4/19/2009
1
Chapter 11
Evaluating Inferences
Spring 2009
San Francisco State University
Instructor Mike Olsen
Statistical Syllogisms
Standard Form
N% of As are Bs.
X is an A.
Therefore, X is a B.
99% of people who jump from the Golden Gate Bridge die.
Jim is going to jump from the bridge.
Thus, Jim will probably die from the jump.
In arguments of this form,
the inference will be of N% strength.
An Example
(1) 5% of all college graduates have taken
calculus.
(2) Mike is a college graduate.
Therefore, (3) Mike has taken calculus.
The inference is of 5% strength. In our
terminology from Inductive evaluation, the
inference is very weak.
The Scope of Premises: “Some”
•
“Some” statements or conclusions are
easy to prove and difficult to disprove
Example:
•
Human beings once walked on the moon.
–
Easy to prove, difficult to disprove
•
Some men are mortal.
–
Easy to prove, difficult to disprove
The Scope of Premises: “All”
Statements
•
When we make “All or None” statements,
these are EASY to disprove, and
hard to
prove.
•
This is why you will see the
Straw Man
committed in this fashion.
–
All Roman Catholics are against abortion.
–
Bill Clinton has never visited Hong Kong.
Logical Relationships: Consistency
•
Two statements (S
1
and S
2
) are consistent
when it is
logically possible
that all of them
are true.
–
Mike is over 30. Mike is over 20.
•
Any age over 30 would make both of these
statements true.

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