A syllogism can play a role in persuasion, but they have to be worded carefully. The general formula is:
1. Major Premise
2. Minor Premise
1. All humans are mammals. (All A is B)
2. All mammals are animals. (All B is C)
3. All humans are animals. (All A is C)
Where it gets tricky, is when you get in to relative or slippery terms.
1. I am nobody.
2. Nobody is perfect.
3. Therefore, I am perfect.
This seems like a silly example, but "nobody" is a relative term. In certain contexts, it means "no person." In other contexts (like this one), it means "no one of significance or popular importance." When you have any term (A,B, or C) with different contextual meanings, a syllogism can backfire on you. This is especially true and controversial when it comes to ethical or moral arguments.
1. Murder is never okay.
2. Murder is justifiable in a justifiable war.
3. Murder is both justifiable and never justifiable.
This is not a strict syllogism, but you get the idea. The problems with using syllogisms for persuasive purposes is the context and the multiple interpretations of the terms. Justifiable and war primarily.
Syllogisms work best with strict, rigorous logic and math problems.
1. 3 people can do x amount of work in 60 minutes.
2. 12 people can do x amount of work in 15 minutes.
3. x = 4.