Unit 3: Mediate Inference and Syllogism

1. Introduction to Mediate Inference
2. Categorical Syllogism: Structure and Rules
3. Figure and Mood of Syllogism
4. Copi's Six Rules for Validity
5. Venn Diagram Techniques for Testing
6. Exam Essentials & Fallacies

Introduction to Mediate Inference

Mediate Inference is a type of deductive reasoning where a conclusion is derived from more than one premise. Unlike immediate inference, which moves from a single premise directly to a conclusion, mediate inference requires a "middle" ground to connect the terms of the argument.

The most common form of mediate inference is the Categorical Syllogism, which consists of exactly two premises and one conclusion.

Categorical Syllogism: Structure

A standard-form categorical syllogism contains three categorical propositions and three distinct terms, each appearing exactly twice in the argument.

The Three Terms

Major Term (P): The predicate of the conclusion.
Minor Term (S): The subject of the conclusion.
Middle Term (M): The term that appears in both premises but never in the conclusion.

The Two Premises

Major Premise: Contains the major term and the middle term.
Minor Premise: Contains the minor term and the middle term.

Figure and Mood of Syllogism

The logical form of a syllogism is uniquely identified by its Mood and Figure.

1. Mood

The mood is determined by the types (A, E, I, or O) of the categorical propositions it contains in order. For example, if both premises and the conclusion are universal affirmatives, the mood is AAA.

2. Figure

The figure refers to the position of the Middle Term (M) in the premises. There are four possible figures:

Figure	Major Premise	Minor Premise	M-Position Description
First	M - P	S - M	M is Subject in Major, Predicate in Minor.
Second	P - M	S - M	M is Predicate in both premises.
Third	M - P	M - S	M is Subject in both premises.
Fourth	P - M	M - S	M is Predicate in Major, Subject in Minor.

Copi’s Six Rules for Testing Validity

Irving Copi provided six essential rules to determine if a categorical syllogism is valid. Violating any of these results in a specific formal fallacy.

Rule 1: A valid categorical syllogism must contain exactly three terms, each used in the same sense throughout.
Fallacy: Fallacy of Four Terms (Quaternio Terminorum).
Rule 2: The middle term must be distributed in at least one premise.
Fallacy: Undistributed Middle.
Rule 3: If a term is distributed in the conclusion, it must be distributed in the premises.
Fallacy: Illicit Process (Illicit Major or Illicit Minor).
Rule 4: No categorical syllogism with two negative premises is valid.
Fallacy: Fallacy of Exclusive Premises.
Rule 5: If either premise is negative, the conclusion must be negative.
Fallacy: Fallacy of drawing an Affirmative conclusion from a Negative premise.
Rule 6: From two universal premises, no particular conclusion can be drawn (in modern Boolean interpretation).
Fallacy: Existential Fallacy.

Venn Diagram Technique

The Venn Diagram technique is a graphical method used to test the validity of categorical syllogisms by representing the relationships between the three classes: S, P, and M.

Execution Steps:

Draw three overlapping circles representing S, P, and M.
Diagram the universal premises first (shading the empty areas).
Diagram particular premises (placing an 'X' in the relevant area).
Test of Validity: If, after diagramming both premises, the conclusion is already represented in the diagram, the syllogism is Valid. If not, it is Invalid.

Exam Essentials: Tips & Pitfalls

Exam Tip: Always look for the Middle Term (M) first. It is the bridge. If it doesn't appear in both premises, it isn't a syllogism!
Common Mistake: Confusing "Illicit Major" with "Illicit Minor." Remember: Illicit Major occurs when the major term is distributed in the conclusion but not in the premise.
Mnemonic: To remember the 4 Figures, visualize the shape made by 'M':
- Fig 1: \ (Top Left to Bottom Right)
- Fig 2: | (Both on Right)
- Fig 3: | (Both on Left)
- Fig 4: / (Top Right to Bottom Left)
FAQ: Why is AAA-2 invalid?
Because M is the predicate in both premises (Fig 2). In 'A' propositions, the predicate is not distributed. Thus, M is never distributed, violating Rule 2 (Undistributed Middle).