When we deduce a conclusion, we put things together, like any good detective. We establish that a general principle is true, that a specific case is an example of that principle, and that therefore a particular conclusion about that case is a certainty.

Deductive reasoning can often be structured in a three-step argument called a syllogism. The three steps are

Syllogism

Deductive arguments break down if one of the premises is not true or if the conclusion does not logically follow from one of the premises.

Faulty deduction

In the following short argument, the major premise is very likely untrue.

ARGUMENT WITH A QUESTIONABLE PREMISE

The police do not give speeding tickets to people driving less than five miles per hour over the limit. Sam is driving fifty-nine miles per hour in a fifty-five-mile-per-hour zone. Therefore, the police will not give Sam a speeding ticket.

The conclusion is true only if the premises are true. If the police sometimes give tickets for driving less than five miles per hour over the limit, Sam cannot safely conclude that he will avoid a ticket.

In the following argument, both premises might be true, but the conclusion does not follow logically from them.

CONCLUSION DOES NOT FOLLOW

All members of our club ran in this year’s Boston Marathon. Jay ran in this year’s Boston Marathon. Therefore, Jay is a member of our club.

The fact that Jay ran the race is no guarantee that he is a member of the club. Presumably, many runners in the Boston Marathon are nonmembers.

Assuming that both premises are true, the following argument holds up.

CONCLUSION FOLLOWS

All members of our club ran in this year’s Boston Marathon. Jay is a member of our club. Therefore, Jay ran in this year’s Boston Marathon.