Study Moods & Figure - Logical Reasoning Notes

What are mood and Figures?

Mood 

The mood of a categorical syllogism is a series of three letters corresponding to the type of proposition the major premise, the minor premise, and the conclusion is (A, E, I, or O).
Medieval logicians invented a simple method of labelling the various forms in which a categorical syllogism may occur by simply stating its mood and figure.

Categorical propositions are represented by letters: A, E, I, and O.

Figure

It depends on the arrangement of the middle term in the proposition.
The figure of the syllogism is based on the arrangement of Subject and predicate and middle term or the common term.

The different types of figures in syllogism are 

table: M stands for “middle term”, S stands for “subject”, P stands for “predicate”

Exploring the Four Figures with Examples

Figure I

• Middle term: This is the subject of the major premise and the predicate of the minor premise.
• Example: “All philosophers are thinkers. Some thinkers are writers. Therefore, some philosophers are writers.”

Figure II

• Middle term: This is the predicate of both premises.
• Example: “All mammals are animals. Some animals are carnivores. Therefore, some mammals are carnivores.”

Figure III

• Middle term: This is the subject of both premises.
• Example: “Some humans are artists. Some artists are painters. Therefore, some humans are painters.”

Figure IV

• Middle term: This is the predicate of the major premise and the subject of the minor premise.
• Example: “No politicians are honest. Some honest people are activists. Therefore, some activists are not politicians.”

Mood and Figure Combinations

Determining Validity:

• By mixing mood and figure, we can sort syllogisms and check if they are valid or not.
• Each combination of mood and figure has its own rules that tell us if a syllogism is valid or invalid.
• For a syllogism to be valid, it is necessary to have the correct distribution of terms.

Examples of Valid and Invalid Syllogisms:

• A valid syllogism is when the mood is AAA in Figure I, as long as the terms are correctly distributed in the premises.
• Example: “All insects are arthropods. All arthropods have exoskeletons. Therefore, all insects have exoskeletons.”
•  Invalid Syllogism: AAA in Figure III 
• Example: “All mammals are animals. All animals are living beings. Therefore, all mammals are living beings.”
  

The Importance of Mood and Figure in Syllogistic Reasoning

Ensuring Coherence:

• Mood and figure help to clearly organize syllogisms.
• They establish the logical connections in arguments.

Facilitating Critical Thinking:

• Looking at moods and figures improves critical thinking skills.
• This helps to spot logical mistakes and strengthens reasoning abilities.

Mood and Figure: Essential parts of syllogistic reasoning that help us check the validity of arguments. 

• Mood shows how categorical statements are arranged.
• Figure indicates where the middle term is placed.
• By understanding these ideas and how they work together, we can better analyze the logical structure of syllogisms.