Lesson 14 - Review

Syllogisms: A Review

Agenda

• The Structure of Syllogisms
• Proving Syllogisms

1. Syllogism Form & Structure

The Standard Categorical Syllogism Structure

A standard categorical syllogism consists of:

• 3 Propositions
• 2 Premises
• 1 Conclusion

Standard Form Components:

1. Quantifier _______ copula _______ { Major premise (contains major term)
2. Quantifier _______ copula _______ { Minor premise (contains minor term)
3. Quantifier _______ copula _______ { Conclusion
   • Minor term
   • Major term

Mood

Definition: The order of the categorical propositions (A, E, I, and O) that comprise the premises and the conclusion.

Example:

• Some Marvel movies are not popular titles. → O
• All Marvel movies are expensive productions. → A
• Some expensive productions are not popular titles. → O

Mood: OAO

Figures

Definition: The placement of the middle term in the premises.

Rules of Validity

ดูยังไงว่า Distributed? ก็จำได้มั้ยว่า A จะ ขีดเส้นใต้อันไหนบ้างที่ Distributed

• A distributes Subject
• E distributes Both
• I distributes Neither
• O distributes Predicate???

Distribution Rules:

1. The middle term must be distributed in at least one of the premises.

   • Violation: Undistributed middle term

2. If either the major or the minor term in the conclusion is distributed, it must be distributed in the premise in which it occurs.

   • Violation: Illicit major term, illicit minor term

Negation Rules:

3. The premises cannot both be negative.

   • Violation: Two negative premises

4. If either premise is negative, the conclusion must be negative; and if the conclusion is negative, one premise must be negative.

   • Violations:
     • Negative premise, affirmative conclusion
     • Affirmative premises, negative conclusion

Quantity Rule:

5. If the conclusion is particular, one premise must be particular. [Required only on the modern view of existential import.]
   • Violation: Universal premises, particular conclusion

Reminder on Distributed Terms

Example: "Unprepared Students Never Pass"

Key Rules:

• Universals distribute Subjects → "All" or "No"
• Negatives distribute Predicates → "No" or "is not/are not"

Supplementary Activity A

In your groups of 3-4, create at least one valid syllogism for every form.

Use these terms:

• Subject: LAS101 Topics
• Predicate: Things that need practice

Supplementary Activity B

Swap papers with another group and check each other's syllogisms using the rules of validity.

Instructions:

• Double underline the distributed terms
• Indicate which rules are followed/not followed

2. Syllogism: Proving Validity - The Venn Diagrams

Diagramming the Premises

Example:

• No European cars are Chinese products.
• Some European cars are electric vehicles.
• ∴ Some electronic vehicles are not Chinese products.

Symbolic Form:

• No M are P.
• Some M are S.
• ∴ Some S are not P.

Steps for Diagramming:

A. Diagram the combined premises:

1. Diagram the universal premise first (shade before X)
2. Diagram the particular premise (place the X)
   • 2.1 If a subarea is shaded, the X should avoid it
   • 2.2 If no shaded subareas exist, the X should be on the line separating the unshaded subareas
3. After diagramming the combined premises, check if the premises give you the shaded area or X that you need in the conclusion

[Venn diagram with three circles labeled P, S, M with numbered regions 1-7 and an X marking]

Diagramming the Conclusion

Example:

• No European cars are Chinese products.
• Some European cars are electric vehicles.
• ∴ Some electronic vehicles are not Chinese products.

Symbolic Form:

• No M are P.
• Some M are S.
• ∴ Some S are not P.

Steps for Diagramming:

B. Diagram the conclusion:

1. Diagram the conclusion
2. Compare it with the combined premises
3. It is valid if the combined premises give you the shaded area or the X the conclusion requires

[Venn diagram showing the conclusion validation]

Supplementary Activity C

Instructions:

• Prove the validity of your own syllogism by diagramming it
• Swap your diagrams with another group and check each other's proof/diagram

The ONLY Reasons to Support Your Judgment of Validity

3. Syllogism: Unconditionally Valid Forms - The Boolean Perspective

Aristotelian vs. Boolean Perspective

"The Aristotelian perspective requires that the terms in the syllogism must relate to reality, while the Boolean perspective does not have this requirement—the Boolean perspective results in unconditionally valid forms."

Deductive Reasoning and Patterns

Because deductive reasoning strictly follows rules, it reveals patterns and relationships of ideas.

Following the Boolean perspective, these syllogisms are unconditionally valid:

Unconditionally Valid Forms

Centerpiece Supplementary Activity

The teams must create diagrams of (all or 3) unconditionally valid syllogisms for each form.

Take-aways

The diagrams remind us of the nature of deductive arguments:

• The conclusion only makes explicit what is implicitly given by the premises
• The conclusion cannot give information beyond what the premises gave