Conversely, you can use a syllogism to bring out some essential part of the reasoning of an opponent which you know will not commend itself to the audience, as did Lincoln in his debate with Douglas at Galesburg.  Douglas had defended the Dred Scott decision of the United States Supreme Court, which decided that the right of property in a slave is affirmed by the United States Constitution.  Lincoln wished to make the consequences of this doctrine as glaringly evident as possible.  He did so as follows: 

    I think it follows, and I submit to the consideration of men capable
    of arguing, whether as I state it, in syllogistic form, the argument
    has any fault in it.

    Nothing in the Constitution or laws of any State can destroy a right
    distinctly and expressly affirmed in the Constitution of the United
    States.

    The right of property in a slave is distinctly and expressly
    affirmed in the Constitution of the United States.

    Therefore, nothing in the Constitution or laws of any State can
    destroy the right of property in a slave.

    I believe that no fault can be pointed out in that argument;
    assuming the truth of the premises, the conclusion, so far as I have
    capacity at all to understand it, follows inevitably.[43]

Lincoln knew that this doctrine that no state could interfere with slavery would be intolerable to the people of Illinois, before whom he was carrying on his campaign; and this syllogism made clear to them the consequences of the decision of the Supreme Court.

Or you can use a syllogism to make obvious a flaw in the reasoning of your opponent, as in the following example: 

In view of the history of commission government in this country so far as it has been made, the burden of proof rests with those who attempt to show that a government which has been so successful in cities of moderate size will not be successful in our largest cities.  The syllogism they are required to prove runs briefly thus: 

Commission government is acknowledged to have been successful in cities as large as one hundred and thirty thousand inhabitants, but

It has not been tried in cities containing more than one hundred and thirty thousand inhabitants;

Therefore, it will not be successful in cities of four hundred thousand or larger, which is a reductio ad absurdum.

The folly of the attempt is shown by the very statement of the conclusion.[44]

44.  The Dilemma.  One special form of the syllogism is at times so strong an argument that it deserves special mention here, namely, the dilemma.  This is a syllogism in which the major premise consists of two or more hypothetical propositions (that is, propositions with an “if” clause) and the minor of a disjunctive proposition (a proposition with two or more clauses connected by “or").