¡¡¡¡R¡ª¡ª>~T
¡¡¡¡~R
¡¡¡¡Therefore£¬ T
¡¡¡¡[Note£º Two negatives make a positive£¬ so the conclusion ~£¨~T£© was reduced to
¡¡¡¡T.] This diagram clearly shows that the argument is committing the fallacy
¡¡¡¡of denying the premise. An if-then statement is made£» its premise is negated
¡¡¡¡£» then its conclusion is negated.
¡¡¡¡Transitive Property
¡¡¡¡A¡ª¡ª>B
¡¡¡¡B¡ª¡ª>C
¡¡¡¡Therefore£¬ A¡ª¡ª>C
¡¡¡¡These arguments are rarely difficult£¬ provided you step back and take a bir
¡¡¡¡d's-eye view. It may be helpful to view this structure as an inequality in m
¡¡¡¡athematics. For example£¬ 5 > 4 and 4 > 3£¬ so 5 > 3.
¡¡¡¡Notice that the conclusion in the transitive property is also an if-then sta
¡¡¡¡tement. So we don't know that C is true unless we know that A is true. Howev
¡¡¡¡er£¬ if we add the premise ¡°A is true¡± to the diagram£¬ then we can conclude t
¡¡¡¡hat C is true£º
¡¡¡¡A¡ª¡ª>B
¡¡¡¡B¡ª¡ª>C
¡¡¡¡A
¡¡¡¡Therefore£¬ C
¡¡¡¡As you may have anticipated£¬ the contrapositive can be generalized to the tr
¡¡¡¡ansitive property£º
¡¡¡¡A¡ª¡ª>B
¡¡¡¡B¡ª¡ª>C
¡¡¡¡~C
¡¡¡¡Therefore£¬ ~A
¡¡¡¡Example£º £¨Transitive Property£©
¡¡¡¡If you work hard£¬ you will be successful in America. If you are successful i
¡¡¡¡n America£¬ you can lead a life of leisure. So if you work hard in America£¬ y
¡¡¡¡ou can live a life of leisure.
