufficient one in various arguments.
Explain the main ideas and terminology related to assumptions and logical gaps.

What is an Assumption?

An assumption is an unstated premise that must be true for an argument's conclusion to hold. It serves as the logical bridge that connects the premises to the conclusion. When evaluating an argument, it is crucial to identify assumptions to determine the strength and validity of the reasoning presented.

Recognizing the Logical Gap

The logical gap occurs when an argument's conclusion does not logically follow from its stated premises without the assumptions. To find this gap, we must analyze the structure of the argument closely.

Example:

Premise 1: All humans are mortal.

Premise 2: Socrates is a human.

Conclusion: Therefore, Socrates is mortal.

In this simple argument, there are no assumptions needed. However, consider this:

Premise 1: If it rains, the ground will be wet.

Premise 2: The ground is wet.

Conclusion: Therefore, it rained.

Here, there is a logical gap. For the conclusion to be valid, we must assume that wet ground is only the result of rain, which is not explicitly stated. This assumption may lead to other alternatives that cause the ground to be wet (e.g., watering the lawn, someone spilling a drink).

Necessary vs. Sufficient Assumptions

To evaluate arguments more effectively, we differentiate between necessary and sufficient assumptions.

Necessary Assumptions

A necessary assumption is one that must be true for the conclusion to be valid. If a necessary assumption is false, the conclusion cannot be logically derived, making the argument invalid.

Example of Necessary Assumption:

Argument: If A is true, then B must also be true.

Premise: If it is cloudy, it will rain.
Conclusion: Therefore, it must be raining.

To validate this conclusion, we need the necessary assumption that cloudy skies always result in rain. If this assumption is false (e.g., it is cloudy but there is no rain), the conclusion becomes invalid.

Sufficient Assumptions

A sufficient assumption is one that, if true, guarantees that the conclusion is also true. This type of assumption supports the argument but is not essential for its validity.

Example of Sufficient Assumption:

Argument: If the package is delivered, then the customer will be happy.

Premise: The package was delivered.
Conclusion: The customer is happy.

In this case, the assumption that the delivery is satisfactory (the package is not damaged, the customer wanted it) is a sufficient assumption. Even if it were false, the conclusion might still stand valid.

Identifying Assumptions in Arguments

To identify assumptions in arguments, follow these steps:

Identify the conclusion: Determine what the argument is trying to prove.
Identify the premises: What evidence is provided?
Analyze the relationship: Look for gaps between the premises and the conclusion.
Formulate assumptions: Ask yourself, "What must be true for the conclusion to follow from the premises?"

Example:

Argument: Many students who attend tutoring sessions improve their grades. Therefore, attending tutoring sessions improves students' grades.

Conclusion: Tutoring improves grades.
Premise: Many students who attend tutoring sessions improve their grades.

Identifying the Assumption: The unstated assumption might be that the only factor affecting grades is the tutoring itself and not the student's initial skill level or study habits.

Common Misconceptions

Misconception: An assumption is always a false statement.

Clarification: An assumption can be either true or false, but it must be accepted for the argument’s conclusion to hold.

Misconception: All assumptions are necessary.

Clarification: Some assumptions are sufficient but not necessary; they can support conclusions but are not essential for validity.

Misconception: An argument with true premises must have a true conclusion.

Clarification: True premises do not guarantee a true conclusion without valid reasoning and correct assumptions.

Conclusion

In this lesson, we have dissected the important role that assumptions play in the structure of arguments and their relationship to logical gaps. Understanding how to identify necessary and sufficient assumptions is crucial for critical reasoning and will significantly enhance your performance on the LSAT. As you practice, remember to analyze arguments carefully, paying attention to unstated assumptions that might affect validity.

Study Notes

An assumption is an unstated premise in an argument.
The logical gap is the space between premises and conclusions that assumptions fill.
Necessary assumptions must be true for the conclusion to be valid, while sufficient assumptions ensure the conclusion holds but are not essential.
Identify the conclusion first, then examine premises and the relationship to find assumptions.
Be aware of common misconceptions regarding assumptions to strengthen your reasoning skills.