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# The Writer’s Reference Book

### Module N – Deductive Reasoning – Hint Sheet

Deduction is a reasoning process that proceeds from a general statement or a general law and leads to a specific and necessary conclusion.

The Categorical Syllogism is a structured deduction.

Categorical Statements place their subjects into larger classes or categories.

A categorical syllogism has three parts:

1. Major Premise – a proposition which states that ALL members of a given category are included in a larger category.
2. Minor Premise – a proposition identifying a particular case as a member of the general class.
3. Conclusion – states that what is true of all members must be true of one member of the general class.

#### The Syllogism as a Formula

• Major Premise: A = B All CATS are FURRY ANIMALS.
• Minor Premise: C = A MORRIS is a CAT.
• Conclusion: C = B Therefore, MORRIS is a FURRY ANIMAL.

#### Tests for Validity

Validity is concerned with the structure of the argument.

Truth is concerned with the factual content of the argument.

• Rule 1: The statement of the Major Premise must be clear and precise.
• Rule 2: There must be three and only three terms in a categorical syllogism.
• Rule 3: Only one premise can be negative. And if either premise is negative, then the conclusion must be negative.
• Rule 4: The relationships among all three terms of a categorical syllogism must be so definite and certain as to allow only one possible conclusion.
• Rule 4a: In a positive categorical syllogism, the term which appears in both the major and minor premises must be the category in one premise and the subject in the other.
• Rule 4b: In a negative categorical syllogism, the term which appears in both the major and minor premises must be the category in the positive premise.

#### Other Forms of the Syllogism

Alterative Syllogisms (either/or) – Alternative syllogisms are easily identifiable because the major premise will always contain the two key terms either and or.

The Exclusive Alternate Syllogism presents alternatives of which only one can be true.

The Hypothetical Syllogism presents a set of conditions which, if met, will cause a specific and necessary result (if ... then)

• The Major Premise states conditions & results (If A, then B).
• The Minor Premise demonstrates satisfaction of the conditions (A).
• The Conclusion reaffirms the results (B).

#### Other Deductive Forms

The Enthymeme is an abbreviated form of the syllogism used in everyday discourse and based upon unexpressed but commonly shared assumptions.

The Chain of Deduction is a complex series of deductions of which only the conclusion is expressed.