Determining if a Statement Contains Faulty Logic

How to Determine if a Statement Contains Faulty Logic

Step 1: Rewrite the statement in "If-then" format.

Step 2: Identify the hypothesis and conclusion of the logical statement.

Step 3: Ask questions about the hypothesis and conclusion of the statement. Consider whether there are more options. enough information, etc. Then determine which, if any, of the common faulty logic/logical fallacies are present in the statement.

What is Faulty Logic?

Hypothesis: The hypothesis of a logical statement is the premise or known information with which we begin. When written in "if-then" format, the hypothesis is the phrase that follows the word "if" and stops right before the word "then."

Conclusion: The conclusion of a logical statement is the fact (conclusion) we draw as a result of the hypothesis holding true. When written in "if-then" format, the conclusion is the phrase that follows the word "then."

Faulty Logic: Faulty logic is often referred to as logical fallacies. These are instances in which a claim or conclusion is made based on unsound arguments.

Hasty Generalization: A hasty generalization occurs when a conclusion is drawn from not enough information.

Circular Reasoning: Circular reasoning occurs when the conclusion is also the starting point. Mathematically, this means because we have A, we can conclude B and because we have B we can conclude A.

False Cause: A false cause fallacy occurs when an event, A, is concluded to be the cause of another event, B, simply because A happened first.

Limited Choice: In a limited choice, the options are boiled down to very few options that are often unrelated and not the only options.

Let's practice identifying faulty logic/fallacies by working through two examples.

Examples for Determining if a Statement Contains Faulty Logic

Example 1

Ben got a good grade on his last math test because Ben is good at math. Determine which fallacy the statement contains.

Step 1: Rewrite the statement in "If-then" format.

We rewrite the statement as "If Ben got a good grade on his last math test, then Ben is good at math."

Step 2: Identify the hypothesis and conclusion of the logical statement.

The hypothesis of the statement is "Ben got a good grade on his last math test" and the conclusion is "Ben is good at math."

Step 3: Ask questions about the hypothesis and conclusion of the statement. Consider whether there are more options. enough information, etc. Then determine which, if any, of the common faulty logic/logical fallacies are present in the statement.

Working through some of the common logical fallacies, we can see this is not a case of a false cause or a limited choice. The statement is not implying unrelated events are related simply because of the order in which they occurred, so we are not dealing with a false cause. The statement is not a limited choice, as the options have not been arbitrarily reduced. The statement could be a hasty generalization, but since we're speaking specifically of Ben and not a group, it's probably not a hasty generalization. This leaves circular reasoning. In circular reasoning, we start with our conclusion and draw the same conclusion. We say that Ben got a good grade on his test because he is good at math. This reasoning has us wondering "how can we be sure?" What if Ben struggles with math, but worked really hard to do well on this particular test? We are using the conclusion "Ben is good at math" to justify the hypothesis "Ben got a good grade on his last math test" and the hypothesis to justify the conclusion. Therefore, the statement "Ben got a good grade on his last math test because Ben is good at math" contains the logical fallacy of circular reasoning.

Example 2

Jennifer did not enjoy the food at the two restaurants in which she ate in Springfield. Therefore, there are no good restaurants in Springfield.

Step 1: Rewrite the statement in "If-then" format.

If Jennifer did not enjoy the food at the two restaurants in which she ate in Springfield, then there are no good restaurants in Springfield.

Step 2: Identify the hypothesis and conclusion of the logical statement.

Hypothesis: Jennifer did not enjoy the food at the two restaurants in which she ate in Springfield

Conclusion: There are no good restaurants in Springfield

Step 3: Ask questions about the hypothesis and conclusion of the statement. Consider whether there are more options. enough information, etc. Then determine which, if any, of the common faulty logic/logical fallacies are present in the statement.

We can discard the fallacies of circular reasoning and false cause. The statement neither uses the hypothesis to justify the conclusion and vice versa nor claims one event caused another unrelated event. We are not dealing with a limited choice, as we haven't narrowed any choices arbitrarily or otherwise. This leaves the fallacy of hasty generalization. The restaurant sample size in the statement is only 2 restaurants. There is not a sufficient sample size to claim there are no good restaurants in an entire city. Therefore, the statement makes use of the logical fallacy of hasty generalization.