What is the rule about distributed terms in a valid syllogism?

• A. No term may be distributed in any premise.
• B. Any term distributed in the conclusion must be distributed in at least one premise; otherwise the argument is invalid.
• C. The middle term must be distributed in both premises.
• D. A term distributed in the premises must be undistributed in the conclusion.

Answer: (B)

In syllogistic validity, a term is distributed when we assert something about all of its members. The essential rule is: if a term is distributed in the conclusion, it must be distributed in at least one premise. This guarantees that the universal claim about that term in the conclusion is supported by a premise that distributes that term.

For example, from premises “All Greeks are humans” and “All humans are mortal,” you can conclude “All Greeks are mortal.” The term Greeks is distributed in the conclusion (as the subject of a universal proposition) and is distributed in the second premise as well, so the rule is satisfied.

If you tried to derive “All mortals are Greeks” from the same premises, the term mortals is distributed in the conclusion but is not distributed in any premise (it’s only the predicate in the first premise). That violates the rule and makes the argument invalid, even though the other premise connects the terms.

Other statements about distribution, like requiring the middle term to be distributed in both premises, aren’t correct, and a term distributed in premises isn’t required to be distributed in the conclusion. The key point is the one-way condition: a distributed term in the conclusion must be distributed in at least one premise.