Unit 4: Mediate Inference (Syllogism)

Mediate Inference: Categorical Syllogism

As defined in Unit 3, a Mediate Inference is one where the conclusion is drawn from two or more premises.
The most famous type is the Categorical Syllogism.

A Categorical Syllogism is a deductive argument consisting of three categorical propositions (two premises and one conclusion) that together contain exactly three terms.

This is the classic "All men are mortal..." argument structure. Its purpose is to link two terms (S and P) by "mediating" them through a third, common term (M).

Structure of a Syllogism

Let's analyze a standard-form example:

1. All mammals are animals.
2. All dogs are mammals.
3. Therefore, all dogs are animals.

The Three Terms

Each of the three terms appears exactly twice in the syllogism.

1. Major Term (P): The predicate term of the conclusion. (In example: "animals")
2. Minor Term (S): The subject term of the conclusion. (In example: "dogs")
3. Middle Term (M): The term that appears in both premises but not in the conclusion. It is the "mediating" term. (In example: "mammals")

The Three Propositions

• Major Premise: The premise that contains the Major Term (P). (In example: "All mammals are animals.")
• Minor Premise: The premise that contains the Minor Term (S). (In example: "All dogs are mammals.")
• Conclusion: The proposition that is inferred, which always has the form S-P. (In example: "All dogs are animals.")

Standard Form

A syllogism is in "Standard Form" when:

1. The Major Premise is listed first.
2. The Minor Premise is listed second.
3. The Conclusion is listed last.

Example (Standard Form):

• Major Premise: All M are P
• Minor Premise: All S are M
• Conclusion:      All S are P

Mood of Syllogism

The Mood of a syllogism is a statement of the proposition types (A, E, I, O) of its major premise, minor premise, and conclusion, in that order.

Example 1:

• All M are P       (A proposition)
• All S are M       (A proposition)
• All S are P        (A proposition)

The Mood of this syllogism is A-A-A.

Example 2:

• No M are P       (E proposition)
• Some S are M   (I proposition)
• Some S are not P (O proposition)

The Mood of this syllogism is E-I-O.

There are 64 possible moods (4 x 4 x 4), but only a few are valid.

Figure of Syllogism

The Figure of a syllogism is determined by the position of the Middle Term (M) in the two premises.

There are only four possible figures. You must memorize these patterns.

Figure 1	Figure 2	Figure 3	Figure 4
M - P S - M ------- S - P	P - M S - M ------- S - P	M - P M - S ------- S - P	P - M M - S ------- S - P
(M is Subject in major, Predicate in minor)	(M is Predicate in both)	(M is Subject in both)	(M is Predicate in major, Subject in minor)