The formal analysis of deductive arguments consisting of three propositions.
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.
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:
- A syllogism must contain exactly three terms used in the same sense.
- The Middle Term must be distributed at least once in the premises.
- If a term is distributed in the conclusion, it must be distributed in the premise where it occurs (Rule of Illicit Process).
- No conclusion can be drawn from two negative premises.
- If one premise is negative, the conclusion must be negative.
- 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.