Syllogistic Patterns and Valid Moods

Logical Syllogisms

Introduction to Syllogisms

Syllogisms are structured forms of reasoning consisting of premises and a conclusion that derive logical inferences. Each syllogism involves a major premise, a minor premise, and a conclusion, typically represented in standard forms.

Figure 1 Pattern

• Major Premise: M - P
• Minor Premise: S - M
• Conclusion: S - P
• Valid Moods:
    - Barbara (AAA)
    - Celarent (EAE)
    - Darii (AII)
    - Ferio (EIO)

Figure 2 Pattern

• Major Premise: P - M
• Minor Premise: S - M
• Conclusion: S - P
• Valid Moods:
    - Cesare (EAE)
    - Camestres (AEE)
    - Festino (EIO)
    - Baroco (AOO)

Figure 3 Pattern

• Major Premise: M - P
• Minor Premise: M - S
• Conclusion: S - P
• Valid Moods:
    - Darapti (AAI)
    - Disamis (IAI)
    - Datisi (AII)
    - Felapton (EAO)
    - Bocardo (OAO)
    - Ferison (EIO)

Figure 4 Pattern

• Major Premise: P - M
• Minor Premise: M - S
• Conclusion: S - P
• Valid Moods:
    - Bramantip (AAI)
    - Camenes (AEE)
    - Dimaris (IAI)
    - Fesapo (EAO)
    - Fresison (EIO)

Summary of Moods

• AAA: Barbara
• EAE: Celarent, Cesare
• AII: Darii, Datisi
• EIO: Ferio, Festino, Ferison
• AOO: Baroco
• AAI: Darapti, Bramantip
• IAI: Disamis, Dimaris
• EAO: Felapton, Fesapo
• OAO: Bocardo

Application of Syllogisms

Understanding these patterns and moods is crucial for logical reasoning, argumentation, and philosophy. Knowing how to form valid syllogisms assists in evaluating the soundness of arguments in various fields such as law, ethics, and logic itself.