Categorical Syllogism and Fallacies
A categorical syllogism is a deductive argument with two premises and a conclusion, all categorical, containing exactly three terms. This domain tests rules of validity, mood and figure, and the standard fallacies that break those rules.
Core rules
- The middle term must be distributed at least once. A term distributed in the conclusion must be distributed in its premise: no illicit major or illicit minor.
- No conclusion follows from two negative premises. If one premise is negative, the conclusion must be negative; if both are affirmative, the conclusion must be affirmative.
- No conclusion follows from two particular premises. If one premise is particular, the conclusion must be particular.
- Mood is the letter sequence of major, minor and conclusion; figure depends on the middle term's position.
Worked example
All poets are imaginative; some writers are poets; therefore some writers are imaginative. Terms: imaginative = P, writers = S, poets = M. Major premise is All M are P (A); minor is Some S are M (I); conclusion is Some S are P (I). Mood AII, figure 1, traditionally Darii. The middle term poets is distributed in the major premise, and no term is illicitly distributed. The argument is valid.
Traps
The undistributed middle is the classic error: All dogs are mammals; all cats are mammals; therefore all cats are dogs. Watch illicit process of the major or minor. Do not draw a negative conclusion from two affirmative premises. Do not ignore the difference between contrary and contradictory premises when testing validity.