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The Conditional Syllogismotherwise knows as:
The Hypothetical Syllogism
“If I had a millions dollars, then I’d buy you a house”
The Barenaked Ladies
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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.
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These arguments are not always valid.
In fact, many are invalid, like the argument above
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The conditional syllogism takes the following form:
If p, then q p q
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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
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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.
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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.
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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
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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.
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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
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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
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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
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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
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Which forms are valid? Which are invalid?
Affirming the AntecedentDenying the Antecedent
Affirming the ConsequentDenying the Consequent
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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.
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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**