Is it valid to have two negative premises in a syllogism?

• A. Yes
• B. No
• C. Only in Figure III
• D. Sometimes depending on terms

Answer: (B)

Two negative premises cannot yield a valid syllogism. In Aristotelian syllogistic, the two premises must establish a bridge through the middle term that connects the subject to the predicate term in the conclusion. Negative premises deny membership or relation rather than affirm a link, so if both premises are negative there’s no affirmative connection left to transfer to the conclusion. As a result, nothing in the premises guarantees a true relation between the major and minor terms, so a valid conclusion cannot follow. A basic rule here is that at least one premise must be affirmative to form a legitimate link between terms. For example, if we have No S are M and No M are P, there’s no guarantee about the relation between S and P—both possibilities can hold, so the argument isn’t valid.