R――~T
~R
Therefore, 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――B
B――C
Therefore, A――C
These arguments are rarely difficult, provided you step back and take a birds-eye view. It may be helpful to view this structure as an inequality in mathematics. For example, 5 4 and 4 3, so 5 3.
Notice that the conclusion in the transitive property is also an if-then statement. So we dont know that C is true unless we know that A is true. However, if we add the premise A is true to the diagram, then we can conclude that C is true:
A――B
B――C
A
Therefore, C
As you may have anticipated, the contrapositive can be generalized to the transitive property:
A――B
B――C
~C
Therefore, ~A
Example:
If you work hard, you will be successful in America. If you are successful in America, you can lead a life of leisure. So if you work hard in America, you can live a life of leisure.
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