The Conditional Syllogism otherwise knows as: The Hypothetical Syllogism “If I had a millions dollars, then I’d buy you a house” The Barenaked Ladies

The Conditional Syllogism Sometimes an argument can take a conditional or hypothetical form. For example, consider the following: Look, I know criminals. If John is innocent, he’ll be willing to testify. But John is willing to testify. It follows that he’s not guilty.

These arguments are not always valid. In fact, many are invalid, like the previous argument… Look, I know criminals. If John is innocent, he’ll be willing to testify. But John is willing to testify. It follows that he’s not guilty.

The conditional syllogism takes the following form: If p, then q p q P represents the antecedent Q represents the consequent

For example: If Johnnie eats cake every day, then he is placing himself at risk for diabetes. Johnnie eats cake every day. Therefore, Johnnie is placing himself at risk for diabetes.

If Johnnie eats cake every day, then he is placing himself at risk for diabetes. Johnnie eats cake every day. Therefore, Johnnie is placing himself at risk for diabetes. Affirming the antecedent in the second premise… Consider the following. Ask yourself whether or not they might be valid.

If Johnnie eats cake every day, then he is placing himself at risk for diabetes. Johnnie does not eat cake every day. Therefore, Johnnie is not placing himself at risk for diabetes. Denying the antecedent in the second premise…

If Johnnie eats cake every day, then he is placing himself at risk for diabetes. Johnnie is placing himself at risk for diabetes. Therefore, Johnnie is eating cake every day. Affirming the consequent in the second premise…

If Johnnie eats cake every day, then he is placing himself at risk for diabetes. Johnnie is not placing himself at risk for diabetes. Therefore, Johnnie is not eating cake every day. Denying the consequent in the second premise…

The major premise in this kind of syllogism is a conditional proposition: "If Johnnie eats cake every day, then he is placing himself at risk for diabetes". There are two parts to the conditional proposition. Notice that one clause begins with "if", another with "then". The "if" clause is called the antecedent, (subject) the "then" clause is called the consequent, (predicate)

If Johnnie eats cake every day, then he is placing himself at risk for diabetes. Johnnie eats cake every day. Affirming the Antecedent in minor premise Therefore, Johnnie is placing himself at risk for diabetes. Affirm the consequent in the conclusion This is called: Affirming the Antecedent

If Johnnie eats cake every day, then he is placing himself at risk for diabetes. Johnnie does not eat cake every day. Denying the Antecedent in minor premise Therefore, Johnnie is not placing himself at risk for diabetes. Deny the consequent in the conclusion This is called: Denying the Antecedent

If Johnnie eats cake every day, then he is placing himself at risk for diabetes. Johnnie is placing himself at risk for diabetes. Affirming the Consequent in minor premise Therefore, Johnnie is eating cake every day. Affirm the antecedent in the conclusion This is called: Affirming the Consequent

If Johnnie eats cake every day, then he is placing himself at risk for diabetes. Johnnie is not placing himself at risk for diabetes. Denying the Consequent in minor premise Therefore, Johnnie is not eating cake every day. Deny the Antecedent in the conclusion This is called: Denying the Consequent

Which forms are valid? Which are invalid? Affirming the Antecedent Denying the Antecedent Affirming the Consequent Denying the Consequent

Affirming the Antecedent: A A = Alcoholics Anonymous Denying the Consequent: D C = Washington D.C AA is a good program, and Washington is a great place to visit.

Affirming the Consequent: A C = Anti-Christ Denying the Antecedent: D A = Dumb A** No one wants to meet the anti- Christ, and no one wants to be a dumb a**

A note on conditional reasoning … It was autumn and the Indians on the reservation asked their new chief if it was going to be a cold winter. Raised in the new ways of the modern world, the chief had never been taught the old secrets and had no way of knowing the answer for sure. To be on the safe side, he advised his tribe to collect wood and prepare for a cold winter. A few days later as a practical thought he decided to call the national weather service and asked whether they were forecasting a cold winter. The meteorologist replied that he indeed determined that the winter would be quite cold. The chief advised the tribe to collect more wood. A couple of weeks later, the chief called the national weather service again and asked, “Does it still look like a cold winter.” “It sure does.” replied the meteorologist. The chief advised the tribe to collect more wood. A few more weeks later the chief calls the national weather service again to confirm the forecast. The meteorologist states, “We’re now forecasting that it will be one of the coldest winters on record!” “Really” says the chief, “How can you be so sure?” The meteorologist replies, “Because, the Indians are collecting wood like crazy.”