Syllogistic Figure

Understanding Syllogistic Figures

A syllogistic figure is the arrangement of the middle term within the two premises of a categorical syllogism. This arrangement dictates the logical structure and potential validity of the argument. There are four historically recognized figures.

The Four Figures

• Figure 1: Middle term is the subject of the major premise and the predicate of the minor premise (M-P, S-M).
• Figure 2: Middle term is the predicate in both premises (P-M, S-M).
• Figure 3: Middle term is the subject in both premises (M-P, M-S).
• Figure 4: Middle term is the predicate of the major premise and the subject of the minor premise (P-M, M-S).

Importance of Figure

The figure is crucial because it, along with the mood (the types of propositions used), determines the validity of the syllogism. Different figures have different sets of valid moods.

Examples

Figure 1 Example:
All men are mortal. (Major Premise: M-P)
Socrates is a man. (Minor Premise: S-M)
Therefore, Socrates is mortal. (Conclusion: S-P)

Figure 2 Example:
No reptiles have fur. (Major Premise: P-M)
All snakes have scales. (Minor Premise: S-M)
Therefore, no snakes are reptiles. (Conclusion: S-P)

Conclusion

Mastering syllogistic figures is fundamental to understanding and constructing valid logical arguments in classical logic.