4. If Either Premise of a Valid Syllogism
Is Negative, the Conclusion Must Be Negative; if the
Conclusion Is Negative, One Premise Must Be Negative
If a premise is negative, it tells us that one class (either S or
P, depending on which premise it is) is excluded from another
class (M). From this information, we might be able to infer that
S is excluded from P--if the other rules are satisfied. However,
we could never infer that S is included in P.
Conversely, if the conclusion is negative, it says that S is
excluded from P. The only information that would justify this
conclusion is the information that S is excluded from M (which is
included in P) or that S is included in M (which is excluded from
P). In either of those cases, we have one negative premise.