Rule 4: A syllogism cannot contain two negative premises.
 
Intuitively, most of you are already familiar with this Rule. Since your earliest days most of you have been taught that “two wrongs don’t make a right!” This is nothing more than a simple truism that has been derived by application of the logic principle stated in this Rule. Consider the following example:
 
1. No man is a mother. (negative major premise)

2. My mother is not my father. (negative minor premise)

3. No man is my father. (conclusion)

crying dad holding crying baby

             
Even though both the major and the minor premise statements are true, the conclusion is completely nonsensical. That is because this syllogism violates Rule 4: it contains two negative premise statements. No valid logical conclusion can be derived from two negative premises. Of course, any logical syllogism can certainly have one negative premise statement (either a major premise or a minor premise), just not both.

[Note: This rule is also the basis for a similar rule in English grammar prohibiting the use of “double negatives.” Thus, statements like, “I don't never ...” are generally to be avoided altogether, because they contain two negatives. In effect, these double negatives “cancel each other out,” leaving the exact opposite meaning from what was actually intended. (i.e., “I DO ...”; or “I EVER ...”).