Analyzing the Figure and Mood of a Syllogistic Argument

To correctly represent the figure and mood of a syllogistic argument, we need to identify the type of each proposition (its quantity and quality) and the position of the middle term in the premises.

Steps to Determine Figure and Mood

Let's break down the given argument:

Premise 1: All businessmen are self-confident

Premise 2: No self-confident men are religious

Conclusion: Therefore, No religious men are businessmen

Step 1: Identify the Subject, Predicate, and Middle Terms

• The Major Term (P) is the predicate of the conclusion. In this case, it is 'businessmen'.
• The Minor Term (S) is the subject of the conclusion. In this case, it is 'religious men' (or 'religious').
• The Middle Term (M) is the term that appears in both premises but not in the conclusion. In this case, it is 'self-confident men' (or 'self-confident').

Let's rewrite the argument using the identified terms:

• Premise 1: All P are M (All businessmen are self-confident)
• Premise 2: No M are S (No self-confident are religious) - Note: We swap S and P from the conclusion's perspective to match the premise terms. So S is religious, P is businessmen, M is self-confident.
• Conclusion: No S are P (No religious are businessmen)

Step 2: Determine the Mood of the Syllogism

The mood is determined by the type of each proposition (Universal Affirmative - A, Universal Negative - E, Particular Affirmative - I, Particular Negative - O) in the order: Premise 1, Premise 2, Conclusion.

• Premise 1: "All businessmen are self-confident" is a Universal Affirmative proposition (A).
• Premise 2: "No self-confident men are religious" is a Universal Negative proposition (E).
• Conclusion: "No religious men are businessmen" is a Universal Negative proposition (E).

So, the mood of the argument is AEE.

Step 3: Determine the Figure of the Syllogism

The figure is determined by the position of the Middle Term (M) in the two premises. There are four possible figures:

• Figure I: M - P, S - M
• Figure II: P - M, S - M
• Figure III: M - P, M - S
• Figure IV: P - M, M - S

In our argument:

• Premise 1: All businessmen (P) are self-confident (M). The Middle Term (M) is the predicate.
• Premise 2: No self-confident (M) are religious (S). The Middle Term (M) is the subject.

The position of the Middle Term is Predicate in Premise 1 and Subject in Premise 2. This corresponds to Figure IV (P - M, M - S).

Step 4: Combine Mood and Figure

The combined figure and mood of the argument is AEE - IV.

Based on the analysis:

• Mood: AEE (A from Premise 1, E from Premise 2, E from Conclusion)
• Figure: IV (Middle Term is Predicate in Premise 1, Subject in Premise 2)

Thus, the correct representation is AEE - IV.

Revision Table: Syllogism Figure and Mood

Additional Information: Categorical Propositions (A, E, I, O)

Understanding the types of categorical propositions is crucial for determining the mood of a syllogism.

• A (Universal Affirmative): All S are P. States that every member of the subject class is a member of the predicate class.
• E (Universal Negative): No S are P. States that no member of the subject class is a member of the predicate class.
• I (Particular Affirmative): Some S are P. States that at least one member of the subject class is a member of the predicate class.
• O (Particular Negative): Some S are not P. States that at least one member of the subject class is not a member of the predicate class.

Identifying these types for each part of the syllogism (both premises and the conclusion) gives you the mood, which is the first part of the answer.