In a valid syllogism, which statement is true about the middle term?

• A. It must be distributed in both premises.
• B. It must be non-distributed in any premise.
• C. It must be distributed in at least one premise.
• D. It must not appear in the conclusion.

Answer: (C)

Understanding how the middle term functions is the key. The middle term is the term that appears in both premises but not in the conclusion, and it must be distributed in at least one premise. Distribution means the term is taken to refer to all of its class in that premise. When the middle term is distributed in at least one premise, it provides a definite link that connects the other two terms and makes the conclusion follow (assuming the other rules of syllogism hold).

For example, consider: All M are P, and All S are M. Here the middle term M is distributed in the first premise, establishing that every M is within P. Since every S is M, it follows that every S is P. This shows how the middle term’s proper distribution in at least one premise allows the two outer terms to be linked to yield a valid conclusion.

If the middle term were not distributed in any premise, the link between the outer terms isn’t guaranteed, and you could end up with an undistributed middle that does not support a solid conclusion.