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Chapter 6: Problem 23

A poor farmer was fond of telling his children: "In this world, you are either rich or poor, and you are either honest or dishonest. All poor farmers are honest. Therefore, all rich farmers are dishonest." The farmer's conclusion is properly drawn if the argument assumes that (A) every honest farmer is poor (B) every honest person is a farmer (C) everyone who is dishonest is a rich farmer (D) everyone who is poor is honest (E) every poor person is a farmer

Short Answer

Expert verified
The correct assumption is (A) every honest farmer is poor.

Step by step solution

01

Understanding the Premise

The farmer makes two key claims: all poor farmers are honest, and he concludes that all rich farmers are dishonest. We need to find the assumption that allows this conclusion to be properly drawn from these claims.
02

Analyzing the Conclusion

The conclusion by the farmer is that 'all rich farmers are dishonest.' For this to hold valid from the premise, the logic must inherently connect poverty with honesty and richness with dishonesty in a necessary and mutually exclusive manner.
03

Evaluating the Options

Look at option (A): It states that every honest farmer is poor. This creates a direct link that the only way a farmer can be honest is if they are poor, implying rich farmers cannot be honest and thus must be dishonest. This supports the conclusion drawn by the farmer. Option (B): It incorrectly broadens the scope to include all honest people as farmers, which isn't directly related to the farmer's conclusion about rich and poor farmers. Option (C): Assumes all dishonest individuals are rich farmers but does not directly relate to the given premise about poor and rich. Option (D): Suggests everyone poor is honest but does not establish the necessity of rich farmers being dishonest. Option (E): Incorrectly limits the category of poor to farmers, failing to address rich farmers' honesty.
04

Deriving the Correct Assumption

Given the analysis, the assumption in option (A) serves as the missing link to logically deduce the farmer's conclusion. If every honest farmer is indeed poor, then any farmer who is not poor (i.e., rich) must be dishonest, supporting the conclusion.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Argument Analysis
The first step in understanding logical reasoning exercises such as this one is to perform a thorough analysis of the argument presented. Here, we encounter a statement made by a farmer about the honesty of farmers based on their economic status鈥攚hether they are rich or poor.
The argument begins with the assertion that all poor farmers are honest. Consequently, the farmer makes a sweeping conclusion that all rich farmers are dishonest.
To analyze this argument effectively, it's vital to identify:
  • The claims made (premises)
  • The conclusion derived
By breaking down the argument into these components, we can understand the structure and intention behind it.
Premise Evaluation
Evaluating the premises of an argument is crucial as they form the foundation on which the conclusion rests. In the given scenario, the premise states all poor farmers are honest. This serves as the primary basis for the argument.
When evaluating premises, consider if they adequately support the conclusion. Here, the farmer believes the premise leads directly to the conclusion that all rich farmers must be dishonest.
However, premises need to be:
  • Clear and unambiguous
  • Relevant to the conclusion
  • Necessary and sufficient for the conclusion
In this exercise, the premise alone doesn鈥檛 logically lead to the conclusion. Therefore, the relationship between poverty and honesty needs further inspection before accepting the conclusion.
Conclusion Drawing
Drawing a conclusion is where the argument effectively ties together the premises to make a logical deduction. In this example, the farmer concludes that all rich farmers are dishonest.
This conclusion appears to stem directly from the premise about poor farmers being honest. However, for clear conclusion drawing, it鈥檚 imperative to have a logical and necessary linkage between the premises and the conclusion.
The farmer's conclusion fails unless there's an underlying assumption that bridges the logical gap. This is why merely observing that poor farmers are honest doesn鈥檛 suffice to deduce the dishonesty of rich farmers without additional support or assumption.
Assumption Identification
Assumptions are unstated premises that are crucial for an argument鈥檚 conclusion to hold. Identifying these is often where students struggle.
In the context of the farmer's argument, we are looking for an assumption that connects the given premise to the conclusion logically.
After evaluating the options, we find that the critical assumption needed鈥攑resented in option (A)鈥攊s that every honest farmer is indeed poor.
This assumption establishes that rich farmers must lack the honesty that only poor farmers hold, thereby implying they are dishonest. Without identifying this assumption, the conclusion lacks validity.
Looking for such hidden premises is essential in logical reasoning tasks to draw conclusions concretely.

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