Illicit Minor

Taxonomy: Logical Fallacy > Formal Fallacy > Syllogistic Fallacy > Illicit Process > Illicit Minor

Sibling Fallacy: Illicit Major

Alias: Illicit Process of the Minor Term

Form:

Any form of categorical syllogism in which the minor term is distributed in the conclusion but not in the minor premiss.

Example Counter-Example
All Marxists are communists.
All communists are socialists.
Therefore, all socialists are Marxists.
All whales are mammals.
All mammals are animals.
Therefore, all animals are whales.
Venn diagram

Venn Diagram:

This diagram represents both the Example and Counter-Example. It does not show the conclusion, "All S is P", to be true, which shows that both arguments are invalid.

Exposition:

"Illicit minor" does not refer to underage drinking, but to an illicit process—that is, distribution—of the minor term in a categorical syllogism. The minor term in the Example, above, is "socialists" since it is the subject term of the conclusion. "Socialists" is distributed in the conclusion because the subject term of an A-type proposition is distributed. The minor premiss of the Example is the second premiss, since it contains the minor term. "Socialists" is undistributed in the minor premiss since the predicate term of an A-type proposition is undistributed. Thus, there is an illicit distribution of the minor term in the Example.

The same points apply to the Counter-Example, except that its minor term is "animals". The difference between the Example and the Counter-Example is that the former is intended to be at least somewhat plausible. In contrast, the Counter-Example has obviously true premisses and a clearly false conclusion, which means that it is invalid. However, the Example is also invalid, and whatever plausibility it has probably comes from the fact that its conclusion is true for some senses of the terms "socialist" and "Marxist".

Source:

Irving Copi & Carl Cohen, Introduction to Logic (Tenth Edition) (Prentice Hall, 1998), p. 277.