The Conditional Syllogism otherwise knows as: The Hypothetical Syllogism

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The Conditional Syllogismotherwise knows
asThe Hypothetical Syllogism

• If I had a millions dollars, then Id buy you a
  house
• The Barenaked Ladies

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(No Transcript)
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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,
  hell be willing to testify. But John refuses to
  testify. It follows that hes 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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Consider the following
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.
Valid or invalid?
Invalid He might drink pop every day.
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Or, the following
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.
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 Antecedent
• Denying the Antecedent
• Affirming the Consequent
• Denying the Consequent

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Affirming the Antecedent A A Alcoholics
AnonymousDenying the Consequent D C
Washington D.CAA is a good program, and
Washington is a great place to visit.
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Affirming the Consequent A C AcneDenying the
Antecedent D A Dumb ANo one wants acne,
and no one wants to be a dumb a