Write a short note on the mood and figure of the following arguments. Find out the formal fallacy committed by these arguments : All household pets are harmless animals. No unicorns are harmless animals. Therefore, some unicorns are not household pets.

Mood and Figure in Categorical Syllogisms: Identifying a Fallacy

Categorical syllogisms, characterized by mood and figure, are essential tools in formal logic. They help assess the validity of arguments and uncover potential fallacies. Let's delve into the mood and figure of the given argument and pinpoint the committed fallacy.

1. Mood and Figure:

Breaking down the provided argument:

• Mood:

  • Premise 1: All household pets are harmless animals. (A)
  • Premise 2: No unicorns are harmless animals. (E)
  • Conclusion: Therefore, some unicorns are not household pets. (O)

• Figure:

  • The middle term (harmless animals) appears in both premises, connecting the major term (household pets) and minor term (unicorns).

The mood of this syllogism is AEO, and the figure is the first figure, as the middle term (harmless animals) appears in the subject of the major premise and the predicate of the minor premise.

2. Analysis of the Argument:

The argument, "All household pets are harmless animals. No unicorns are harmless animals. Therefore, some unicorns are not household pets," commits a formal fallacy known as the fallacy of illicit major. This fallacy occurs when the middle term (harmless animals) is distributed in the conclusion but not in the major premise.

• In the major premise (All household pets are harmless animals), the term "harmless animals" is not distributed because it refers only to household pets.
• In the minor premise (No unicorns are harmless animals), the term "harmless animals" is distributed because it refers to all unicorns.

However, in the conclusion, the term "harmless animals" is distributed, stating "some unicorns are not household pets." This violates the rules of valid categorical syllogisms.

3. Correction:

To rectify the fallacy, the argument needs to ensure that the middle term is distributed in at least one of the premises. For instance, the major premise could be modified to "All harmless animals are household pets," ensuring the distribution of the middle term and preserving logical coherence.

Understanding the principles of mood and figure is crucial for constructing valid categorical syllogisms. The fallacy of illicit major in the given argument emphasizes the importance of proper distribution of terms to ensure logical validity and avoid erroneous conclusions.

In conclusion, dissecting the mood and figure of categorical syllogisms provides a structured approach to evaluating their logical soundness. Recognizing and addressing formal fallacies enhance our ability to engage in rigorous and valid reasoning.