The Conditional Syllogismotherwise 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 refuses to testify. It follows that he’s guilty.

These arguments are not always valid.

In fact, many are invalid, like the argument above

The conditional syllogism takes the following form:

If p, then q p q

For example, consider whether this conclusion follows

from the given premises:

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 you think it is valid, you are correct

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.

Consider the following

Valid or invalid?

Invalid: He might drink pop every day.

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.

Or, the following:

Invalid: He might be drinking pop every day, or eating chocolate bars, etc.

Or,

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.

Valid?

It is valid

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,

the "then" clause is called the consequent.

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

Johnnie eats cake every day. Affirming the Antecedent

Therefore, Johnnie is placing himself at risk for diabetes.

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

Therefore, Johnnie is not placing himself at risk for diabetes.

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

Therefore, Johnnie is eating cake every day.

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

Therefore, Johnnie is not eating cake every day.

This is called: Denying the Consequent

Which forms are valid? Which are invalid?

Affirming the AntecedentDenying the Antecedent

Affirming the ConsequentDenying 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 = Acne

Denying the Antecedent: D A = Dumb A**

No one wants acne, and no one wants to be a dumb a**