Can a syllogism be valid with two positive premises and a negative conclusion?

• A. Yes
• B. No
• C. Sometimes
• D. Not determinable

Answer: (B)

In a categorical syllogism, the quality of the premises determines the quality of the conclusion. When both premises are affirmative, they establish a positive link between the terms, and the conclusion must also be affirmative. A negative conclusion (such as no S are P or some S are not P) would require showing a exclusion or non-membership that isn’t supported by two positive connections.

For example, if we have all dogs are mammals and all mammals are animals, we can conclude all dogs are animals. That chain of inclusion cannot yield a negative assertion about dogs and animals. Therefore a syllogism with two positive premises cannot validly yield a negative conclusion.