Knowlet

Unit 4: Categorical Syllogisms

The formal analysis of deductive arguments consisting of three propositions.

Table of Contents

1. Structure of a Syllogism

A categorical syllogism is a deductive argument in which a conclusion is inferred from two premises. It must contain exactly three categorical propositions (A, E, I, or O).

Major Premise: All mammals are mortal.
Minor Premise: All dogs are mammals.
Conclusion: Therefore, all dogs are mortal.

2. The Three Terms

Every valid syllogism contains exactly three terms, each occurring twice across the propositions.

Term Name Definition Location
Major Term (P) The predicate of the conclusion. Found in Major Premise and Conclusion.
Minor Term (S) The subject of the conclusion. Found in Minor Premise and Conclusion.
Middle Term (M) The term that connects the premises. Found in both premises, but never in the conclusion.

3. Figures and Moods

Figure: Determined by the position of the Middle Term (M) in the premises.

Mood: Determined by the types of propositions (A, E, I, O) used. For example, a syllogism with two 'A' premises and an 'A' conclusion has the mood AAA.

4. General Rules of Validity

For a syllogism to be formally valid, it must obey these six fundamental rules:

  1. A syllogism must contain exactly three terms used in the same sense.
  2. The Middle Term must be distributed at least once in the premises.
  3. If a term is distributed in the conclusion, it must be distributed in the premise where it occurs (Rule of Illicit Process).
  4. No conclusion can be drawn from two negative premises.
  5. If one premise is negative, the conclusion must be negative.
  6. From two particular premises (I or O), no conclusion can be drawn.

5. Formal Fallacies

Breaking any of the rules above results in a Formal Fallacy. Common ones include:

  • Fallacy of Four Terms (Quaternio Terminorum): Using four terms instead of three.
  • Undistributed Middle: When the Middle Term is not distributed in either premise.
  • Illicit Major/Minor: When a term is distributed in the conclusion but not in the premise.
  • Fallacy of Exclusive Premises: Drawing a conclusion from two negative premises.

Exam Essentials

  • Identifying Terms: Always identify the conclusion first. Its subject is 'S' and its predicate is 'P'. The remaining term in the premises is 'M'.
  • Standard Form: Ensure the Major Premise is listed first, followed by the Minor Premise, then the Conclusion.
  • Validity Testing: Be prepared to test a given syllogism by checking all six rules. If it passes all, it is valid.

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